A = 12C (2017KE05)

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¹²C (2017KE05)

(See Energy Level Diagrams for ¹²C and Isobar Diagram)

See also 2 [Electromagnetic Transitions in A = 12] (in PDF or PS), 12.13 [Energy levels of ¹²C] (in PDF or PS) and 12.14 [The decay of some ¹²C levels] (in PDF or PS).

Isotopic abundance: (98.93 ± 0.08)%. < r²_charge >^1/2 = 2.4829 ± 0.0019 fm (1984RU12: charge radius). See also reaction 40.
< r²_matter >^1/2 ≈ 2.35-2.48 fm; i.e., see (1985TA18, 2001OZ04, 2011AL23, 2016KA37).
¹²C*(4.44): Q = 6 ± 3 e ⋅ fm², indicating a substantial oblate deformation (1983VE01).
g_J (¹²C⁵⁺)[electronic g-factor] = 2.0010415963 (10)_exp (44)_me (2002BE82).

1. ⁶Li(⁶Li, γ)¹²C Q_m = 28.1738

The γ_0-3 excitation functions from the ⁶Li + ⁶Li capture reaction were measured for E_cm = 1 to 8 MeV (1991EU01). Evidence is found for a state at E_x = 30.33 MeV with Γ ≈ 0.8 MeV. A comparison with other data, mainly from other ⁶Li + ⁶Li decay channels and ⁹He(³He, γ) suggests the resonance results from a concentration of J^π; T = 2⁺; 0 and 2^-; 1 strength.

2. (a) ⁶Li(⁶Li, n)¹¹C Q_m = 9.4521 E_b = 28.1738
(b) ⁶Li(⁶Li, p)¹¹B Q_m = 12.2169
(c) ⁶Li(⁶Li, d)¹⁰B Q_m = 2.9873
(d) ⁶Li(⁶Li, α)⁸Be Q_m = 20.8072
(e) ⁶Li (⁶Li, 2α)⁴He Q_m = 20.8990
(f) ⁶Li (⁶Li, 2d)⁴He⁴He Q_m = -2.9475
(g) ⁶Li(⁶Li, ⁶Li)⁶Li E_b = 28.1738

The excitation functions for some final states in ¹¹B and ¹¹C (reactions (a) and (b)) are structureless while others (to states with J^π = 3/2^-, 5/2^-, 5/2⁺) exhibit pronounced structures. The most prominent of these is observed at E(⁶Li) = 8.4 MeV [¹²C*(32.4)] in the p₂ and n₂ yields with a width Γ_cm ≈ 1 MeV (1987DO05). Reaction (d) has been studied in kinematically complete experiments at E(⁶Li) = 2.4 to 6.7 MeV (1988LA11) and at E(⁶Li) = 2.5 and 3.1 MeV (2015SP01, 2015TU06). See also (1984LA19, 1987LA25). For reactions (e) and (f) see (1983WA09). Broad structures have been observed in the elastic scattering at E(⁶Li) ≈ 13 and 26 MeV: see (1980AJ01). See also (1990AJ01).

3. ⁸Be(α, γ)¹²C Q_m = 7.3666

This reaction and the Hoyle state ¹²C*(7.65) resonance state are of great importance to nucleosynthesis and the formation of heavy elements; see (1985CA41, 1987DE13, 1998TH07, 2000FI14, 2001CS04, 2010OGZX, 2010UM01, 2013EP01, 2013NG01, 2015FI03, 2016ME03, 2016SU25). In (2010UM01), non-resonant capture to a linear configuration that transitions to a triangular orientation is suggested. Production rate sensitivities to stellar environment variables are investigated in (2010DE18, 2011AU01), and the impact of time variation of the fundamental constants is studied in (2012CO19). Also see a prediction for the J^π = 0₃⁺ state at E_res = 1.66 MeV in (2010KAZK).

4. ⁹Be(³He, γ)¹²C Q_m = 26.2797

Excitation functions and angular distribution studies have been carried out at E(³He) = 1.0 to 6.0 MeV (1972BL17: γ₀, γ₁, γ₂), E(³He) = 1.5 to 11 MeV (1972LI29: γ₀, γ₁, γ₂, γ₃), E(³He) = 2 to 4.5 MeV (1964BL12: γ₀, γ₁) and E(³He) = 3 to 26 MeV (1974SH01: γ₀, γ₁, γ₂, γ₃). Observed resonances are shown in 12.15 (in PDF or PS). See (1980AJ01) for references.

¹²C*(28.2) appears to be formed by s- and d-wave capture. The γ₀ and γ₂ transitions to the 0⁺ states ¹²C*(0, 7.7) are strong and show a similar energy dependence. A strong non-resonant contribution is necessary to account for the γ₁ yield (1972BL17). The resonance structure reported by (1974SH01) appears to confirm the role of 3p-3h configurations for ¹²C excitations somewhat above the giant resonance region. The γ₃ yield is relatively unstructured (1972LI29, 1974SH01: to E(³He) = 26 MeV). See also (1975AJ02).

(1970BL09) had reported a capture resonance at E(³He) = 1.74 MeV which subsequently decayed via ¹²C*(15.11) and which was assumed to correspond to the first J^π = 0⁺; T = 2 state in ¹²C [E_x = 27.585 ± 0.005 MeV]. However, neither (1972HA63) nor (1972WA18) have been able to repeat this observation: Γ_³HeΓ_γ/Γ < 1.5 meV (1972WA18), < 2 meV (1972HA63).

5. (a) ⁹Be(³He, n)¹¹C Q_m = 7.5580 E_b = 26.2797
(b) ⁹Be(³He, p)¹¹B Q_m = 10.3228
(c) ⁹Be(³He, d)¹⁰B Q_m = 1.0932
(d) ⁹Be(³He, t)⁹B Q_m = -1.0866
(e) ⁹Be(³He, ³He)⁹Be
(f) ⁹Be(³He, α)⁸Be Q_m = 18.9131
(g) ⁹Be(³He, α)⁴He⁴He Q_m = 19.0049

Excitation functions for neutrons, production cross sections for ¹¹C and polarization observables have been measured at E(³He) = 1.2 to 10 MeV for several neutron groups. No sharp structure is observed, but there is some suggestion, from angular distribution data and the excitation function at forward angles, for a structure (Γ ≈ 350 keV) at E(³He) ≈ 2 MeV: E_x = 27.8 MeV (1963DU12, 1965DI06). The total cross section for ¹¹C production shows a broad maximum, σ = 113 mb at E(³He) = 4.3 MeV. In the range E(³He) = 5.7 to 40.7 MeV the yield decreases monotonically. Excitation functions and angular distributions for protons (reaction (b)) have been measured for E(³He) = 1.0 to 10.2 MeV for a number of proton groups. No pronounced structures are reported.

Analyzing powers have been measured at E(pol. ³He) = 33.3 MeV for nine deuteron groups (reaction (c)). The cross section for ground-state tritons (reaction (d)) increases monotonically for E(³He) = 2.5 to 4.2 MeV and then shows a broad maximum at E(³He) ≈ 4.5 MeV. See also (1993AR14, 1996AR07: E = 22.3 to 34 MeV).

The excitation function for elastic scattering (reaction (e)) decreases monotonically for E(³He) = 4.0 to 9.0 MeV and 15.0 to 21.0 MeV. See also (1992AD06: E = 50, 60 MeV). At θ_cm = 111° a slight rise is observed for E(³He) = 19 to 21 MeV. Polarization observables have been reported at E(³He) = 18, 31.4 and 32.8 MeV.

Excitation functions for the α₀ group (reaction (f)) have been reported for E(³He) = 2 to 10 MeV (1978BI15): evidence is found for a resonance at E_x ≈ 29.3 MeV. See also (1992AD06). Analyzing powers have been measured at E(pol. ³He) = 33.3 MeV. For reaction (g) see (1986LA26, 1987WA25).

See references and additional work in (1968AJ02, 1975AJ02, 1980AJ01, 1985AJ01, 1990AJ01).

6. (a) ⁹Be(α, n)¹²C Q_m = 5.7020
(b) ⁹Be(α, ¹²C)n Q_m = 5.7020

Neutron groups have been observed to ¹²C*(0, 4.4, 7.7, 9.6, (10.1), (10.8)). Angular distributions of neutrons, mainly for n_0-3, have been measured at energies in the range E_α = 1.75 to 32 MeV. Gamma-ray angular distributions have been studied by (1955TA28, 1959SM98, 1963SE04). Observation of the γ-decay of the 15.1 MeV level is reported by (1954RA35, 1957WA04). At E_α = 35 MeV the members of the K^π = 0⁺ band and ¹²C*(9.63) are strongly populated (1981HAZV).

Doppler shift measurements on the transition ¹²C*(4.4 → g.s.) yield mean life values of τ_m = 50 ± 6 fsec (1961DE38); 57⁺²³_-17 fsec, Γ_γ = (11.5⁺⁵_-3.2) meV (1966WA10); < 48 ± 10 fsec (1967CA02). The internal pair conversion coefficient indicates an E2 transition (1954MI68): the pair angular correlation permits M1 or E2 and favors the latter (1954HA07, 1956GO1K, 1956GO73, 1958AR1B). Angular distributions of n₁ and n₁-γ correlations strongly indicate a direct interaction mechanism even at E_α = 3.3 and 5.5 MeV (1960GA14, 1962KJ01); also see correlation studies at E_α = 1.4 to 4.5 MeV (2010GI07). ¹²C*(7.65[J^π = 0⁺]) decays predominantly into ⁸Be + α with a small radiative branch. In (1960AL04, 1972OB01) the pair decay is measured Γ_π/Γ = (6.9 ± 2.1) × 10^-6; this supercedes the earlier value Γ_π/Γ = (6.6 ± 2.2) × 10^-6 (1959AL97, 1960AJ04, 1960AL04, 1961GA03). However, see 12.14 (in PDF or PS).

Neutron catalyzed helium burning, i.e. ⁴He(αn, γ)⁹Be(α, n)¹²C, is analyzed in (1994WR01, 1996KU07, 2009GI03, 2011GI05). The ratio, Yield(E_γ = 4.44 MeV)/Yield(neutrons) = 0.596 ± 0.017, was measured for an AmBe source in (2004MO18). The energy dependent reaction cross sections have been evaluated at E < 10 MeV for actinide-Be neutron source energy distributions (2003SH22). Also see (1997HE11, 2000MI34, 2007AH07, 2007MA58, 2015VL01).

Reaction (b) was measured at E_α = 22 to 30 MeV, along with ¹²C(α, 3α)⁴He, in search of ¹²C resonances above E_x = 7 MeV that could have structures related to the Hoyle state (2011FR02). The analysis separately considered both events populating natural parity states involving ¹²C* → ⁸Be_g.s.(J^π = 0⁺) + α and events that excluded ¹²C* → ⁸Be_g.s. + α. Known states at E_x = 9.64, 10.84, 11.83, 12.71, 14.08 are observed in the ⁹Be(α, ¹²C) reaction along with a state consistent with E_x = 13.3 ± 0.2 MeV and Γ = 1.7 ± 0.2 MeV. Analysis of the angular correlations from the ¹²C(α, 3α) reaction support J^π = 4⁺ for the new state.

7. ⁹Be(⁶Li, t)¹²C Q_m = 10.4855

At E(⁶Li) = 32 MeV angular distributions have been studied to ¹²C*(0, 4.4, 7.7, 9.6, 10.8, 11.8, 12.7, 14.1); ¹²C*(9.64) is relatively strongly populated. There is no indication of the T = 1 states (1986AS02: FRDWBA). Similar results are found for E(⁹Be) = 26 MeV in (1975VE10).

8. ⁹Be(⁹Be, ⁶He)¹²C Q_m = 5.1048

At E(⁹Be) = 40 MeV, angular distributions to ¹²C*(0, 4.44, 7.65, 9.64, 13.35, 14.08) were measured (1992CO05); the data are consistent with direct ³He cluster transfer. Cluster spectroscopic factors are deduced. Also see measurements at E(⁹Be) = 26 MeV, θ = 10° to ¹²C*(4.4, 7.7, 9.6) (1975VE10).

9. ⁹Be(¹⁰C, ¹²C)⁷Be Q_m = 11.2783

At E(¹⁰C) = 10.7 MeV, the α-particle correlations from ¹²C*(7.65, 9.64) were studied in search of evidence supporting direct 3-body breakup (2012MA10), as suggested in (2011RA43). Results were consistent with 100% decay via ⁸Be_g.s. + α in both cases.

10. ¹⁰Be(³He, n)¹²C Q_m = 19.4674

At E(³He) = 13 MeV neutron groups are observed to ¹²C*(0, 4.4, 7.7, 16.1, 17.8) and to excited states at E_x = 23.53 ± 0.04 [Γ < 0.4 MeV] and 27.611 ± 0.020 MeV. The latter is formed with a 0° cross section of ≈ 200 μb/sr and is taken to be the first 0⁺; T = 2 state of ¹²C (1974GO23).

11. ¹⁰B(d, γ)¹²C Q_m = 25.1864

The (d, γγ) excitation function [via the J^π = 1⁺; T = 1 state at E_x = 15.1 MeV] has been measured for E_d = 2.655 to 2.84 MeV. The non-resonant yield of 15 MeV γ-rays is due to direct capture processes or to a very broad resonance: no sharp resonances are observed corresponding to the E_x ≈ 27.6, T = 2 state reported in other reactions [Γ_d₀Γ_γ/Γ ≲ 0.2 eV] (1970BL09).

12. ¹⁰B(d, n)¹¹C Q_m = 6.4648 E_b = 25.1864

The thin-target excitation function, measured at E_d = 0.3 to 4.6 MeV, shows some indication of a broad resonance in the forward direction near E_d = 0.9 MeV. Above E_d = 2.4 MeV, the cross section increases rapidly to 210 mb/sr at 3.8 MeV and then remains constant to 4.6 MeV (1954BU06, 1955MA76). Also see activation measurements reported at E_d = 0.5 to 6 MeV (1990MI11). The 0° excitation function for ground state neutrons shows no structure for E_d = 3.2 to 9.0 MeV (1967DI01). Excitation functions have been measured for E_d = 7.0 to 16.0 MeV (1981AN16). The excitation function for neutrons to ¹¹C*(6.48) increases monotonically for E_d = 4.0 to 4.8 MeV (1972TH14). The branching ratios at 90° for the transitions to the ground states of ¹¹C and ¹¹B [n₀/p₀] have been measured for E_d = 1.0 to 2.0 MeV by (1973BR24). At E_d = 1 to 5 MeV, cross sections have been obtained for the neutrons and protons to the second, third, fourth, and fifth excited states of the ¹¹B and ¹¹C mirror nuclei (1967SC1K). The angular distributions all show a sharp peak around 20° and a smaller contribution in the backward direction; DWBA produces a satisfactory fit to these distributions (1967DI01).

Polarization measurements have been carried out for E_{pol. d} = 2.5 to 4.0 MeV (1967ME1N), E_{pol. d} = 1.20 to 2.90 MeV (1968BR26: n₀) and E_{pol. d} = 2.4 to 4.0 MeV (1972ME06: n₀, n₁, n₂₊₃). The transitions to ¹¹C*(0, 4.32 + 4.80) appear to involve a direct reaction mechanism (1972ME06).

Cross sections and astrophysical S-factors for n₀ are reported for E_d < 160 keV (2008ST10). Thick-target yields and astrophysical S-factors are reported for neutrons at E_d = 24 to 111 keV (2001HO23) and for 4.3 MeV γ-rays at E_d = 111 to 170 keV (1982CE02).

Methods of ¹¹C production for position emission tomography are discussed in (1989ST09, 2005VO15, 2011KI04).

13. ¹⁰B(d, p)¹¹B Q_m = 9.2296

Angular distributions and yields of protons have been measured for E_d = 0.9 to 2 MeV (2007KO69) and E_d = 15.3 MeV (2005GA59); also see results reported at E_d = 0.18 to 3.1 MeV (1959AJ76), 0.14 to 12 MeV (1968AJ02) and 0.7 to 2.9 MeV (1975AJ02). Although the excitation functions show several broad peaks, no clear resonances can be identified, and it is assumed that many overlapping resonances are involved (1956MA69) except possibly at E_d = 2.3 MeV (E_x = 27.1 MeV) where the effect of a broad resonance influences the cross section of the p₁ and p₃ groups. An analysis given in (2005RU16) suggests the broad peaks correspond to fragmented J^π = 1^- components of the GDR at E_res(cm) = 0.38, 0.61, 1.61 MeV with Γ = 0.37, 0.37 and 1.24 MeV, respectively, as well as a J^π = 2⁺ contribution from the GQR at E_res(cm) = 1.36 MeV with Γ = 710 keV. The p₂-γ-ray correlations were measured in (2005GA59). Cross section ratios for the (d, n) and (d, p) reactions to mirror states have been measured by (1967SC1K, 1973BR24).

The astrophysical relevant region has been studied at E_d = 57 to 141 keV (1993CE02, 1997YA02, 1997YA08), 91 to 161 keV (1981CE04) and 120 to 340 keV (2001HO22) and at E_cm = 100 to 300 keV (2004RU10).

Polarization studies have been carried out at E_{pol. d} = 6.9, 10, 11 to 13.8, 11.4 and 21 MeV [See (1968AJ02)] and at E_{pol. d} = 1.15, 1.40 and 1.85, 10, 12 and 13.6 MeV [see (1975AJ02)].

14. ¹⁰B(d, d)¹⁰B E_b = 25.1864

The yield of elastically scattered deuterons has been measured for E_d = 1.0 to 2.0 MeV: resonances at E_d = 1.0 and 1.9 MeV are suggested by (1969LO01). Excitation functions for the deuterons to ¹⁰B*(1.74, 2.16) [J^π; T = 0⁺; 1 and 1⁺; 0, respectively] have been measured at several angles for E_d = 4.2 to 16 MeV: they are characterized by rather broad, slowly varying structures. The ratio σ_1.74/σ_2.16 varies from (0.69 ± 0.04)% at E_d = 6.5 MeV to (0.16 ± 0.04)% at E_d = 12.0 MeV corresponding, respectively, to isospin impurities of ≈ 2% and ≈ 0.5% (1974ST01). No resonance structure is observed in the elastic yield for E_d = 14.0 to 15.5 MeV (1974BU06). Polarization measurements are reported at E_{pol. d} = 12.5 MeV (1975ZA08) and at 15 MeV (1974BU06).

15. (a) ¹⁰B(d, α)⁸Be Q_m = 17.8198 E_b = 25.1864
(b) ¹⁰B(d, 2α)⁴He Q_m = 17.9117

Excitation functions have been measured for the α₀ and α₁ groups for E_d = 0.4 to 12 MeV [see (1968AJ02, 1975AJ02, 1980AJ01)] and for E_d = 0.9 to 2.0 MeV (2007KO70: α₀). Maxima in the α₀ yields are reported at E_d = 1, 2, 4.5 and (6) MeV. The first is attributed to an s-wave resonance corresponding to a state with E_x ≈ 26.0 MeV, Γ ≈ 0.5 MeV (1968FR07). The resonance structures at ≈ 2.0 and 4.5 MeV (Γ ≳ 1 MeV) may both involve the isoscalar giant resonance: E_x ≈ 28 MeV, Γ ≈ 4 MeV (1978BU04). No evidence for the T = 2 state was found in the α₀ and α₁ yield curves taken in 2 keV steps for 27.35 < E_x < 27.65 MeV (1970BL09). For yields of the α-particles to ⁸Be*(17.6, 18.1) see (1970CA12). Cross sections, angular distributions and S-factors are deduced in (2001HO22: E_d = 120 to 340 keV) and (1993CE02, 1997YA02, 1997YA08: E_d = 57 to 141 keV).

Reaction (b) has been studied for E_d = 2.7 to 5.0 MeV (1975RO09, 1975VA04, 1977GO16), E_d = 0.36 MeV (1977NO10), E_d = 2.5 and 3 MeV (1992KO26), E_d = 13.6 MeV (1981NE08, 1992PU06) and E_d = 48 MeV (1993PA31). The work of (1977NO10) suggests that J^π = 3^- and 4⁺ ¹²C compound states with unidentifiable energies and widths contribute dominantly to the sequential decay. Also see (1990NE15, 1991AS02).

16. (a) ¹⁰B(³He, p)¹²C Q_m = 19.6929
(b) ¹⁰B(³He, pα)⁸Be Q_m = 12.3264
(c) ¹⁰B(³He, 2p)¹¹B Q_m = 3.7361
(d) ¹⁰B(³He, pn)¹¹C Q_m = 0.9713

Observed proton groups are displayed in 12.16 (in PDF or PS). Angular distributions of many of these groups have been measured for E(³He) = 2.0 to 3.0 MeV (1965BH1A), 3.7 MeV (1962BR10), 10.1 MeV (1962AL01) and 14 MeV (1967CO1F). Also see 12.17 (in PDF or PS), which has results from complete kinematics studies of ¹⁰B(³He, p3α) and ¹¹B(³He, d3α) given in (2007BO49, 2009KI13, 2010KI08, 2011AL28, 2012AL22, 2012KI07, 2013KI07). 12.14 (in PDF or PS) summarizes the electromagnetic decay parameters of some of the excited states of ¹²C including results below.

Pair emission from ¹²C*(7.65) has been measured: Γ_π/Γ = (6.6 ± 2.2) × 10^-6 [see 12.14 (in PDF or PS)] as has the cascade through ¹²C*(4.4): Γ_γ/Γ = (3.3 ± 0.9) × 10^-4 (1961AL27). By observation of ¹²C recoils, a value Γ_rad/Γ = (3.5 ± 1.2) × 10^-4 is found by (1964HA23).

For ¹²C*(12.71) Γ_γ₀/Γ = (1.93 ± 0.12)%, Γ_γ₁/Γ_γ₀ = (15.0 ± 1.8)% and Γ_α/Γ = (97.8 ± 0.1)% (1977AD02). See earlier reported results of Γ_γ/Γ_α = (3 ± 1)% (1958MO99) and (2 ± 1)% (1959AL96): the γ-decay branching ratios are reported; see comments in 12.16 (in PDF or PS). The α breakup of ¹²C*(12.71) shows a triple-peaked α-particle spectrum, characteristic of the breakup of a J^π = 1⁺ state (1967BH1B).

For ¹²C*(14.08) the branching ratio Γ_α₀/Γ is 0.1 - 0.4. Proton-α correlations require J ≥ 2 (1966WA16).

¹²C*(15.11: J^π = 1⁺; T = 1) decays by γ-emission mainly to ¹²C_g.s. and has weaker transitions to ¹²C*(4.4, 7.7, (10.3), 12.7) (1972AL03, 2009KI13): see 12.16 (in PDF or PS). Earlier measurements reported the feeding to ¹²C_g.s. as 97% and to ¹²C*(4.4) as (3.1 ± 0.6)% (1959AL96), (4 ± 1)% (1960AL14); Γ_α/Γ < 0.2 (1960MI1E), < 0.05 (1965AL1B), < 0.10 (1966WA16), respectively. The strong inhibition of the transition to ⁸Be*(2.9) is cited as evidence for a high isospin purity (1965AL1B). For a study of the charge-dependent matrix element between ¹²C*(12.7, 15.1) see 12.18 (in PDF or PS).

Decays of ¹²C*(16.11, 16.57) populate both ⁸Be*(0, 2.9). The consequent assignment of natural parity is consistent with J^π = 2⁺ for the former but not with the accepted J^π = 2^- for the latter. For ¹²C*(16.1) Γ_γ₁/Γ = (2.42 ± 0.29) × 10^-3, Γ_γ₀/Γ_γ₁ = (4.6 ± 0.7)%, Γ_γ(16.1 → 9.6)/Γ_γ₁ = (2.4 ± 0.4)%, and Γ_γ(16.1 → 12.7)/Γ_γ₁ = (1.46 ± 0.25)% (1976AD03, 1977AD02). Also see (1974AN19) who reported Γ_p/Γ = (3.24 ± 0.27) × 10^-3 and Γ_γ/Γ = (3.23 ± 0.50) × 10^-3. Reported values of Γ_α₀/Γ are 0.05 - 0.12; the decay to 3α occurs rarely, if at all (1966WA16: see however, ¹¹B(p, α)⁸Be: (1965DE1A)).

