A=12C (1959AJ76)

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¹²C (1959AJ76)

(See the Energy Level Diagram for ¹²C)

GENERAL: See also Table 12.4 [Table of Energy Levels] (in PDF or PS).

Theory: See (1955FE1A, 1955HE1E, 1956CA1F, 1956EL1C, 1956GL1B, 1956HA1C, 1956HA1D, 1956KU1A, 1956MO1D, 1956NA1A, 1956PE1A, 1956RE1C, 1956WI1F, 1957BA1H, 1957BI1C, 1957HE1B, 1957KU58, 1957PA1A, 1957RE1A, 1957SA1B, 1958CA1G, 1958FR1C).

1. ⁷Li(⁶Li, n)¹²C Q_m = 20.931

See (1957NO17).

2. (a) ⁹Be(³He, n)¹¹C Q_m = 7.565 E_b = 26.286
(b) ⁹Be(³He, p)¹¹B Q_m = 10.329
(c) ⁹Be(³He, α)⁸Be Q_m = 18.911
(d) ⁹Be(³He, d)¹⁰B Q_m = 1.093

The yields and angular distributions of protons leading to the ground state and several excited states of ¹¹B have been investigated by (1956AL1E: E(³He) up to 2.7 MeV), by (1955HO1D, 1956HL01: E(³He) = 2.0 MeV), by ((1956WO1A, 1956WO1C, 1957JO1B) and E. Wolicki, private communication: 2 to 4.5 MeV) and by (D.R. Sweetman, private communication: 6.05 MeV). The yield rises rapidly to E(³He) = 1.8 MeV and remains approximately constant to 4.5 MeV, with no indication of resonance. Angular distributions show fore and aft asymmetry and vary only slowly with energy. At E(³He) = 2 MeV, it appears that both direct interaction and compound nucleus formation, involving interfering resonances with l ≤ 3, may be taking place. At higher energies the forward peaking suggestive of direct interaction becomes more obvious. See also ¹¹B. For reactions (a), (c) and (d), see ¹¹C, ⁸Be and ¹⁰B.

3. ⁹Be(α, n)¹²C Q_m = 5.709

Neutron groups corresponding to states of ¹²C*(0, 4.4, 7.6) have been observed with E_α up to 5.3 MeV. At E_α = 5.3 MeV the forward yield of the group leading to the 7.6 MeV state is about 1/8 of that leading to the 4.4 MeV state: see (1952GU1A, 1955ST1C, 1956ME1B, 1957RI38); see also (1957DI1B).

The energy of the γ-ray from the first excited state is 4.425 ± 0.020 (1954MI68), 4.48 ± 0.06 MeV (1955BE1G) (both values corrected for Doppler shift). The internal pair conversion, coefficient indicates an E2 transition (1954MI68); the angular correlation of pairs admits M1 or E2, favoring the latter (1954HA07, 1956GO1K, 1956GO73, 1958AR1B). The angular distribution of γ-rays observed at several bombarding energies is consistent with J = 2⁺ (1955TA28, 1956PR1A). The n-γ correlation at E_α = 5.3 MeV (thick target) is isotropic within 6.5% (1956ST1E: see also (1958TA05)). The mean lifetime of the 4.4 MeV level is (2.6 ± 0.9) × 10^-14 sec, about one-eighth of the single-particle value for an E2 transition (1956DE22).

The 7.7 MeV state appears to decay predominantly into ⁸Be + α (see ¹²B(β^-)¹²C and ¹²C(α, α')¹²C*). A gamma ray of energy 3.1 MeV has been reported by (1953BF01, 1954UE01, 1956ST1E, 1956ST1F, 1957ST1E), but (1955BE1G, 1957GO89, 1957KR1A) find no evidence of the 7.7 MeV nuclear pairs which should accompany the decay to the ground state. (1955BE1G) estimate that at least 96% of the decays proceed to ⁸Be + α; (1957KR1A, 1958KR70) find < 1.6 × 10^-5 7-MeV pairs per 4.4 MeV γ-ray; assuming a population ratio of 1 : 8, this result yields Γ_π/Γ < 1.3 × 10^-4. An upper limit of 1/600 for the ratio of 7.6/4.4 MeV pairs is reported by (1957GO89). (1954DI1A) find no n-γ coincidences other than those associated with the 4.4 MeV level. See also (1957RO1E).

At E_α = 21.7 and 175 MeV, γ-radiation from the 15 MeV, J = 1⁺; T = 1 state (see ¹²C(p, p')¹²C*) is reported (1954RA35, 1957WA04). At the higher energy, the ratio of 15 MeV to 4.4 MeV radiation is 1.2 × 10^-2 (1957WA1F). See also (1954EL1B, 1955BR1A, 1955HA1E, 1956GO1N, 1957BR1J) and (1955MA1J; theor.).

4. ¹⁰B(d, γ)¹²C Q_m = 25.195

At E_d = 0.95 MeV, the upper limit to the capture cross section is 0.1 μb (1955SA1B).

5. ¹⁰B(d, n)¹¹C Q_m = 6.473 E_b = 25.195

The thin-target excitation function in the forward direction in the range E_d = 0.3 to 4.6 MeV shows some indication of a broad resonance 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). Angular distributions seem to be dominated by the stripping process: see ¹¹C. The yield of 6.5 MeV γ-rays has been measured at four bombarding energies between 0.8 and 2.2 MeV (1955SA1B). See also ¹¹C.

