(See the Energy Level Diagram for 13C)
At Eα = 1.60 MeV, the capture cross section is less than 30 μb (1955AL16).
Resonances for neutrons and for γ-rays from 12C*(4.4) are given in Table 13.3 (in PDF or PS). Absolute cross sections for several resonances are reported by (1956BO61, 1959GI47). For the prominent 1.9 MeV resonance, dσ/dΩ (90°) for 4.4 MeV γ-rays is given as 12 mb/sr (lab) by (1956BO61) and as 26 mb/sr by (1955TA28). For Eα = 2.5 to 8.2 MeV, absolute neutron yields have been measured by (1958MA1J, 1959GI47).
Separate excitation curves (at 0°) for ground state neutrons (n0) and for neutrons to the 4.4 MeV state (n1) are reported by (1957RI38) in the range Eα = 1.7 to 4.8 MeV (n0) and 3.1 to 4.8 MeV (n1). The n0 yield curves show broad maxima at Eα = 1.9, 2.0, 2.6, 4.2 and 4.5 MeV. The sharp 3.98 MeV resonance is strong for n1, but quite weak for n0. Angular distributions of ground-state neutrons suggest two broad resonances in the region Eα = 3.9 to 4.6 MeV, probably J = 3/2+ and 5/2+ (1957RI38).
Extensive angular distribution studies have been made for Eα < 2 MeV by (1955TA28, 1956JA28). According to (1956JA28), the best fit to the distributions in the range Eα = 0.4 to 1.3 MeV is obtained from the assignments J = 1/2+, 7/2-, 1/2- for the 0.5, 1.9 and 2.6 (?) MeV resonances (see also (1955TA28)). The angular correlation of neutrons and 4.4 MeV gamma-rays is isotropic at Eα = 1.2 and 2.8 MeV, indicating that stripping plays only a minor role at these energies (1958TA05). See also (1955MA1J; theor.) and (1956BE98).
Four proton groups are observed, corresponding to the 13C levels at 0, 3.09, 3.68 and 3.85 MeV (1953SH64, 1954FA1A, 1954FA1B, 1956PI1A). Additional groups are reported by (1957RO1F). The relative intensities depend strongly on bombarding energy (see 14N, (1953SH64)). See also (1955AJ61).
A study of gamma rays from this reaction and from 12C(d, p)13C shows three lines with Eγ = 0.1695 ± 0.0004, 3.844 ± 0.015 and 3.69 ± 0.02 MeV. The 3.85 MeV γ-ray exhibits no Doppler shift and therefore has a lifetime greater than 3 × 10-13 sec; the 3.69 MeV line shows approximately the maximum possible Doppler shift (τ < 3 × 10-13 sec). The 170 keV line is due to the cascade transition between the 3.84 and 3.68 MeV states; the internal conversion coefficient is consistent with E1, although M1 cannot be excluded. The probability of this cascade decay of the 3.84 MeV state is 0.24 ± 0.05. Cascade transitions to the 3.1 MeV excited state have not been observed. Their intensities are less than 3% of the ground state transitions (1956MA1Q, 1956MA52): see Energy Level Diagrams for 13C. (For earlier work see (1953SH64) and (1954ST20)). The angular distributions and p - γ correlations for the 3.8 MeV radiation contain terms in (cos4θ), indicating J = 5/2+ for the 3.84 MeV state (1954ST20: see 12C(d, p)13C). If the 170 keV line is due to an E1 transition, the Jπ of the 3.68 MeV state is then 3/2- (Jπ = 1/2-, 3/2- follows from 12C(d, p)13C); the angular distribution of the 3.7 MeV radiation is consistent with M1 (1954ST20).
Angular distributions of the grounds state protons are reported at Eα = 4.9, 6.0, 7.0 and 8.1 MeV (1957VO25) and at Eα = 30.5 MeV (1957HU1E): in both cases direct interaction appears to be involved. See also (1957BA1K) and (1955BR1A).