An unpublished result at E(³He) = 14 MeV, referenced in (1968AJ02), reported two peaks in the giant resonance excitation region corresponding to ¹²C* ≈ 20.6 and 24.5 MeV, with Γ ≈ 200 and 50 keV, respectively; the angular distributions show forward maxima.

Reactions (c) and (d) have been studied by (1970BO39). The latter, at E(³He) = 11 MeV, appears to proceed via a state in ¹²C at E_x = 20.5 ± 0.1 MeV, which is suggested to be J^π = 3⁺; T = 1. The relative intensities of the decays of ¹²C states with 20 < E_x < 25 MeV via channels (c) and (d) is estimated. The α₀-decay is very small, consistent with the expected population of T = 1 states (1970BO39).

17. ¹⁰B(α, d)¹²C Q_m = 1.3399

Angular distributions of the deuterons corresponding to ¹²C*(0, 4.4) have been measured at E_α = 15 to 31 MeV [see references in (1968AJ02, 1980AJ01, 1985AJ01, 1990AJ01)]. The dγ_4.4 angular correlations have been measured for E_α = 19 to 30 MeV [see references in (1975AJ02, 1990AJ01)], and see (1989VA07, 2001LE50: E_α = 25 MeV). Thick target γ-ray yields were measured in (1995HE40, 1997HE11). At E_α = 39.9 MeV, the relative populations of ¹²C*(12.71, 15.11) [both 1⁺; the latter isospin forbidden] leads to the value of 285 ± 30 keV (1977LI02) for the charge-dependent matrix element between these two states. The spin-tensor components for ¹²C*(4.44) formation (1990BO54, 1991BA23, 1998GA46) and induced polarization effects (1999GA43, 2003ZE06) are deduced from analysis of angular distributions at E_α = 25 and 30 MeV.

18. ¹⁰B(⁶Li, α)¹²C Q_m = 23.7127

At E(⁶Li) = 4.9 MeV (1966MC05) angular distributions have been obtained for the α-particles to ¹²C*(0, 4.4, 7.7, 9.6); the population of ¹²C*(11.8, 12.7) is also reported. At E(⁶Li) = 3.8 MeV the intensity ratio for populating the isospin forbidden ¹²C*(15.11; T = 1) state is (3 ± 2)% of the intensity to ¹²C*(12.7; T = 0) (1964CA18).

19. ¹⁰B(¹⁴N, ¹²C)¹²C Q_m = 14.9141

Angular distributions involving ¹²C*(0, 4.4) have been measured at several energies to E(¹⁴N) = 93.6 MeV (1969IS01, 1977MO1A).

20. (a) ¹¹B(p, γ)¹²C Q_m = 15.9569
(b) ¹¹B(p, e⁺ + e^-)¹²C Q_m = 14.9349
(c) ¹¹B(p, α)⁸Be Q_m = 8.5903 E_b = 15.9569

(a) Measurements relevant to the astrophysical capture reaction have been carried out at E_p = 40 to 180 keV (1992CE02), E_{pol. p} = 80 to 100 keV (2000KE10), E_p = 140 to 260 keV (1993AN06) and E_p = 160 to 310 keV (2016HE05). (1992CE02) produced γ₀ and γ₁ yields and S-factor related to the measured α-particle yields. A study of the E_x = 16.1 MeV state in (2016HE05) found E_res = 150.0 ± 0.5 keV and Γ = 5.0 ± 0.8 keV. See related discussion in (1990BR12, 1996RE16, 1999AN35, 2000LI06, 2012CO19, 2012MI24, 2014DU09).

In (2012DI19, 2012FY01), a kinematic energy reconstruction of the 3α energy was used to study α-unbound states populated in the γ-decay of ¹²C*(16.1, 16.57). Capture reactions with E_p = 165 keV and 350 keV beams populated the higher-states, while ¹²C*(9.63, 10.8, 12.7) were observed in the low-energy region of the 3α spectrum. In (2012DI19), the E_x = 11.5-12 MeV region shows evidence for a state that may be associated with J^π = 2⁺ strength. An update of this work, (2016LA27) observed evidence for ¹²C*(16.1) decay to ¹²C*(10.8) with Γ_γ = 0.48 ± 0.04 (stat.) ± 0.11 (sys.) eV; in that work, they gave an overview of the partial decay widths for ¹²C*(16.1). At E_p = 0.675, 1388, 2626 keV (E_x = 16.58, 17.23, 18.37 MeV), the relative intensities of the capture γ rays to ¹²C*(0, 4.44, 7.65, 9.64, 12.71, 15.11) were measured at θ_lab = 55° (1990ZI02). See also (1992HO11).

In the range 4 < E_p < 14.5 MeV, σ(γ₀) is dominated by the giant dipole resonance at E_p = 7.2 MeV (E_x = 22.6 MeV, Γ_cm = 3.2 MeV), while the giant resonance in γ₁ occurs at E_p ≈ 10.3 MeV (E_x = 25.4 MeV, Γ_cm ≈ 6.5 MeV): see (1964AL20). Absolute cross-section measurements from E_p = 5 to 14 MeV suggest that dσ/dΩ(90°) = 13.1 ± 1.3 μb/sr be used as a standard at the E_p = 7.25 MeV peak of the GDR (1982CO11; also derived σ(E2) for E_p = 7 to 14 MeV). The E2 strength is found to be centered near E_p = 12 MeV: it exhausts ≳ 30% of the isoscalar E2 sum rule (1976MAZG, 1976MAZL).

A study of the giant dipole resonance region with polarized protons (E_{pol. p} = 6 to 14 MeV) sets limits on the configuration mixing in the γ₀ giant resonance (1972GL01). The analysis of γ₁ is more complicated: the asymmetry results are constant either with a single J^π = 2^- state or with interference of pairs of states such as (1^-, 3^-), (2^-, 3^-) and (1^-, 2^-) (1972GL01). The 90° yield of γ₀, γ₁, γ₂ and γ₃ [to ¹²C*(0, 4.4, 7.7, 9.6)] has been studied by (1977SN01): the γ₂ yield shows a peak at E_p ≈ 14.3 MeV with a cross section ≈ 2.3% that of γ₀ [in γ₀ yield, E_res = 15.0 MeV (1977SN01)] and perhaps a low-intensity structure at E_p = 11.8 MeV as well. The γ₃ yield exhibits two asymmetric peaks at E_p = 12.5 and 13.8 MeV (Γ ≈ 0.7 and 2.5 MeV) and a weaker structure at ≈ 9.8 MeV (1977SN01).

Resonances populated with E_p = 7 to 24.5 MeV beams were studied via γ-γ techniques by measuring the cascades feeding into the ¹²C*(15.1) state. In (2008CH13) peaks were found in the excitation function corresponding to E1 transitions from E_x = 24.41 ± 0.15 and 28.81 ± 0.10 MeV with Γ_cm = 1.3 ± 0.3 MeV and 2.0 ± 0.2 MeV, and (2J + 1) Γ_p₀Γ_γ/Γ = 20.8 ± 2.8 and 150 ± 18 eV, respectively. The peaks were found on a smooth excitation function that had previously been analyzed in (2004CH06).

(1983AN09, 1983AN16) have measured the cross sections for γ₀ and γ₁ for E_p = 18 to 43 MeV. They report giant resonances based on various excited states of ¹²C at E_x = 22.5 and 25.5 MeV (γ₀), 25.5, 27.4 and (31) MeV (γ₁), 27.4, 31 and (37) MeV (γ₃), as well as in the γ-yield to higher states. At E_p = 40, 60 and 80 MeV, radiative capture is observed to a state, or a narrow group of states, at E_x = 19.2 ± 0.6 MeV (1979KO05); see also (1982WE08). At E_{pol. p} = 50 MeV, angular distributions and analyzing power measurements are reported to ¹²C*(0, 4.4, 9.6, 18.8 ± 0.5 [u], 22.3 ± 1.0 [u]) by (1985NO01) [u = unresolved].

At E_p = 98 MeV, radiative capture to ¹²C*(0,4.4, 7.6, 9.6, 12.7, 15.1, 16.1 + 16.6, ≈ 19) (1990HO23, 1992HO04, 1996BR20: E_p = 98 and 176 MeV) and internal pair production to ¹²C*(0, 4.4, 9.64) (1993HO07, 1997TR01) are studied to gain insight into exchange current effects. See also (2000LI06). See other measurements in (1991CA25: E_p = 14.24 MeV, 1992KE03: E_p = 7 MeV, 1998MA85: E_p = 7.2 MeV).

(b) In (1993HO07, 1997TR01) radiative capture at E_p = 98 MeV followed by decay via internal pair conversion to ¹²C*(0, 4.4, 9.64) was measured; the internal conversion cross section was roughly two times larger than expected. At E_p = 1.6 MeV, the pair decay of ¹²C*(17.2) was studied (1996DE51) in a search for evidence of a massive neutral boson. See also (1994VA17).

(c) Excitation functions have been measured for E_p = 0.15 to 18.9 MeV (see 1975AJ02), 35.4 keV to 18 MeV (see 1980AJ01), 4.5 to 24 MeV (see 1985AJ01). Also see references listed below and in the comments of 12.19 (in PDF or PS), 12.20 (in PDF or PS) and 12.21 (in PDF or PS).

Astrophysically relevant ¹¹B(p, α) cross sections were measured in (1993AN06: E_p = 17 to 134 keV); see additional comments on electron screening in (1993AN06, 1997BA95, 2002HA51, 2002BA77) and other discussions in (1995YA07, 1996RA14, 2004RO27, 2004SP03, 2008LA18, 2010LA11, 2011ST01, 2012CO19, 2013KI06). The use of this reaction for clean fusion energy generation is discussed in (1996YU04: E_p = 0.165 to 2.58 MeV, 1998LI51: E_p = 667 and 1370 keV, 1999LI13, 2015BE28). Surface analysis techniques and related cross sections are given in (1991BA61: E_p = 660 keV, 1992LA08: E_p = 650 keV, 1996VO23: E_p = 160 to 800 keV, 1998MA54: E_p = 1.7 to 2.7 MeV, 2002LI29: E_p = 0.4 to 1.6 MeV, 2010KO33: E_p = 2.2 to 4.2 MeV). See additional theoretical analysis in (1992KO26, 1994SH21, 2006DM01).

The total cross section shows the 162 keV resonance and a broad peak centered at 600 keV. At E_cm = 300 keV σ(α₀) = 1.03 ± 0.06 mb and σ(α₁) = 165 ± 10 mb (1987BE17). The parameters of the 162 keV resonance are E_res(cm) = 148.3 ± 0.1 keV, Γ_cm = 5.3 ± 0.2 keV (1987BE17), 149.8 ± 0.2 keV, 5.2^+0.5_-0.3 keV (1979DA03). Derived S-values lead to S(0) = 197 ± 12 MeV ⋅ b (1987BE17).

The reaction proceeding via 3α breakup into the 3-body continuum is of astrophysical importance; however the reaction proceeds predominantly by sequential two-body decays via ⁸Be*(0, 2.9). In past reviews, the reactions ¹¹B(p, α)⁸Be and ¹¹B(p, α)⁴He⁴He were distinct in that experiments grouped with the later reaction detected both α particles from the decay of ⁸Be.

In (2016LA27) the 3-body decay of ¹²C*(16.11) was analyzed using Dalitz plots, which indicated primarily sequential decay. Analysis of the multiplicity = 2α and 3α events yields Γ_α₀/Γ = 0.054 ± 0.011 and 0.051 ± 0.005 respectively. The text includes discussion on the "ghost" of the ground state; it is suggested that a correction for the "ghost" could raise the Γ_α₀/Γ value by ≈ 25% to around 0.065, as in (2012AL22).

Beams of E_p = 0.675 and 2.64 MeV protons were used to study the decay mechanisms of ¹²C*(16.576, 18.38) (2011ST01); the decays were found to proceed primarily via l = 3 and 1 α₁ emission, respectively.

At higher energies, resonances are observed at E_p = 4.68, 5.10, 6.08, 6.58 and 7.11 MeV [E_x = 20.25 to 22.47 MeV] (1983BO19) and some broad structures are reported by (1983BU06). Contributions from ¹²C*(23.0, 23.6, 25.4) are reported in (1975VA04). A wide resonance-like structure centered at E_p = 13 MeV [¹²C*(28)] with Γ ≈ 6 MeV is reported by (1977BU07): the angular distributions of α₀ show prominent backward peaking. No marked structure is observed above E_x = 28 MeV (1972TH1C: Ph.D. thesis).

The parameters of the observed resonances are displayed in 12.19 (in PDF or PS) and 12.20 (in PDF or PS). The following summarizes the information on the low-lying resonances: for a full list of references see (1968AJ02, 1980AJ01).

E_p = 0.16 MeV [¹²C*(16.11)]. This is the J^π = 2⁺; T = 1 analog of the first excited states of ¹²B and ¹²N. The γ-decay is to ¹²C*(0, 4.4, 9.6): the angular distribution of γ₃, together with the known α-decay of ¹²C*(9.6), fix J^π = 3^- for the latter (1961CA13).

E_p = 0.67 MeV [¹²C*(16.58)]. The proton width [Γ_p ≈ 150 keV] indicates s-wave protons and therefore J^π = 1^- or 2^-. This is supported by the near isotropy of the two resonant exit channels, α₁ and γ₁. The α₁ cross section indicates 2J + 1 ≥ 5: therefore J^π = 2^-. [This is consistent with the results of an α-α correlation study via ⁸Be*(2.9) (1972TR07)]. The γ₁ E1 transition has |M|² ≈ 0.01 W.u., suggesting T = 1 (1957DE11, 1965SE06). (1962BL10) report a γ branch to ¹²C*(12.71) (≈ 6% of the intensity of the γ₁ transition). Such a branch may also be present for ¹²C*(17.23).

E_p = 1.4 MeV [¹²C*(17.23)]. (2J + 1) Γ_γ₀ ≥ 115 eV. This indicates J^π = 1^-, with T = 1 most probable (1965SE06). J^π = 1^- is also required to account for the interference at lower energies in α₀ and γ₀: see (1957DE11) and is consistent with the α-α correlation results of (1972TR07). Two solutions for Γ_p are possible; the larger (chosen for 12.19 (in PDF or PS) and 12.20 (in PDF or PS)) is favored by elastic scattering data (1965SE06).

E_p = 2.0 MeV [¹²C*(17.76)]. The resonance in the yield of α₀ requires natural parity, the small α-widths suggest T = 1. For J^π = 1^- or 3^- the small γ-widths would be surprising; J^π = 2⁺ would lead to a larger anomaly than is observed. J^π is then 0⁺; T = 1 (1965SE06). A study of E_p = 0.82 to 2.83 MeV reports that E_x = 17.80 MeV [Γ_cm = 96 ± 5 keV] decays via a 5.10 ± 0.03 MeV γ-ray to ¹²C*(12.71): Γ_γ = 3.7 ± 1.5 eV. The angular distribution is isotropic, as expected (1982HA12).

E_p = 2.37 MeV [¹²C*(18.13)]. Seen as a resonance in the yield of 15.1 MeV γ-rays: σ_R = 0.77 ± 0.15 μb, Γ_cm = 600 ± 100 keV, (2J + 1) Γ_γ ≥ 2.8 ± 0.6 eV. The results are consistent with J^π = 1⁺; T = 0, but interference with a non-resonant background excludes a definite assignment (1972SU08).

E_p = 2.64 MeV [¹²C*(18.38)]. The resonance for α₀ requires natural parity; the presence of a large P₄ term in the angular distribution requires J ≥ 2 and l_p ≥ 2. The assignment J^π = 3^- is consistent with the data (1965SE06, 1972CH35, 1972VO01, 1974GO21). (1982HA12) report E_x = 18.38 MeV, Γ_cm ≈ 400 keV, Γ_γ (to ¹²C*(9.6)) = 5.7 ± 2.3 eV, consistent with J^π = 3^-; T = 1. The total peak cross section is 4.2 ± 1.7 μb. Transitions to ¹²C*(0, 4.4) are also observed: Γ_γ ≈ 2 × 10^-3 eV and 3.2 ± 1.0 eV, respectively.

E_p = 2.66 MeV [¹²C*(18.40)] is not observed in these reactions: see ¹¹B(p, p).

E_p = 3.12 MeV [¹²C*(18.80)]. The angular distribution of γ₀ indicates E2 radiation, J^π = 2⁺. This assignment is supported by the angular correlation in the cascade γ₁ and by the behavior of σ(α₀); T = 1 is suggested by the small Γ_α (1965SE06). The yield of γ₃ (to ¹²C*(9.6)) shows a peak corresponding to E_x ≈ 18.9 to 19.0 MeV. It may be due to ¹²C*(18.8) with an energy shift due to interference (1982WR01).

The structure near E_p = 3.5 to 3.7 MeV [¹²C*(19.2, 19.4)] seems to require at least two levels. The large Γ_γ₀ requires that one be J^π = 1^-; T = 1 and interference terms in σ(α₀) require the other to have even spin and even parity: J^π = 2⁺; T = 0 is favored (1963SY01, 1965SE06). (1982WR01) do not observe any evidence for an isospin mixed doublet near E_x = 19.5 MeV [E_p = 2.9 to 4.6 MeV (60° and 90°)].

Levels at E_p = 4.93 and 5.11 MeV, seen in σ(γ₁) (1955BA22) also appear in σ(α₁), but not in σ(α₀). Angular distributions suggest J^π = 2⁺ or 3^- for the latter [¹²C*(20.64)]; the strength of γ₁ and absence of γ₀ favors J^π = 3^-; T = 1 (1963SY01, 1965SE06).

The first seven T = 1 states in ¹²B and ¹²C have been identified by comparing reduced proton widths obtained from this reaction and reduced widths obtained from the (d, p) and (d, n) reactions: see 12.12 (in PDF or PS) of (1980AJ01) and (1971MO14, 1974AN19).

21. ¹¹B(p, n)¹¹C Q_m = -2.7647 E_b = 15.9569

Excitation functions have been studied at E_p = 2 to 5, 2.6 to 5.5, 3 to 4, 4 to 11.5, 4 to 14 and 4.9 to 11.4 MeV [see (1968AJ02)], from threshold to 6.0, 5.4 to 7.5 and 10.87 to 27.50 MeV [see (1985AJ01)], E_p = 13.7 to 14.7 and 16 to 26 MeV [see (1990AJ01)]. At the higher energies the excitation function decreases essentially monotonically (1981AN16). At the lower energies many peaks are observed whose positions correspond with structures seen in ¹¹B(p, γ)¹²C and ¹¹B(p, α)⁸Be and ¹²C(γ, n) and ¹²C(γ, p) reactions, suggesting that resonances, and not fluctuations, are involved; see 12.21 (in PDF or PS). Angular distributions do not change as rapidly as might be expected from the pronounced structures in the excitation function (1965OV01). The strength of the pronounced peak at E_p = 6.03 MeV (E_x = 21.49 MeV) appears to demand J ≥ 4 (1961LE11). See also (1994SH21, 1995SH44, 1999AN35, 2009EL09).

Polarization measurements have been carried out for E_{pol. p} = 186 MeV (1994RA23, 1994WA22, 1995YA12) and 295 MeV (1995WA16) and at E_{pol. p} = 7.0 to 26.5 MeV [see articles cited in (1975AJ02, 1980AJ01, 1985AJ01)]. For high-energy interactions see (1994GA40, 1994GA49) and work cited in (1990AJ01).

22. ¹¹B(p, p)¹¹B E_b = 15.9569

States shown in 12.21 (in PDF or PS) are revealed in the excitation functions, which have been studied at E_p = 0.3 to 1.0, 0.6 to 2.0, 2 to 5.3 MeV [see (1959AJ76)], E_p = 0.5 to 4.0, 1.8 to 4.1 MeV [see (1968AJ02)], E_p = 1.9 to 3.0, 3.5 to 10.5, 7.5 to 21.5 MeV [see (1975AJ02)], E_p = 1.8 to 3.1, 1.9 to 3.0, 3.0 to 5.2, 3 to 8, 7.5 to 10.5 and 19.2 to 47.4 MeV [see (1980AJ01)], E_p = 4.5 to 7.5, and 5.4 to 7.0 MeV [see (1985AJ01)], and E_cm ≈ 0.15 to 1.1 MeV (1990AJ01), E_p = 0.3 to 1.05 MeV (2011AM02), 0.5 to 3.3 MeV (2001CH78), 1.7 to 2.7 MeV (1998MA54), 2.2 to 4.2 MeV (2010KO33). No pronounced structure is observed above E_x = 28 MeV (1969TH1B, 1971TH1F, 1972TH1C). It is reported that in all the channels and throughout this energy range a strong 2⁺ background is observed. It is suggested that it may be the low-energy tail of the isoscalar giant quadrupole resonance (1983BO19).

Polarization measurements are reported in (1975AJ02, 1980AJ01, 1990AJ01) and in (2003HA11, 2003HA12, 2004KA53). For studies of high-energy interactions see (2004KA53, 2004KA56). Applied uses of this reaction are discussed in (1990BO15, 1994MI21, 1998MA54, 2010KO33) Also see (1994SH21, 1998DO16, 2013HA17).

23. ¹¹B(p, d)¹⁰B Q_m = -9.2296

At E_{pol. p} = 11.34 to 11.94 MeV the VAP angular distributions and excitation functions of the deuterons have been studied by (1982BU03). See also (1991AB04, 1994SH21).

24. ¹¹B(d, n)¹²C Q_m = 13.7323

Angular distributions of the neutrons to many ¹²C states up to E_x = 17.23 MeV have been reported (see 12.22 (in PDF or PS)) for energies in the range E_d = 0.5 to 10 MeV [see (1968AJ02)], E_d = 2.5 to 4 MeV (1972ME06), E_d = 5.5, 6 and 11.8 MeV [see (1975AJ02)], E_d = 0.9 and 1.2 MeV (1975SI22), E_d = 7 to 16 MeV (1981AN16), E_d = 12 MeV (1983NE11), E_{pol. d} = 79 MeV (1985FO05, 1987FO22), and E_d = 111 keV (2001HO23), E_d = 120 to 160 keV (2006PA27) and E_d < 5 MeV (2013CO12).

Proton- and α-decay from excited states are reported in (1965OL01, 1985NE01). J^π = 3^- for the 9.64 MeV state is favored on the basis of the angular distribution of the α-particles to ⁸Be_g.s.. There is no evidence for direct 3α-decay of ¹²C levels in the range E_x = 9 to 13 MeV, nor does ¹²C*(10.3) appear to participate in this reaction (1965OL01). Relative spectroscopic factors obtained in several (d, n) and (³He, d) studies are summarized in (1975AJ02), but see (1971MU18) for a discussion of the problems involved in comparing spectroscopic factors obtained in these different reactions.

See a comparison of cross section calculations from the TALYS nuclear reaction code with reaction rates from the NACRE data base in (2012CO01). Angular correlations of neutrons and 4.4 MeV γ-rays and neutrons and 15.1 MeV γ-rays are reported in (1968AJ02, 1975AJ02). For polarization measurements see references in (1990AJ01).

25. (a) ¹¹B(³He, d)¹²C Q_m = 10.4634
(b) ¹¹B(³He, np)¹²C Q_m = 8.2388

Observed deuteron groups are displayed in 12.22 (in PDF or PS). Also see 12.17 (in PDF or PS), which has results from ¹⁰B(³He, p3α) and ¹¹B(³He, d3α) complete kinematics studies given in (2007BO49, 2009KI13, 2010KI08, 2011AL28, 2012AL22, 2012KI07, 2013KI07). Angular distributions have been measured at E(³He) = 5.1 to 44 MeV [see (1968AJ02)], 10, 11, 12, 18 and 44 MeV [see (1975AJ02)], 23.2 MeV [see (1980AJ01)], 43.6 MeV [see (1985AJ01)], 18.3 and 22.3 MeV [see (1990AJ01)] and 44 MeV (2012SM06). The angular distributions exhibit characteristic direct interaction features (1967CR04). A J^π = 2⁺ state at E_x = 11.16 was reported at E(³He) = 44 MeV in (1971RE03): the group appeared as an enhancement on the high energy side of the E_x = 10.84 MeV peak; however a study under the same kinematic conditions found no evidence for such a peak (2012SM06). The R-matrix analysis of (2012SM06) showed that the fit to their data was improved by including a J^π = 2⁺ resonance at E_x = 9.7 MeV: note there is no visible peak in the spectrum at this energy. At E(³He) = 22.3 MeV, spectroscopic factors of S = 1.6 and 0.33 are deduced for ¹²C*(0,4.4), respectively (1993AR14); See 12.14 (in PDF or PS) in (1980AJ01) for earlier reported values and see (2010TI04, 2016CO14). The d₁-γ angular correlations are studied in (1988IG03).