6. ¹⁰B(d, p)¹¹B Q_m = 9.237 E_b = 25.195

Absolute yields and angular distributions are reported for various proton groups by (1952EN19, 1954BU06, 1954PA28, 1956MA69, 1956VA17) for E_d = 0.18 to 3.1 MeV. Although the excitation functions show several broad peaks, no clear resonances can be identified, and it must be assumed that many overlapping resonances are involved (1956MA69). Angular distributions indicate both stripping and compound nucleus processes even at low bombarding energies (1954PA1D). However, the p₁ group, leading to ¹¹B*(2.1), shows no stripping even at E_d = 3 MeV; it is suggested that an orbital angular momentum selection rule is operative here (1956MA69: see ¹¹B). Absolute cross sections reported by (1954BU06, 1954PA28, 1956MA69) differ rather greatly.

The yields of 6.8 and 7.3 MeV γ-rays have been measured at four bombarding energies between 0.8 and 2.2 MeV (1955SA1B). At E_d = 1.70 MeV, θ(lab) = 58°, the cross section for protons leading to the 6.76 MeV state is 6.1 (± 15%) mb/sr (1956KA1A).

7. ¹⁰B(d, d)¹⁰B E_b = 25.195

See ¹⁰B.

8. ¹⁰B(d, α)⁸Be Q_m = 17.819 E_b = 25.195

Excitation curves for ground state α-particles have been measured for E_d = 0.9 to 2.6 MeV at 45°, 90° and 150°. Broad maxima are observed at 1.0, (1.4) and 2.0 MeV. At E_d = 0.91 MeV, the angular distribution of α₀ particles shows a peaking in the forward direction (1956MA69). See also ⁸Be.

9. ¹⁰B(t, n)¹²C Q_m = 18.937

Not reported.

10. ¹⁰B(³He, p)¹²C Q_m = 19.702

Proton groups reported by (1955BI26) and (1958MO99) are listed in Table 12.5 (in PDF or PS). A careful search, at E(³He) = 1.25 MeV, reveals no other level in the range E_x = 4.4 to 7.7 MeV (1958MO99: region at E_x = 6.4 MeV obscured). At E(³He) = 2.0 MeV, the proton group leading to the 15.11 MeV level was found to be in coincidence with a 15.10 MeV γ-ray: Γ_γ/Γ for this level is 0.77 ± 0.20. The ratio of the width for γ-emission to the 4.4 MeV level to the ground state Γ_γ is ≈ 0.03. The 12.76 MeV level also emits γ-rays: Γ_γ/Γ ≈ 0.02, suggested J^π = 1⁺ ((1957GO1B) and H.E. Gove, private communication). Coincidence studies by (1958MO99) lead to Γ_γ/Γ < 0.9% for the 7.7 MeV level, Γ_γ/Γ = 3 ± 1 % for the 12.76 MeV level, and 50 ± 25 % for the 15 MeV level. See also ¹¹B(d, n)¹²C, (1958BR1D, 1958SW63) and ¹³N.

11. ¹⁰B(α, d)¹²C Q_m = 1.351
Q₀ = 1.341 ± 0.002 (1956DO41).
Q₀ = 1.36 ± 0.09 (1956PI1A).
Q₀ = 1.39 ± 0.01 (1953SH64).

See also ¹⁴N.

12. (a) ¹¹B(p, γ)¹²C Q_m = 15.958
(b) ¹¹B(p, α)⁸Be Q_m = 8.582 E_b = 15.958

In the range E_p = 0 to 3 MeV, five principal resonances occur, at E_p = 0.16, 0.67, 1.4, 2.0 and 2.6 MeV (see Table 12.6 (in PDF or PS)). All except the second and fourth exhibit resonance for α₀, α₁, γ₀ and γ₁ (to ⁸Be*(0, 2.9) and ¹²C*(0, 4.4)); at E_p = 0.67 MeV, only α₁, γ₁ are resonant. It follows from angular momentum selection rules that resonances for α₀ must have the character J^π = 0⁺, 1^-, 2⁺, 3^-...; J = 0⁺ is excluded by observation of γ₀.

The E_p = 0.16 MeV resonance (¹²C*(16.11)) is well established as J = 2⁺; probably the T = 1 analogue of ¹²B*(0.95). The angular distribution of α₀ particle is strongly anisotropic at resonance and shows a (cos θ) term varying with energy near resonance. The assumption J = 2⁺, l_p = 1, with interference from an s-wave state at higher energy gives a good account of the observed angular distributions from E_p = 0.13 to 0.3 MeV. The channel spin ratio χ = 0.42 ± 0.02; the relative amplitude of the interfering J = 1^- state is 0.022 ± 0.002 (1952TH1B). The angular correlation of α₁ and the subsequent breakup of ⁸Be*(2.9) also requires J = 2⁺, with the ratio of reduced matrix elements for outgoing d to s-waves, B = 0.80, phase difference cos β = 0.60 (1955GE1A). The angular distribution of γ₁ and of the following 4.4 MeV radiation is consistent with the scheme 2⁺(M1)2⁺(E2)0⁺ with the channel spin ratio χ = 0.42 (1954GR1C); (1956CR1C) obtain χ = 0.51 ± 0.03. Angular distributions of the 16 MeV radiation, γ₀, require J = 2⁺, with interference from a J = 1^- level at E_p = 1.4 MeV (1954GR1C); (1956CR1C). (γ₀ is not resonant at E_p = 0.67 MeV, so this state cannot be involved here.) The resonant energy is 163.1 ± 0.2 keV; Γ_lab = 6.5 ± 0.6 keV (see (1955AJ61)). The very small α-width suggests T = 1 (1953BE61).

