Study of the reaction 16O(7Li, 3He)20F

Angular distributions for the ¹⁶O(⁷Li,³He)²⁰F reaction, at a bombarding energy of 24 MeV, have been measured for all states below 6.25 MeV excitation, using a gas target and a multi-angle spectrograph. Low-lying core-excited states are populated much less strongly than known (sd)⁴ states. Cross sections decrease rapidly with excitation energy, but states at 4.20, 4.52, 4.58 and 5.41 MeV are quite strong — suggesting they have high spin and (sd)⁴ configurations. Previously suggested high-spin states at 4.73 and 4.76 MeV are weak, implying they are probably of core-excited character.     

Search for 8+ strength in 16O via the 12C(α, α2)12C1(7.66 MeV) reaction

Closely spaced angular distributions have been measured for the ${}^{12}\text{C}\text{(α, α}{}_2\text{)}{}^{12}\text{C}\text{1(7.66}\text{MeV}\text{)}$ reaction between E_α = 17.39 and 20.5 MeV in a search for 8⁺ strength in ¹⁶O. No evidence of 8⁺ strength is found, but evidence is found for a narrow 7^? resonance at 21.52 MeV excitation.     

The 12C(7Li, α)15N triton transfer reaction

The ¹²C(⁷Li, α) reaction was studied up to 16 MeV excitation energy in ¹⁵N. Excitation functions for eight α-groups were measured in the 28–38 MeV incident energy range. A high resolution angular distribution was taken at E_7Li = 35 MeV with the aid of a multi-gap magnetic spectrograph. The contribution of the compound nucleus channel to the α-intensities was estimated. A finite range DWBA calculation in which the three transferred nucleons enter the sd shell was attempted. Results of the above-mentioned studies and the strong selectivity of the reaction indicate a predominant direct reaction mechanism at the present relatively high bombarding energy. Comparison between the experimental results and calculations based on the weak coupling model of Lie and Engeland, exhibit reasonable correlation between the strongly excited states in the present study and the 3p-4h model states for which the contribution of the core excitation is small, and this gives a possible interpretation of the high selectivity of the reaction.     

Cross sections for the 11.08 (3+) and 11.096 MeV (4+) states in 16O by 12C(6Li,d) and 13C(6Li,t)

Particle and particle-γ measurements were performed to determine the cross sections for population of the 8.87 (2^?), 10.35 (4⁺), 11.08 (3⁺) and 11.096 MeV (4⁺) states in ¹⁶O by the ¹²C(⁶Li, d) and ¹³C(⁶Li, t) reactions in the energy range from 20—34 MeV. In general, statistical compound nuclear calculations correctly predict the magnitude of the cross sections of the unnatural parity states and underpredict those for the natural parity states. The population of the 10.35 MeV 4⁺ state in the ¹³C(⁶Li, t) reaction is correctly predicted by these calculations. These measurements support earlier claims that the large ¹²C(⁶Li, d) cross section to the 11.096 MeV 4⁺ state is a result of multistep processes.     

The 12C(α, γ)16O reaction and stellar helium burning

The cross section for the reaction ¹²C(α, γ)¹⁶O has been measured for a range of c.m. energies extending from 1.41 MeV to 2.94 MeV, by using ¹²C targets of high isotopic purity, large NaI(T1) crystals, and the time-of-flight technique for the suppression of prompt neutron background and time-independent background. Gamma-ray angular distributions were measured at c.m. energies of 2.18, 2.42, 2.56 and 2.83 MeV. By means of theoretical fits, which include the coherent effects of the 1^? states of ¹⁶O at 7.12 MeV, 9.60 MeV, and those at higher energies, the electric-dipole portion of the cross section at astrophysically relevant energies has been determined. A three-level R-matrix parametrization of the data yields an S-factor at E_c.m. = 0.3 MeV, S(0.3 MeV) = 0.14^+0.14_?0.12 MeV · b. A “hybrid” R-matrix optical-m parameterization yields S(0.3 MeV) = 0.08^+0.05_?0.04 MeV · b. This S-factor is of crucial importance in determining the abundances of ¹²C and ¹⁶O at the end of helium burning in stars.     