26. ¹¹B(α, t)¹²C Q_m = -3.8570

Angular distributions of t_0-3 and to ¹²C*(12.7) have been measured at several energy between E_α = 15.1 to 120 MeV [see references in (1968AJ02, 1975AJ02, 1980AJ01, 1985AJ01 1990AJ01)]. Single-proton transfer seems to be the dominant reaction mode (1967DE1K). Angular correlation measurements of t₁-γ are reported at E_α = 21 to 30 MeV: see (1972EL09, 1987VA04, 1988IG04). See also reaction mechanism studies in (1989BA86, 1990BO23, 1990BA62, 1991BA23, 1998GA46, 1999GA43, 1999LE48).

27. ¹¹B(⁷Li, ⁶He)¹²C Q_m = 5.9829

At E(⁷Li) = 18.3 and 28.3 MeV, angular distributions to ¹²C_g.s. were measured and analyzed via DWBA to determine the ⁶He + ¹²C and ⁷Li + ¹¹B optical Model parameters (2009WU01). At E(⁷Li) = 34 MeV, angular distributions have been measured and spectroscopic factors deduced for the groups to ¹²C*(0, 4.4, 7.7, 9.6, 10.8, 11.8, 12.7, 15.1, 16.1, 18.35) (1983NE11, 1987CO16). It is concluded on the basis of these and other works, that the group corresponding to E_x = 18.35 ± 0.05 MeV (Γ = 350 ± 50 keV) consists of unresolved ¹²C states with J^π = 3^- (T = 1) and 2^- (T = 0 plus some mixing of T = 1). No states were observed with E_x > 18.35 MeV.

28. ¹¹B(¹¹B, ¹⁰Be)¹²C Q_m = 4.7283

Angular distributions involving ¹²C*(0, 4.4) and ¹⁰Be*(0, 3.4) have been measured at E(¹¹B) = 11 MeV (1985PO02).

29. ¹¹B(¹³N, ¹²C)¹²C Q_m = 14.0134

The ¹³N valence proton wave function was evaluated using the (¹³N, ¹²C) reaction on ¹¹B at E(¹³N) = 29.5 and 45 MeV (1998DI14). States at ¹²C*(0, 4.44, 15.1) are found to participate, along with 3α unbound states. Further studies on ²⁴Mg states, some of which are found to possess significant components of 3^-₁ + 3^-₁, 3^-₁ + 1^-₁ and 0⁺₂ + 3^-₁, are given in (1999DI04, 2001DI12).

30. (a) ¹¹B(¹⁴N, ¹³C)¹²C Q_m = 8.4063
(b) ¹¹B(¹⁶O, ¹⁵N)¹²C Q_m = 3.8295

Angular distributions to ¹²C_g.s. were measured at E(¹⁴N) = 41, 77 and 113 MeV (1971LI11) and optical model parameters were deduced. For reaction (b), angular distributions to ¹²C*(0, 4.44, 9.6) have been measured at E(¹⁶O) = 27, 30, 32.5, 35 and 60 MeV (1972SC03): at the highest energy the ratio of relative spectroscopic factors, θ²/θ²_g.s., for the transitions ¹¹B_g.s. + p → ¹²C* is 0.12 and 0.05, respectively, for ¹²C*(4.4, 9.6). See (1975SC35) for analysis of reactions to the ground state at E(¹⁶O) = 27 to 35 MeV, and see (1992KA19) for analysis of multi-cluster transfer processes in the reaction.

31. ¹¹C(d, p)¹²C Q_m = 16.4971

The impact of reactions such as ¹¹C(n, γ), ¹¹C(n, α) and ¹¹C(d, p) on nucleosynthesis is analyzed (2012CO01).

32. ¹²B(β^-)¹²C Q_m = 13.3694

¹²B decay to ¹²C is complex. Most of the decay populates ¹²C_g.s. with small branches populating ¹²C*(4.4) and several α-particle unbound states (see 12.24 (in PDF or PS)). See general discussion in (1992BA11, 1993CH06). The ground state decay branch is determined by subtracting all other observed decay branches from unity. Early studies were motivated by evaluation of the ¹²B and ¹²N mirror decays to states in ¹²C and by parity violation studies. The decay rates to ¹²C*(4.4) measured in (1981KA31) are deduced while taking significant care to decrease systematic effects that could distort the results; they are the most precise and have been used as normalization factors in modern experiments to deduce the relative and absolute branching ratios of weaker decay branches. We adopt the branching ratios of (1981KA31) to ¹²C*(4.4).

Significant efforts have focused mainly on the ratio of the β-decay branches of ¹²B and ¹²N to ¹²C*(4.4) and the relevance of mirror asymmetries in β-decay; see 12.23 (in PDF or PS). In the case of ¹²N, the measurement is complicated because the high-energy 17.3 MeV β⁺ particles can produce Bremsstrahlung photons and give rise to a huge background. A lower Q-value in the case of ¹²B β^--decay makes these measurements less complicated. Discussion on systematic effects in the measurements is given in (1974MC11, 1978AL01).

In (1963PE10, 1963WI05) the experimental layout used a scintillator β-counter that covered only part of the total solid angle along with NaI detectors; the β-γ coincidence data were analyzed. Other experimental efforts surrounded the targets with well-type scintillators while also detecting γ-rays in a NaI detector and analyzing the β-γ coincidence events (1972AL31, 1974MC11). The use of Ge(Li) and HPGe detectors significantly improved results from the measurements reported in (1978AL01, 1981KA31, 1988NA09). In most cases, the ratio of ¹²B-to-¹²N β-γ(4.44) coincidences was measured by using an essentially identical configuration for the two decays; then in some cases the configuration was modified to permit an absolute measurement of the ¹²B decay branch to ¹²C*(4.4) (1978AL01). In (1963PE10, 1981KA31) absolute ¹²N decay intensities were measured along with the mirror decay ratio.

In the early study of (1957CO59) β-delayed α particles were studied in an effort to validate the prediction of a narrow "3α" state located just above the breakup threshold. The Hoyle state was reported in ¹²B decay with the branching ratio (1.3 ± 0.4)%, J^π = 0⁺ and Q(¹²C-⁸Be-α) = 278 ± 4 keV (E_x = 7.65 MeV). Analysis of a higher energy α group (1958CO66) was consistent with a broad J^π = 0⁺ (or 2⁺) state near 10.1 MeV with a (0.13 ± 0.04)% branching ratio. Later, in (1963WI05) the α, β and γ products were measured and analyzed for evidence of states in the E_x = 9 to 12 MeV region; their best fit included states at E_x = 10.1 and ≈ 11.8 MeV. It is later pointed out in (1967AL03, 2009HY02) that the early works such as (1958CO66, 1963WI05) assigned too much intensity to the E_x = 10.3 MeV strength because they were unaware of the presence of the E_x = 12.71 MeV state. The work of (1966SC23) found evidence for ¹²C*(10.3 ± 0.3) decaying primarily to ⁸Be_g.s. + α₀ with a likely J^π = 0⁺ and for ¹²C*(12.71) decaying > 96% to ⁸Be*(2⁺) + α, hence J^π = 1⁺. The relative ratio of I_β(10.3)/I_β(12.7) was found as 0.20 ± 0.05.

On the other hand, the studies of (1962MA22, 1963GL04) used magnetic spectrometers to measure the β^∓-particle energy spectra. While the main thrust of these measurements focused on the energy dependence of the shape factors, results on intensities to ¹²C*(7.65, 10.3) were also obtained in the analysis. See also (2015MO10).

In (1963AL15), the γ_3.23-γ_4.44 sequential de-excitation γ rays from ¹²C*(7.65) and the β-γ_3.23-γ_4.44 events are analyzed to determine Γ_γ/Γ(7.65) = (3.8 ± 1.5) × 10^-4 and the (1.7 ± 0.5)% for the ¹²B β-decay branching ratio to ¹²C*(7.65). A similar measurement was carried out using the Gammasphere array (2016MU06); in that work (0.64 ± 11)% is determined for the β-decay branching ratio to ¹²C*(7.65) and E_γ = 3216.9 ± 0.4 (stat.) ± 0.7 (sys.) keV and 4439.5 ± 0.7 (sys.) keV are determined for the transitions between the J^π = 0⁺₂ → 2⁺₁ and J^π = 2⁺₁ → 0⁺₁ states. This corresponds to E_x = 7657.8 ± 1.0 keV, which is in poor agreement with the adopted value in 12.13 (in PDF or PS), E_x = 7654.07 ± 0.19 keV (1976NO02). In 12.24 (in PDF or PS) it is highlighted that some of the differences in published branching ratios are connected with the use of updated values in their computations.

In (1973BA73) the energy of the Hoyle state was determined by implanting ¹²B activity, produced via the ¹¹B(d, ¹²B) reaction, into a thick Si detector and measuring the 3-α breakup energy, Q = 379.6 ± 2.0 keV.

Prior to development of rare isotope facilities, the ¹²B and ¹²N activities were typically produced in the target using the ¹¹B(d, n) and ¹⁰B(³He, n) reactions, respectively. These approaches have the disadvantage of producing unwanted activities such as ¹¹C, ¹³N and ¹⁴O in the targets. Renewed interest in the higher-lying J^π = 0⁺ and 2⁺ states led to measurements where ¹²B and ¹²N were produced at rare isotope facilities. An early series of experiments (2002FY02, 2003FY02, 2003FY04, 2004BO43, 2004FY02, 2004FY03) focused on identifying ¹²C*(10.3) → ⁸Be_g.s. + α and ¹²C*(12.71) → ⁸Be*(2⁺) + α₁ as the dominant breakup mechanisms for these states by analyzing the α-particle correlations. These data also gave indications of important interference effects between the E_x = 7.65 and 10.3 MeV J^π = 0⁺ states, as had been suggested in (1963WI05). In follow up measurements, two different experimental approaches enhanced the available data (2005DI16, 2009DI06, 2009HY01, 2009HY02, 2014TE01); in one case the ions were implanted into a thin carbon foil and the full decay kinematics of breakup α-particles was measured. Analysis yielded the decay intensity of ¹²C excited states along with an assessment of the decay mechanism. In the second approach, ions were implanted in a segmented strip detector whose thickness stopped the full decay energy of breakup α-particles; this calorimeter approach provided a measure of the energies populated in ¹²C with fewer systematic effects than prior experiments. The general shapes of spectra observed in (2009HY01, 2009HY02) were found in reasonable agreement with prior results. Implementation of HPGe detectors in the setups of (2009HY01, 2009HY02) permitted a simultaneous and absolute normalization of the β branching ratios to all unbound states using the known branching ratio to the ¹²C*(4.44) state. In this case, the total intensities of ¹²C*(12.71, 15.11) must be adjusted to account for the Γ_γ decay branches. See 12.24 (in PDF or PS).

The work of (2009HY01, 2009HY02, 2010HY01) focused on a search for unknown and unresolved J^π = 0⁺ and 2⁺ strength in the E_x = 9-16 MeV region. Their analysis found that interference of the J^π = 0⁺₂ state with other J^π = 0⁺ strength around E_x ≈ 11.2 MeV leads to "the very broad component from 8.5 to 11 MeV, which has been mistaken for a 10.3-MeV resonance with a 3-MeV width". Rather than attribute their observed strength to a 10.3 MeV group, they provided the β feeding strength for the E_x = 9-12 MeV and 12-16.3 MeV regions [excluding the 12.7 MeV state]. In (2010HY01), a multi-level many-channel R-matrix analysis of the data was carried out. The data was best fit with a J^π = 0⁺ state at E_x = 11.2 ± 0.3 MeV with Γ = 1.5 ± 0.6 MeV and B(GT) = 0.06 ± 0.02 and a J^π = 2⁺ state at E_x = 11.1 ± 0.3 MeV with Γ = 1.4 ± 0.4 MeV and B(GT) = 0.05 ± 0.03.

33. ¹²C decay

Violation of the Pauli exclusion principle could permit ¹²C to decay by converting a p-shell nucleon into as 1s_1/2-shell nucleon followed by emission of a ≈ 20 MeV γ ray. The reaction has not been observed. The limit on the mean lifetime of ¹²C for this decay is τ_m ≥ 5.0 × 10³¹ yr (2010BE08); see also (1979LO13, 1998BA57, 1999AR22). Lifetimes for other ¹²C_g.s. exotic decays are > 8.9 × 10²⁹ yr (2010BE08); see also (2003BA42).

34. (a) ¹²C(γ, n)¹¹C Q_m = -18.7217
(b) ¹²C(γ, 2n)¹⁰C Q_m = -31.8414

The total absorption, mainly (γ, n) + (γ, p), is dominated by a giant resonance peak at E_x = 23.2 MeV, Γ = 3.2 MeV [σ_max = 21 mb] and by a smaller structure at E_x = 25.6 MeV, Γ ≈ 2 MeV [σ_max ≈ 13 mb]: see (1975AH06) and references tabulated in (1968AJ02, 1975AJ02).

The (γ, n) cross section shows a giant resonance, σ_max ≈ 7 - 8 mb, centered at about 23 MeV and consisting of an ≈ 1 MeV-wide group at 22.3 MeV and an ≈ 2 MeV-wide group at ≈ 23.3 MeV. A secondary maximum occurs at 25.5 MeV, Γ ≈ 2 MeV with evidence for other structures at ≈ 30 - 31 and possibly at ≈ 35 MeV (1966FU02, 1966LO04); see also (1999AB39, 1999AB40, 2000AB35: E_brem = 20 MeV), (2003CH80, 2016HE07) and the atlas of photo-neutron cross sections (1988DI02).

The (γ, n₀) cross section has been measured at θ = 90° for 21 < E_x < 40 MeV and compared with the (γ, p₀) cross section (1968WU01): the isospin mixing averages about 2% in intensity and shows structure at the giant resonance. Angular distributions of n₀ measured over the giant resonance region indicate that the main excitation mechanism is of a 1p_3/2 → d_5/2 E1 single-particle character. No significant E2 strength is observed (1968RA21). At E_γ = 60 MeV a comparison of the (γ, n₀) and (γ, p₀) cross sections indicates the reaction mechanism is absorption and suggests the reaction is useful for studying correlated n-p pairs (1980GO13). A comparison of the ¹²C(γ, p)³H2α and ¹²C(γ, n)³He2α reactions at E_γ = 30 to 120 MeV is given in (2007AF02). See also results in (1993AN17: E_brem = 58 MeV), (2001KO62: E_brem = 70 to 140 MeV) and (1994RY03, 2000LE38, 2003VA20, 2011DZ02).

The (γ, 2n) cross section (reaction (b)) is much smaller than that for (γ, n): the highest value is 0.15% of the maximum value for reaction (a) in the energy range E_γ = 20 to 140 MeV (1970KA37). The reaction has been studied for E_brem = 100 to 800 MeV with an emphasis on ¹¹C production (1977JO02): see other references in (1975AJ02, 1980AJ01, 1985AJ01, 1990AJ01).

35. ¹²C(γ, p)¹¹B Q_m = -15.9569

The photoproton cross section exhibits two broad peaks, the giant resonance peak at 22.5 MeV, Γ = 3.2 MeV, σ_max = 13.1 ± 0.8 mb and a 2 MeV broad peak at 25.2 MeV, σ_max = 5.6 ± 0.3 mb: see (1976CA21) and values listed in 12.19 (in PDF or PS) in (1968AJ02). The (γ, p₀) cross section at the giant resonance is 11.0 ± 1.1 mb (1986KE06). While the E1 component dominates in the GDR, a 2% E2 contribution may be present (1976CA21). In contrast with the giant resonance peak in the (γ, n) cross section, the (γ, p) cross section shows a sharp peak in the center of the broad giant resonance peak. See also (1991IS09). Above 24.5 MeV the ground state (γ, p) and (γ, n) excitation functions have the same shape up to at least 36 MeV: see (1985FU1C).

The (γ, p) results of (1968FR12, 1968FR14, 1969CA22) are in good agreement with those of (1964AL20) for the inverse reaction, ¹¹B(p, γ₀)¹²C [see reaction 20], when the population of ¹¹B*(4.4, 5.0) is taken into account: the required cross sections for the (γ, p₂) and (γ, p₃) processes peak at 1.5 mb at 29 and 30 MeV, respectively (1973DI1C, 1974DI17).

The population of ¹¹B states has been determined at various energies. The ground state is predominantly populated in these reactions; see measurements and discussion in (1980AJ01, 1985AJ01, 1990AJ01) and (1986AN25, 1986MC15, 1990SP06, 1990VA07, 1990VA09, 1991IS09, 1993IR01, 1994NI04, 1994ZO01, 1995HA03, 1995MO18, 1996KU36, 1996RU15, 1997AS01, 1997ZO02, 1998KU23, 1998SO18, 2001ME29, 2006MO11). Nuclear transparency, as well as the roles of different reaction mechanisms, including quasi-deuteron knockout, are investigated in (1990VA07, 1992RY02, 1992VA01, 1993HA12, 1993IR01, 1994IR01, 1994NI04, 1994RY03, 1995MO18, 1996AS02, 1996JO15, 1996RU15, 1997AS01, 1997BO22, 1997JO07, 2000LE38, 2002ME17, 2005GL05, 2005KA54, 2006CO19, 2013RO17).

Reactions in the Δ resonance region are discussed in (1992BA57, 1992GL04, 1995CR04, 1997JO07, 1997LI30, 1998GL14, 1999FI01, 2000DE58, 2000GL08, 2001MA31, 2002ME17, 2003GL03, 2006AN22, 2008GL05, 2010GL02, 2012GL02, 2013GL03, 2014GL03). In this region peaks corresponding to the removal of s-shell or p-shell protons from ¹²C are observed in the missing mass spectrum, and quasi-free photo pion production is an important reaction mechanism. Searches for Δ components in the ¹²C_g.s. are discussed in (2001BY01, 2002BY03). Evidence for η-mesic ¹¹B atoms is claimed in (1999SO18, 2000SO19, 2000YO02, 2002BA21); also see (1995LE26, 1996LE11, 1996RO06, 1997FI07, 1997HE14, 1998AB13, 1998EF09, 1998HE18, 1998PE12, 1999LE35, 1999TR09, 2000EF04, 2001BL13, 2001TR06, 2003HE18, 2003VA08, 2004MA27, 2005MO04, 2005NA17, 2005NA25, 2005NA35, 2006NA34, 2007HE29, 2008JI06, 2008ME15, 2015NE10).

36. (a) ¹²C(γ, π⁰)¹²C Q_m = -134.9766
(b) ¹²C(γ, π⁺)¹²B Q_m = -152.9396
(c) ¹²C(γ, π^-)¹²N Q_m = -156.9083

Photo-pion production has been measured at E_γ = 111 to 160 MeV (1997BE22), 120 to 819 MeV (2008TA05), 130 to 165 MeV (1995VO17), 141 to 159 MeV (2008BA24), 170 to 177 MeV (1995GO27, 2008GO20), 200 to 350 MeV (2002KR02), 200 to 800 MeV (1998KR28, 2004KR16), 300 to 400 MeV (1991BE16) and 4.5 GeV (1993EG06). The 2π⁰ correlations were measured at E_γ = 200 to 820 MeV (2003ME32) and at 400 to 460 MeV (2002JA10, 2002ME22). General discussion, for example on photo-pion production in the Δ-resonance region, can be found in (1991TR02, 1992CA16, 1994BE31, 1994KO23, 1994OS02, 1995BA92, 1995HO12, 1996MA20, 1997EF03, 2000GL08, 2002BA23, 2004MU17, 2006DA17, 2007TR04, 2008CO04). Coherent photo-pion production is discussed in (1991BO26, 1993CA35, 1993LA07, 1993OL06, 1996TR07, 1997KA65, 1998PE09, 1999AB42, 1999DR17, 2005KR18, 2010NA04, 2012ZH39), and in-medium effects are discussed in (1996OS02, 1999LE35, 2002RO28, 2003RO20, 2003VI09, 2003VI11, 2005KR10, 2005RO13, 2006SC18). For ¹²C(γ, π⁺) see ¹²B reaction 23 and for ¹²C(γ, π^-) see ¹²N reaction 8.

37. (a) ¹²C(γ, d)¹⁰B Q_m = -25.1864
(b) ¹²C(γ, pn)¹⁰B Q_m = -27.4110
(c) ¹²C(γ, t)⁹B Q_m = -27.3663
(d) ¹²C(γ, pd)⁹Be Q_m = -31.7731

Cross sections and angular distributions of the deuterons corresponding to transitions to ¹⁰B_g.s. and/or low excited states have been measured at E_γ ≈ 40 MeV: the results are consistent with E2 strength. There is some evidence for the excitation of higher states of ¹⁰B via non-E2 transitions (1972SK08). For E_brem = 90 MeV, the ratio of the yields of deuterons to protons is ≈ 2%, for particle energies 15 to 30 MeV. For higher particle energies, the ratio decreases (1962CH26). The excitation function for deuterons to E_γ = 1.4 GeV is given in (1969AN10, 1971AN15, 1972AN09, 1972AN22). The (γ, pn) reaction has been studied at E_γ = 83 to 133 MeV by (1988DA16), at E_brem = 150 MeV by (1999KH06) and in the Δ-resonance region by (1987KA13, 1996HA17, 1996LA15, 1998HA01, 1998MA02, 1998YA05, 1999FR32, 2000WA20, 2001PO19); see also (1996OS01, 1998RY01, 1999IR01, 2000GR13, 2003WA01).

Momentum spectra for deuterons and tritons (reactions (a) and (c)) are reported at E_γ = 300 to 600 MeV by (1986BA07). The yield of tritons has been measured for E_γ = 35 to 50 MeV: see (1967KR05) and E_γ < 1.2 GeV (1972AN09). For reaction (d) see (1987VO08: E_brem = 80 MeV), (1999MC06: E_brem = 150 to 400 MeV) and (2007WA12: E_{pol. brem} = 170 to 350 MeV).

38. ¹²C(γ, α)⁸Be Q_m = -7.3666

A study of the α breakup cross section using quasi-monoenergetic and polarized beams with E_γ = 9.0 to 10.7 MeV found enhanced E2 strength corresponding to E_x = 10.03 ± 0.11 MeV with Γ = 0.80 ± 0.13 MeV and Γ_γ = 60 ± 10 meV (2013ZI03); in the analysis the α-⁸Be breakup angular distribution was analyzed to determine the E1/E2 contributions and the mixing phase. This state is interpreted as the J^π = 2⁺ excitation of the E_x = 7.65 MeV astrophysically important Hoyle state. Also see (2011GA09, 2012GA39), (2016HA05: theory) and (1994OB03, 2011GA47, 2011IS14, 2013IS05, 2014IS06, 2015GA17: astrophys.).

At higher energies, the total cross section exhibits broad peaks at E_x = 17.47 ± 0.12 MeV with Γ = 6.12 ± 0.14 MeV and 27.12 ± 0.34 MeV with Γ = 4.56 ± 0.14 MeV (2008AF04). A pronounced minimum occurs at 20.5 MeV: to what extent the peaks have fine structure is not clear; see (1964TO1A) and references in (1968AJ02). Alpha energy distributions show surprisingly strong E1 contributions below E_γ ≈ 17 MeV (1955GO59, 1964TO1A). For E_γ < 22 MeV, transitions are mainly to ⁸Be_g.s. and ⁸Be*(2.9) with the g.s. transition dominating for E_γ ≲ 14 MeV. For E_γ > 26.4 MeV, ⁸Be (T = 1) levels near 17 MeV are strongly excited (1955GO59, 2008AF04). The mechanism for formation of various ⁸Be excited states up to E_x ≈ 23 MeV was carefully studied for photon energies below E_brem = 40 MeV (2008AF04), and resonances have been deduced; see 12.25 (in PDF or PS). See also (1992DZ02, 1993KI15, 1997GO16, 1998KO77, 2001KI33, 2002KO65).