The yield of neutrons has been measured for Ed = 0.2 to 5.4 MeV. The total cross section for ground state neutrons in the 0.5 to 1.15 MeV range rises from 0.5 to 30 mb; both direct and exchange stripping processes seem to be involved (1956PA23, 1957AM48). The yield of the excited-state group, 12C*(4.4) rises smoothly from Ed = 0.5 to 1.1 MeV and is essentially flat from Ed = 1.1 to 2.0 MeV (1959NE1A). At Ed = 600 keV, angular distributions indicate that stripping is important for the ground-state group. For the excited-state group (12C*(4.4)), the interpretation is less clear; the observed distribution can be accounted for by p-wave formation of a J = 7/2+ level in 13C (1955WA30). (1959NE1A) find evidence of strong "heavy-particle" stripping for this group in the range Ed = 0.5 to 2.0 MeV. The cross section for emission of neutrons in the forward direction is ≈ 270 mb/sr at Ed = 5.4 MeV (1955MA76). For Ed = 1.6 to 3.2 MeV, the yield of 15.1 MeV γ-rays shows resonances at Ed = 2.180 ± 0.010 and 3.080 ± 0.015 MeV, corresponding to 13C*(20.52, 21.28) with Γc.m. = 115 ± 10 and 160 ± 15 keV, respectively; the cross section at Ed = 2.2 MeV is 29 ± 7 mb (1958KA31). See also (1954BU06, 1955RI1B) and 12C.
The thin-target yield rises smoothly from Ed = 0.3 to 3.1 MeV with no evidence of resonances (1949HU41, 1958KA31). At Ed = 1.5 MeV, σ ≈ 0.38 b (1958KA31: see, however, (1949HU41)). See also 12B and (1957JA37).
Levels derived from reported proton groups are listed in Table 13.4 (in PDF or PS). The levels at 5.5 and 6.1 MeV have not been observed in any other reaction. From the fact that they do not appear in 12C(n, n)12C, an upper limit of Γ = 10 keV is estimated; the mirror levels in 13N must be assumed to have θ2p < 0.02 (1958MO99).
Angular distributions have been measured for the p0, p1 and (p2 + p3) groups at E(3He) = 4.5 MeV. The p0 group appears to be peaked in both the forward and the backward direction. The other groups do not exhibit a strong angular variation (1957HO61). At E(3He) = 6.05 MeV the p0 group is strongly peaked forward ((1958SW63), and D.R Sweetman, private communication).
The thermal capture cross section is 3.3 ± 0.2 mb (1958HU18). In addition to the 4.95 MeV ground state transition (Eγ = 4948 ± 8 keV), a γ-ray is reported with an energy of 3.68 ± 0.05 MeV and an intensity of 0.3 γ/capture. If 3.1 and 3.9 MeV γ-rays occur, their intensities are less than 0.10 and 0.06 γ/capture, respectively (1953BA18).
The cross section is approximately constant to 160 keV, then decreases monotonically to En = 2 MeV. There follows a region of resonances to 8.5 MeV, followed by a smooth variation of the cross section to En = 100 MeV (1958HU18). (1958CO07) finds a minimum of 1.3 b at En = 14 MeV, followed by a rise to 1.5 b at En = 15.5 MeV: see also 12C(n, p)12B. The average total cross section in the range En = 14 to 10000 eV is 4.69 ± 0.10 b (1956BR99).
The parameters of observed resonances are displayed in Table 13.5 (in PDF or PS). A careful search for resonances in the region En = 20 to 1360 keV with 10 and 22 keV resolution revealed no deviation > 5% from a smooth monotonic decrease in σt (1950MI1A) (see, however, 11B(3He, p)13C). The course of the cross section in this region can be accounted for by the broad s1/2 state at 13C*(3.09) (1952TH1D). A similar search, with 5 keV resolution, in the range En = 2.73 to 2.80 MeV revealed no deviations > 0.2 b from a smooth function (1958WI01: see 12C(d, p)13C).
Below En = 4.0 MeV, three d-wave resonances occur, at 2.08, 2.95, and 3.67 MeV. The total cross section and angular distributions establish the first as D5/2 (1958WI36); phase shift analyses of angular distributions yield D3/2 for the other two. The s-wave phase shift is everywhere negative and decreases slowly with energy: the behavior for En = 0 to 4 MeV can be accurately reproduced by a static potential well with a diffuse boundary (1958WI36). See also (1954HU1A). The p1/2 and p3/2 phase shifts are negative and small, not inconsistent with hard-sphere scattering (1954ME95, 1955BU56, 1958WI36). Polarization of scattered neutrons is discussed in these three papers and in (1956MC70, 1957MC1B). Other angular distribution studies in this range are reported by (1957LA14: En = 0.06 to 1.8 MeV), (1955WI25: En = 0.55 to 1.5 MeV), (1956MU96: En = 1.66 MeV), (1955LI50: En = 2.7 MeV), (1955WA27: En = 4.1 MeV).