Gross structure in γ-ray yields following the 16O + 12C reaction

The γ-ray yield of discrete transitions from evaporation residues formed in the reaction ¹⁶O + ¹²C has been measured between E_{c.m. = 6 and 31 MeV}. Data for a backed and self-supporting target were compared to check the consistency of the observed results. Channels in which α-particles are emitted carry most of the oscillatory structure which was previously observed for the total fusion cross section. Relative yields of the different evaporation channels can be reproduced by statistical model calculations. Optical model calculations with a parity-dependent exchange contribution reproduce the periodicity of the gross structure but underestimate the magnitude of the oscillations.     

The 16O(6Li,dγ)20Ne reaction

The discrepancy between observed reaction streghts and those predicted from SU(3) considerations in the ¹⁶O(⁶Li, d) reaction has been studied. The effects of both ¹⁶O ground state correlations and of inelastic couplings on the reaction strengths are included. Particle-gamma angular correlations are presented as a test of the reaction predictions. It is found that inclusion of both the ground state correlations and the inelastic coupling does help to resolve the theoretical- experimental discrepancy, and results in generally improved representations of both cross section and angular correlation data.     

Isospin mixing observed in the reaction 12C(6Li, α)14N

The reaction ¹²C(¹²Li, α)¹⁴N was studied to investigate the isospin mixing of high-lying levels in ¹⁸F. Excitation functions and angular distributions of the α-transitions to the ground, first and second excited states in ¹⁴N were measured for bombarding energies from 3.2 to 8.0 MeV. The isospin-forbidden cross section for the excitation of the lowest T = 1 state in ¹⁴N at 2.31 MeV was found to lie between 1–2 % of that of the allowed transitions. A partial wave analysis of the α₁ angular distribution data revealed a strong resonance with J^π = 2⁺ at E_x = 15.99 MeV. Arguments are presented which tentatively identify this resonance as being due to two close-lying 2⁺ levels with different isospin.     

Cross sections for 6Li production in the reactions 10B + 16O and 12C + 14N at low energies

Absolute cross sections have been measured for the reactions ¹⁰B(¹⁶O, ⁶Li)²⁰Ne and ¹²C(¹⁴N, ⁶Li)²⁰Ne at several energies in the range E_c.m. = 7.5–16.2 MeV, and 13.8–16.6 MeV, respectively. The predictions of Hauser-Feshbach calculations show generally good agreement with the experimental data without parameter variation. The consequences of an angular momentum cutoff in the entrance channel and in the compound nucleus are discussed.     

Large-angle enhancements in the 16O(6Li, α)18F reaction at 48 MeV

The elastic scattering of ⁶Li + ¹⁶O at 48 MeV has been measured and fitted with an optical model calculation. Measurements have been made of the ¹⁶O(⁶Li, α)F reaction at 48 MeV populating the 1⁺ g.s., 3⁺ 0.927 MeV and 5⁺ 1.122 MeV states in ¹⁸F. The data exhibit cross sections at large angles comparable to those at forward angles, and have been compared with exact finite-range DWBA calculations. Exchange contributions were included for the 1⁺ g.s. and were unable to account for the large-angle data. Calculated statistical compound nucleus cross sections were approximately a factor of 100 below the data. The same conclusions are reached for previously published data at 34 MeV.     

The K-matrix parametrization of the 12C(α, γ)16O cross section

The experimental data on the El part of the ¹²C(α, γ)¹⁶O cross section and the l = 1 phase shift of ¹²C(α, α)¹²C are analyzed in terms of a two-channel, two-level approximation of a modified K-matrix. The latter allows a unitary parametrization, avoids computing Coulomb wave functions and does not require introducing channel radii; at low energies, it differs very little from the conventional K-matrix. Simple results are obtained which allow the extrapolation of the ¹²C(α, γ)¹⁶O cross section to lower energies of astrophysical interest (E_α(c.m.) ≈ 300 keV). Our results are compared with those of other parametrizations and suggestions are made to improve the uncertainties resulting from the best data presently available.     