The ratio for σ(γ, α₀)/σ(γ, p₀) is 0.029 ± 0.012 at E_γ = 28 MeV (1989FE01). For other breakup processes see (1975AJ02, 1985AJ01).

39. ¹²C(γ, γ)¹²C

Inelastic scattering has also been reported to ¹²C*(4.4, 9.6 ± 0.2, 11.8 ± 0.2, 12.7, 13.3 ± 0.2, 17.2 ± 0.2, 18.3 ± 0.2, 20.5 ± 0.2, 22-24 (giant resonance), 26.5 ± 0.4, 29.5 ± 0.3): see details in (1980AJ01) and (1980IS09, 1980IS13, 1982NOZV).

The E_x of ¹²C*(4.4) is reported as 4439.4 ± 1.6 keV (1977WE1C), and the lifetime of the 4.4 MeV state was determined as τ_m = 65 ± 12 fsec (1958RA14).

Resonance scattering and absorption by ¹²C*(15.11) have been studied by many groups: see 12.15 (in PDF or PS) in (1968AJ02). The branching ratios and partial widths are displayed in 12.9 (in PDF or PS) in (1975AJ02) and 12.14 (in PDF or PS). The scattering angular distribution indicates dipole radiation (1959GA09), the azimuthal distribution of scattered polarized radiation indicates M1 (1960JA01) and the large Γ_γ indicates T = 1. The branching ratio for the cascade decay via ¹²C*(4.4) was reported as (3.6 ± 0.7)% (1970AH02).

The ground-state width of ¹²C*(16.11) was first reported as Γ_γ₀ = 7.5 ± 1.9 eV (1959KE19): see, however, 12.14 (in PDF or PS) which shows a much smaller accepted value. For ¹²C*(17.22), the scattering cross section is 1.0 ± 1.0 μb, consistent with Γ_γ from ¹¹B(p, γ) (1963SC21).

At higher energies, elastic scattering studies show the giant resonance peak at ≈ 24 MeV. A considerable tail is visible, extending to > 40 MeV (1959PE32). At E_γ = 23.5 MeV, the peak of the giant resonance, the total photonuclear absorption cross section is 19.7 ± 0.4 mb (1983DO05), and Γ₁/Γ₀ = 0.23 ± 0.07.

In (1990SC02) the cross sections were measured for E_γ = 15 to 140 MeV using tagged Bremsstrahlung photons. At low energies, ¹²C*(15.1) and the GDR are prominent, while the scattering cross section is essentially flat above E_γ = 30 MeV. The ¹²C*(16.1) state and additional strength are observed in the inelastic scattering to ¹²C*(4.4). The ratio of dσ(150°)/dσ(60°) was studied in this range to reveal E1/E2 interference effects; E2 states are suggested near E_x = 28 and 32 MeV. Previous measurements of the cross section at θ = 90° and 135° for E_γ = 23.5 to 39 MeV indicated a significant E2 strength [1.9^+0.8_-0.7 total isoscalar + isovector energy weighted sum rule] in addition to the dominant E1 strength (1980DO04, 1983DO05). However, measurements of the elastic differential cross sections for E_γ = 22.5 to 52.0 MeV (θ = 45°, 90°, 135°) reported by (1984WR01, 1985WR02) were inconsistent with the results of (1980DO04, 1983DO05). The difference between the measured energy-integrated values of σ(γ) and the E1 part of the photo-absorption cross section σ_E1(γ) was small and not sufficient to verify E2 strength (1985WR02).

The scattering cross section has been measured for E_γ = 150 to 400 MeV by (1984HA08). Angular distributions for elastic and inelastic scattering are measured at E_brem = 158.8, 195.2, 197.2, 247.2 and 290.2 MeV (1995IG01). Measurements of elastic and inelastic scattering to ¹²C*(4.4) at E_γ = 200 to 500 MeV, including the Δ-resonance region, are given in (1993AH01, 1994WI13). A measurement of the total photoabsorption cross section for E_γ = 600 to 1500 MeV is given in (2010RU16). See theoretical analyses in (1996PA06, 1998HU01, 2002SC15, 2002VA01). For pair-production measurements at E_brem = 4.2 to 31.1 MeV see (1983NO06).

The polarizabilities of bound nucleons in ¹²C and ¹⁶O were measured at E_γ = 61 and 77 MeV (1992LU01). The deduced values, α̃_N = (11.5 ± 0.8 (stat.) ± 2.1 (sys.)) × 10^-4 fm³ and β̃_N = (2.5 ∓ 0.8 (stat.) ± 2.1 (sys.)) × 10^-4 fm³, are in close agreement with the values for free nucleons. However, see the analysis of (2001WA24: E_γ = 84 to 105 MeV), which suggests that definite conclusions are severely hampered by model dependencies. See also (1995HA23: E_γ = 58 and 75 MeV, 2014MY01: E_γ = 65 to 115 MeV).

40. ¹²C(e, e)¹²C

Elastic scattering has been studied up to several GeV. The form factor is well accounted for by a harmonic-well model. Measurements of the elastic scattering form factor indicate the nuclear charge radius is < r² >^1/2 = 2.471 ± 0.009 fm [2.478 fm with dispersion corrections] (1991OF01), 2.464 ± 0.012 fm [2.468 fm with dispersion corrections] (1982RE12) and 2.472 ± 0.015 fm (1980CA07). This compares with < r² >^1/2 = 2.4829 ± 0.0019 fm from muonic X-ray studies (1984RU12). Other values are reported in (1968AJ02, 1975AJ02). See also (1995AN02, 1995AN13, 2010HA14). (1991OF01) reports evidence for an energy dependence of the elastic form factors.

The isoscalar vector hadronic coupling constant, γ = 0.136 ± 0.032 (stat.) ± 0.009 (sys.) (1990KO47, 1990SO03, 1991SO08), is determined from analysis of parity violating electro-weak asymmetry in elastic scattering. Use of the parity violating elastic scattering asymmetries to obtain neutron densities is discussed in (2011MO35, 2012AB04, 2014MO03). See also (1990SU15, 1992MI09, 1993AL07, 1993AL20, 1993HO03, 1995KA14, 1998HO12, 2005ME10, 2009MO35).

Sharp inelastic peaks are reported along with widths in 12.26 (in PDF or PS). See also (2009DE14, 2011AN17).

A study of the (e, e'γ) reaction by (1985PA01) shows that the relative phase of the longitudinal and transverse form factors of ¹²C*(4.4) is negative.

Inelastic scattering data for the ¹²C*(7.65) Hoyle state at E_e = 73 MeV was collected and analyzed along with the world data resulting in the value Γ_π = 62.3 ± 2.0 μeV for radiative decay (2009CHZX, 2010CH17, 2011VO16). This value is compared with prior measurements and other analyses; see (2005CR03) and (2014FR09) for references. Analysis of data in (2007CH04) suggests that the Hoyle state is dilute with a radius about 1.5 times larger than that of the ground state.

The longitudinal form factor for the J^π; T = 1^-; 0 isospin forbidden transition to ¹²C*(10.84), which is sensitive to isospin mixing, was analyzed and indicates a transition strength B(E1) = 0.39 ± 0.20 × 10^-5 e² ⋅ fm² (1995CA14).

The isospin mixing between ¹²C*(12.71) and ¹²C*(15.11) [both J^π = 1⁺; T = 0 and 1, respectively] has been measured by (1974CE01): β = 0.19 ± 0.01 or 0.05 ± 0.01. The inelastic scattering to ¹²C*(12.71, 15.11) was analyzed at q < 0.5 fm^-1, Γ_γ₀ = 0.32 ± 0.02 eV and 35.0 ± 1.1 eV were deduced, respectively (2000VO04). The results were combined with (1972SP1C) and (1973CH16) (other low q results) and produced an average of 35.9 ± 0.06 eV for the later transition. These compare with 38.5 ± 0.8 eV from (1983DE53). The Coulomb matrix element was also analyzed in (2000VO04); ME = +118 ± 8 keV was deduced.

The longitudinal form factors show ¹²C*(16.1, 18.6, 20.0, 21.6, 22.0, 23.8, 25.5) while the transverse form factors show ¹²C*(15.1, 16.1, 16.6, 18.1, 19.3, 19.6, 20.6, 22.7, (25.5)). At E_e = 150.6 MeV (θ = 180°) two peaks are observed at 16.1 and at 19.6 MeV corresponding to E2 and M2-M4 excitations (1984RY01).

There appears to be evidence for structures at 18.1 ± 0.05, 19.5 ± 0.05 (Γ = 0.5 ± 0.1), ≈ 24 and ≈ 34 MeV (1964GO14). The variation of F(q²) with q² in the range 0-0.6 fm^-2 shows good agreement with the calculations of (1964LE1D) which assumes four 1- particle-hole states at E_x = 19.6, 23.3, 25.0 and 35.8 MeV (see also (1967CR02)). The behavior of the 19.2 MeV level suggests ascription to the expected giant magnetic quadrupole state J^π = 2^-; this state is not likely to have been seen in ¹¹B(p, γ)¹²C (1965DE1C, 1965DE1K, 1967BI1K, 1967CR02). A positive parity state with a large longitudinal matrix element may also be present (1967BI1K).

No ΔT = 2 excitations were observed in a search for isotensor components of the electromagnetic interaction (1993LO13).

Results and general analysis on scattering at medium to high energies are given in (1990DA14, 1991BR13, 1991BU04, 1991DE32, 1991ER06, 1991TA23, 1992PR01, 1992WA19, 1993AM11, 1993AR06, 1993DE33, 1994AM06, 1994JE04, 1995AV01, 1995DO23, 1995JO21, 1995MO11, 1995VA12, 1995VA33, 1997GI12, 1998RI01, 1999GU20, 2001CA04, 2001GU16, 2002CA26, 2003KI06, 2003KI09, 2003ME09, 2004KI21, 2005KI26, 2006KU01, 2006MA62, 2008CE01, 2009LI04, 2010AM01, 2010HA14, 2014KI06, 2015LO05, 2015MO24, 2015PA35, 2016RO32).

Reviews on the scaling and superscaling behavior of quasielastic electron scattering reaction cross sections are found in (2009MA57, 2010CA14). See other detailed discussion on scaling approaches in (1999DO05, 2003HA44, 2005AM03, 2005NA03, 2006BA62, 2006CA22, 2006CO15, 2007AM01, 2007KI16, 2007MA18, 2009AN06, 2009CI01, 2009MA57, 2009ME07, 2010AM01, 2011AN09, 2015AM02, 2015BE26, 2015KI01, 2016IV03).

Electro-production of hypernuclei is discussed in (1998HI15, 2003MI11, 2003TA41, 2005GA09, 2006YU03, 2007IO02, 2007TA25, 2008HA14, 2008LE08, 2010FU13, 2010GA29, 2014TA26).

41. (a) ¹²C(e, e'p)¹¹B Q_m = -15.9569
(b) ¹²C(e, e'n)¹¹C Q_m = -18.7216
(c) ¹²C(e, e'α)⁸Be Q_m = -7.3666
(d) ¹²C(e, eπ⁺)¹²B Q_m = -152.9396
(e) ¹²C(e, eπ^-)¹²N Q_m = -156.9083

In (1984CA34) evidence for a monopole, J^π = 0⁺, state near E_x ≈ 20.5 MeV which exhausts at least 1% of the energy weighted sum rule is found in (e, e'p₀). The decay of states in the giant resonance region via α-particles has been studied by (1993DE10, 1995DE23): the E2 decay is primarily to ⁸Be*(2.9[J^π = 2⁺]) and reveals a peak with E_x = 21.6 and Γ ≈ 1.5 MeV; see also (1991PO06, 1994CA08, 1999SA27).

Electron spectra in the region of large energy loss show a broad peak which is attributed to quasi-elastic processes involving ejection of single nucleons from bound shells; studies of e'-p coincidences reveal peaks corresponding to ejection of 1p and 1s protons (at 700 MeV the energies of the peaks are 15.5 ± 0.1 and 36.9 ± 0.3 MeV with Γ = 6.9 ± 0.1 and 19.8 ± 0.5 MeV, respectively [1976NA17: DWIA]). Spectroscopic factors for 1s [ = 1.50 ± 0.08 (2000LA23)] and 1p [= 3.56 ± 0.12 (2000LA23)] shell single-particle knockout reactions are discussed in (1990CA14, 1990DE16, 1990WE06, 1991WE10, 1991WE16, 1994IR01, 1994IR02, 1995BL10, 1995KE03, 1998WO01, 1999DO30, 1999RY06, 2000DU12, 2000LA23, 2002MA12).

At 500 MeV the quasi-elastic scattering cross section has been analyzed and indicates the Fermi momentum is 221 ± 5 MeV/c (1971MO06).

Studies of the quasielastic longitudinal and transverse response functions versus missing energy have been carried out. (1987UL03) find in the longitudinal response a broad bump at missing energies between 28 and 48 MeV, attributed to knockout from the s-shell. In the transverse response they find this bump on top of a broader feature with a threshold at 28 MeV extending beyond 65 MeV. This broad feature is attributed to two-particle knockout, a non-quasielastic reaction mechanism; it may account for the observed (e, e') transverse-longitudinal difference. This feature is also observed in unseparated data at larger momentum transfers: it appears to grow with momentum transfer (1988WE1E). See also (1992BO10, 1992WA19, 1994MA26, 1995JO21, 2003AN15, 2003DE10, 2005MO04).

Multi-nucleon correlations and few-body interactions are discussed in (1993KE02, 1995KE03, 1995KE06, 1996KE03, 1996RY04, 1997RY01, 1998AL03, 1998BL06, 1998RY05, 2000DE58, 2000RO17, 2004MU29, 2005HO18, 2005KE06, 2006EG02, 2007PI05, 2009CI01, 2014CO05). Nucleon excitation studies are discussed in (1993RO13, 1995NI01, 1995ZO01, 1997GI02, 1997GI12, 1998GA25, 1999BA31, 2004BO47, 2008BO24, 2011VA11).

Effects such as transparency of the nuclear medium have been studied by (1990FR11, 1992BE23, 1992FR17, 1992GA02, 1992JE03, 1992PA03, 1993LO01, 1993NI11, 1994FR12, 1994FR16, 1994GR05, 1994IR02, 1994KO21, 1994MA23, 1994NI05, 1995FR04, 1996KE14, 1996NI13, 1997AL20, 1997IW03, 1999RY06, 2000DU12, 2000LA23, 2001FR06, 2002DE11, 2002GA43, 2002ME11, 2002ME17, 2003DU23, 2003RY02, 2004BA99, 2004BO47, 2004HA63, 2004LA13, 2005RO38, 2006RO37, 2007CL04, 2009KA02, 2010QI02, 2013RO06). Discussion on other final state effects is given in (1991CA09, 1994IR02, 1994JE04, 1994RY04, 1995BI07, 1995BI19, 1995NI02, 1996BI01, 1996BI21, 1996JE04, 1999KE04, 2002DE07, 2004BA99, 2004BB15, 2005BA07, 2005BA23, 2005PR02, 2007AL14, 2007PI05), and discussion on the reaction mechanism is found in (1990LO09, 1991VA05, 1992DR02, 1993CI05, 1993OF01, 1994IR01, 1994RY03, 1994TA11, 1994WE06, 1999MO02, 2002ME17, 2004FR27, 2004MU29, 2004RO35, 2004TA18, 2011RY03). See also (1993KE02, 1993KO12, 1994BI05, 1994VE08, 1994WA19, 1995RY02, 1996JO15, 1997BI06, 1997GI13, 1998HO20, 1999JO06, 2000DE38, 2000UD01, 2005KE04, 2009TA34, 2014MO25, 2014TO14).

42. (a) ¹²C(μ^±, μ^±)¹²C
(b) ¹²C(μ^±, X)

Parity violating muon scattering is discussed in (1993MI03). A review of μ^--e^- conversion reactions is given in (2006DE31). Cosmogenic production of nuclides, such as ¹¹C, is discussed in (2005GA19, 2006BA66, 2000HA33).

43. (a) ¹²C(π^±, π^±)¹²C
(b) ¹²C(π^±, π^±p)¹¹B Q_m = -15.9569

Angular distributions of the elastic and inelastically scattered pions have been measured at many energies: see 12.27 (in PDF or PS). See theoretical analysis in (1990BE53, 1990ER06, 1990FR02, 1990LI10, 1990MI08, 1990TA13, 1991AL01, 1991AR12, 1991OS01, 1991TA01, 1992BI06, 1993CH04, 1993CH16, 1993CH25, 1993MO27, 1993NI02, 1993PE09, 1994CH30, 1995AR02, 1995BA92, 1995KA49, 1996BI12, 1996CH16, 1996EB02, 1997SC09, 1998AH06, 1998CH42, 1998NU02, 1998PE09, 1998RO15, 1999HO13, 1999TA33, 2000EB05, 2000KH17, 2002NO13, 2004SA28, 2005EB03, 2005HA26, 2006AH02, 2006KA47, 2009FA02, 2010IO02, 2011EB03, 2013EB02, 2013KH17).

Angular correlations for π'-γ_4.4 and π'-γ_15.1 reactions have been studied by (1984SO12, 1984VO04, 1986OL07, 1988OL02) and (1988BA27), respectively. A detailed analysis of the sum rules for population of the J^π = 1^-; T = 0 ¹²C*(10.84) state is given in (1993KO17). The possible group to ¹²C*(15.4) has a width of ≈ 2 MeV (1981MO07); ¹²C*(14.1, 16.1) were also populated. J^π = 2^- for ¹²C*(18.25, 19.4) and J = 4 for ¹²C*(19.25) are suggested in (1987CO17); ¹²C*(19.65) is also populated. Study of the giant resonance region suggests states at E_x = 19.85, 22.10, 22.94, 23.70 and 25.40 MeV with Γ ≈ 330, 198, 192, 79 and 232 keV, respectively (1993KO17). See also E_x = 20.0 ± 0.2 and 22.7 ± 0.4 MeV, with Γ = 3.2 ± 0.3 and 1.0 ± 0.2 MeV (1984BL12) and E_x ≈ 18.3, 19.3, 22.1, 23.7 and 25.6 MeV (1982MO25).

A strong energy-dependent enhancement in the pion scattering to ¹²C*(15.1) but not to ¹²C*(12.7) is observed at E_π^± = 100, 180 and 230 MeV: this is interpreted as possible evidence for direct (Δ-h) components in the wave function of the T = 1 state (1982MO01). The charge-dependent matrix element between the J^π = 1⁺; T = 0 and 1⁺; T = 1 states, ¹²C*(12.71, 15.11), was studied by (1990JA05); ME = 157 ± 35 keV was deduced. See the results of (1981MO07) along with other values in 12.18 (in PDF or PS). The ratio of the cross sections to, ¹²C*(12.7, 15.1) at E_π^± = 50 MeV is 7.1 ± 1 [isospin averaged] (1988RI03). The excitation of these two states has also been studied for E_π^± = 80 to 295 MeV by (1988OA03). A preliminary value for the isospin mixing matrix element between ¹²C*(18.4, 19.4), 250 ± 50 keV, was given in (1979BO2D, 1979MO1W: E_π = 116, 180 MeV).

The emission of 2 photons in the capture of stopped pions, i.e. (π^-, γγ), occurs at a rate of (1.3 ± 0.3) × 10^-5/capture (1979DE06).

Strong energy dependence is observed in the π⁺ absorption (1981AS07, 1983NA18). At E_π^± = 50 MeV the absorption of π^- is about twice that of π⁺ (1983NA18). Analysis of 4.4 MeV γ-rays produced at E_π = 73 MeV yields σ(π⁺) = 14.5 ± 3.0 mb and a cross section ratio, σ(π^-)/σ(π⁺), of 1.23 ± 0.22 (1970HI10).

The Fermi-momentum distribution of protons was measured using reaction (b) at E_π^- = 0.7, 0.9 and 1.25 GeV (2000AB25).

44. (a) ¹²C(n, n)¹²C
(b) ¹²C(n, nα)⁸Be Q_m = -7.3666

Angular distributions and differential cross sections of elastically and inelastically scattered neutrons have been measured at many energies up to 350 MeV [see 12.28 (in PDF or PS)]. See other results in (1995TI10, 1995ZH49, 2013NE11). Discussion on polarization measurements is given in (1995CH12, 1995CH44, 2005CH58, 2006SV01, 2010WE06). For Optical Potential analyses see (1990NI02, 1991SH08, 1997EL13, 2001KA58, 2009WE04, 2011JA09, 2011RA34, 2012JA03, 2012PA09, 2015GH04, 2016AL14, 2016XU07); for Coupled Channels analyses see (2003AM08, 2005CA16, 2006SV01); for other analyses see (1990BE54, 1991BA39, 1992GA26, 1992KA14, 1992KA21, 1994IS08, 1994XI04, 1996CH33, 1996CH49, 1996GO48, 1997HA21, 1998SU23, 1999SU01, 2000CH31, 2000KE13, 2005PI16, 2008FR02, 2008FR11, 2008GE04, 2009AL05, 2009AL10, 2010NA18, 2016AR13, 2016FR09).

Angular correlations of (n, n'γ_4.4) have been studied at E_n = 13.9 MeV (1973DE45) and 15.0 MeV (1971SP01), and at 14 to 14.7 MeV [see (1968AJ02)]. The spin-flip probability for the transition to ¹²C*(4.4) has been studied at E_n = 7.48 MeV (1971MC1K, 1972MC20) and at 15.0 and 16.9 MeV (1973TH08, 1974ME29). Its shape at E_n = 7.48 MeV is similar to that measured by (1964SC07) in the (p, p') reaction at E_p = 10 MeV (1972MC20); while that at E_n = 16.9 MeV the shape is similar to that measured by (1969KO07) at E_p = 20 MeV (1974ME29). The quadrupole deformation parameter β₂ = -0.67 ± 0.04 (1983WO02).

For reaction (b), complete kinematics involving ¹²C*(7.65, 9.64, 10.84, 11.8, 12.7, 14.0, 15.1, 16.1) were studied at energies between E_n = 11.5 to 19 MeV (1991AN06). At E_n = 14.4 MeV ¹²C*(9.6, 10.8, 11.8, 12.7) have been reported: see (1975AJ02). A detailed study on the population of ¹²C*(9.6) at E_n = 11 to 35 MeV is given in (1983AN02): the decay is dominated by sequential feeding of ⁸Be_g.s. at the higher energies; see also (1953JA1C). The α-decay of the 10.8 and 11.8 MeV states, together with stripping results, suggest J^π = 1^- and 2^- for these states (1964BR25, 1971DO1K, 1975AN01, 1975AN02; see also (1966MO05)).

45. (a) ¹²C(p, p)¹²C
(b) ¹²C(p, p')¹²C

Angular distributions of elastically and inelastically scattered protons have been measured at many energies up to E_p = 1040 MeV: see 12.29 (in PDF or PS). 12.30 (in PDF or PS) displays the information on excited states of ¹²C. A summary of the decay of some excited states is shown in 12.14 (in PDF or PS).

The angular distributions have been analyzed by DWBA (and CCBA), DWIA (including microscopic calculations) and DWTA (DW t-matrix approximation with density-dependent interactions). Microscopic DWIA calculations give good results for transitions which proceed through the S = T = 1 part of the effective interaction and also give a reasonable description of the S = T = 0 transition. However the mechanism for the excitation of ¹²C*(12.71) (S = 1, T = 0) remains a puzzle (1980CO05: E_p = 122 MeV). The angular distributions of the inelastically scattered protons to ¹²C*(12.71) are usually poorly fitted: see e.g. (1990IE01). In (1995SA28) the 0° cross sections were measured for ¹²C*(12.71, 15.11) at E_p = 65 to 400 MeV; the cross sections, which maintained a nearly consistent ratio at all energies, were evaluated via microscopic DWIA analysis that reproduced the data best by reducing the isovector tensor terms of the effective interactions. Also see the analysis of spin observables at E_p = 198 MeV, for ¹²C*(12.71, 15.11) up to q ≈ 200 MeV/c (2001OP01).

At E_p = 402 MeV the differential cross sections for ¹²C*(12.7, 15.1) (J^π = 1⁺) are very similar for large q. This may be due to the smallness of precursor effects [precursor to a pion condensate] (1981ES04).