For En = 4 to 8 MeV, several additional resonances are reported by (1950FR61, 1956BE98, 1956HA1E, 1957BO13): see Table 13.5 (in PDF or PS) and (1958HU18). The structure above En = 7 MeV is undoubtedly quite complex: see 9Be(α, n)12C and 12C(n, n')12C*. Further angular distribution measurements are reported by (1955JE27: 4.4 MeV), (1958HI68: 5 MeV), (1958BR1F: 5.6 MeV), (1956BE32: 7 MeV), (1956DO1D, 1958NA09: 14 MeV), (1958CO77: 14.5 MeV) and (1957KH1B: 14.8 MeV): see also (1956HU1A). Optical model effects become apparent at the higher energies; see (1956CU1A; theor.).
In the region beyond the resolved resonances, recent measurements of the total cross section have been made by (1958BR16: En = 7 to 14 MeV), (1958CO07: En = 13.1 to 15.6 MeV), (1958VE15, 1958VE21: En = 13.6 to 14.75 MeV) and (1957KH1A: En = 14.8 MeV). For a review of the earlier work, see (1955AJ61) and (1957HU1D). Non-elastic cross section measurements are reported by (1956BE32: En = 7 MeV), (1958BA03: En = 7 to 14 MeV), (1955TA29: En = 12.7 and 14.1 MeV), (1955GR21, 1956FL1B, 1957ST1F: En = 14 MeV) and (1958MA54: En = 21, 26 and 29 MeV): see also (1947HU03, 1955MA1G, 1957ZA1A). See also (1956LA1C) and (1956KA1B; theor.).
In the range En = 4.4 to 8 MeV, four resonances are observed in the yield of 4.4 MeV γ-rays, at En = 6.30, 6.49, 7.6, 7.87 and 8.15 MeV, corresponding to 13C*(10.76, 10.94, 12.0, 12.21, 12.47). The differential cross section at 90° reaches a maximum of 60 mb/sr at 7.87 MeV (1956HA1E, 1958HU18). At En = 6.58 MeV, the cross section for production of 4.4 MeV γ-rays is 353 ± 59 mb (1956DA23); at 14 MeV, it is 245 ± 35 mb (1955BA95). (1955GR21) estimate 160 mb for the inelastic cross section at En = 14 MeV to 12C levels at 9.6 to ≈ 13 MeV and 100 to 300 mb as the cross section to the 12C states at 4.4 and 7.6 MeV. See 12C(n, n)12C above, for further references on non-elastic cross sections.
Reaction (b) has been studied for En = 12.3 to 20.1 MeV. The cross section is 190 ± 50 mb at 12.9 MeV. It goes through a broad maximum of ≈ 300 ± 60 mb at ≈ 16.5 MeV and then decreases to 240 ± 50 mb at En = 20.1 MeV (1955FR35). See also (1955BE1D, 1955BF01, 1958VA1D), (1956SA1E; theor.) and (1955AJ61).
Measurements on the proton groups are summarized in Table 13.6 (in PDF or PS). The level assignments were obtained by analysis of angular distributions (with deuterons of energies up to 24 MeV) in terms of direct interaction theories. A careful search with Ed = 5 to 8.5 MeV (θ = 90°) reveals no further proton groups corresponding to levels in the range 0 to 4.9 MeV with intensity greater than 0.5% of the ground state group (1954SP01). At Ed = 14.8 MeV, all groups show pronounced stripping distributions except that corresponding to 13C*(9.50), for which the distribution is roughly isotropic. The proton spectrum exhibits a conspicuous broad structure attributed to a 13C level at Ex = 8.4 MeV, Γ = 1.1 ± 0.3 MeV. (It seems probable that this level is to be identified with the D3/2 level of similar width observed in 12C(n, n)12C at Ex = 8.33 MeV: see Table 13.5 (in PDF or PS).) Only one other level has a measurable width: Ex = 7.64 MeV, Γlab = 70 ± 15 keV (compare Table 13.5 (in PDF or PS)) (1955MC75). It is of interest that the 7.47 and 7.53 MeV levels do not appear in 12C(n, n)12C (1958WI01).
