A=13C (1959AJ76)

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¹³C (1959AJ76)

(See the Energy Level Diagram for ¹³C)

GENERAL: See also Table 13.2 [Table of Energy Levels] (in PDF or PS).

Theory: See (1955AU1A, 1955LA1A, 1956DA1G, 1956DE1C, 1956KU1A, 1957BA1H, 1958FR1C, 1958SK1A).

1. (a) ⁶Li(⁷Li, p)¹²B Q_m = 8.338 E_b = 25.876
(b) ⁶Li(⁷Li, n)¹²C Q_m = 20.931
(c) ⁶Li(⁷Li, 2n)¹¹C Q_m = 2.209

See (1957NO17).

2. ⁷Li(⁷Li, n)¹³C Q_m = 18.624

See (1957NO17).

3. ⁹Be(α, γ)¹³C Q_m = 10.654

At E_α = 1.60 MeV, the capture cross section is less than 30 μb (1955AL16).

4. ⁹Be(α, n)¹²C Q_m = 5.709 E_b = 10.654

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 E_α = 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 E_α = 1.7 to 4.8 MeV (n₀) and 3.1 to 4.8 MeV (n₁). The n₀ yield curves show broad maxima at E_α = 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 E_α = 3.9 to 4.6 MeV, probably J = 3/2⁺ and 5/2⁺ (1957RI38).

Extensive angular distribution studies have been made for E_α < 2 MeV by (1955TA28, 1956JA28). According to (1956JA28), the best fit to the distributions in the range E_α = 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 E_α = 1.2 and 2.8 MeV, indicating that stripping plays only a minor role at these energies (1958TA05). See also (1955MA1J; theor.) and (1956BE98).

5. ⁹Be(α, p)¹²B Q_m = -6.884 E_b = 10.654

See ¹²B.

6. ⁹Be(α, d)¹¹B Q_m = -8.022 E_b = 10.654

See ¹¹B.

7. (a) ⁹Be(α, α')⁹Be* E_b = 10.654
(b) ⁹Be(α, α'n)⁸Be Q_m = -1.667
(c) ⁹Be(α, n)⁴He⁴He⁴He Q_m = -1.572

For reaction (a) see ⁹Be and (1955TA28). For reactions (b) and (c), see (1952AJ38).

8. ¹⁰B(t, α)⁹Be Q_m = 13.210 E_b = 23.882

See ⁹Be.

9. ¹⁰B(α, p)¹³C Q_m = 4.070
Q₀ = 4.064 ± 0.012 (W.J Fader, quoted in (1957VA11)).
Q₀ = 4.08 ± 0.03 (1956PI1A).
Q₀ = 4.10 ± 0.03 (1956PA1B).

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 E_γ = 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 J^π of the 3.68 MeV state is then 3/2^- (J^π = 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 E_α = 4.9, 6.0, 7.0 and 8.1 MeV (1957VO25) and at E_α = 30.5 MeV (1957HU1E): in both cases direct interaction appears to be involved. See also (1957BA1K) and (1955BR1A).

10. ¹¹B(d, n)¹²C Q_m = 13.731 E_b = 18.677

The yield of neutrons has been measured for E_d = 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 E_d = 0.5 to 1.1 MeV and is essentially flat from E_d = 1.1 to 2.0 MeV (1959NE1A). At E_d = 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 E_d = 0.5 to 2.0 MeV. The cross section for emission of neutrons in the forward direction is ≈ 270 mb/sr at E_d = 5.4 MeV (1955MA76). For E_d = 1.6 to 3.2 MeV, the yield of 15.1 MeV γ-rays shows resonances at E_d = 2.180 ± 0.010 and 3.080 ± 0.015 MeV, corresponding to ¹³C*(20.52, 21.28) with Γ_c.m. = 115 ± 10 and 160 ± 15 keV, respectively; the cross section at E_d = 2.2 MeV is 29 ± 7 mb (1958KA31). See also (1954BU06, 1955RI1B) and ¹²C.

11. ¹¹B(d, p)¹²B Q_m = 1.138 E_b = 18.677

The thin-target yield rises smoothly from E_d = 0.3 to 3.1 MeV with no evidence of resonances (1949HU41, 1958KA31). At E_d = 1.5 MeV, σ ≈ 0.38 b (1958KA31: see, however, (1949HU41)). See also ¹²B and (1957JA37).