The spin-flip probability (SFP) for the transition to ¹²C*(4.4) has been measured for E_p = 15.9 to 41.1 MeV: two bumps appear at E_x ≈ 20 and ≈ 29 MeV. It is suggested that the lower one is due to a substructure of the E1 giant dipole resonance while the upper one results from the E2 giant quadrupole resonance (1975DE32, 1982DE02). The SFP has also been studied at E_{pol. p} = 24.1, 26.2, 28.7 MeV (1981FU12: to ¹²C*(4.4)), at E_p = 42 MeV (1981CO08: to ¹²C*(12.7)), at E_{pol. p} = 397 MeV (1982SE12: to ¹²C*(9.6, 12.7, 15.1, 16.1)) [the SFP to ¹²C*(9.6) is consistent with zero; the others exhibit large SFP at forward angles] and at E_p = 398, 597 and 698 MeV (1983JO08: to ¹²C*(18.3, 19.4)). The SFP has also been measured for ¹²C*(12.71) at E_p = 42 MeV (1977MO18) and for ¹²C*(12.7, 15.1) at E_p = 23.5 to 27 MeV (1978HOZJ) and E_p = 500 MeV (1991CH31). The SFP was measured in the region of 5 < E_x < 30 MeV (1999TA22) and 10 < E_x < 40 MeV (1993BA37); see also (1990BA14, 1990BA61).

(1980HO07) have measured the angular distribution of γ-rays from the decay of ¹²C*(12.7, 15.1) at E_p = 21.5 to 27 MeV. Microscopic DW calculations were performed for the A₀ and a₂ coefficients from these and earlier data. The theoretical calculations underestimate A₀ for energies below 35 MeV and are in agreement with the experimental A₀ for higher energies. The calculations also predict significant differences in the a₂ values for the transitions from ¹²C*(12.7, 15.1), and these are observed (1980HO07).

Angular distributions show that a large deformation exists: β₂ = -0.72 (1972DE13) and 0.6 (1967SA13); β₂ = -0.663 and β₄ ≈ 0 (1983DE36); β₂ = 55 ± 11, β₀ = 0.15 ± 3 and β₃ = 0.39 ± 8 (2010OK01). A DWBA analysis in (2010OK01) suggests ¹²C*(7.65) has a structure that is consistent with the assumption of a dilute α-cluster condensed state as suggested by (2001TO23).

The p-γ_4.4 angular distributions have been studied at E_p = 7.5 MeV (2006LE45). The p-γ_15.1 angular correlations have been studied at E_{pol. p} = 100 to 180 (1990PI06) and E_p = 200 MeV (1995WE10), 318 MeV (1992LY01) and 400 MeV by (1988HI12). See also (1990PI06, 1995SU30).

A study at E_p = 66 MeV measured Γ(9.64) = 48 ± 2 keV (2013KO14). Evidence for the J^π = 2⁺ excitation of the E_x = 7.65 MeV "Hoyle state" has been reported in (2009FR07, 2010FR03, 2012FR05: E_x = 9.75 ± 0.15 MeV with Γ = 0.75 ± 0.15 MeV) and (2011ZI01: E_x ≈ 9.6 MeV). In these different experiments, the known states at (7.65, 9.6, 9.64, 10.83, 11.80, 12.71) were also observed. The Γ ≈ 600 keV width initially reported in the (p, p') work of (2009FR07) was reanalyzed in (2012FR05) along with the (α, α') data of (2011IT08) yielding the slightly higher Γ = 0.75 ± 0.15 MeV value. In (2009FRZV), the authors question the validity of the E_x = 11.16 MeV state reported previously in ¹¹B(³He, d) reactions and they reiterate the likely ¹²C*(13.35) J^π = 4^- spin assignment previously suggested in (2007FR17). In (1997TE14), inclusive (p, p') and exclusive (p, p'p) and (p, p'α) reactions populated levels between 0 < E_x < 24.4 MeV.

The GT₊ strength distribution in ¹²B was analyzed in (2001WO07) by comparing the ¹²C*(15.1, 16.1, 18.35, 19.4, 21.6) excitations with the corresponding J^π = 1⁺, 2⁺, 2^-, 2^- and 2^- excitations from ¹²C(d, ²He)¹²B.

For theoretical analysis of elastic and inelastic scattering see (1990TA13, 1990TA16, 1991LI07, 1991TA01, 1992WA19, 1993BY02, 1993DE33, 1995MA23, 1996BE25, 1997DO02, 1997TE14, 1998GI01, 1998GU13, 1998KI17, 1998SU23, 1999GU17, 1999NA43, 2000CH31, 2000DE37, 2000LO20, 2004YA24, 2005PI16, 2006GU23, 2008FR02, 2013WE05, 2015TO11). Analyses of spin observables and polarized beam results are found in (1990BA14, 1990HA45, 1990ST32, 1990TA17, 1991BE45, 1992BE03, 1992BE24, 1992SH01, 1993CH14, 1993CO02, 1993KA45, 1993LA27, 1994DO03, 1994HI02, 1994PH02, 1994WI09, 1995BU37, 1995CH12, 1995CH44, 1995DE32, 1995DO31, 1995KA24, 1996DE31, 1996KA65, 1997BB17, 1997DO01, 1998DO16, 1998HI02, 1999AN32, 2000WE01, 2001HI10, 2001RA06, 2004CU02, 2005DE32, 2006ON03, 2007KH12, 2007YA13, 2008FU13, 2008KI13, 2009CO17, 2010NA18, 2011FU16, 2013PL02, 2014PL05). Global studies evaluating protons on a variety of targets are given in (1990BA14, 1990BA61, 1990HU09, 1990KA05, 1990PH02, 1990ST32, 1992KO04, 1993BE10, 1993CH14, 1993CO02, 1993KA45, 1994HA48, 1994WI09, 1995CH12, 1995CH44, 1995ER10, 1996GO48, 1997DO01, 1998DO16, 1999KU07, 2000DE43, 2000KE13, 2001KA58, 2002DI04, 2002FA14, 2002SA49, 2002TR12, 2005DE32, 2005KI04, 2005KO28, 2007KH12, 2007TA27, 2008FU13, 2008HA03, 2008KI13, 2009CO17, 2009WE04, 2010NA18, 2012DY01, 2012PA09, 2013ZU04, 2014HL01, 2015AR01, 2015BE12, 2016AR13). See also (1997IL02, 1998BA59, 1998KI15, 2001KI25, 2001WO07, 2010AZ01, 2011DU06: astrophysics).

46. (a) ¹²C(p, 2p)¹¹B Q_m = -15.9569
(b) ¹²C(p, pn)¹¹C Q_m = -18.7216
(c) ¹²C(p, pd)¹⁰B Q_m = -25.1864
(d) ¹²C(p, pα)⁸Be Q_m = -7.3666
(e) ¹²C(p, 3p)¹⁰Be Q_m = -27.1854

The (p, 2p) reaction has been studied up to energies above 1 GeV. At E_p = 56.5 MeV, p₀-decay from a state at ¹²C*(20.3 ± 0.5) was reported (1969EP01). 12.31 (in PDF or PS) shows states populated in reactions with 156 MeV protons. The analysis suggests the region above E_x = 21 MeV is dominated by J^π = 1^-; T = 1 resonances that mainly de-excite via single-nucleon emission. States in ¹¹B are studied in (2004YA20, 2004YO06). At higher energies, quasifree knockout reactions from distinct shells are observed; see experimental results reported in (1997HA15, 1998MA67, 1998NO04, 1999AC03, 1999CA11, 1999CA15, 2000NO03, 2003TA03, 2004AC08, 2004AN01, 2007RY02, 2008NO01). Discussions include p-p correlations, initial and final state effects, such as color transparency and nuclear modifications to the NN interaction; see (1992LE03, 1994FR12, 1994FR16, 1994KO21, 1995GA46, 1997GA16, 2000ST17, 2006DA15, 2006HI15, 2006VA08, 2007DA19, 2009CO10, 2011RY03, 2014CR05, 2015MO21, 2015OG03).

Although the shapes of the momentum distributions in the (p, pn) reaction (reaction (b)) at 400 MeV are consistent with quasifree knockout, the magnitude of the cross section relative to that for the (p, 2p) process is inconsistent with the PWIA model (1979JA20). However, a study of inclusive (p, p') reactions along with exclusive (p, p'n) and (p, 2p) reactions at E_p = 200 MeV (1999CA11, 1999CA15) found that a comprehensive accounting of p-shell knockout and s-shell knockout to excited states in the residuals was consistent with DWIA calculations, and apparently validated the impulse approach at this energy regime and lower. See also (2015MO21: theory) and ¹¹C yield measurements in (1993KO48).

The ¹²C(p, pd) missing energy spectrum at E_p = 670 MeV (reaction (c)) shows a strong bump at E_miss = 25 MeV and a weaker one at E_miss = 45 MeV, corresponding to the ¹⁰B ground-state and ¹⁰B*(20) regions, respectively (1981ER10). See also (1990LO18).

For reaction (d), at E_p = 56.5 MeV (1969EP01) T = 0 states at ¹²C*(22.2 ± 0.5, 26.3 ± 0.5) were reported to α₀-decay (natural parity) while states at ¹²C*(19.7, 21.1, 26.3) were found to α₁-decay. It is suggested that ¹²C*(21.1) has unnatural parity. At E_p = 44.2 MeV ¹²C*(12.7, 14.1, 21.6, 26.6) are observed in the angular correlations involving α₀; states at ¹²C*(21.6, 24.1, 26.6) decay via α₁ to ⁸Be*(3.0) [suggesting 2⁺ for these states, assuming that only resolved states are involved (1981DE08)]. A detailed analysis of the ¹²C(p, p3α) reaction at E_p = 14, 18 and 26 MeV (1999HA27) indicates the involvement of ¹²C(p, p'α)⁸Be and ¹²C(p, α)⁹B reaction channels. Other measurements at E_p = 101 MeV (2009CO01, 2009MA21) and E_p = 296 MeV (1998YO09) probed the cluster nature of ¹²C by evaluating alpha cluster spectroscopic factors and quasifree scattering; consistency with free scattering was found. See also (1994NE05, 1995GA39, 1995NE11, 1995TC01, 1997NE05, 1997SA04).

47. (a) ¹²C(d, d)¹²C
(b) ¹²C(d, pn)¹²C Q_m = -2.2246
(c) ¹²C(d, dα)⁸Be Q_m = -7.3666

The angular distribution of elastically and inelastically scattered deuterons has been studied at many energies: see 12.32 (in PDF or PS). Measurements aimed at refining global model parameters are found in (1993BE43, 2001BA18); see also (1990GO28, 1990HU09, 1990ST32, 1992RA31, 2003EL08, 2004KE08, 2006AN14, 2006HA42, 2006PR13, 2008CHZT, 2010GU03, 2011MI20, 2012PA22, 2012UP01, 2016ZH26). Few-body and cluster model analyses are given in (1997MI29, 1999BR09, 2000MI36, 2007AL28, 2008FO06, 2009DE08, 2013BE27, 2014BE17). In (2009DA22, 2010OG03) a method is suggested for determining nuclear radii of unstable states by analysis of diffractive scattering; root-mean-square radii are estimated for ¹²C*(7.65. 9.64, 9.9, 10.3, 10.84).

In addition to well-known states in ¹²C such as ¹²C*(4.4) [E_x = 4440.5 ± 1.1 keV (1974JO14)] and ¹²C*(12.7, 15.1) [see 12.18 (in PDF or PS) for charge-dependent matrix element results], the population of ¹²C*((10.8 ± 0.2), (11.8 ± 0.2), 18.3 ± 0.3, 20.6 ± 0.3, 21.9 ± 0.3 (broad), ≈ 27 (broad)) is also reported (1975AS06). The J^π = 2^- state here at 18.3 MeV is different from the 18.4 ± 0.2 MeV J^π = 2⁺ state observed in α inelastic scattering (1995JO06). DWIA analysis indicates J^π = (1⁺) for E_x = 20.4 MeV and L = (1) for E_x ≈ 30 MeV (1994MO21). The GDR region was studied in (2008GR22). A preliminary report (1977CH1L) suggested two structures at E_x = 26 ± 1 and 29 ± 1 MeV, with Γ = 2 ± 1 and 4 ± 1 MeV, respectively, and determine L = 3 in the excitation of ¹²C*(18.4).

Isoscalar spin strengths and spin-flip probabilities are reported at E_{pol. d} = 53 MeV (1993IS04), E_{pol. d} = 270 MeV (2001SA68) and E_{pol. d} = 400 MeV (1995JO06); S₁ shows peaks for E_x = 12.71 and 18.35 MeV and suggestions of peaks above 20 MeV while S₂ is consistent with zero up to E_x = 24 MeV range (2001SA68). Polarization observables are reported at, for example, E_d = 200 MeV (2004KA53), E_d = 393 MeV (1995FU03: E_x = 12.7 MeV) and E_d = 1.8 GeV (1995TO15). See also theoretical analysis in (1990SA45, 2001HI10, 2009DE02, 2009DE13).

The quadrupole deformation parameter is calculated to be β₂ = -0.48 ± 0.02 independent of incident energy [E_d = 60.6, 77.3, 90.0 MeV] (1975AS06: coupled channels analysis). (1971DU09: E_d = 80 MeV) report β₂ = 0.47 ± 0.05 and β₃ = 0.35 ± 0.06 for ¹²C*(4.4, 9.6), respectively. See also β₂ = -0.5 (2007GA07).

Reaction (b) was measured at E_d = 56, 140 and 270 MeV (1994OK01, 1998OK04); the results indicate sensitivity to Coulomb-dissociation and dissociation-diffraction mechanisms (1990SA45, 1991EV03, 1995SA39, 1996SA10, 1998NA42, 1998TO08, 1998TO10, 2002ZA10, 2006EV05, 2012UP01). See also (2002EV01, 2003EV01, 2009DE08, 2014YE03, 2016OG02). Earlier results are reported at E_d = 5.00 to 5.50, 9.20 and 9.85 MeV (1973SA03), 5.1 to 6.25 MeV (1973SH04), 5.4 and 6.0 MeV (1968BO02), 5.5 to 6.5 MeV (1972VA10), 56 MeV (1983BA37) and 2.1 GeV (1989PU01).

For reaction (c) see ⁸Be in (1979HE06).
48. ¹²C(t, t)¹²C

Angular distributions of elastically scattered tritons have been measured at E_t = 1 to 20 MeV. See (1968AJ02: E_t = 1 to 12 MeV), (1975AJ02: E_t = 1.11 to 20 MeV), (1980AJ01: E_t = 9.0 to 17 MeV) and (1990AJ01: E_t = 33, 36 MeV). See also the optical model analyses for E_t < 40 MeV in (2007LI55, 2009PA07, 2015PA10).

49. ¹²C(³He, ³He)¹²C

Angular distributions of ³He ions have been measured for E(³He) = 2 to 217 MeV: see 12.33 (in PDF or PS). Parameters of observed ³He groups are displayed in 12.34 (in PDF or PS). See analysis on angular distributions in (1995GA22, 1997KH07, 2000MO34, 2001KU20, 2003BE70, 2003KH01, 2004BE42, 2007LU04, 2007OH01, 2008DE35, 2009GU16, 2009PA07, 2010HA19, 2015PA10). In (2003KH01), E(³He) = 72 MeV data are analyzed and the deformation length δ₂ = 1.05 fm is deduced for ¹²C*(4.44). The ³He-γ_4.44 angular correlations were measured in (1994IG01). See (2003KA24: E = 443 MeV) for polarization observables.

Rainbow effects and Airy patterns are discussed in (1990DE31, 1990KU25, 1991GO25, 1991KU29, 1992AD06, 1992DE18, 1995DA08, 1995DA21, 1995GA22, 2010OG03). The radius of the ¹²C*(7.65) Hoyle state is reported as 2.94 fm or 1.2-1.3 times larger than the g.s. radius (2008DE35); see additional comments on the dilute nature of the Hoyle state structure in (2006OG04, 2007OH01, 2008DE35, 2009DA22, 2010OG03, 2013HA01).

Angular distributions of the ³He groups to ¹²C*(15.11, 16.11, 16.58, 19.56) have been compared with those for the tritons to ¹²N*(0, 0.96, 1.19, 4.25) in the analog (³He, t) reaction: the correspondence is excellent and suggests strongly that these are T = 1 isobaric analog states (1969BA06: E(³He) = 49.8 MeV). See also 12.12 (in PDF or PS) in (1980AJ01) and 12.34 (in PDF or PS). At E(³He) = 46 MeV, the inelastically scattered ³He projectiles were detected along with the 3α particles from the breakup of α-unbound states (2014WH02); levels up to E_x = 25.1 MeV are observed.

The states reported by (1977BU03) at E(³He) = 130 MeV [see 12.34 (in PDF or PS)]: ¹²C*(4.4, 15.2, 18.4, 18.9, 21.3, 23.5, 25.9, 28.8) are all suggested to correspond to E2 transitions: their strengths add up to 46% of the EWSR (energy-weighted sum rule). The quadrupole deformation parameter β₂ = 0.30 can account for both the elastic and inelastic data providing that the ratio of the spin orbit and central deformation β_s.o./β_cent. is energy dependent (E(³He) = 20.5 to 33 MeV) (1977KA25).

In (1980LE25) states were reported at E_x = 9.15 ± 0.2 and 20.3 ± 0.2 MeV [Γ = 1.8 ± 0.2 and 1.1 ± 0.2 MeV, respectively]: it was suggested that both are E0 states whose intensities are (2.1 ± 0.4)% and (2.6 ± 0.2)% of the EWSR: however these states are not confirmed, see (1981EY02, 1981YO04) in reaction 46 of (1985AJ01).

Cross sections are discussed in (1998BO39, 2008KO29, 2009LI01, 2011CH11).

For discussion on Δ-resonance excitation and coherent π⁺ production see (1990UD01, 1991DE31, 1992HE08, 1993DM01, 1993FE10, 1993HE03, 1993OL06, 1993RO09, 1993RO30, 1994DM03, 1994JA12, 1994KO23, 1994OS02, 1994OS03, 1994SN01, 1994UD01, 1995KE13, 1995ST29, 1996GA20, 1996OS02, 1997KA52, 1998DA25, 2000BO47, 2002DA20, 2005AL37, 2005BO22).

50. (a) ¹²C(α, α)¹²C
(b) ¹²C(α, 2α)⁸Be Q_m = -7.3666

Angular distributions have been measured at many energies up to 1.37 GeV: see 12.35 (in PDF or PS). Parameters of observed states of ¹²C are displayed in 12.34 (in PDF or PS). See general theoretical analyses of the angular distributions in (1990AB10, 1990AL05, 1990BO23, 1990CO29, 1990HU09, 1990LE18, 1991AN21, 1991BA23, 1991KU30, 1991LI25, 1991OK02, 1991ZH27, 1992ZH06, 1992ZH40, 1993AL10, 1993TA30, 1994AH05, 1994IN01, 1994RU12, 1994RU15, 1995AI03, 1995KH07, 1996ZH36, 1997CH48, 1998EL14, 1998GA46, 1999GA43, 1999IG02, 2000AB16, 2000EB02, 2000EL03, 2000GU07, 2001EL05, 2001KH02, 2001KI25, 2002HI07, 2002KH01, 2003MO11, 2003ZE06, 2004YA03, 2005AL18, 2005GR40, 2005KU23, 2006FA09, 2006FU11, 2006KU16, 2008KH14, 2008ZO03, 2010IZ01, 2010KA21, 2011AL23, 2011BE20, 2011BE42, 2011GU15, 2012DY01, 2012GI01, 2012PA22, 2013LA28, 2015SU14, 2016AN08, 2016HU08, 2016MI13, 2017BE01). Structures in large angle scattering are discussed in (1990DA23, 1991GO25, 1994DA32, 1995DA08, 2004OH13, 2008DE35, 2011BE42) and studies of backward angles scattering are emphasized in (1990TO09, 1994DA16, 1994YO06, 1995EN09, 1996SO20, 1998BE56, 2002AN26, 2002AR16, 2004JI10, 2012MA26). The large radii deduced for ¹²C*(7.65), R_rms = 2.89 ± 0.04 fm and ¹²C*(9.9: J^π = 2⁺), R_rms(2⁺₂) = 3.07 ± 0.13 fm, are significantly larger than for ¹²C*(4.44) and have been suggested as evidence for Bose-Einstein condensate structures (2008DE35, 2009DA22, 2010OG03, 2011OG10, 2013OG05); see also (2004IT09, 2006OG04, 2006TA27, 2008KH02, 2008OHZX, 2008TA21, 2010BE32, 2010OG03, 2011IT08, 2016NA22).

In (2004IT09), an L = 2 component of the reaction was identified near E_x = 9.9 MeV with Γ ≈ 1.0 MeV; the strength is associated with a rotational excitation of the Hoyle state. In (2011IT08), the state is identified at E_x = 9.84 ± 0.06 MeV with Γ = 1.01 ± 0.15 MeV. In (2012FR05) the (p, p') data from (2009FR07) and the (α, α') data from (2011IT08) are simultaneously analyzed via R-matrix analysis, and the J^π = 2⁺₂ state is identified at E_x = 9.75 ± 0.15 MeV with Γ = 0.75 ± 0.15 MeV. The large α width associated with this J^π = 2⁺₂ state suggests a highly clustered structure.

In addition to the discovery of the J^π = 2⁺₂ state, evidence is observed for other previously unreported states in the E_x = 9-12 MeV region. A group at E_x = 9.93 ± 0.03 MeV with Γ = 2.71 ± 0.08 MeV is identified with J^π = 0⁺ strength; it is suggested as a J^π = 0⁺₃ + 0⁺₄ doublet (2011IT08); this state is seen at E_x = 9.8^+0.2_-0.4 MeV with Γ = 2.7 ± 0.3 MeV in (2003JO07). Analysis in (2011IT08) suggests E_x = 9.04 ± 0.09 MeV and Γ = 1.45 ± 0.18 MeV for 0⁺₃ and E_x = 10.56 ± 0.06 MeV and Γ = 1.42 ± 0.08 MeV for 0⁺₄ states. Additional support for the interpretation of doublet J^π = 0⁺ states is found in the GCM calculations of (2016ZH43) and in the cluster model analyses of (2016FU07, 2016IS15). See also (2015FU09, 2016KA19, 2016YO09).

At E_α = 240 MeV (2003JO07), some evidence for J^π = 2⁺ strength at E_x is reported at E_x =11.46 ± 0.20, but no evidence was seen for this state in the E_α = 386 MeV data of (2011IT08). In addition, the results of (2011IT08) don't find support for the J^π = 0⁺ and 2⁺ strength at E_x = 11.2 and 11.1 MeV, respectively, deduced in the analysis of the ¹²B/¹²N β decay data (2010HY01); however, differences in analysis approaches may explain the different findings. At present it is difficult to suggest a clear picture of the J^π = 0⁺ and 2⁺ strength has emerged. See a review of Eλ transition strengths for E_x ≤ 10.84 MeV in (2013CU05).

Evidence for a Γ = 1.7 ± 0.2 MeV broad J^π = (4⁺) state at E_x = 13.3 ± 0.2 MeV is seen in the reconstructed kinematics of 3α ejectiles (2011FR02). It is suggested that this state, along with the J^π = 0⁺₂ and 2⁺₂ states form a rotational band. Alpha-alpha correlations from ¹²C*(14.1) to ⁸Be_g.s. lead to an assignment of J^π = 4⁺ for that state (1977MC07); see also (1978RI03).

States at E_x = 7.65, 9.64, 10.84 and 14.08 MeV were observed along with a new state at E_x = 22.4 ± 0.2 MeV (2014MA37); the angular correlations of breakup α-particles indicate a J^π = 5^- assignment for the later. A ground state rotational band including ¹²C*(0[J^π = 0⁺], 4.44[2⁺], 9.64[3^-], 14.08[4⁺] and 22.4[5^-]) is suggested.

In the region of the GDR, prominent structures are observed consisting of two ≈ 2 MeV wide peaks at 26.2 and 29.2 MeV (1987KI16: see also for a discussion of deformation parameters). J^π assignments have been suggested for ¹²C states with 9.6 ≤ E_x ≤ 39.3 MeV on the basis of their decay into 3α-particles: see (1973JA02: E_α = 90 MeV).