For the E_p = 1.4 MeV state (¹²C*(17.23)), the possible assignments are 1^- (s-wave), 2⁺ (p-wave), 1^- or 3^- (d-wave); d-wave formation would seem to be excluded by the observed width. As indicated above, J = 1^- appears to be required to account for the interference at lower energies in α₀ and γ₀; known higher resonances are probably too narrow to produce the observed effects. (1957DE11) find that the α₀-dsitributions for E_p = 0.6 to 1.4 MeV are well accounted for by the assumption of s-wave formation of J = 1^- through channel spin (χ = 0) with a relative d-wave amplitude A = 0.5, and interference by the 2.6 MeV, J = 2⁺, state, with relative amplitude C = 0.25. A qualitative fit to the behavior of α₁ can be obtained with the same assumptions (1957DE11). Angular distributions of γ₀ at E_p = 1.4 MeV admit either J = 2⁺ or 1^-; for the latter, however, formation in channel spin 2 (χ = ∞, d-waves) is required (1955GO10). The angular correlation of internal pairs indicates E1 for γ₀ (1956GO1K, 1956GO1N, 1958AR1B). The large E1 width suggests T = 1 for this state (1953BE61).

The E_p = 0.67 MeV state (¹²C*(16.58)) may be formed by s- or p-waves; d-waves are excluded by the width (1953BE61). The angular distribution of α₁ at E_p = 0.64 and 0.93 MeV indicates s-wave formation: if J = 2^- is assumed, the d-wave admixture is < 10%. The correlation of α₁ with the subsequent ⁸Be*(2.9) breakup is consistent with J = 2^- and excludes 1^-; an appreciable f-wave admixture in outgoing α₁-particles is indicated (1957DE11). Correlation results at E_p = 270 keV can be accounted for by J = 2^- with interference from the 1^-, E_p = 1.4 MeV state (1955GE1A, 1957DE11). The angular distribution of γ₁ is reported to require J = 2⁺, with interference from the 1^-, E_p = 1.4 MeV state (1954GR1B): according to (1957DE11), however, the distributions observed by (1954GR1C, 1955GO10) can equally well be ascribed to J = 2^-, with interference from a broad, even parity state, possibly at E_p = 2.0 or 2.6 MeV (see, however, (1954GI1B)). The angular correlation of internal pairs indicates E1 for the γ₁ radiation (1956GO1K, 1956GO1N, AR57). The relatively large E1 width suggest T = 1 for this state (1953BE61).

The E_p = 2.0 MeV level is reported to be resonant for α₀ and α₁; the relative weakness of α₁ suggests J = 0⁺ (1953PA26). These seems to be no clear indication of resonance for γ₀ or γ₁ at this energy (1955GO10: see also (1953HU29)). At E_p = 2.65 MeV, resonance occurs for α₀, α₁ (1953PA26) and, weakly, for γ₀, γ₁ (1955BA22, 1955GO10). A large P₂ coefficient in the angular distribution of γ₀ suggests J = 2⁺ (1955GO10). (1955HO48) find E_p = 1.98 and 2.61 MeV for the resonant energies for α₀. Additional resonances for γ₀ and γ₁, reported by (1955BA22) are listed in Table 12.6 (in PDF or PS). (1959GE33) have examined the excitation function for ground-state transitions from E_p = 4 to 7.7 MeV. The experiment locates the maximum of the ¹²C giant resonance at E_x = 22.55 ± 0.1 MeV but does not resolve individual levels. Two additional peaks, at E_x = 21.4 and 22.1 MeV are suggested. The maximum value of σ(γ, p) is calculated to be 29 ± 5 mb.

An upper limit for the total cross section (average value, E_p = 1.7 to 4.0 MeV) for the production of nuclear pairs with E_π = 6.5 to 9.5 MeV is 0.03 μb (1955BE62). See also (1955AJ61, 1956MA1T), (1957SI1B; theor.) and ⁸Be.

13. ¹¹B(p, n)¹¹C Q_m = -2.764 E_b = 15.958

Observed maxima in the (p, n) cross section are listed in Table 12.7 (in PDF or PS) (1951BL1A, 1955BA22, 1957KA1C, 1959GI47). The region covered is characterized by considerable overlapping of resonances (1959GI47). See also (1956KO1D, 1958MA1F, 1958TA03).