12. ¹¹B(d, d)¹¹B E_b = 18.677

See ¹¹B.

13. ¹¹B(d, α)⁹Be Q_m = 8.022 E_b = 18.677

Some absolute cross sections are given by (1958KA31). See also ⁹Be.

14. ¹¹B(t, n)¹³C Q_m = 12.419

Not reported.

15. ¹¹B(³He, p)¹³C Q_m = 13.184

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 θ²_p < 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).

16. ¹¹B(α, d)¹³C Q_m = -5.167

Not reported.

17. ¹²C(n, γ)¹³C Q_m = 4.946

The thermal capture cross section is 3.3 ± 0.2 mb (1958HU18). In addition to the 4.95 MeV ground state transition (E_γ = 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).

18. ¹²C(n, n)¹²C E_b = 4.946

The cross section is approximately constant to 160 keV, then decreases monotonically to E_n = 2 MeV. There follows a region of resonances to 8.5 MeV, followed by a smooth variation of the cross section to E_n = 100 MeV (1958HU18). (1958CO07) finds a minimum of 1.3 b at E_n = 14 MeV, followed by a rise to 1.5 b at E_n = 15.5 MeV: see also ¹²C(n, p)¹²B. The average total cross section in the range E_n = 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 E_n = 20 to 1360 keV with 10 and 22 keV resolution revealed no deviation > 5% from a smooth monotonic decrease in σ_t (1950MI1A) (see, however, ¹¹B(³He, p)¹³C). The course of the cross section in this region can be accounted for by the broad s_1/2 state at ¹³C*(3.09) (1952TH1D). A similar search, with 5 keV resolution, in the range E_n = 2.73 to 2.80 MeV revealed no deviations > 0.2 b from a smooth function (1958WI01: see ¹²C(d, p)¹³C).

Below E_n = 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 D_5/2 (1958WI36); phase shift analyses of angular distributions yield D_3/2 for the other two. The s-wave phase shift is everywhere negative and decreases slowly with energy: the behavior for E_n = 0 to 4 MeV can be accurately reproduced by a static potential well with a diffuse boundary (1958WI36). See also (1954HU1A). The p_1/2 and p_3/2 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: E_n = 0.06 to 1.8 MeV), (1955WI25: E_n = 0.55 to 1.5 MeV), (1956MU96: E_n = 1.66 MeV), (1955LI50: E_n = 2.7 MeV), (1955WA27: E_n = 4.1 MeV).

For E_n = 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 E_n = 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: E_n = 7 to 14 MeV), (1958CO07: E_n = 13.1 to 15.6 MeV), (1958VE15, 1958VE21: E_n = 13.6 to 14.75 MeV) and (1957KH1A: E_n = 14.8 MeV). For a review of the earlier work, see (1955AJ61) and (1957HU1D). Non-elastic cross section measurements are reported by (1956BE32: E_n = 7 MeV), (1958BA03: E_n = 7 to 14 MeV), (1955TA29: E_n = 12.7 and 14.1 MeV), (1955GR21, 1956FL1B, 1957ST1F: E_n = 14 MeV) and (1958MA54: E_n = 21, 26 and 29 MeV): see also (1947HU03, 1955MA1G, 1957ZA1A). See also (1956LA1C) and (1956KA1B; theor.).

19. (a) ¹²C(n, n')¹²C* E_b = 4.946
(b) ¹²C(n, n')⁴He⁴He⁴He Q_m = -7.281

In the range E_n = 4.4 to 8 MeV, four resonances are observed in the yield of 4.4 MeV γ-rays, at E_n = 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 E_n = 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 E_n = 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 E_n = 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 E_n = 20.1 MeV (1955FR35). See also (1955BE1D, 1955BF01, 1958VA1D), (1956SA1E; theor.) and (1955AJ61).

20. ¹²C(n, 2n)¹¹C Q_m = -18.722 E_b = 4.946

See (1952BR61, 1958AS63).

21. ¹²C(n, p)¹²B Q_m = -12.593 E_b = 4.946

The cross section has been measured from threshold to E_n = 17.5 MeV. At E_n = 17.5 MeV, the cross section is 29.1 ± 4 mb (1958KR65, 1959KR1B). See also (1956KR1A, 1956KR1B).

22. ¹²C(n, α)⁹Be Q_m = -5.709 E_b = 4.946

See (1955GR21) and ⁹Be.