The quadrupole deformation, β₂, is -0.29 ± 0.02 (1971SP08), -0.30 ± 0.02 (1976PA05), -0.40 ± 0.02 (1983YA01); β₃ = 0.24 (1973SM03), 0.23 (1977BU19) and β₄ = +0.16 ± 0.03 (1983YA01: see also for a review of deformation parameters). In (2003JO07) β₂ = 0.753 ± 0.049, β₀(7.65) = 0.187 ± 0.13, β₃ = 0.556 ± 0.066, β₀(10.3) = 0.157 ± 0.011, β₁ = 0.026 ± 0.005 deformation parameter values are deduced.

In (2003JO07) strength was identified corresponding to (27 ± 5)%, (78 ± 9)%, and (51 ± 7)% of the isoscalar E0, E1, and E2 energy weighted sum rule (EWSR), respectively, with centroids of 21.9 ± 0.3, 27.5 ± 0.4, and 22.6 ± 0.5 MeV and rms widths of 4.8 ± 0.5, 7.6 ± 0.6, and 6.8 ± 0.6 MeV. Less than 7% of the E3 EWSR strength was identified. See also (1998YO02, 2008KH02) and earlier work in (1976KN05, 1978RI03, 1981EY02).

Angular correlation measurements α₁-γ_4.4 have been carried out for E_α = 10.2 to 104 MeV (see 1980AJ01, 1985AJ01, 1990AJ01). Measurements of the radiative widths for ¹²C*(7.7, 9.6) are reported in (1974CH32, 1976MA46) and 12.14 (in PDF or PS). The value for Γ_rad for ¹²C*(7.65) implies a 45% faster rate for the (3α) astrophysical process (1974CH32). A detailed study of the ¹²C*(7.65) de-excitation finds the decay is 99.1% via sequential α-decay to ⁸Be_g.s. and < 0.9% via direct decay into 3α-particles (2013RA20).

For cross sections analyses relevant to ¹⁶O see (1990AR24, 1991DE15, 1992SA26, 1993DE03, 1996VO18, 1997AB52, 1997GO10, 1999AN35, 2000AN17, 2001BU20, 2001HU14, 2002TI03, 2004SP02, 2004SP04, 2005PA58, 2005SP06, 2006BU32, 2007FR22, 2007ST21, 2009AS01, 2009TI02, 2010KA21, 2011DU06, 2011IR01, 2011SP03, 2012CU04, 2012DE08, 2012SO20, 2013CU04, 2013DE03, 2013GA05, 2013KA03, 2014CH06, 2015IR01, 2015SH22). For reaction (b) and α-cluster knockout studies see (1999NA05, 1999ST06, 2007FR22, 2012CU04, 2012SO20, 2013CU04: exp.) and (2008JA02, 2009JA07, 2011CO10, 2014JA07: theory).

51. ¹²C(⁶He, ⁶He)¹²C

Angular distributions of elastic scattering have been measured at E(⁶He) = 5.9 to 492 MeV; see 12.36 (in PDF or PS). At E(⁶He) = 10 MeV (1995WA01) the elastic angular distribution was found to fall off more quickly than expected when compared with the Rutherford cross section; on the other hand, measurements at E(⁶He) = 38.3 and 82 MeV/A found an enhancement of cross section at angles larger than about 15° (2002LA20, 2011LO07). At E(⁶He) = 30 MeV, scattering to ¹²C*(0, 4.4) was measured and analyzed for θ_cm ≈ 20° - 100° using a coupled-channels approach (2014SM01). The nuclear forward glory effect was studied at E(⁶He) = 5.9 MeV in (1998OS02, 1999OS04, 2002OS04), and the analysis indicated the low ⁶He binding energy leads to a loss of flux from the elastic channel, even at very forward scattering angles.

See theoretical analyses in (1993GO06, 1995GA24, 1998TO05, 2000BO45, 2000KR13, 2000MI36, 2002AB16, 2002SU18, 2003AB26, 2003LE25, 2003ZA15, 2004AB12, 2004AB13, 2004MA57, 2005AL18, 2005MI29, 2007RO29, 2008BO19, 2008DE38, 2008EL03, 2008KE06, 2008RO16, 2009DO20, 2009KU25, 2010AY08, 2010DEZW, 2010LA09, 2010LU08, 2010MA61, 2011BA03, 2011LU14, 2012AL24, 2012GI01, 2014KU09, 2015IS03, 2016IB01, 2016SU13).

52. (a) ¹²C(⁶Li, ⁶Li)¹²C
(b) ¹²C(⁶Li, αd) ¹²C Q_m = -1.4738
(c) ¹²C(⁷Li, ⁷Li)¹²C

See 12.37 (in PDF or PS) for a summary of reported measurements on ¹²C(⁶Li, ⁶Li) and ¹²C(⁶Li, dα). The inelastic angular distributions to ¹²C*(4.4, 7.7, 9.6) have been used to obtain deformation parameters (1996KE09); see earlier work in (1994RE15, 1974BI04). Measurements of large angle scattering are reported in (1996GA29, 2004CA46) and analyzed in (1990DA23, 1990SA05, 1993GO06, 1995GA22, 2003LE25, 2005MI29, 2012CA21). A method for determining nuclear radii of excited states, such as ¹²C*(7.65. 9.64, 9.9, 10.3, 10.84), is suggested in (2009DA22). A study of the E0 strength distribution determines 10%, (5 ± 1)% and (5 ± 2)% of the EWSR, respectively for ¹²C*(7.7, 10.3) and for 19 < E_x < 21.5 MeV (1987EY01). See general theoretical analyses in (1990KA14, 1991BO48, 1991EV04, 1991SA26, 1992GA17, 1994NA03, 1994SA10, 1994SA33, 1994SK04, 1995BE60, 1995EM03, 1995GA24, 1995KH03, 1995MO28, 1996CA01, 1997SA57, 1997ZE04, 1998PI02, 1999BE59, 2000BE49, 2000EL11, 2000MI36, 2002EL01, 2002EL10, 2003ZA15, 2004EL02, 2005AL18, 2006DA05, 2008KE06, 2009DA22, 2011PA37, 2013BA13, 2015AY05, 2016CA36).

At E(pol. ⁶Li) = 30 MeV the angular distributions and polarization observables corresponding to ¹²C*(0, 4.4, 9.64) have been studied (1994RE01, 1994RE15); see also E(pol. ⁶Li) = 50 MeV measurements to ¹²C*(0, 4.4, 7.65, 9.64) reported in (1995KE10, 1996KE09) and theoretical analyses given in (1990FI12, 2011BA23, 2011PA37).

At E(⁶Li) = 60 MeV reaction (b) takes place via ¹²C*(0, 4.4, 7.7) (1982AR20) and can involve structures in ¹⁶O. See other measurements and analysis of the ⁶Li breakup mechanism in (2000SC11, 2004SO23: exp.) and (1991EV04, 1991EV05).

See 12.37 (in PDF or PS) for a summary of reported measurements on ¹²C(⁷Li, ⁷Li). Analyses of elastic scattering distributions are given in (1991BO48, 1994SK04, 1997BE05, 2000EL11, 2002EL01, 2004EL02, 2005AL18, 2011BA23, 2014PI02) At E(pol. ⁷Li) = 34 MeV the angular distributions and polarization observables corresponding to ¹²C*(0, 4.4, 7.65, 9.64) and ¹²C*(0, 4.4) + ⁷Li*(0.48) have been studied (2000BA75, 2002KE04); see other results in (2001BA29, 2001BA57, 2006MO24) and (2011BA23: theory). For fusion and yield measurements see (2007PA33).

For the ⁶Li and ⁷Li + C interaction cross sections at 790 MeV/A see (1985TA18).

53. ¹²C(⁷Be, ⁷Be)¹²C

Angular distributions for elastic and inelastic scattering have been measured at E(⁷Be) = 8 to 280 MeV; see 12.36 (in PDF or PS). See theoretical analyses and discussion in (1995FA17, 1996KN05, 1997KN07, 2006DA05, 2010HO08).

Reaction cross sections and interaction cross sections are reported at E(⁷Be) = 245 and 420 MeV (1999FU08) and 280 MeV (1995PE09). See also (1993FE12, 2000AB31, 2002AB16).

54. (a) ¹²C(⁸Li, ⁸Li)¹²C
(b) ¹²C(⁸Li, X)

Angular distributions for elastic and inelastic scattering have been measured at E(⁸Li) = 13 to 24 MeV; see 12.36 (in PDF or PS). See theoretical analyses and discussion in (2014AY05).

Reaction cross sections and interaction cross sections are reported at E(⁸B) = 30 to 110 MeV (2014FA18, 2015FA03). See also (2000AB31, 2000BH09, 2001BH02, 2002AB16, 2002WA08, 2003WE07, 2004KH06, 2006SH20).

55. (a) ¹²C(⁸B, ⁸B)¹²C
(b) ¹²C(⁸B, X)

Angular distributions for elastic and inelastic scattering have been measured at E(⁸B) = 25.8 to 320 MeV; see 12.36 (in PDF or PS). See theoretical analyses and discussions in (1995FA17, 1996AL13, 1996KN05, 1997KN07, 2000BO45, 2006DA05, 2006DA27, 2010HO08).

Reaction cross sections and interaction cross sections are reported at E(⁸B) = 206.4 MeV (2011BA25), 280 and 480 MeV (1999FU08), 288 MeV (2015JI07), 320 MeV (1995PE09) and 616 MeV (2003EN05). See also (1998KN03, 2000AB31, 2001LE21, 2002AB16, 2002PA51, 2004EV02, 2006HU12, 2006TR07, 2011HA38).

56. ¹²C(⁹Be, ⁹Be)¹²C

Angular distributions for elastic scattering have been obtained at E(⁹Be) = 3 to 158.3 MeV; see recent studies listed in 12.36 (in PDF or PS). At E(⁹Be) = 158.3 MeV angular distributions to ¹²C*(0, 4.4) were measured by (1984FU10), and at E(¹²C) = 65 MeV angular distributions to ¹²C*(0, 4.4, 7.7, 9.6) were measured by (1985GO1H).

Excitation functions were measured for elastic scattering at E_lab = 13 to 21 MeV (2011OL01) and for elastic and inelastic scattering to ⁹Be*(2.43) or ¹²C*(4.44) at E_cm = 2 to 16 MeV (1995CA26); analysis indicated significant components of ³He transfer in the reactions (1995CA26); see also (1998GR21).

The interaction cross section of ⁹Be ions on ¹²C at 790 MeV/A is reported in (1985TA18). See estimates of the total reaction cross sections for E(⁹Be) = 3 to 26 MeV (2011ZA05); also see (1993FE12, 2000BH09, 2002AB16, 2002BR01, 2003CA07, 2006SH20, 2008KO29, 2013YA01, 2016TR10). For fusion and yield measurements see (1978CH02, 1981JA09, 1982DEZL, 1982HU06, 1983JA09, 1985DE22, 1992FI04, 1998CA27).

57. (a) ¹²C(¹⁰Be, ¹⁰Be)¹²C
(b) ¹²C(¹¹Be, ¹¹Be)¹²C

Angular distributions of ¹⁰Be and ¹¹Be elastic scattering are summarized in 12.36 (in PDF or PS). For theoretical analyses, see (¹⁰Be: 1999BR09, 2000AB31, 2009RO31) and (¹¹Be: 1995EV01, 1996EV01, 1996VO04, 1997AL05, 1997JO16, 1998TO05, 1999BR09, 1999FO13, 2000BO45, 2000JO21, 2002AL25, 2002BO25, 2002SU18, 2002TA31, 2003TA04, 2005BA72, 2005TA34, 2009HA18, 2010LA09, 2011OG09, 2011OG10, 2015IS03, 2015LU04).

The interaction cross section of ¹⁰Be ions on ¹²C at 790 MeV/A is reported in (1985TA18). See estimates of the total reaction cross sections for E_cm = 12.7 MeV (2011ZA05); see also (1993FE12, 1996AL24, 2000BH09, 2002AB16, 2002BR01, 2006SH20). For ¹¹Be (reaction (b)), see measurements on the reaction cross sections in (1991FU10) and see other theoretical analyses in (1993FE02, 1993MA25, 1994SA30, 1996AL13, 1997FO04, 2000BH09, 2002BR01, 2003CA07, 2006GO05, 2006SH20, 2007SH33, 2008AL06, 2013SH17).

58. (a) ¹²C(¹⁰B, ¹⁰B)¹²C
(b) ¹²C(¹¹B, ¹¹B)¹²C

Angular distributions in reaction (a) have been measured at E_cm = 3.18 to 6.82 MeV (1977HI01) and at E(¹⁰B) = 18 (1969VO10, 1988DI08) and 100 MeV (1977TO02).

The ¹¹B + ¹²C reaction has been studied for E(¹¹B) = 10 to 100 MeV and for E(¹²C) = 15 to 87 MeV; see 12.36 (in PDF or PS), 12.20 (in PDF or PS) in (1985AJ01), 12.20 (in PDF or PS) in (1990AJ01) and discussion in (1980AJ01). Proton spectroscopic factors for elastic transfer reactions ranging from C²S = 2 - 5.6 have been deduced from measurements at E_cm = 15 to 40 MeV (1991AL12), and 2.15 ± 0.23 was deduced at E(¹¹B) = 50 MeV (2014LI49). Spectroscopic factors for ¹²C*(0, 4.4, 9.64) from analysis of measurements at E(¹²C) = 18 MeV (2014HA34) and E(¹²C) = 344.5 MeV (1990JA12, 1992JA12) are given in 12.38 (in PDF or PS). See other analyses in (1990KA17, 1998KH16, 2001RU14, 2003ME36). For fusion and yield studies see references in (1985AJ01, 1990AJ01) and (1993HA14, 1994BA41, 1996JA12, 1996KI17, 1999CA50, 2000TAZK, 2006JI01, 2009JI04).

59. (a) ¹²C(¹¹Li, ¹¹Li)¹²C
(b) ¹²C(¹¹Li, X)

Angular distributions for elastic and inelastic scattering have been measured at E(¹¹Li) = 550 to 660 MeV; see 12.36 (in PDF or PS). See theoretical analyses and discussion in (1991CA14, 1992TA16, 1992YA04, 1993DA09, 1993ME02, 1993TH01, 1994AL02, 1994CA07, 1994HU04, 1994SA16, 1995AL01, 1995AL02, 1995CO01, 1995DA04, 1995EV03, 1995FA17, 1995FO08, 1995GA24, 1995HU08, 1995KH11, 1996CA01, 1996KH03, 1996KN05, 1996RA18, 1996UE01, 1996UE07, 1997CH32, 1997KN07, 1997MO42, 1998CH18, 1998MO27, 1999MO37, 2000MO34, 2000PA14).

Reaction cross sections are reported at E(¹¹Li) = 341 and 451 MeV (2013MO21). See other theoretical analyses mainly related to the ¹¹Li density distribution and structure in (1992OG02, 1992YA02, 1993FE02, 1993MA17, 1993MA25, 1996AL13, 1996AL24, 1996BU09, 1997FO04, 1997ZA08, 1998BE09, 1998GA37, 1998KN03, 2000BO45, 2001BH02, 2001OG10, 2002WA08, 2004CA18, 2004LO12, 2007AL07, 2007SH33, 2008CA08, 2009SH25, 2011IB02).

60. (a) ¹²C(¹²C, ¹²C)¹²C
(b) ¹²C(¹²C, α⁸Be)¹²C Q_m = -7.3666

Angular distributions have been measured at E(¹²C) = 10 to 2400 MeV: see 12.39 (in PDF or PS).

See analyses of elastic and inelastic scattering at E < 100 MeV (1990DE13, 1991AL03, 1991TR03, 1991VE02, 1992AP01, 1994AP01, 1995AP01, 1995LI27, 1997AP06, 1997BR05, 1998AP03, 2000EB03, 2001BO18, 2001BO41, 2001EL08, 2002BO17, 2003AL17, 2005ER05, 2006KU06, 2011HA36), at E = 100 MeV to 1 GeV (1990JA12, 1990WA01, 1991AL16, 1992AY03, 1992GA08, 1992KA36, 1992LE02, 1993LI13, 1993MC01, 1994KH02, 1995FA17, 1996BE25, 1996EL05, 1997BR04, 1997BR30, 1997CH48, 1997IN02, 1997KH04, 1997KN07, 1997SI21, 1997ZE04, 2000KH06, 2000KI05, 2001FA24, 2002AH05, 2002BO58, 2002YA15, 2004AH11, 2005AL18, 2005CH48, 2007KI19, 2010BA45, 2012FU04, 2012FU09, 2013FU01, 2013WE05, 2016MI03), and at E > 1 GeV (1990AL10, 1990AM02, 1990DA12, 1990DA23, 1991CE09, 1991ZH20, 1992CH30, 1993CE01, 1994CH35, 1994GU20, 1995BE26, 1995GA24, 1996FA08, 1998CH18, 1998EL14, 1999MA18, 2000AB31, 2000EL03, 2001LU09, 2002AB16, 2002AH02, 2002FA10, 2002VA17, 2003BE31, 2004FA08, 2004GH02, 2006CH45, 2007CH42, 2009FU11, 2012GI01, 2013WE05, 2014MI22, 2016FU13). See also (1991PU01, 1991SA29, 1996AD04, 1996RA25, 1997AB50, 2007CH62, 2011FU16, 2012FU04). For comments on "rainbow" scattering and Airy minima see (1991BR04, 1992MC07, 1995GA22, 2000ME04, 2000ME05, 2002KI15, 2003SZ12, 2004KI13, 2004MI12, 2010DE32, 2010FU12, 2016KH09).

The nuclear sizes of ¹²C*(0, 4.4, 7.65) were determined by a Frauenhofer analysis of the small angle diffraction pattern at E(¹²C) = 121.5 MeV; results indicate R_diffraction = 6.35 ± 0.09, 6.26 ± 0.10 and 6.86 ± 0.11 fm, respectively (2011MA04). See also (2009DA22), who evaluated ³He, α, ⁶Li and ¹²C scattering data, deduced the diffractive radii for ¹²C*(0, 4.4, 7.65, 9.64) and deduced R_rms = 2.34, 2.36 ± 0.04, 2.89 ± 0.04, 2.88 ± 0.11 fm for those states, respectively.

The relative population of elastic and inelastic channels is very energy dependent, for example, because of structure effects and molecular-like states in ²⁴Mg; see references listed in (1975AJ02, 1980AJ01, 1985AJ01, 1990AJ01), and see footnote ^a in 12.40 (in PDF or PS). The spin alignment of ¹²C*(9.64) was studied in (1993DA22, 1995DA05) and shows little energy dependence. See also (1990SA07, 1990SA48, 1992GR15, 1992RA25, 1993AB05, 1993ME04, 1994AD13, 1994ME18, 1994SA07, 1995BE33, 1995HI21, 1996AD04, 1996SC02, 1998KO29, 1999IT02, 2000SA57, 2001BO18, 2002IT05, 2003SA36, 2003SA39, 2003SZ12, 2005GA33, 2006PE23, 2007FR22).

For reaction (b), several states are observed by reconstructing the complete kinematics of decay α particles, see 12.40 (in PDF or PS). In (2007FR17), the three-α breakup systematics are analyzed to determine spin values for states with E_x ≥ 7.65 MeV; the analysis found no evidence for the J^π = 2⁺ excitation of the Hoyle state that is expected near 10 MeV. Contradictory results for previous J^π value assignments for states such as ¹²C*(11.83, 13.35) were also found along with suggestive evidence for new broad states nears E_x = 11.8 and 12.5 MeV. In (2007FR17) analysis of the E_x = 11.16 MeV region is given that showed limited evidence for a previously accepted state; however, in light of the findings in (2012SM06), the result of (2007FR17) does not provide sufficient evidence for the state's existence (private communication, M. Freer, June 2017). In (2010MU05) analysis of the α-particle angular correlations found no evidence for excess J^π = 2⁺ strength in the E_x ≈ 9 to 10 MeV excitation region.

In (1991CA01) no evidence for direct 3α-decay was observed from any state. Detailed measurements of the ¹²C*(7.65) decay systematics, which are relevant for astrophysical ¹²C formation, are given in (1994FR05, 2014IT01); see also (1996RA08). In (2014IT01) the decay kinematics of ¹²C*(7.65) are analyzed, and the results are consistent with 100% sequential decay via ⁸Be_g.s., with limits of < 0.2% decay via 3-body phase space and < 0.08% decay into 3 equal energy α particles. The α-α correlation data is analyzed in (2007FR05), and discussion relating the correlations to the nuclear radii of excited states is given.

61. (a) ¹²C(¹³C, ¹³C)¹²C
(b) ¹²C(¹⁴C, ¹⁴C)¹²C

Elastic and inelastic angular distributions are reported at E(¹²C) = 127.2 MeV (2010AL10) and E(¹³C) = 16.3, 20, 29.5 MeV (1995LI23) and 240 MeV (2010DE32). See previous measurements reported at E(¹²C) = 15 to 36 MeV and 87 MeV (1975AJ02), at E(¹²C) = 20 to 35 MeV and E(¹³C) = 12 and 36 MeV (1980AJ01), at E(¹²C) = 15 MeV and E(¹³C) = 87 MeV (1985AJ01), and at E(¹²C) = 94.5 MeV and E(¹³C) = 16.3 to 26.5 MeV, 36 MeV and 260 MeV (1990AJ01).

The spin-flip probability to ¹²C*(4.4) has been studied at E(¹³C) = 36 and 56 MeV by (1985BY01); also see (1981TA21). The mirror scattering reactions of ¹²C + ¹³C and ¹²C + ¹³N are compared in (1995LI10, 1995LI23, 1997IM01). Rainbow scattering and Airy minima are discussed in (2003BE70, 2004BE42, 2010DE32, 2015OH02). See also (1990BA03, 1993IM02, 1999RA24, 2010AL10).

For reaction (b) elastic angular distributions are reported at E(¹²C) = 12 to 20 MeV (1972BO68) and E(¹⁴C) = 31.0 to 56 MeV (1985KO04). Excitation functions to ²⁶Mg resonances are studied for ¹²C(¹⁴C, ¹⁴C) at E_cm = 22 to 30 MeV (1992FR13) and E_cm = 6 to 35 MeV (2003SZ11).

62. ¹²C(¹³N, ¹³N)¹²C

Elastic and inelastic scattering has been measured at E(¹³N) = 16.3, 20 and 29.5 MeV (1995LI10, 1995LI23) and at 153.4 MeV (2004TA15). The ¹²C + ¹³C and ¹²C + ¹³N systems appear to comply with charge symmetry, see (1995LI10, 1995LI23, 1997IM01).

63. ¹²C(¹⁴N, d)²⁴Mg* → ¹²C + ¹²C Q_m = -10.2723

This reaction has been used to populate ¹²C-¹²C quasi-molecular states in ²⁴Mg, see for example measurements at E(¹⁴N) = 30 to 45 MeV (1994ZU03) and analyses in (1994BE55, 1999SA54, 2002BE71, 2002BE73).

64. (a) ¹²C(¹⁴N, ¹⁴N)¹²C
(b) ¹²C(¹⁵N, ¹⁵N)¹²C

Elastic and inelastic angular distributions are reported at E(¹⁴N) = 80.73, 100.3 MeV (1990DE13), 116 MeV (1997ZI05) and 280 MeV (1990BR21). See previous measurements reported at E(¹⁴N) = 21.5 to 27.3 and 62.5 MeV (1968AJ02), E(¹⁴N) = 21 to 155 MeV (1975AJ02), E(¹⁴N) = 37 to 155 MeV (1980AJ01), E(¹⁴N) = 48 to 78 MeV (1985AJ01) and E(¹⁴N) = 150 MeV (1990AJ01). At E(¹⁴N) = 155 MeV ¹²C*(0, 4.4, 7.7, 9.6, 10.8, 11.8, 12.7, 13.4, 14.1) are reported; see (1975AJ02). High-energy γ-ray emission has been studied at E(¹⁴N) = 280 to 560 MeV (1986ST07). See also (1994AD08, 1997IN02, 2003AU04).

For reaction (b), angular distributions are reported at E(¹⁵N) = 31.5 to 47 MeV (1978CO20) and the spin-flip probability to ¹²C*(4.4) has been studied at E(¹⁵N) = 94 MeV (1981TA21).