14. (a) ¹¹B(p, p)¹¹B E_b = 15.958
(b) ¹¹B(p, p')¹¹B*

Absolute elastic scattering cross sections are reported for one angle for E_p = 0.6 to 2.0 MeV by (1956TA16), for four angles for E_p = 0.3 to 1.0 MeV by (1957DE11). A pronounced anomaly is observed near E_p = 0.67 MeV at all angles; the level is therefore formed by s-waves. The 0.3 to 1.0 MeV results are well accounted for by two resonances: E_p = 0.67 MeV, s-wave, J = 2^-, Γ = 0.33 MeV, Γ_p/Γ = 0.5, d-wave < 10%, and E_p = 1.4 MeV, s-wave, J = 1^-, Γ = 1.27 MeV, Γ_p/Γ = 0.05 (1957DE11). (The reported Γ_p/Γ for the 1.4 MeV resonance appears to be inconsistent with the values 0.8 or 0.2 derived by (1953BE61) from (p, γ) and (p, α) cross sections.) (1956TA16) find no rapid variation in cross section near E_p = 2.0 MeV. The absence of a detectable anomaly near E_p = 0.16 MeV confirms the small value of Γ_p assumed for this resonance; Γ_p < 200 eV (J.C. Overley, private communication). See also (1956KI54).

Maxima in the yield of 2.1 MeV γ-radiation from ¹¹B*(2.1) are observed at E_p = 2.664 MeV, Γ = 48 keV: (1953HU29, 1955BA22) and at E_p = 3.15, 3.4, 3.78, 4.28, 4.68 and 5.13 MeV (1955BA22: see Table 12.7 (in PDF or PS)). (Judging form the width, the 2.66 MeV resonance is not that observed, e.g., in ¹¹B(p, γ)¹²C.)

15. ¹¹B(p, d)¹⁰B Q_m = -9.237 E_b = 15.958

See ¹⁰B.

16. ¹¹B(d, n)¹²C Q_m = 13.731
Q₀ = 13.63 ± 0.05 (1957BI78).

Reported neutron groups are listed in Table 12.8 (in PDF or PS). The group corresponding to the 7.6 MeV state is weak, relative to neighboring groups, at all bombarding energies investigated, and the stripping pattern is poorly developed. The relative weakness of the 7.6 MeV state in this reaction and in the ¹²C(e, e')¹²C* and ¹²C(p, p')¹²C* reactions is attributed to lack of parentage overlap with the ground state of ¹²C (1955LA1C). At E_d = 0.92 MeV, there is no indication of a state in the range E_x = 5.1 - 6.6 MeV: the upper limit of the intensity of the corresponding neutron group is ≲ 1% of the intensity of the group corresponding to the 4.4 MeV state (1957BI78). For E_d = 1.1 to 2.0 MeV only the groups corresponding to ¹²C*(4.4, 12.76) are accompanied by γ-radiation; an upper limit for (n, γ) coincidences from ¹²C*(7.6) is 0.2% of ¹²C*(4.4) (1958DA11, 1958NE38, 1959NE1A).

Angular distributions of the neutrons to the first four states of ¹²C have been reported for a number of energies in the range E_d = 0.5 to 10 MeV. At the higher energies, the distributions are understood in terms of simple stripping theory (except for the 7.6 MeV state). At the lower energies, E_d = 0.5 to 5 MeV, a good account of the angular distributions of ground-state neutrons is obtained with the theory of (1957OW03) which includes not only stripping of the deuteron but also the possibility of stripping a neutron from ¹¹B, and the interference between the two processes. The relative probability of the exchange stripping increases with energy until the Coulomb barrier is surmounted. The exchange process seems to involve s-wave deuteron capture by a ¹⁰B core with J = 1⁺ (1956PR1B, 1957AM48, 1957OW03: see also (1959NE1A)). Angular distributions at E_d = 9 MeV indicate odd parity for the 9.6 MeV state (1956MA83: see also (1954GR53) and Table 12.8 (in PDF or PS)). For other work on angular distributions, see (1957AM48, 1958AM13: E_d = 0.50 to 1.15 MeV), (1955WA30: E_d = 0.6 MeV), (1955IH1B: E_d = 0.69 MeV), (1954GR53: E_d = 0.85 MeV), (1957BI78: E_d = 0.92 MeV), (1956PR1B: E_d = 1.5 to 5 MeV), (1953GI05: E_d = 8.1 MeV), and (1957ZE1A: E_d = 10 MeV). See also (1954BU06, 1956BO1F, 1956BO43, 1956KO1E, 1957RA1A) and (1955MA1J, 1958ED1C; theor.).

In the range E_d = 1.0 to 5.5 MeV, two slow neutron thresholds are observed at 1.627 ± 0.004 MeV (E_x = 15.11 ± 0.01 MeV) and near 4.1 MeV (broad; E_x = 17.23 MeV) (1955MA76). Gamma rays are observed with E_γ = 4.44 ± 0.05 (1951RU1A) and 12.8 ± 0.3 MeV (1958KA31). If the latter γ-ray is properly attributed to decay of the 12.8 MeV level, it is not clear why the level should so decay in view of its instability with respect to ⁸Be and ⁸Be*(2.9) (1958KA31: see also ¹⁰B(³He, p)¹²C). A 15.1 MeV γ-ray is observed with a threshold of E_d = 1633 ± 3 keV, attributed to the first T = 1 state of ¹²C at 15.11 MeV. The observed width is < 2 keV. A search for α-particles to ⁸Be and ⁸Be* gives Γ_α/Γ_γ < 1.5. At E_d = 2.96 MeV the cross section for production of the 16.1 MeV T = 1 state is < 1 mb/sr (1958KA31). See also (1955AJ61) and (1957WA04).