23. ¹²C(d, p)¹³C Q_m = 2.719
Q₀ = 2.721 ± 0.002 (1957VA11).

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 E_d = 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 E_d = 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 E_x = 8.4 MeV, Γ = 1.1 ± 0.3 MeV. (It seems probable that this level is to be identified with the D_3/2 level of similar width observed in ¹²C(n, n)¹²C at E_x = 8.33 MeV: see Table 13.5 (in PDF or PS).) Only one other level has a measurable width: E_x = 7.64 MeV, Γ_lab = 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: E_d = 0.52 to 0.84 MeV), by (1956JU1E, 1956JU1F, 1957JU1A: E_d = 0.60 to 1.45 MeV), by (1955AL1D, 1955AL1E: E_d = 1.4 to 2.0 MeV), by (1956BE1H, 1956MC88: E_d = 1.86 to 2.86 MeV for the p₀ group - on and off resonances - and E_d = 2.74 and 2.89 MeV for the p₁ group), by (1954HO48, 1956BO08: E_d = 3.2 to 4.4 MeV) and by (1956KO26, 1956VA17: E_d = 0.26 to 0.59 MeV). In the range E_d = 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 E_d = 2 to 6 MeV, angular distributions of the p₀ group (to ¹³C_g.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 E_d = 2.68 and 3.26 MeV indicates equality of the ground-state reduced widths (1956BE1H, 1958MC63). At E_d = 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 E_γ = 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 ¹³C_g.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 l_n and s_n: P = ± when j = l -/+ 1/2 (1958HE47). See (1954CH1C, 1957SA1C; theor.). See also (1952CA1B, 1954CA1B, 1955KH31, 1956CA1H, 1957SE1C), (1957DA1C; theor.) and ¹⁴N.

24. ¹²C(t, d)¹³C Q_m = -1.313

Not reported.

25. ¹²C(α, ³He)¹³C Q_m = -15.632

Not reported.

26. ¹³C(γ, n)¹²C Q_m = -4.946

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 E_γ = 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).

27. ¹³C(γ, p)¹²B Q_m = -17.539

The yield of β-particles from the ¹²B decay has been determined to 45 MeV. The cross section shows a broad maximum of 8.8 mb near 25.5 MeV (1956CO72, 1957CO57).

28. ¹³C(γ, α)⁹Be Q_m = -10.654

See (1953MI31).

29. ¹³C(p, p')¹³C*

Angular distributions of the 3.09 MeV γ-rays are isotropic for E_p = 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 E_p = 4.5 MeV resonance (1957BA29). See also (1952CO1C).

30. ¹³N(β⁺)¹³C Q_m = 2.222

See ¹³N.

31. ¹⁴C(p, d)¹³C Q_m = -5.947

Not reported.

32. ¹⁴C(d, t)¹³C Q_m = -1.915

At E_d = 14.8 MeV, triton groups have been observed leading to the ¹³C states at 0, 3.09, 3.68 and 3.85 MeV (1958MO97). See ¹⁴C.

33. ¹⁴C(³He, α)¹³C Q_m = 12.404

Not reported.

34. ¹⁴N(n, d)¹³C Q_m = -5.319

At 14 MeV, deuteron groups to the 0 and 3.68 MeV (but not to the 3.09 and 3.84 MeV) states of ¹³C have been observed (1957CA07). See also (1952LI24) and ¹⁴N.

35. ¹⁴N(p, 2p)¹³C Q_m = -7.546

At E_p = 185 MeV, the summed proton spectrum shows two peaks, corresponding to ejection of p_1/2 and p_3/2 protons, with binding energies of ≈ 7 and ≈ 15 MeV, ¹³C* = 0 and ≈ 8 MeV (1958MA1B, 1958TY49).

36. ¹⁴N(d, ³He)¹³C Q_m = -2.052

Not reported.

37. ¹⁴N(t, α)¹³C Q_m = 12.267

This reaction has been observed at E_t = 1.9 MeV (1958JA06).

38. ¹⁵N(n, t)¹³C Q_m = -9.903

Not reported.

39. ¹⁵N(p, ³He)¹³C Q_m = -10.668

Not reported.

40. ¹⁵N(d, α)¹³C Q_m = 7.683

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 E_d = 21 MeV shows a maximum at 70° (c.m.) (1958FI27).

41. ¹⁶O(n, α)¹³C Q_m = -2.203

See (1951HU1A, 1952LI24) and ¹⁷O.