65. ¹²C(¹⁶C, ¹⁶C)¹²C

The angular distribution for quasielastic scattering at E(¹⁶C) = 47.5 MeV/A is reported for θ_cm = 5 ° - 40° (2009FA07).

66. (a) ¹²C(¹⁶O, ¹⁶O)¹²C
(b) ¹²C(¹⁶O, α)¹²C¹²C Q_m = -7.1619

Angular distributions involving ¹²C and ¹⁶O states have been measured at E(¹⁶O) = 17.3 to 1503 MeV and at E(¹²C) = 65 to 76.8 MeV: see 12.41 (in PDF or PS). See general analyses in (1990DA12, 1991ST07, 1992CH29, 1992CO01, 1993MA09, 1994KH02, 1994SA24, 1996EL05, 1997BR04, 1997CH23, 2000EL03, 2000KI30, 2000ME04, 2002AN35, 2002KU41, 2003BE31, 2005CH48, 2005KO52, 2006HO04, 2007GO35, 2009CH46, 2009FU11, 2011GR11, 2011MO07, 2012FU04, 2012GR16, 2013GR13, 2014FA04, 2014FA11, 2016FU13, 2016MA52).

The reaction dynamics leading to the Airy patterns at large scattering angles are discussed in (1997RI08, 2001AN04, 2001GO46, 2001MI06, 2002MI19, 2002MI39, 2002SZ03, 2003GO34, 2003OG04, 2003SZ12, 2008GR12, 2008GR14, 2008KO16, 2009KO05, 2010BA45, 2010DE10, 2014OH02, 2015MA12, 2016HA01).

In (1979DO01) excitation of the giant quadrupole resonance is observed in groups at ¹²C*(25.3, 26.7) with Γ ≈ 4 MeV that contain (25⁺¹⁵_-10)% of the energy-weighted E2 sum rule strength; states at ¹²C*(0, 4.4, 9.6, 10.8, 15.8, 21.6) were also populated.

For fusion resonant excitation function studies to states in ²⁸Si see (1992SA21, 1993BE17, 1993ES01, 1994GA06, 1995BU29, 1995FR12, 1995SI13, 1997FU12, 1997GY02, 1998KE02, 2008LE27, 2011LE19, 2011CO05, 2012RU02, 2012LE04, 2013KU04, 2014KU06, 2014GO03) and (1994GR26, 2004KO38, 2007FR22: theory). For studies of other nuclides see (²⁰Ne: 1994RA04, 1995SU06), (²⁴Mg: 1991CO09, 1994CO01, 1994KU18, 1995FR12, 1997FU12, 1998FR03, 2001FR19, 2001TU06, 2001WI18, 2011JO02, 2012DI04 and theory: 2007FR22) and (²⁶Al: 1993BE17, 1997BA51, 1998BA19). See also (1993HA14, 1993WA16, 1994CZ03, 1994DE21, 1995SC30, 2006YA14, 2007GA43, 2009CH35, 2009LO01, 2012UM02, 2015AB01). For discussions on fragmentation reactions see (1990WE15, 1992MA13, 1992ME02, 1999BO46, 2000CH20, 2000FA12, 2001DE50, 2002MO22, 2008KU15, 2011DE09).

67. (a) ¹²C(¹⁷O, ¹⁷O)¹²C
(b) ¹²C(¹⁸O, ¹⁸O)¹²C

Elastic and inelastic angular distributions are reported at E(¹⁷O) = 22 to 38 MeV (1993TI05) and E(¹⁸O) = 66 to 120 MeV (2001SZ05, 2006SZ06), 84 MeV (2011CA33), 94.5 MeV (2009AD08), 105 MeV (2010RU03, 2010RU13, 2010RU15, 2011RU07) and 216 MeV (2014AL05, 2014AL11). See previous measurements reported at E(¹⁷O) = 35 MeV (1975AJ02), 30.5 and 33.8 MeV (1980AJ01), 40 to 70 MeV (1990AJ01), and E(¹⁸O) = 35 MeV (1975AJ02), 32.3, 35, 47.5, 55 and 57.5 MeV (1980AJ01) and 32.0 to 140 MeV (1985AJ01). Fusion yields and other reactions to isotopes in, for example, Ne and Si are reported in (1990XE01, 1993BE17, 1993TI05, 1996FO16, 1999BO46, 2000CH20, 2000FA12, 2006FR16, 2006YI01, 2011BA22, 2011GI03, 2014ST22) and (1980AJ01, 1985AJ01, 1990AJ01). See also analyses in (1991TH02, 1991TH04, 1997KI22, 1999MA96, 2002BR01, 2004KH06, 2006BH01, 2008KO29, 2009AB07, 2011KU06, 2011SH26, 2012HO19, 2012RA29, 2014HO02).

68. (a) ¹²C(¹⁷F, ¹⁷F)¹²C
(b) ¹²C(¹⁹F, ¹⁹F)¹²C

Angular distributions for elastic scattering and quasielastic scattering have been measured at E(¹⁷F) = 60 MeV (2012ZH21) and 170 MeV (2005BL23). For reaction (b), elastic scattering and fusion angular distributions are reported at E(¹⁹F) = 10 to 16 MeV (1990XE01), 19 to 56 MeV (1999CA50), 22 to 24 MeV (2004SU02), 48 to 72 MeV (2002AN11), 57 to 64 MeV (2002SU17), 83.6 MeV (2003WO17, 2004KI07, 2006WO04), 92 MeV (1997AI01, 1997AI06), 96 MeV (1996BH06, 1999BA11, 2001BB02, 2002BA50), 111 to 136.9 MeV (1997PO07, 2001PO01), 121.7 MeV (1995VA05) and 912 MeV (2001ME26). See previous measurements reported at E(¹⁹F) = 40, 60 and 68.8 MeV (1975AJ02), E(¹⁹F) = 18.0 to 60.1 MeV (1985AJ01) and E(¹⁹F) = 29.3 to 60.1 MeV (1990AJ01). The substate population probability for ¹²C*(4.4) has been studied by (1986IKZZ) at E(¹⁹F) = 63.8 MeV.

69. (a) ¹²C(²⁰Ne, ²⁰Ne)¹²C
(b) ¹²C(²²Ne, ²²Ne)¹²C

Elastic angular distributions are reported at E(²⁰Ne) = 390 MeV (1993BO28) and E(²²Ne) = 264 MeV (2010AL10). See previous measurements for reaction (a) reported at E(²⁰Ne) = 65.7 MeV (1980AJ01) and at E(¹²C) = 37 MeV (1975AJ02), 20 to 34.4, 60.7, 72.6 to 75.2 MeV [to ²⁰Ne*(0, 1.6)] and 77.4 MeV (1985AJ01). Fusion to sulfur, reaction cross section, fragmentation yield and evaporation residue studies are also reported in the literature. See also (1990SL01, 1997BR05, 1997FR04, 2004FA08, 2007FR22).

70. (a) ¹²C(²⁴Mg, ²⁴Mg)¹²C
(b) ¹²C(²⁶Mg, ²⁶Mg)¹²C

Elastic angular distributions are reported for reaction (a) at E(¹²C) = 19, 21 and 23 MeV (1993LE08), 32 to 48 MeV (1997SC14), 85 MeV (2000SI36) and 104 MeV (2017JO03), and at E(²⁴Mg) = 130 MeV (2004BE08, 2004BE18, 2009BE34) and 768 MeV (2001CH11, 2001CH56). See previous measurements for reaction (a) at E(¹²C) = 20 to 36, 20 to 60, 24.8, 27.7 to 34.8 and 40 MeV (1985AJ01) and for reaction (b) at E(¹²C) = 20 to 56 MeV (1985AJ01). The B(E2) values and deformation parameters for the first J^π = 2⁺ states of ^24,30,32Mg are measured at E ≈ 32 MeV (2001CH11, 2001CH56). See also analyses of scattering distributions given in (1991LI34, 1992GR15, 1994LI33, 1996FR23, 1997FR04, 1999KU01, 1999LE14, 1999LE38, 1999LI34, 2000LU03, 2001BO41, 2001BO46, 2001KU01, 2002BO17, 2002BO58, 2002KU33, 2004BE31, 2005BO28, 2005BO31, 2006KA23, 2006KA43, 2006MA33, 2007FR22). Reaction induced fission of ²⁴Mg to ¹²C-¹²C cluster states is studied at E(²⁴Mg) = 170 and 180 MeV (1991BE27, 1991FU03, 1991FU09, 1994CU05, 1995CU01, 1995LE22, 2000CU02, 2001SH08) and E_cm = 43.3 to 60 MeV (1994GY01). Studies on fusion to ³²S and ³⁶Ar, fragmentation yields, and other reaction cross sections can be found in the literature.

71. ¹²C(²⁷Al, ²⁷Al)¹²C

Elastic angular distributions have been measured at E(¹²C) = 21 MeV (2011HA47) and 30.0 to 39.9 MeV (1979RO11), while that of the transition to ¹²C*(4.4) has been studied at E(¹²C) = 82 MeV (1977BE42) and E = 344.5 MeV (1990JA12). See also (2004FA08, 2004GA16, 2006ZA10). Results on fusion, fragmentation yield, and other reaction studies are found in the literature.

72. (a) ¹²C(²⁸Si, ²⁸Si)¹²C
(b) ¹²C(²⁹Si, ²⁹Si)¹²C
(c) ¹²C(³⁰Si, ³⁰Si)¹²C

Elastic scattering for reaction (a) was studied at E(¹²C) = 60, 65, 75 and 85 MeV (1998YA02) and E(²⁸Si) = 145 and 160 MeV (1991RA05). See previous measurements at E(¹²C) = 19 to 36, 24, 27, 30, 40.2, 49.3, 70 and 83.5 and 186.4 MeV and at E(²⁸Si) = 58.3 to 116.7 MeV see (1980AJ01), at E(¹²C) = 19 to 48, 41.3, 56.0 to 69.5 and 131.5 MeV see (1985AJ01), and at E(¹²C) = 56, 59, 66, 69.5 and 65 MeV see (1990AJ01). The α-γ angular correlations have been studied at E(²⁸Si) = 112.3 and 142.7 MeV: ¹²C*(4.4) is found to be produced almost entirely in the m = 0 magnetic substate (1986RA08). Elastic and inelastic scattering on ²⁹Si was studied at E(¹²C) = 36.8 MeV (1968AN21). See theoretical analysis of elastic scattering on ²⁸Si in (1992GR15, 1997CH41, 1999LE14, 1999LE38, 1999RA24, 2001EL08, 2004PA17, 2010BA45) and see specific discussion on "forward glory" scattering in (2000DA15, 2003LE25, 2004DA27, 2011DA04). Results on fusion, fragmentation yield, and other reaction studies on ^28,29,30Si targets are found in the literature.

73. ¹²C(³²S, ³²S)¹²C

Elastic and inelastic angular distributions and B(E2) values are reported at E(³²S) = 65 to 67 MeV (2006SP01). See previous measurements at E(¹²C) = 35.8 MeV and E(³²S) = 73.3 to 128.3 MeV (1980AJ01), E(³²S) = 60 to 99 MeV and 160 MeV (1985AJ01), and E(³²S) = 194, 239 and 278 MeV (1990AJ01). See also (1990ME07, 1991AR15, 1991BE27, 1991FI04, 2001PI10, 2003BE75), references in (1980AJ01, 1985AJ01, 1990AJ01) and other references in the literature for discussion on fusion, fragmentation yield and other reaction studies.

74. (a) ¹²C(³⁹K, ³⁹K)¹²C
(b) ¹²C(⁴⁰Ar, ⁴⁰Ar)¹²C

Elastic angular distributions for reaction (a) have been studied at E(¹²C) = 54 and 63 MeV (1980GL03). For reaction (b) see measurements in (1989PL02, 1990LE08, 1990LE10, 1991PA08, 1993YO03, 2004MO48).

75. (a) ¹²C(⁴⁰Ca, ⁴⁰Ca)¹²C
(b) ¹²C(⁴²Ca, ⁴²Ca)¹²C
(c) ¹²C(⁴⁸Ca, ⁴⁸Ca)¹²C

The elastic scattering in all three reactions has been studied at E(¹²C) = 51.0, 49.9 and 49.9 MeV, respectively (1979RE03) and for reaction (a) at E(¹²C) = 180, 300 and 420 MeV (1986SA29). See theoretical analysis of elastic scattering on a ⁴⁰Ca target in (1994SA37, 2003AL17, 2008KI20, 2013XU06). Results on fusion, fragmentation yield, and other reaction studies are found in the literature.

76. ¹²N(β⁺)¹²C Q_m = 17.3381

¹²N decay to ¹²C is complex. Most of the decay populates ¹²C_g.s. with small branches populating ¹²C*(4.4) and several α-particle unbound states (see 12.42 (in PDF or PS)). The ground state decay branch is determined by subtracting all other observed decay branches from unity. Early studies were motivated by evaluation of the ¹²B and ¹²N mirror decays to states in ¹²C and by parity violation studies. The decay rates to ¹²C*(4.4) measured in (1981KA31) are most precise and have been used as normalization factors in modern experiments to deduce the relative and absolute branching ratios of weaker decay branches, see 12.23 (in PDF or PS). In most articles, measurements on ¹²N and ¹²B were published together; see reaction 32 ¹²B β^--decay for detailed discussion on the experiments.

Studies on ¹²N decay are more complicated than those on ¹²B decay because the high-energy 17.3 MeV β⁺ particles can produce Bremsstrahlung photons while interacting in the β-counter, which can be detected in the γ-counter giving rise to a huge background under the discrete photo-peaks. The Q-value for ¹²B decay is 13.37 MeV, which leads to a significantly lower background radiation. In addition, the β⁺ annihilation photons can sum with decay γ-rays in the detector causing a distortion away from the expected response function. Discussion on systematic effects is given in (1974MC11, 1978AL01).

A detailed study of the high-energy portion of the γ-ray spectrum identified decay branches populating the ¹²C*(12.71, 15.11) states (1967AL03). The β-γ spectra were analyzed to determine the ratios I(E_γ = 12.72)/I(E_γ = 4.4) = 2.9 × 10^-3 ± (26%) and I(E_γ = 15.11)/I(E_γ = 4.4) = 1.78 × 10^-3 ± (20%). Using the known Γ_γ and γ-decay branching ratios the β-decay intensities to these states can be deduced.

Interest in the higher-lying J^π = 0⁺ and 2⁺ states led to measurements where ¹²N and ¹²B ions were produced at rare isotope facilities. Analysis of these data gave precise details on the α breakup channel for ¹²C states up to E_x = 15.11 MeV populated in the decays, see for example (2004FY03, 2005DI16, 2009DI06, 2014TE01). In (2009HY01, 2009HY02, 2010HY01) it is found that interference of the J^π = 0⁺₂ state with other J^π = 0⁺ strength around E_x ≈ 11.2 MeV leads to "the very broad component from 8.5 to 11 MeV, which has been mistaken for a 10.3-MeV resonance with a 3-MeV width". Rather than attribute their observed strength to a 10.3 MeV group, they provided the β feeding strength for the E_x = 9-12 MeV and 12-16.3 MeV regions [excluding the 12.7 MeV state]. A multi-level many-channel R-matrix analysis of the data (2010HY01) indicated a J^π = 0⁺ state at E_x = 11.2 ± 0.3 MeV with Γ = 1.5 ± 0.6 MeV and B(GT) = 0.06 ± 0.02 and a J^π = 2⁺ state at E_x = 11.1 ± 0.3 MeV with Γ = 1.4 ± 0.4 MeV and B(GT) = 0.05 ± 0.03.

77. ¹³B(β^-n)¹²C Q_m = 8.4908

The β-decay of ¹³B primarily populates bound states in ¹³C with an intensity > 99%. However weak decay branches to ¹³C*(7.54, 8.86, 9.90) and possibly ¹³C*(9.50) lead to β-delayed neutron emission to ¹²C*(0.4.4) with P_n = (0.28 ± 0.04)% (1962MA19, 1969JO21, 1974AL12); see Fig. 4 [¹³B β^-n-decay scheme].

78. ¹³C(γ, n)¹²C Q_m = -4.9463

The decay of the giant resonance in ¹³C takes place predominantly to ¹²C*(15.1, 16.1) [and to their analogs in ¹²B]. Below E_γ = 21 MeV transitions to ¹²C*(4.4) are dominant (1975PA09). A review on isospin component splitting in ¹³C up to E_γ ≈ 30 MeV is given in (1993MC02).

79. ¹³C(e, e'n)¹²C Q_m = -4.9463

The neutron decay of the pygmy and giant dipole resonances of ¹³C were studied using E_e = 129 MeV electron scattering (1999SU12). Neutron decay from the pygmy resonance tends to populate ¹²C*(0, 4.4), while neutron decay from the GDR tends to populate ¹²C*(12.7, 15.11).

80. ¹³C(π⁺, p)¹²C Q_m = 135.4062

Angular distributions have been measured at E_π⁺ = 90 to 170 MeV to ¹²C*(0, 4.4, 7.7, 9.6, 12.7, 14.1, 15.1, 16.1, 19.1, 20.6, 22.9, 25.3) (1981AN10): an energy dependent ratio for the excitation of ¹²C*(12.7, 15.1) is reported along with similarities in the population of states seen in this reaction and in the (p, d) reaction. Angular distributions are reported to ¹²C*(0, 4.4) at E_π⁺ = 32 MeV (1982DO01). The population of ¹²C*(4.4) is more than 10 times that of ¹²C_g.s..

81. (a) ¹³C(p, d)¹²C Q_m = -2.7217
(b) ¹³C(p, pn)¹²C Q_m = -4.9463

Angular distributions have been measured at E_p = 8 to 800 MeV; see (1995TO03) for E_p = 35 MeV to ¹²C*(0, 4.4), see (1982BU03) for E_{pol. p} = 123 MeV^† to ¹²C*(0, 4.4), see (1990AJ01) for E_p = 18.6 MeV^† to ¹²C*(0, 4.4), 41.3 MeV to ¹²C*(0, 4.4, 12.7, 15.1, 16.1), 800 MeV to ¹²C*(0, 4.4, 12.7, 14.1, 15.1, 16.1) and E_{pol. p} = 119 MeV^† to ¹²C*(0, 4.4, 7.7, 9.6, 12.7, 14.1, 15.1, 16.1, 16.6, 17.8, 18.16 ± 0.07, 18.8, 19.9, 20.3, 20.6) and 500^† MeV to ¹²C_g.s., see (1985AJ01) for E_p = 800 MeV to ¹²C*(0, 4.4, 12.7, 14.1, 15.1, 16.1) and E_{pol. p} = 65^† MeV to ¹²C*(0, 12.7, 15.1, 16.1) and 200 and 400 MeV to ¹²C*(0, 4.4), see (1980AJ01) for E_p = 16.7 and 17.7 MeV to ¹²C*(0, 4.4) and 200 to 500 MeV to ¹²C*(0. 4.4), see (1975AJ02) for E_p = 50^† and 54.9^† to ¹²C*(0, 4.4, 12.7, 15.1, 16.1), and 62^† MeV to ¹²C*(15.11, 16.1, 17.76, 18.8, 21.5, 22.55), and see (1968AJ02) for E_p = 8, 12 and 17 MeV to ¹²C*(0, 4.4). Spectroscopic factors are deduced in measurements highlighted with the symbol ^†. See also (1990GU26, 1990MU19, 1991AB04, 2004LI41, 2005DE33, 2005TS03, 2009DE02, 2009DE07, 2009DE13, 2012KU35).

The population of ¹²C*(10.3, 15.4) is reported in (1987LE24) along with structures at E_x = 18.2, 18.8, 19.9, 20.3 and 20.6 MeV that have Γ_cm = 240 ± 50, 120 ± 30, ≈ 400, ≈ 220 and ≈ 210 keV, respectively. (1984SM04) report structures at 20.61 ± 0.04 and 25.4 ± 0.1 MeV, the latter with Γ ≥ 0.5 MeV. At E_p = 62 MeV, (1974PA01) report the excitation of states having widths [Γ (keV)] of E_x = 15112 ± 5, 16110 ± 5 [< 20], 17760 ± 20 [80 ± 20], 18800 ± 40 [80 ± 30], 21500 ± 100 [< 200] and 22550 ± 50 [< 200] keV: l_n = 1 for all states except ¹²C*(21.5) and (22.55) for which l_p = (1) and ≠ 1, respectively. ¹²C*(14.1) is not excited, consistent with J^π = 4⁺ (1970SC02, 1974PA01). For d-γ correlations via ¹²C*(15.1) see (1987CA20).

For reaction (b), cross sections and angular distributions for deuterons and small-relative angle p-n pairs with small relative angles (¹S₀ state pairs) were measured at E_p = 35 MeV (1995TO03); both angular distributions were reproduced in coupled channels calculations, and the angular distribution for the singlet state pairs was found to fall off more slowly at large angles. Also see (1996GO07). In a kinematically complete experiment at E_p = 7.9 to 12.5 MeV (1971OT02), it was found that sequential decay via states in ¹³C and ¹³N is strongly involved in the reaction. Near E_p = 12.5 MeV there is some indication of sequential decay via singlet deuteron formation.

82. ¹³C(d, t)¹²C Q_m = 1.3109

Angular distributions, mainly for t₀, t₁ and t₂, have been measured for E_d = 0.41 to 29 MeV. See (1985AJ01) for E_d = 18 MeV, see (1980AJ01) for E_d = 24.1, 26.2 and 27.5 MeV and E_{pol. d} = 13 and 29 MeV, see (1975AJ02) for E_d = 0.41 to 0.81, 1.0 to 2.7, 2.2, 3.3 8, 12, 12.1, 13.3, 13.6, 14, 14.8, 15 and 28 MeV, see (1968AJ02) for E_d = 2.2, 3.3, 8, 12 and 14.8 MeV. Also see analyses in (1990GU26, 1995GU22, 2007CO01).

The relative yields of triton groups to ¹²C*(12.7, 15.1, 16.1) [(J^π; T) = (1⁺; 0), (1⁺; 1) and (2⁺; 1), respectively] and ³He groups to ¹²B*(0, 0.95) [(J^π; T) = (1⁺; 1) and (2⁺; 1), respectively] give information on a possible short range charge dependent nuclear force. Ratios were measured at E_d = 62 MeV (1972BR27), 24.1 to 27.5 (1977LI02) and 29 MeV (1979CO08) yielding charge-dependent matrix element values of 250 ± 50 keV, 180 ± 80 keV and 120 ± 30 keV, respectively. If the j = 1/2 component is excluded, which appears to be unwarranted, the charge dependent matrix element of (1979CO08) increases to 140 ± 40 keV. For a comparison of reported charge-dependent matrix element values between ¹²C*(12.7, 15.1) see 12.18 (in PDF or PS).

83. (a) ¹³C(³He, α)¹²C Q_m = 15.6313
(b) ¹³C(³He, 2α)⁸Be Q_m = 8.2647
(c) ¹³C(³He, pt)¹²C Q_m = -4.1826

Angular distributions, mainly involving α_0-3 have been measured at many energies up to 60 MeV; see (1990ES01): E_cm = 1.05 and 1.20 MeV, (1994BU01): E(³He) = 37.9 MeV, (1990MU19): E(³He) = 39.6 MeV, (1992AD06): E(³He) = 50 and 60 MeV, (1959AJ76): E(³He) = 2 and 4.5 MeV, (1968AJ02): E(³He) = 1.6 to 3.3, 1.8, 4.5, 8.8, 9.4, 10.3, 12, 15, 18, 40 to 45 MeV, (1975AJ02): E(³He) = 1.5 to 5.3, 19.1, 27.3, 35.7, 36.8 MeV, (1980AJ01): E(³He) = 18, 20, 29.2 MeV, (1985AJ01): E(³He) = 18.3 and 23.1 MeV and (1990AJ01): E(³He) = 22.7 MeV. A DWBA analysis of α_0-3 and ¹²C*(10.84, 11.8, 12.7, 13.3) distributions (1966KE08) finds l = 1 or 0 for all the groups except α₃ (to ¹²C*(9.6)) for which l = 2. Rainbow scattering effects are discussed in (1992AD06, 1994BU01). See also (1968AR12, 1990GU26).