17. ¹¹B(³He, d)¹²C Q_m = 10.464

At E(³He) = 4.5 MeV, the ground state deuteron group is strongly peaked in the forward direction (1957HO61).

18. ¹¹B(α, t)¹²C Q_m = -3.855

Not reported.

19. ¹²B(β^-)¹²C Q_m = 13.376

The half-life is 20.34 ± 0.5 msec (weighted mean of (1955AJ61, 1956NO1A, 1957CO57, 1958KR65, 1958VE20, 1959KR1B), excluding (1948JE03)). E_β(max) = 13.40 ± 0.05 MeV (1958VE20). Branches are observed leading to ¹²C*(0, 4.4, 7.65, 10.1): see Table 12.9 (in PDF or PS). The fact that the transition to the 0⁺ ground state is allowed establishes J = 1⁺ for ¹²B. This assignment is confirmed by the allowed character of the transition to ¹²C*(4.4), J = 2⁺. The 7.7 MeV level decays mainly by α-emission to ⁸Be(0) with Q = 278 ± 4 keV; E_x = 7.653 ± 0.008 MeV (1957CO59). Gamma transitions with E_γ > 6 MeV accompany < 10^-4 of all β-decays (1956KA1A, 1958KA31); an upper limit of 3 × 10^-5 is obtained in a search for β-γ (7.6) coincidences (1958KA14). Upper limits for (3.2 + 4.4) MeV cascades are given as (0.4 ± 2) × 10^-3 and 10^-5 of all decays by (1956TA07) and (1958KA14) respectively. It follows that the relative partial width of the 7.6 MeV level is < 3 × 10^-3 for 7.6 MeV γ-rays and < 10^-3 for 3.2 MeV γ-rays (see also ⁹Be(α, n)¹²C). Since the β-transition is allowed, the 7.7 MeV state has J = 0⁺, 1⁺ or 2⁺; J = 1⁺ is ruled out by the α-decay. The preponderance of α-decay over γ-decay speaks for J = 0⁺ (1957CO59).

The 10.1 MeV level decays mainly via α-emission to ⁸Be(0); transitions to ⁸Be*(2.9) amount to < 4%. The c.m. width is about 2.5 MeV (after removing the E_β⁵ factor): the best account of the observed α-spectrum is obtained with J = 0⁺, E_λ = 1 0.4 MeV, θ²_α = 1.5, R = 5.21 × 10^-13 cm (1958CO66).

The β-spectrum has been reported by (1950HO01, 1958VE20). (1958GE1C) discusses a possible distortion of high-energy β-spectra in axial-vector coupling due to a "weak-magnetic" interaction.

See also (1957CH25), (1955JA1C, 1957FE1C, 1959SC1B; theor.).

20. ¹²C(γ, γ')¹²C*

The lifetime of the 4.4 MeV state has been determined by resonance scattering and resonant absorption (of γ-radiation from ¹⁵N(p, α)¹²C*) as τ_mean = (6.5 ± 1.2) × 10^-14 sec (1958RA14).

Excitation of the 15.1 MeV level by bremsstrahlung is reported by (GA57B, 1957HA13, 1959GA09). From measurement of the yield of resonance scattered radiation and of the self-absorption coefficient, the integrated scattering cross section ∫ σ_sdE, and the peak absorption cross section σ⁰_n are deduced. The resulting values for partial widths are given in Table 12.10 (in PDF or PS). It is noted the γ-ray width for the ground state transition is near the single-particle M1 value of 65 eV, and that the very small α-width strongly suggests T = 1 for this level (1957HA13). The scattering angular distribution indicates dipole radiation (1956LE1E, GA57B, 1959GA09). The strength of the M1 radiation also indicates T = 1: see (1958MO17). Inelastic scattering in the giant-resonance region has been studied by (1959GA09). See also (1957GO1F, 1958AX1A, 1958MC1D).

21. ¹²C(γ, n)¹¹C Q_m = -18.722

The cross section for production of ¹¹C exhibits a broad peak at E_γ = 22.5 MeV, Γ ≈ 4 MeV, σ_max = 8.3 mb (1955BA63). Other reported values for σ_max are summarized by (1957CO57: note a 10% correction in this work). See also (1957CA1D). AT high energies, the cross section exhibits a long tail, falling off approximately as E_γ^-3. The integrated cross section to E_γ = 250 MeV is 80 MeV-mb, accounting for about 1/3 of the sum-rule limit for all absorption processes. It is noted that the relative prominence of the high-energy tail is not a general feature of (γ, n) reactions in heavy elements (1955BA63, 1957CO57). Comparison of (γ, n) and (e, n) cross section for 28 to 145 MeV are consistent with the assumption that the transitions are predominantly E1 (1958BA60). The angular distribution of photoneutrons at the giant resonance is W(θ) = 1 + (1.35 ± 0.88)sin²θ, indicating considerable emission of neutrons with l > 0 (1956FA30). See ¹²C(γ, p)¹¹B and (1954TE1A, 1955MO1B, 1957BA1K; theor.).