Structure of 14C from 12C(t,p)

The reaction ¹²C(t, p)¹⁴C has been investigated with an 18 MeV triton beam. Twenty energy levels of ¹⁴C were identified up to 13 MeV excitation. Angular distributions were measured and compared with DWBA calculations. A previously unreported 0⁺ level at 9.75 MeV was observed; it undoubtedly corresponds to the second predominantly sd shell 0⁺ state in ¹⁴C. Additional spin and parity assignments have been made in the present work: 9.81 MeV, (1^?); 10.43 MeV, 2⁺; 10.50 MeV, (3^?); 10.74 MeV, 4⁺; 11.40 MeV, 1^?; 11.67 MeV, (1^?); 11.73 MeV, (5^?); 12.58 MeV, (2⁺, 3^?); 12.87 MeV. 2⁺, 3^?; and 12.96 MeV, (1^?); none of which had a definite spin and parity assignment previously. Our results confirm the previous information on the level structure of ¹⁴C below 8.5 MeV. The cross section for the unnatural parity state at 7.34 MeV, J^π = 2^?, is well reproduced by a two-step reaction calculation. The results are compared with the predictions of a weak coupling model.     

The j-dependence of the (19F, 16O) reaction

The total angular momentum transfer (j) dependence was studied for orbital angular momentum transfers l = 1, 2, and 3 in the (¹⁹F, ¹⁶O) reactions on ^{28, 30}Si and ⁶⁰Ni. In contrast to the strong j-dependence for the l = 2 transitions to ^{31, 33}P states, no distinct j-dependence was found for the l = 1 and l = 3 transitions to ⁶³Cu states. Previously reported results for the ${}^{28}\text{Si}\text{(}{}^{19}\text{F}\text{,}{}^{16}\text{O)}{}^{31}\text{P}$ reaction were re-analyzed using optical-potential sets which fit the elastic-scattering data for both the entrance and exit channels. Results of DWBA calculations without use of spin-orbit potentials were found to be out of phase with the data for all l-transfers and the j-dependence could not be reproduced. Both of these problems were alleviated by including spin-orbit forces in the optical potentials. However, a good fit to the ²⁸Si(¹⁹F, ¹⁶O)³¹P data was obtained only if the optical potentials that fit the elastic scattering data were modified for the exit channel.     

Direct and compound nuclear contributions to the 13C(6Li,t) reaction at Elab = 25 MeV

The reaction ¹³C(⁶Li, t)¹⁶O has been studied in the incident energy range 24–26 MeV. Complete angular distributions have been measured at E_⁶Li, = 25 MeV in the angular range θ_lab = 8°–172°, with the reaction ⁶Li(¹³C, t)⁶O being used for the backward angle measurements. Cross sections for evaporation residues from the fusion of the ⁶Li + ¹³C system have been measured in the incident ⁶Li energy range 9.2–35.1 MeV. Compound nuclear contributions to the transfer cross sections have been calculated using the Hauser-Feshbach statistical theory with the assumption that the compound-nucleus formation cross section is equal to the measured fusion cross section. By comparison of the compound nuclear calculations with backward angle data it is found that the sharp cutoff approximation commonly used to represent the initial angular momentum distribution of the compound nucleus is not adequate for the ¹³C(⁶Li, t)¹⁶O reaction. Good fits to the backward angle data can be obtained by using a smooth cutoff approximation. The forward angle cross sections have been compared with exact finite-range distorted-wave Born approximation calculations to extract transferred angular momenta and spectroscopic strengths. The present results differ from those of an earlier study. These differences are due to the inclusion of forward angle data in the present study.     

Experimental determination of the total reaction cross section of the stellar nuclear reaction 16O + 16O

The total reaction cross section for ¹⁶O + ¹⁶O has been measured at six energies between E_c.m. = 6.8 and 11.9 MeV. Cross sections for the production of protons, alphas, neutrons, deuterons, ³¹S, ³⁰P, ¹²C(g.s.) + ²⁰Ne(g.s.) and the relative γ-yield were obtained with a variety of experimental methods. No ³H or ³He were found. All cross sections are normalized to ¹⁶O + ¹⁶O elastic scattering at θ_c.m. = 90°, which was measured separately with high precision between E_c.m. = 7.3 and 14.4 MeV. The elastic scattering and relative γ-yield of ¹²C + ¹²C were measured between E_c.m. = 3.9 and 7.5 MeV. The elastic scattering and neutron yield of ¹²C + ¹⁶O were measured between E_c.m. = 5.4 and 10.1 MeV.     

