
^{13}C (1959AJ76)(See the Energy Level Diagram for ^{13}C) GENERAL: See also Table 13.2 [Table of Energy Levels] (in PDF or PS). Theory: See (1955AU1A, 1955LA1A, 1956DA1G, 1956DE1C, 1956KU1A, 1957BA1H, 1958FR1C, 1958SK1A).
See (1957NO17).
See (1957NO17).
At E_{α} = 1.60 MeV, the capture cross section is less than 30 μb (1955AL16).
Resonances for neutrons and for γrays from ^{12}C*(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 γrays 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 (n_{0}) and for neutrons to the 4.4 MeV state (n_{1}) are reported by (1957RI38) in the range E_{α} = 1.7 to 4.8 MeV (n_{0}) and 3.1 to 4.8 MeV (n_{1}). The n_{0} 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 n_{1}, but quite weak for n_{0}. Angular distributions of groundstate 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 gammarays 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).
See ^{12}B.
See ^{11}B.
For reaction (a) see ^{9}Be and (1955TA28). For reactions (b) and (c), see (1952AJ38).
See ^{9}Be.
Four proton groups are observed, corresponding to the ^{13}C 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 ^{14}N, (1953SH64)). See also (1955AJ61). A study of gamma rays from this reaction and from ^{12}C(d, p)^{13}C shows three lines with E_{γ} = 0.1695 ± 0.0004, 3.844 ± 0.015 and 3.69 ± 0.02 MeV. The 3.85 MeV γray 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 ^{13}C. (For earlier work see (1953SH64) and (1954ST20)). The angular distributions and p  γ correlations for the 3.8 MeV radiation contain terms in (cos^{4}θ), indicating J = 5/2^{+} for the 3.84 MeV state (1954ST20: see ^{12}C(d, p)^{13}C). 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 ^{12}C(d, p)^{13}C); 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).
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 excitedstate group, ^{12}C*(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 groundstate group. For the excitedstate group (^{12}C*(4.4)), the interpretation is less clear; the observed distribution can be accounted for by pwave formation of a J = 7/2^{+} level in ^{13}C (1955WA30). (1959NE1A) find evidence of strong "heavyparticle" 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 γrays shows resonances at E_{d} = 2.180 ± 0.010 and 3.080 ± 0.015 MeV, corresponding to ^{13}C*(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 ^{12}C.
The thintarget 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 ^{12}B and (1957JA37).
See ^{11}B.
Some absolute cross sections are given by (1958KA31). See also ^{9}Be.
Not reported.
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 ^{12}C(n, n)^{12}C, an upper limit of Γ = 10 keV is estimated; the mirror levels in ^{13}N must be assumed to have θ^{2}_{p} < 0.02 (1958MO99). Angular distributions have been measured for the p_{0}, p_{1} and (p_{2} + p_{3}) groups at E(^{3}He) = 4.5 MeV. The p_{0} 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(^{3}He) = 6.05 MeV the p_{0} group is strongly peaked forward ((1958SW63), and D.R Sweetman, private communication).
Not reported.
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 γray 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 γrays 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 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 ^{12}C(n, p)^{12}B. 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, ^{11}B(^{3}He, p)^{13}C). The course of the cross section in this region can be accounted for by the broad s_{1/2} state at ^{13}C*(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 ^{12}C(d, p)^{13}C). Below E_{n} = 4.0 MeV, three dwave 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 swave 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 hardsphere 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 ^{9}Be(α, n)^{12}C and ^{12}C(n, n')^{12}C*. 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). Nonelastic 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.).
In the range E_{n} = 4.4 to 8 MeV, four resonances are observed in the yield of 4.4 MeV γrays, at E_{n} = 6.30, 6.49, 7.6, 7.87 and 8.15 MeV, corresponding to ^{13}C*(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 γrays 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 ^{12}C levels at 9.6 to ≈ 13 MeV and 100 to 300 mb as the cross section to the ^{12}C states at 4.4 and 7.6 MeV. See ^{12}C(n, n)^{12}C above, for further references on nonelastic 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).
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).
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 ^{13}C*(9.50), for which the distribution is roughly isotropic. The proton spectrum exhibits a conspicuous broad structure attributed to a ^{13}C 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 ^{12}C(n, n)^{12}C 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 ^{12}C(n, n)^{12}C (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 p_{0} group  on and off resonances  and E_{d} = 2.74 and 2.89 MeV for the p_{1} 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 (^{12}C + d) reactions are characterized by numerous strong, overlapping resonances (see ^{14}N); 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 p_{0} group (to ^{13}C_{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 p_{1}group, ^{13}C*(3.09), show even stronger stripping effects, with a pronounced forward maximum (1956BO08, 1956MC88, 1958MC63). A detailed comparison of distributions for ^{12}C(d, p)^{13}C and ^{12}C(d, n)^{13}N at E_{d} = 2.68 and 3.26 MeV indicates equality of the groundstate reduced widths (1956BE1H, 1958MC63). At E_{d} = 9 MeV, a similar comparison yields γ^{2}(^{13}C)/γ^{2}(^{13}N) = 0.86 (1956CA1D). See also (1955WI43). Observed gamma rays are listed in Table 13.7 (in PDF or PS). No γrays are observed with E_{γ} = 3.9 to 5.8 MeV with intensity > 10% of the 3.85 MeV γray (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 ^{13}C_{g.s.} and ^{13}C*(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 ^{14}N.
Not reported.
Not reported.
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 singleparticle model (1957CO57). Se also (1949SE1B, 1953GO13, 1956CO72).
The yield of βparticles from the ^{12}B decay has been determined to 45 MeV. The cross section shows a broad maximum of 8.8 mb near 25.5 MeV (1956CO72, 1957CO57).
See (1953MI31).
Angular distributions of the 3.09 MeV γrays are isotropic for E_{p} = 3.7 to 4.2 MeV, consistent with the assignment J = 1/2 to ^{13}C*(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).
See ^{13}N.
Not reported.
At E_{d} = 14.8 MeV, triton groups have been observed leading to the ^{13}C states at 0, 3.09, 3.68 and 3.85 MeV (1958MO97). See ^{14}C.
Not reported.
At 14 MeV, deuteron groups to the 0 and 3.68 MeV (but not to the 3.09 and 3.84 MeV) states of ^{13}C have been observed (1957CA07). See also (1952LI24) and ^{14}N.
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, ^{13}C* = 0 and ≈ 8 MeV (1958MA1B, 1958TY49).
Not reported.
This reaction has been observed at E_{t} = 1.9 MeV (1958JA06).
Not reported.
Not reported.
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 ^{12}C(d, p)^{13}C 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 groundstate alpha particles at E_{d} = 21 MeV shows a maximum at 70° (c.m.) (1958FI27).
See (1951HU1A, 1952LI24) and ^{17}O.