Discontinuities in the yield function are reported to indicate levels at 19.3, 19.8, 20.1, 20.5, 20.7, 21.1, 21.6, 22.4, and 22.8 MeV (1954GO39, 1954KA1A). The first two are given as 19.09 ± 0.05 and 19.55 ± 0.05 MeV by (1955SP1A). Eighteen discontinuities observed between E_γ = 18.90 and 22.88 MeV are tabulated by (1958KA1D). A search for resonance absorption near E_γ = 22.8 MeV indicates a width Γ > 580 keV, in apparent contradiction of the activation results (1956TZ1A). (1958WO1B), using monochromatic gamma rays, find no evidence of fine structure in the total cross section from E_γ = 20.3 to 20.8 MeV. The upper limit is, however, not in conflict with the recent report of (1958KA1D). See also (1955JO1B, 1955SA1F, 1958BA1K, 1958SM1A).

22. ¹²C(γ, p)¹¹B Q_m = -15.958

The cross section exhibits a giant resonance at E_γ = 21.5 ± 0.5 MeV, Γ = 1.7 ± 0.5 MeV (1951HA1C). The peak cross section is 22 mb, and the integrated cross section to 24 MeV is 56 MeV-mb (1956CO59): compare ¹¹B(p, γ)¹²C (1959GE33). The photoproton spectrum shows the general features of the inverse reaction, ¹¹B(p, γ)¹²C, and suggests resonances at E_γ = 17.3, (20.8), 22.6, and (23.1) MeV (1956CO59: see, however, (1958WO1B)). (1957LI1A) finds indications of peaks at E_γ = 21.8, 22.6, 23.3 and 25.8 MeV. An absolute measurement, based on σ(¹²C*(γ, 3α)) for E_γ = 17.6 MeV yields σ(γ, p) = 1.19 ± 0.21 mb, in good agreement with the value 1.09 ± 0.16 mb calculated from the inverse reaction (1956MA1T). See also (1956GO1G, 1958CH31, 1958PE1A, 1958WH35).

Angular distributions of photoprotons show a pronounced 90° peaking, somewhat skewed in the forward direction (1952HA1B, 1953HE1B, 1955JO1B, 1956KL19, 1957DO1A, 1957LI1A, 1957MI1A). Such distributions are inconsistent with s-wave proton emission from J = 1^-; ¹²C compound states formed by E1 absorption and suggest a direct interaction involving independent-particle states: L-S coupling seems to be favored (1955MA1H). The angular distributions of ¹²C(γ, n) and (γ, p) are evidently quite similar, as expected on the assumption of charge independence; the difference of about a factor of 2 in total cross section is ascribed to a 1% T = 0 admixture in the intermediate state (1957BA1K). See also (1953HE1B, 1957CH24, 1958BA1M, 1958BA30, 1958PA1B, 1958PE1B, 1958SM1A) and (1955MO1B, 1957SI1B; theor.).

23. ¹²C(γ, 3α) Q_m = -7.281

Maxima in the yield of 3-prong stars are reported at E_γ = 17.3, 18.3, 21.9, 24.3 and 29.4 MeV; some evidence of fine structure is also found. The integrated cross section is 1.21 ± 0.16 MeV-mb for E_γ < 20.5 MeV, 2.8 ± 0.4 MeV-mb for 20.5 ≤ E_γ < 42 MeV, and < 0.2 MeV-mb for 42 ≤ E_γ < 60 MeV (1953GO13, 1955GO59). (1955CA19) summarize cross section measurements for the ⁷Li(p, γ) radiation and find evidence for a resonance near E_γ = 12.3 MeV and possibly others at 15 and 16 MeV. According to (1955JO1C), peaks occur at E_γ = 14.7, 15.8, 16.6, 18.3, 24.3, and > 29 MeV, in fair agreement with (1953GO13). Absolute cross sections are reported for E_γ = 13 to 30 MeV, and integrated cross sections agree well with (1953GO13, 1955JO1C). See also (1953DA1A, 1953GU1A, 1953MI31, 1955HA1D). According to (1955GO59), the three-body reaction is not involved for E_γ < 40 MeV (see, however, (1953MI31, 1954CH1B)). The reaction ¹²C(γ, α)⁸Be*(p)⁷Li is reported by (1956LI05).

Studies of angular distributions indicate that for E_γ = 12 to 15.6 MeV, the reaction involves mainly E2 absorption (¹²C*: J = 2⁺; T = 0); from 15.6 to 20 MeV both E1 (J = 1^-; T = 1) and E2 (J = 2⁺; T = 1), and for E_γ > 20 MeV, mainly E1 (J = 1^-; T = 1). Significant E2 absorption (J = 2⁺; T = 0) also occurs for E_γ = 20 to 25 MeV (1955GO59: see, however, (1951TE1A, 1953GE1B)). See also (1953LI1C, 1954GR1B, 1955CO1A, 1955SO1B, 1955TI1A, 1956MA1T, 1957MU1C).

24. ¹²C(e, e')¹²C

Both elastic and inelastic scattering angular distributions have been studied at E_e = 80, 150 and 187 MeV by (1955FR1G, 1956FR27) and at 420 MeV by (1958EH1B). The elastic data are well accounted for by a modified Gaussian charge distribution of r.m.s. radius 2.50 × 10^-13 cm, derived from a harmonic well with a characteristic length parameter of 1.68 × 10^-13 cm (1956FR27, 1958EH1B). See also (1953HO79, 1956FE1B, 1956HO93, 1957HO1E, 1958EH1A, 1958RA43).