The 18O(18O, 16O)20O reaction at 52 MeV

The structure of the ²⁰O nucleus was studied by the ¹⁸O(¹⁸O, ¹⁶O)²⁰O reaction at E_1ab = 52 MeV. Angular distributions for the transitions to the lowest four states in ²⁰O were obtained and analyzed with finite-range DWBA calculations. Optical potential sets were used which fit the experimental elastic scattering differential cross sections over almost the whole angular range. The two L = 0 transitions to the ground state and the 4.45 MeV state of ²⁰O populated by the ¹⁸O(¹⁸O, ¹⁶O) reaction were analyzed with exact finite-range DWBA calculations using microscopic form factors. These calculations underestimate the absolute cross sections by a factor of 11. The relative strength of the two L = 0 transitions is well reproduced in the ¹⁸O(¹⁸O, ¹⁶O) reaction. However, DWBA calculations for the ¹⁸O(t, p)²⁰O reaction overestimated the relative cross sections for the excited 0⁺ state by a factor of 6. Several model wave functions were tested for the ground-state transition. It was found that the absolute cross sections of the (¹⁸O, ¹⁶O) reaction are very sensitive to the mixing of shell-model configurations. The angular distribution shapes are also slightly dependent on the mixing.     

6Li elastic scattering ON 12C, 16O, 40Ca, 58Ni, 74Ge, 124Sn, 166Er and 208Pb at E(6Li) = 50.6 MeV

The elastic scattering of ⁶Li ions from a variety of targets, A = 12 to 208, has been measured at a bombarding energy of 50.6 MeV. The angular distributions are characteristic of strongly absorbed particles, such as ³He and heavy ions, and less diffractive than for ⁴He. A simple optical model with Woods-Saxon real and imaginary volume potentials is adequate to fit the data. Spin-orbit effects are not apparent in the data.     

High resolution study of the reactions 54, 56, 58Fe(16O, 12C)58, 60, 62Ni and a comparison with (6Li,d) α-transfer spectroscopy

Spectra and angular distributions for the reactions ^{54, 56, 58}Fe(¹⁶O, ¹²C)^{58, 60, 62}Ni (E_x = 0.0–4.5 MeV) have been measured at 50 MeV with an energy resolution of 45–80 keV using a Q3D spectrograph. The selectivity of the (¹⁶O, ¹²C) reaction is found to be very similar to the (⁶Li, d) reaction. The close correspondence recently noted between the (⁶Li, d) spectra and levels strongly excited in (t, p) and (³He, n) two-nucleon transfer reactions is also observed to be present for the (¹⁶O, ¹²C) reaction. Relative α spectroscopic factors for (¹⁶O, ¹²C) and (⁶Li, d) obtained in a DWBA analysis assuming direct one-step α-cluster transfer are in very good quantitative agreement. Unnatural parity states, whose excitation is forbidden in the DWBA α-cluster approximation, are observed to be very weakly populated. These results, together with previous work on s-d shell and Ni targets, strongly suggest that the spectroscopic information provided by the (¹⁶O, ¹²C) and (⁶Li, d) reactions is essentially the same and that this information may be reliably extracted by DWBA analysis.     

The 16O(d, 3He)15N reaction at 29 MeV: Reaction mechanism and nuclear structure

The reaction ¹⁶O(d, ³He)¹⁵N has been investigated using 29 MeV deuterons, and angular distributions were obtained for levels in ¹⁵N up to 10 MeV excitation energy. The measured distributions were subjected to distorted-wave (DWBA), compound nucleus (Hauser-Feshbach) and coupled-channel (CCBA) analyses. Only the strong transitions to the $\text{1}\text{2}$^? ground state and the $\text{3}\text{2}$^? state at 6324 keV exhibit distributions which are well described by DWBA. The spectroscopic factors are in agreement with shell-model estimates. The weak transitions generally show little structure and the spectroscopic factors extracted for these transitions tend to be unreasonably large. Contributions from compound nucleus formation were estimated and found to vary between about 10 % and 100 % of the observed cross sections with an average of the order of 30 %. The CCBA analysis for the transitions to the $\text{5}\text{21}{}^{\mathrm{+}}$, $\text{5}\text{22}$⁺ and $\text{7}\text{2}$⁺ states at 5271, 7155 and 7566 keV, respectively, was performed using the spectroscopic amplitudes from weak coupling shell-model wave functions. Inelastic excitations to one-phonon states in the target and residual nuclei were included. The agreement between calculated and experimental distributions is good for both shape and magnitude, a conclusion which is not disturbed by the addition of small compound nucleus contributions. It is evident that spectroscopic factors extracted for the weak transitions on the basis of a direct one-step reaction mechanism alone are unreliable.