Angular distributions at low energies have been studied by (1954TA1A: Ed = 0.52 to 0.84 MeV), by (1956JU1E, 1956JU1F, 1957JU1A: Ed = 0.60 to 1.45 MeV), by (1955AL1D, 1955AL1E: Ed = 1.4 to 2.0 MeV), by (1956BE1H, 1956MC88: Ed = 1.86 to 2.86 MeV for the p0 group - on and off resonances - and Ed = 2.74 and 2.89 MeV for the p1 group), by (1954HO48, 1956BO08: Ed = 3.2 to 4.4 MeV) and by (1956KO26, 1956VA17: Ed = 0.26 to 0.59 MeV). In the range Ed = 1 to 6 MeV, the (12C + d) reactions are characterized by numerous strong, overlapping resonances (see 14N); the angular distributions show evidence of both stripping and compound nucleus formation, even below 1 MeV (1956JU1E, 1956KO26, 1956VA17, 1957JU1A). From Ed = 2 to 6 MeV, angular distributions of the p0 group (to 13Cg.s.) generally show a stripping maximum near 25°, as expected for an l = 1 transfer; several of the "resonances" appear most conspicuously at the angle. The p1-group, 13C*(3.09), show even stronger stripping effects, with a pronounced forward maximum (1956BO08, 1956MC88, 1958MC63). A detailed comparison of distributions for 12C(d, p)13C and 12C(d, n)13N at Ed = 2.68 and 3.26 MeV indicates equality of the ground-state reduced widths (1956BE1H, 1958MC63). At Ed = 9 MeV, a similar comparison yields γ2(13C)/γ2(13N) = 0.86 (1956CA1D). See also (1955WI43).
Observed gamma rays are listed in Table 13.7 (in PDF or PS). No γ-rays are observed with Eγ = 3.9 to 5.8 MeV with intensity > 10% of the 3.85 MeV γ-ray (1955BE62). An upper limit of 3% is placed on the fraction of cascade transitions from the 3.67 and 3.84 MeV levels via the 3.1 MeV level. The internal conversion coefficient of the 170 keV radiation indicates E1, though M1 is not excluded (1956MA1Q, 1956MA52). The internal pair formation coefficient for the 3.09 MeV level indicates an E1 transition (1952TH24); the angular correlation of internal pairs also indicates E1 (1954GO1E, 1956GO1K, 1958AR1B). Polarization of protons accompanying the formation of 13Cg.s. and 13C*(3.1) has been studied by (1956HI1B, 1958BO67, 1958HE47, 1958HI74, 1958JU39, 1958JU42). The sense of polarization is correlated with the coupling of ln and sn: P = ± when j = l -/+ 1/2 (1958HE47). See (1954CH1C, 1957SA1C; theor.). See also (1952CA1B, 1954CA1B, 1955KH31, 1956CA1H, 1957SE1C), (1957DA1C; theor.) and 14N.
The cross section for neutron production has been determined to 38 MeV. The (γ, n) cross section exhibits two peaks at 13.3 ± 1 MeV (Γ = 5 ± 1 MeV, σ = 3.3 mb) and at ≈ 22 MeV (σ ≈ 6 mb, Γ ≈ 7 MeV). The total absorption cross section, σ(γ, n) + σ(γ, p) shows maxima at Eγ = 13.5 and 25 MeV. The lower resonance is much too large to be explained on a single-particle model (1957CO57). Se also (1949SE1B, 1953GO13, 1956CO72).
Angular distributions of the 3.09 MeV γ-rays are isotropic for Ep = 3.7 to 4.2 MeV, consistent with the assignment J = 1/2 to 13C*(3.09). Angular distributions of the 3.68 MeV radiation have also been studied near the Ep = 4.5 MeV resonance (1957BA29). See also (1952CO1C).
This reaction has been observed at Et = 1.9 MeV (1958JA06).
Observed alpha particle groups are displayed in Table 13.8 (in PDF or PS) (1951MA08, 1957WA01). The broad level at 8.4 MeV observed in 12C(d, p)13C does not appear in the present reaction; it is suggested that the direct (d, α) transition is forbidden by the nature of the configurations involved (1957WA01). The angular distribution of the ground-state alpha particles at Ed = 21 MeV shows a maximum at 70° (c.m.) (1958FI27).