Inelastic peaks corresponding to ¹²C*(4.4, 7.7, 9.6) are observed, in addition to some unresolved structure near 11 MeV. There is no indication of the 15.1 MeV level. The observed angular distributions agree well with shell-model calculations of (1955RA1D, 1956MO1E, 1956TA1C, 1957TA1B) with a harmonic well of r.m.s. radius 2.40 × 10^-13 cm. Predicted absolute cross sections are low by a factor of 2 in L-S coupling, 6 in j-j coupling; it is presumed that some collective modes of excitation are involved.

Excitation of the 4.4 MeV level is electric; a width of (12.5 ± 2.5) × 10^-3 eV, τ_m = (0.53 ± 0.11) × 10^-13 sec, is obtained (1956HE83). The 7.7 and 9.6 MeV levels are also electrically excited; the angular distributions indicate either monopole or quadrupole transitions, J = 0⁺, 2⁺. The matrix element for the 7.7 MeV E0 transition is 50 mb, in good agreement with that observed for the ¹⁶O monopole transition (1955SC1B, 1956FR27). A shell model calculation in intermediate coupling indicates that configuration mixing is required to give a non-zero matrix element for the 0⁺-0⁺ transition and suggests that a semi-collective model is indicated (1955SC1B, 1956SH1F, 1957TA1B: see also (1955LA1C)). According to (1956EL1C), satisfactory agreement is obtained with a 50% admixture of 1s³1p⁸2s and 1s⁴1p⁷2p. (1956RE1C) also finds reasonable agreement using the 1s^-12s configuration and suggests that such a "core" excitation might appear quite generally in the light nuclei (see ¹⁶O, ¹⁴C and (1954CH1A)). Calculations using an independent-particle approach to a collective description give a good account of the form factors for both the 4.4 and 7.7 MeV excitations. The form factor for the 9.6 MeV level is consistent with J = 1^- (1956FE1B: see also (1957PA1B)). See also (1958EL48; theor.).

Neutron production with E_e = 35 to 150 MeV has been studied by (1956GE1B). Comparison of σ(γ, n) and σ(e, e'n) for E_e = 24 to 145 MeV indicates that the transitions are largely E1 (1958BA60).

25. (a) ¹²C(n, n)¹²C
(b) ¹²C(n, n')¹²C*
(c) ¹²C(n, n')⁴He⁴He⁴He Q_m = -7.281

For E_n ≳ 14 MeV, elastic scattering angular distributions show pronounced optical-model effects: see (1956BU95, 1956CU1A, 1958NA09) and ¹³C.

A gamma ray of energy 4.42 ± 0.03 MeV is observed at E_n = 6.58 MeV (1956DA23: see also (1954TH42, 1955BA95, 1955BE1H)). Production of 15.1 MeV γ-rays is observed at E_n = 90 MeV (1957WA04, 1957WA1F). At E_n = 14 MeV, inelastic neutron groups corresponding to ¹²C*(4.4, 9.6) are reported by (1956WO1B: see also (1953WH1A, 1956BE1F, 1956CA1E, 1958AN32)). The angular distributions for neutrons corresponding to ¹²C*(4.4) agree well with (p, p') distributions and with direct interaction theory (1958AN32: E_n = 14 MeV).

Inelastic excitation leading to α-particle states has been studied by (1955FR35); levels of ¹²C at 7.7 and 9.6 MeV are involved. (1953JA1C) find that for E_n < 20 MeV, most events proceed through a level at 10 ± 0.8 MeV, Γ_obs = 1.6 MeV, to ⁸Be(0) (See (1955FR35) and ¹²B(β^-)¹²C). See also ¹³C, (1953LI1C) and (1956LA1D; theor.).

26. (a) ¹²C(p, p')¹²C*
(b) ¹²C(p, p')⁴He⁴He⁴He Q_m = -7.281

Elastic scattering differential cross sections have been determined by (1953BU72, 1957GI14, 1957GR53: E_p = 9.4 to 9.6 MeV), (1954FI1B: E_p = 10 MeV), (1956SH1C: E_p = 12 MeV), (1957PE14: E_p = 14 to 19.4 MeV), (1956DA03: E_p = 17.0 MeV, c.m.), (1955KI43, 1956KI54: E_p = 14.5, 20 and 31.5 MeV), (1952BR52, 1953WRZZ: E_p = 30.6 MeV), (1957HI1C: E_p = 40 MeV) and (1957GE08: E_p = 96 MeV). Calculations based on the diffuse-surface optical model give a good account of the data at higher energies (1957GL58, 1957ME21, 1958GL11). At E_p = 9.5 MeV, some evidence for compound elastic scattering is seen in the marked energy variation at back angles (1957GI14). See also ¹³N. Polarization of elastic and inelastic protons has been studied by (1958BR24) for E_p = 16 to 18 MeV. Polarization of elastic protons for E_p = 5 - 7 MeV is reported by (1958WA1D, 1958WA1E). See also (1957LE1G, 1958KO03, 1958SQ53; theor.). Polarization studies at high energies are discussed by (1956ER1A, 1956NI1B, 1957AL79, 1957HE51, 1957HI98, 1957TY1B, 1958NI1B, 1958NI26).