Angular correlations of α-particles and 4.4 MeV γ-rays have been studied at E(³He) = 4.5 MeV (1962HO13) and 29.2 MeV (1976FU1F). For ¹²C*(15.1), angular correlations have been studied at E = 9.4 and 11.2 MeV (1969TA09) and at E = 24 and 25.5 MeV (1980BA1U): the average ratio between the p_1/2 and p_3/2 amplitudes is -0.086 ± 0.030 in the later measurement; see also (1999LE48, 2003ZE06). See (1990ES01, 2007GA24) for discussion on neutron stripping and ⁹Be cluster transfer, and see (1984VA39, 1985VA1E, 1986ZE1C) for a study of the spin tensors for ¹²C*(4.4). Ion beam analysis of surfaces is discussed in (2017MO06).

For a detailed analysis of the decays of ¹²C*(12.7, 15.1) see (1970RE09) and 12.14 (in PDF or PS). Attempts have been made to study the T mixing between the 1⁺ states ¹²C*(12.71, 15.11). Reported values for Γ_α/Γ for ¹²C*(15.11) are (1.2 ± 0.7)% (1970RE09, 1970RE1F), (6.0 ± 2.5)% (1970AR30) and (4.1 ± 0.9)% (1974BA42). The (1974BA42) value was obtained by observing the decay α-particles (only α₁) in reaction (b); using the ¹²C*(15.11) Γ_γ₀ (1983DE53) and γ-decay branching ratios (1972AL03) leads to Γ_α = Γ_α₁ = 1.8 ± 0.3 eV. If this isospin forbidden Γ_α is the result of the mixing between the 1⁺ states ¹²C*(12.71, 15.11) [T = 0 and 1, respectively] via a charge dependent interaction, the matrix element is 340 ± 60 keV (1974BA42): see, however, 12.18 (in PDF or PS) and (1980AJ01).

For reaction (c), proton unbound states in ¹³N that decay to ¹²C*(0, 4.4, 7.65, 12.7, 14.08, 15.1, 16.1) were studied at E(³He) = 450 MeV (2004FU12).

84. (a) ¹³C(⁶Li, ⁷Li)¹²C Q_m = 2.3048
(b) ¹³C(⁷Li, ⁸Li)¹²C Q_m = -2.9137

At E(⁷Li) = 34 MeV angular distributions have been observed for the reactions to ¹²C*(0, 4.4) + ⁷Li*(0, 0.48) and ⁸Li*(0, 0.95) in all combinations. While ¹²C*(0, 4.4) are dominant in the two spectra, ¹²C*(7.7, 9.6) and, in reaction (a) at E(⁶Li) = 36 MeV, ¹²C*(12.7) are also populated (1973SC26). See also (1987CO16, 2003TR04, 2004CA46).

85. (a) ¹³C(¹³C, ¹⁴C) Q_m = 3.2301
(b) ¹³C(¹⁴C, ¹⁵C) Q_m = -3.7282

Angular distributions have been reported at E(¹³C) = 16.0 to 50.0 MeV by (1983KO15) who have also studied the excitation functions over that energy range. For reaction (b), (2014MC03) deduced spectroscopic factors and asymptotic normalization coefficients at E(¹⁴C) = 168 MeV. See (1988BI11) for measurements at E(¹³C) = 20.0 to 27.5 MeV.

86. (a) ¹³C(¹⁶O, ¹⁷O)¹²C Q_m = -0.8032
(b) ¹³C(¹⁷O, ¹⁸O)¹²C Q_m = 3.0991
(c) ¹³C(¹⁸O, ¹⁹O)¹²C Q_m = -0.9907

Angular distributions for neutron exchange reactions involving oxygen isotopes are reported at E(¹⁶O) = 42 to 65 MeV (1989FR04), 13 and 14 MeV (1976DU04), 14, 17 and 20 MeV (1971BA68) and 41.7 and 46.0 MeV (1973DE21); E(¹⁷O) = 29.8 and 32.3 MeV (1977CH22, 1978CH16), and E(¹⁸O) = 15, 20 and 24 MeV (1971BA68, 1971KN05) and 31.0 MeV (1978CH16). See also (1990IM01).

87. ¹³O(β⁺p)¹²C Q_m = 15.8260

The β-decay of ¹³O populates ¹³N_g.s. in (88.7 ± 0.2)% of all decays. The levels with E_x ≥ 3.50 MeV decay via proton emission to ¹²C*(0, 4.4, 7.65) leading to P_p = (11.3 ± 2.3)%. See (2005KN02) and Fig. 5 [¹³O β⁺p-decay scheme]. Also see (1965MC09, 1970ES03, 1990AS01, 2014TE01).

88. ¹⁴C(p, t)¹²C Q_m = -4.6409

Angular distributions have been measured at E_p = 14.5 (1971CU01), 18.5 (1963LE03), 39.8 (1973HO10), 40.3 (1990YA02), 45 (1978RO08), 46 (1979FR04), 50.5 [unpublished in (1975AJ02)] and 54 MeV (1976AS01).

At E_p = 40.3 MeV, the states at ¹²C*(0, 4.4, 7.65, 9.64, 12.71, 14.08, 15.11, 16.10, 17.76, 18.80) are populated; cross sections for natural parity T = 0 states are enhanced when compared with the T = 1 states (1990YA02). At E_p = 54 MeV the first T = 2 states of ¹²C are observed at E_x = 27.57 ± 0.03 and 29.63 ± 0.05 MeV [Γ_cm ≤ 200 keV] (1976AS01): their identification is supported by the similar angular distributions to the first two T = 2 states in ¹²B, reached in the (p, ³He) reaction [see reaction ¹⁴C(p, ³He) in ¹²B]. The lower T = 2 state is well fitted by L = 0; the angular distribution to ¹²C*(29.63) is rather featureless. It is suggested that its shape is more consistent with L = 0 than with L = 2. It is not excluded that the group to ¹²C*(29.63) may be due to unresolved states. The states are observed with Γ_p/Γ = 0.3 ± 0.1 and Γ_α₁/Γ < 0.1 for the first T = 2 state and Γ_p/Γ = 0.8 ± 0.2, Γ_p₀/Γ ≈ 0.4 and Γ_α/Γ ≈ 0.2 for ¹²C*(29.63). (1976BA24) has suggested that the second T = 2 state in A = 12 may have J^π = 0⁺.

At E_p = 45 MeV, (1978RO08) report E_x = 27595.0 ± 2.4 keV, Γ ≤ 30 keV for the first T = 2 state and calculate the decay properties for two values of the total width, narrow and 30 keV. A subsequent measurement at E_p = 46 MeV reported branching ratios for the decay of ¹²C*(27.6) to ⁸Be_g.s. + α; ¹¹B*(0, 2.12, 4.45, 5.02, 6.74 + 6.79) + p; and ¹⁰B_g.s. + d are, respectively, (10.5 ± 3.0)%; (3.0 ± 2.2)%, (8.0 ± 2.3)%, (0 ± 3.3)%, (8.4 ± 3.2)%, (8 ± 5)%; and (2.8 ± 2.0)% (1979FR04). An additional (9.1 ± 3.5)% of the decay feeds into the ⁸Be* + α continuum. See also (2006FO11).

89. (a) ¹⁴N(p, ³He)¹²C Q_m = -4.7788
(b) ¹⁴N(p, pd)¹²C Q_m = -10.2723

Angular distributions of ³He, mainly to ¹²C*(0, 4.4) and also to ¹²C*(12.7, 14.1, 15.1, 16.1), have been studied at E_p = 7.5 to 52 MeV; see references in (1975AJ02, 1980AJ01). At E_p = 50 MeV, the analysis indicates J^π = 4⁺ for ¹²C*(14.1) (1970SC02). The angular distributions to the first two T = 1 states in ¹²C are compared with those of the analog states in ¹²N obtained in the (p, t) reaction (1976YO03). For reaction (b) the transitions to ¹²C*(0, 4.4) have been studied at E_p = 46 MeV (1970WE1J, 1971WE05) and to ¹²C*(4.4) at E_p = 58 MeV (1985DE17).

90. ¹⁴N(d, α)¹²C Q_m = 13.5742

Alpha groups have been observed corresponding to most known ¹²C states up to ¹²C*(16.11), see (1965BR08, 1965SC12) and 12.34 (in PDF or PS). The reaction proceeds mainly via α_0-3. Angular distributions have been measured at several energies, see (1959AJ76): E_d = 10.8 to 20 MeV, (1968AJ02): E_d = 0.5 to 28.5 MeV, (1975AJ02): E_d = 1.0 to 40 MeV, (1980AJ01): E_d = 2.7 to 40 MeV, (2004PE10): E_d = 0.5 to 2.0 MeV, (2008GU08): E_d = 0.7 to 2.2 MeV and (1999IG03): E_d = 15.4 MeV. The α-γ correlations give J = 2⁺ for the 4.4 MeV state (1954ST1C). At E_d = 1.8 MeV, the α-particles to the 7.65 MeV state were observed in coincidence with recoiling ¹²C_g.s. nuclei; if Γ_rad = (Γ_γ + Γ_π), then the ratio Γ_rad/Γ = (2.8 ± 0.3) × 10^-4 was reported in (1963SE23). The width of the 9.6 MeV state Γ_cm is reported as 30 ± 8 keV (1953DU23, 1956AH32).

Analysis of the angular distributions at E_d = 40 MeV, with a one-step, ZRDWBA, leads to J^π = (1, 2, 3)⁺, (2, 3)⁺ and (2, 3)⁺, respectively for ¹²C*(19.5, 20.6, 22.5) (1976VA07); spectroscopic factors were also deduced for all observed transitions. At E_d = 40 MeV, the upper limits for the ratio of the cross sections to ¹²C*(15.11) and ¹²C*(12.71) are ≈ 0.3% for θ_lab = 6° to 10° and 0.5% at 40° and 50°: these results by (1974VA15) imply a lower isospin mixing between these two 1⁺ states than suggested by the work of (1965BR08, 1972BR27). See also (1991AP03, 1994IV01, 1996TA29: material profiling) and (1995HU15: meteorite analysis).

91. ¹⁴N(α, ⁶Li)¹²C Q_m = -8.7985

The angular distributions of ⁶Li ions corresponding to transitions to ¹²C*(0, 4.4) have been measured at E_α = 27.2 (1995FA21) and 42 MeV (1964ZA1A). At 27.2 MeV, the contributions of the direct and statistical two-nucleon transfer processes are estimated by studying the (α, ⁶Li) reaction on several targets.

92. (a) ¹⁵N(p, α)¹²C Q_m = 4.9655
(b) ¹H(¹⁵N, α)¹²C Q_m = 4.9655

Properties of ¹²C states have been deduced from measurements of the angular distributions of α₀ and α₁ particles for E_p < 18 MeV [see (1968AJ02)], at E_p = 2.99 to 5.14 MeV (1977JA11), E_p = 19.85 to 43.35 MeV (1971GU23) and E_p = 3.5 to 7.5 MeV (2000IG05). Early results on the angular distributions of alpha particles and 4.4 MeV γ-radiation indicated that the 4.4 MeV state has J = 2⁺ or > 4 (1953KR1B). The alpha particles to ¹²C*(4.432 ± 0.010 MeV) were observed along with a transition corresponding to E_γ = 4.443 ± 0.020 MeV (1952SC1B). The lifetime of ¹²C*(4.4) was reported as τ_m = 65 ± 9 fsec (1970CO09). At E_p = 43.7 MeV the angular distributions to the 0⁺ states ¹²C*(0, 7.66, 17.76) are fitted by L = 1, while the distributions to ¹²C*(14.1, 16.1) are consistent with L = 3 [J^π = 4⁺ and 2⁺, respectively] (1972MA21). The energy of the second excited state of ¹²C is 7654.2 ± 1.6 keV (1973MC01), see additional discussion therein; such a high value leads to a sharply reduced rate for the (α-α-α) process.

At E_p = 7.5 MeV, the α-γ correlations to ¹²C*(4.44) were measured and analyzed for θ = 20°-160° to deduce spin tensor components and M = 0, 1 and 2 magnetic sublevel populations (2000IG05). The triton-cluster transfer spectroscopic factor amplitudes to ¹²C*(0, 4.44, 7.65, 14.08, 16.1, 17.76) are deduced from analysis of angular distributions at E_p = 9 to 43.7 MeV (2006AB20). This reaction, which decreases proton and ¹⁵N abundances in the ¹⁹F production sequence, was studied in (1994KA02, 1998AD12, 2003HU10, 2008BA42, 2009LA13, 2011AD03, 2012DE06, 2012IM02); complementary analyses of this reaction using the Trojan Horse Method are found in (2006LA18, 2007LA37, 2008MU07, 2008MU15, 2008PIZZ, 2009LA13, 2010MU16).

Parity non-conserving alpha-decay reactions are discussed in (1990DU01, 1991DU04, 1991KN03, 2000MI37). Depth profiling and material composition studies using reactions (a) and (b) are discussed in (1990FU06, 1991DU04, 1991IW05, 1992FA04, 1992MA14, 1992MA22, 1994EN07, 1994JA16, 1994OL08, 1996MI28, 1996MI29, 2005KU36, 2010MA26, 2016RE12).

93. ¹⁵N(α, ⁷Li)¹²C Q_m = -12.3808

At E_α = 42 MeV angular distributions have been obtained for all four of the transitions: ¹²C_g.s. + ⁷Li*(0, 0.48) and ¹²C*(4.4) + ⁷Li*(0, 0.48) (1968MI05). See (1995BO31) for a study of the ¹⁵N cluster configurations at E_α = 27.3 MeV.

94. ¹⁶N decay

The β-delayed α-decay of ¹⁶N can feed only ¹²C_g.s. from ¹⁶O*(8.871, 9.585, 9.845) states. In early measurements such as (1959AL06, 1984WA07), a (1.0 ± 0.2)% β-decay branch to ¹⁶O*(8.871) was deduced that was based on the beta spectrum following ¹⁶N decay; a subsequent reanalysis by the authors resulted in a revised branching ratio (1.06 ± 0.07)% that was detailed in (1986AJ04). However, the small fraction of α-decay from these states yields a significantly lower α-particle intensity.

The decay to ¹⁶O*(9.585), which α-decays 100% to ¹²C_g.s. dominates the delayed α spectrum; the branching ratio (1.20 ± 0.05) × 10^-5 (1961KA06) has been used extensively in the literature. However the result (1.49 ± 0.05) × 10^-5 (2016RE01) is in poor agreement. A third reported value (1.3 ± 0.3) × 10^-5 (1993ZH13) does little to resolve the discrepancy. In (1961KA06) a gas carrying radioactive ¹⁶N passed sequentially through a proportional counter (α-counting) and a GM-tube counter (β-counting). The delayed α branching ratio was deduced from analysis that considered lifetimes, flow-rates and active volumes. On the other hand, (2016RE01) counted the number of ¹⁶N nuclei deposited into a Si detector and the number of subsequent α-decays. At present, we accept the result of (2016RE01), though additional verification of this result would be useful.

The smaller decay branches to the neighboring states have been measured relative to the ¹⁶O*(9.585) branching ratio, see 12.43 (in PDF or PS). The α-decay of ¹⁶O*(8.871) is parity forbidden, and detailed measurements of this decay branch have set limits on irregular parity amplitudes in the wavefunction (1961KA06, 1969HA42, 1970JO25, 1974NE10). In (1974NE10) Γ_α = (1.03 ± 0.28) × 10^-10 eV is determined for ¹⁶O*(8.87) (1974NE10).

It was proposed in, for example, (1971BA99) that the ¹⁶N delayed α spectrum gives details on the E1 component of the ¹²C + α capture cross section in the relevant E_cm ≈ 300 keV region. At astrophysical energies the reaction is dominated by the tails of subthreshold states; the interference of these states gives rise to a, so called, "ghost peak" in the delayed α-particle energy spectrum that can be used to deduce the E1 component of the capture reaction. Significant efforts focused on determining the shape of the spectrum (1993BU03, 1993BU18, 1993BU21, 1993ZH06, 1994AZ03, 1997FR12, 1998GA20, 2007FR11, 2007TA34, 2009BU12, 2010TA05).

95. (a) ¹⁶O(γ, α)¹²C Q_m = -7.1619
(b) ¹⁶O(γ, 4α) Q_m = -14.4367
(c) ¹⁶O(e, e'α)¹²C Q_m = -7.1619

Reactions (a) and (b) have been studied using Bremstrahling beams with E_γ < 42 MeV (1981MA38), < 50 MeV (1997GO16, 2001KI33), < 100 MeV (1981CH28), < 150 MeV (2012AF07), < 300 MeV (1995GO10, 1995KI04), and with polarized quasi-monoenergetic beams at E_γ = 9 to 11 MeV (2013ZI03). There is evidence for the involvement of many ¹²C states: see (1965RO05) and references therein. A test of time reversal invariance, via comparison of the ¹²C(α, γ) vs. the ¹⁶O(γ, α) rate found no evidence of T-invariance (1970VO13). Astrophysical implications of the photo-breakup reactions are discussed in (1953HO81).

For reaction (c), the dipole and quadrupole decay strengths measured in ¹⁶O(e, e'α) reactions to ¹²C states are discussed in (1990BU27, 1992FR05, 2001DE36, 2008DO15).

96. (a) ¹⁶O(n, n'α)¹²C Q_m = -7.1619
(b) ¹⁶O(p, p'α)¹²C Q_m = -7.1619

These reactions proceed mainly through ¹²C*(0, 4.4). See references in (1968AJ02, 1975AJ02, 1980AJ01, 1985AJ01, 1990AJ01). ¹²C*(14.1) is populated at E_p = 101.5 MeV (1984CA09). See analysis of the E_γ = 4.44 MeV lineshape in (2001KI25). See also (2016OL04).

97. ¹⁶O(d, ⁶Li)¹²C Q_m = -5.6882

Angular distributions, mainly to ¹²C*(0, 4,4), have been measured at E_d = 13 to 55 MeV (1975AJ02), E_d = 12.7 to 80 MeV (1980AJ01), E_d = 50 to 80 MeV (1985AJ01) and E_d = 18 to 55 MeV (1990AJ01). Spectroscopic factors are reported in (1984UM04: E_d = 54.2 MeV to ¹²C*(0, 4.4, 7.7, 9.6, 14.1)), (1978BE1T: E_d = 50, 65 and 80 MeV to ¹²C*(0, 4.4, 14.1)), (1978OE02, 1979OE04: E_d = 80 MeV to ¹²C*(0, 4.4, 7.7, 9.6, 14.1, and broad (or unresolved) structures at 14.1 ± 2.6, 19.5 ± 1.5 MeV)), (1980YA02, 1984UM04: E_d = 54.25 MeV to ¹²C*(0, 4.4, 7.7, 9.6, 14.1)).

98. ¹⁶O(³He, ⁷Be)¹²C Q_m = -5.5748

Reactions involving ¹²C*(0, 4.4, 9.6) + ⁷Be*(0, 0.4) and ¹²C*(7.6) + ⁷Be_g.s. are reported at E(³He) = 25.5 to 30 MeV (1970DE12, 1972PI1A). The α-particle pickup spectroscopic factors are deduced at E(³He) = 26 MeV (1975AU01), 60 MeV (1995MA57) and 70 MeV (1976ST11). See also measurements at E(³He) = 41 MeV (1981LE01).

99. (a) ¹⁶O(α, 2α)¹²C Q_m = -7.1619
(b) ¹⁶O(α, ⁸Be)¹²C Q_m = -7.2538

At E_α = 25 MeV reaction (a) proceeds in part by sequential decay via states in ¹⁶O and ²⁰Ne (1968PA12). Angular distributions involving ¹²C*(0, 4.4) at E_α = 90 MeV have been analyzed by PWIA and DWBA by (1976SH02): S_α = 2.9 ± 0.5 and 0.70 ± 0.23, respectively. In reaction (b), the angular distributions and integrated cross sections of ⁸Be nuclei (identified through the α-decay) leading to the ground and 4.4 MeV states of ¹²C have been determined for E_α = 35.5 to 41.9 MeV (1965BR13). The α pickup spectroscopic factors have been measured at E_α = 55 to 72.5 MeV (1973WO06, 1974WO1D, 1976WO11): S_α = 0.25, 1.07, 0.05, 1.40 for ¹²C*(0, 4.4, 7.7, 14.1) respectively; the excitation of ¹²C*(9.6) is also reported. See also (1990JA09, 1992JA04, 2008JA02, 2009JA07, 2014JA07).

100. (a) ¹⁶O(⁹Be, ¹³C)¹²C Q_m = 3.4864
(b) ¹⁶O(¹⁶O, ²⁰Ne)¹²C Q_m = -2.4321

Reaction (a) was measured at E_cm = 7.2 to 10.2 MeV (1988WE17), see analysis in (1994OS08). For reaction (b), see measurements reported in (1974SP06: E(¹⁶O) = 24 MeV), (1974RO04: 49 to 64 MeV), (1977PO14, 1979PO14: 68 to 90 MeV), (1979MO14: 65 to 92 MeV), (1983ME13, 1984ME10: 50 to 72 MeV), (1988AU03: 72 MeV), (1996FR09: 51 to 66 MeV) and (1977KA26: E_cm = 17 MeV).

101. ¹⁶O(¹¹B, ¹²C)¹⁵N Q_m = 3.8295

At E(¹¹B) = 41.25 MeV the t₂₀ and t₄₀ polarization tensors of ¹²C*(2⁺₁) were measured for θ_cm = 48° - 62° (2000IK02). In addition, analysis of the measured transfer cross sections for reactions leading to ¹²C_g.s. + ¹⁵N_g.s., ¹²C*(4.44) + ¹⁵N_g.s. and ¹²C_g.s. + ¹⁵N*(6.32[J^π = 3/2^-]) appears to indicate significant participation of multistep processes passing through ¹¹B states. See also optical model analysis of measurements at E(¹¹B) = 115 MeV in (1979RA10).

102. ¹⁶O(¹³C, ¹²C)¹⁷O Q_m = -0.8032

The γ-recoil method was used to extract the t₂₀ and t₄₀ polarization tensors of ¹²C*(2⁺₁) at E(¹³C) = 50 MeV for population of ¹²C*(2⁺₁) + ¹⁷O_g.s. and ¹²C*(2⁺₁) + ¹⁷O*(870) (2000IK01). An analysis of the spectroscopic amplitudes is also given. See earlier experimental results in (1975SE03, 1976WE21, 1977DU04, 1979BO36, 1979RA10).

103. ¹⁸O(p, tα)¹²C Q_m = -10.8686

The decay of the lowest T = 2 state of ¹⁶O to ¹²C*(0, 4.4) has been studied by (1973KO02).

104. ¹⁹F(d, ⁹Be)¹²C Q_m = 0.2998

At E_d = 13.6 MeV angular distributions have been obtained for the ⁹Be groups to ¹²C*(0, 4.4) (1981GO16). Angular distributions have also been measured at E_d = 9 to 14.5 MeV: see (1964DA1B, 1967DE03, 1967DE14).

105. ²⁰Ne(α, ¹²C)¹²C Q_m = -4.6170

Angular distributions for the α-induced fission of ²⁰Ne have been measured in the range E_α = 13.4 to 20.8 MeV (1981DA13). See also measurements at E_α = 12 to 17 MeV (1962LA03, 1962LA05, 1962LA15).

106. ²³Na(p, ¹²C)¹²C Q_m = -2.2409

Angular distributions involving ¹²C_g.s. have been studied at E_p = 7.9 to 18.6 MeV (1987KI26).

107. ²⁴Mg(α, ¹⁶O)¹²C Q_m = -6.7717

Angular distributions have been reported in (1978SO10: E_α = 22 to 26 MeV), (1980BE04, 1980BE15: 90.3 MeV), (1986SK01: 24.9 to 27.76 MeV) and (1989ES06: 26 to 37 MeV).

108. ²⁴Mg(¹⁶O, ²⁸Si)¹²C Q_m = 2.8222

Angular distributions for reactions that mainly involve ⁴⁰Ca resonances have been reported in (1978PA04: E = 47 to 57 MeV), (1979LE02: 17 to 31 MeV), (1980PA08, 1980SA12, 1980SA31, 1985SA11: 24 to 54 MeV), (1981NU02: 32 to 48 MeV), (1982FU06: 32 to 36 MeV) and (1989LE19: 46.5 MeV). See also measurements and analyses of the α transfer reaction reported in (1972MA36, 1975ER02, 1976PE05).