Excitation of the 4.4 MeV level is commonly observed for all energies above E_p ≈ 5 MeV: see (1955AJ61) and (1956RE39: E_p = 5 to 6 MeV), (1957GI14, 1957HO1H: E_p = 9.5 MeV), (1957CO53: E_p = 12 MeV), (1957PE14: E_p = 14 to 19 MeV), (1952BR52: E_p = 31.5 MeV), (1958CH26: E_p = 40 MeV), (1956ST65: E_p = 96 MeV), (1957DI28: E_p = 95 and 135 MeV) and (1957AL39, 1957TY36, 1957TY37, 1958MA1B, 1958TY49: E_p = 182 MeV). E_x = 4431 ± 8 keV (1957BU36). The 7.7 and 9.6 MeV levels are reported by (1957CO53, 1957HO1H, 1957PE14, 1957TY37, 1958CH26). Levels at 12.6, 15.0, and ≈ 20 MeV are also reported by (1957TY36, 1957TY37); the last appears strongly in the work of (1956ST65) (E_x = 20.8 MeV) and is there associated with the giant resonance seen in ¹²C(γ, n) and ¹²C(γ, p).

For E_p ≲ 30 MeV, the angular distribution of the proton group corresponding to the 4.4 MeV level exhibits a minimum near 90° - 100° (c.m.) and a definite fore-and-aft asymmetry. Neither the compound nucleus model nor the direct interaction theory appears to give a satisfactory account of these distributions (1957CO53, 1957GI14, 1957PE14). A direct interaction calculation, using distorted waves, does reproduce the general features of the distributions and also fits the observed (p'-γ) correlation of (1956SH1E) and (1958LE06). See also (1956BE1G, 1957BA1L, 1957BU52, 1957MA58, 1958BR83, 1958CH26, 1958MO98).

The angular distribution of protons corresponding to the 7.7 MeV state depends strongly on energy in the range E_p = 14 to 19 MeV, but consistently shows a strong forward peak, indicative of l = 0 and hence J = 0⁺ (1957PE14). See also (1955LA1C). An attempt to observe γ-decay of this level yields an upper limit of 3% for Γ_γ/Γ_α (1956HO1D). The angular distribution of protons leading to the 9.6 MeV level is consistent with l = 1, J = 0^-, 1^-, 2^- (1957PE14).

The angular distribution of pick-up deuterons at E_p = 95 MeV indicates significant contributions of high momentum components in the bound, 1p neutron wave function, suggesting strong interactions, (≈ 200 MeV), for close distances, R ≈ 1 × 10^-13 cm (1955SE1C, 1956SE1A). See also (1956GR1E).

Emission of (15.1 ± 0.2) MeV γ-radiation, ascribed to the first T = 1 level, has been studied in the range E_p = 15 to 340 MeV by (1957WA04, 1957WA1F). The general shape of the excitation function indicates direct nucleon-nucleon interaction for the higher energies; near threshold, emission of s-wave protons is indicated. Estimates of the α-particle width, and comparison with isobaric spin forbidden reactions (e.g. ¹²C(α, α')¹²C*, ¹²C(d, d')¹²C*) indicate a T = 0 admixture a² ≈ 10^-3. At 31 MeV, θ_lab = 80°, γ-rays of energy 15.1, 12.8 and 10.7 MeV are observed, with relative intensities 1/0.090 ± 0.015/0.095 ± 0.014. The 12.8 MeV radiation is ascribed to excitation of a ¹²C level of that energy, while the 10.7 MeV radiation represents a cascade from ¹²C*(15.1) to ¹²C*(4.4) (1957WA1F: see also ¹⁰B(³He, p)¹²C).

A study of reaction (c) at an energy of 29 MeV shows no indication of direct 4-body decay of ¹³N*; 1/4 of the events proceed via ⁸Be(0), and > 1/2 via ⁸Be*(2.9). Evidence is found for the participation of ¹²C*(9.6, ≈ 12, 16, 20, 25) (1955NE18). See also (1955RE16), (1957JA1B) and (1955CU1C, 1956SA1C, 1956SA1D).

See also (1956ST30, 1957AL39, 1957GO1D) and (1957KA1D, 1958EL48; theor.).

27. ¹²C(d, d')¹²C*

The angular distribution of elastic scattering has been studied at E_d = 19 MeV by (1954FR24); several diffraction peaks appear. See also (1958WA07).

Inelastic groups corresponding to ¹²C*(4.4, 9.6) are reported by (1951KE02, 1954FR24, 1956GR37, 1956HA90: see also (1956CA65)). The 7.7 MeV level has not been observed. The angular distribution of the Q = -4.4 MeV group at E_d = 15 MeV has been analyzed in terms of direct nuclear interaction theory and in terms of electric interaction theory by (1956HA90); neither appears to give a satisfactory account of the observations.

A search for 15 MeV γ-radiation at E_d = 85 MeV yielded a negative result; a T = 0 admixture of < 4 × 10^-2 is indicated (1957WA04, 1957WA1F).