Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.     

Fusion cross sections for 10,11B+12C at sub-Coulomb energies

Total fusion cross sections for the ¹⁰B + ¹²C and ¹¹B + ¹²C reactions have been determined over a 5 MeV (c.m.) energy range extending to ≈ 3 MeV below the Coulomb barrier. Absolute γ-ray yields for specific transitions in the de-excitation of the heavy products following compound nucleus decay were measured using a Ge(Li) detector. Statistical model calculations of the decay modes of the compound nucleus have been used to deduce, from the γ-ray data, cross sections for single proton, neutron and α-particle emission, and to determine total cross sections for compound nucleus formation. No evidence has been found for sub-Coulomb resonances in either reaction. The total reaction cross sections are compared with optical model calculations using different parameter sets and the observed trend in the very low energy cross sections is discussed relative to other reactions in the same mass region.     

14N fusion with 13C and 16O at sub-barrier energies

Total fusion cross sections for the ¹⁴N+¹²C and ¹⁴N+¹⁶O reactions have been measured in the c.m. energy ranges 3.6–9.2 MeV and 5.6–12.6 MeV, respectively. Cross sections are also reported for important individual exit channels which were studied by observing discrete γ-ray transitions in the evaporation residues with a Ge(Li) detector. Excitation functions reveal no evidence of intermediate structure in these reactions. The fusion cross sections for ¹⁴N induced reactions on ¹²C, ¹⁴N and ¹⁶O are compared with an IWB calculation using recently published semi-empirical parameters for the real ion-ion interaction potential. Such a comparison supports the view that low-energy fusion studies may be sensitive probes of the nuclear potential in the interior of the interaction barrier.     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.     

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.     

IWB analysis of scattering and fusion cross sections for the 12C+12C, 13C+16O and 16O+16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the ¹²C+¹²C and ¹²C+¹⁶O fusion cross sections. In the case of ¹⁶O+¹⁶O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is discussed.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

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 several (n, 2n) reactions at 14 Mev

Precision measurements of the cross sections of the (n, 2n) reactions to produce ^44mSc, ⁸⁸Y, ⁸⁹Zr, ⁹²Nb, ¹⁵⁰Eu(35y), ¹⁶⁸Tm, ^174m+gLu and ¹⁹⁶Au were made for a range of neutron energies from 13.7 to 15.0 MeV. The samples were irradiated at various positions on the surface of a 20 cm radius sphere centered at the ²H–³H neutron source. This allowed a range of neutron energies to be obtained with good energy resolution. The ²⁷Al(n, )²⁴Na reaction was used to monitor the neutron fluence in the target samples. Particular attention was given to the accurate measurement of the (n, 2n) products, using calibrated Ge(Li) and NaI(Tl) detectors. An uncertainty of about ±5% is assigned to the results, except those for ¹⁵⁰Eu and ¹⁷⁴Lu, which have an additional uncertainty in their decay schemes.     

Mechanisms in d + 6Li three-body reactions at low bombarding energies

The three-body reactions induced by low energy deuterons on ⁶Li have been studied. The contributions from the sequential processes through the excited states of the intermediate ⁴He, ⁵Li, ⁶Li and ⁷Li nuclei dominate the coincidence spectra. The quasi-free d + d → d + d, d + α → d + α, and d + d → p + t reactions have been observed and compared with plane wave impulse approximation (PWIA) calculations.     

Total fusion cross sections for 18, 17, 16O + 27Al at energies near the Coulomb barrier

Total fusion cross sections have been measured for ^{18, 17, 16}O + ²⁷Al systems at bombarding energies 27–42 MeV. The evaporation residues were detected in the angular range 4°–25° (lab) using a $\text{2E?E}$ counter telescope. Barrier radii extracted from total fusion and elastic scattering cross sections are found to increase with the projectile mass. The effect of the yrast levels on the isotopic yields in the evaporation cascade is investigated.     

Comparison of cross sections for C + O reactions in the second regime of complete fusion

Kinetic energy spectra, angular distributions, and elemental yield distributions have been measured for the ¹² C + ¹⁶ O, ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reaction products over an energy range from 2 to 7 times the Coulomb barrier energy. A careful kinematic analysis of the evaporation residues and comparisons with statistical-model calculations show that fusion proceeds with full momentum transfer followed by a statistical decay of the compound nucleus. The competition between complete fusion process and peripheral reactions in the ¹² C + ¹⁶ O system is less important than for the ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reactions. The unexpectedly high ¹² C + ¹⁶ O complete fusion cross sections are related to the possible occurrence of a superdeformation of the ²⁸ Si compound nucleus.     

9Be + 12C, 9Be + 16O,9Be + 19F reactions at energies below the barrier

The ¹⁶O + ⁹Be reactions have been studied from E_c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction ⁹Be(¹⁶O,¹⁷O¹ (0.87 MeV))⁸Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E_c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E_c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the ¹²C + ¹³C reaction, which proceeds via the formation of the same compound nucleus, ²⁵Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions ⁹Be(¹²C, ¹³C¹)⁸Be and ⁹Be(¹⁹F, ²⁰F)⁸Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.     

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.     

Fusion and neutron-transfer cross sections for 13C + 10B and 13C + 11B reactions at subbarrier energies

The cross sections for the ¹⁰B(¹³C, ¹²C)¹¹B neutron-transfer reaction, leading to the ¹¹B 4.45 and 6.74 MeV and ¹²C 4.44 MeV excited states, and for ¹³C + ¹⁰B fusion have been measured by the characteristic and total γ-ray yield methods, respectively, over the energy (c.m.) interval 2.4–5.8 MeV. For ¹³C + ¹¹B, with no transfer reactions present, the fusion cross sections have been measured between E_c.m. = 2.3 and 6.4 MeV. The fusion cross sections for ¹³C + ¹⁰B and ¹³C + ¹¹B are found to be almost equal and slightly enhanced with respect to those for ¹²C + ¹⁰B and ¹²C + ¹¹B.     

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.     

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.     

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.     

Scattering and transfer reactions for 6, 7Li + 90, 91Zr

Elastic scattering data have been measured for the ⁷Li + ⁹⁰Zr, ⁶Li + ⁹⁰Zr, and ⁶Li + ⁹¹Zr systems at E(Li) = 34 MeV. Inelastic scattering data for the ⁷Li + ⁹⁰Zr and ⁶Li + ⁹⁰Zr systems were also measured for the 2⁺(2.18 MeV) and 3^?(2.75 MeV) states in ⁹⁰Zr and the $\text{1}\text{2}{}^{\mathrm{?}}\text{(0.48}\text{MeV}\text{)}$ state in ⁷Li. Optical model analyses of the elastic scattering data and DWBA analyses for the states in ⁹⁰Zr were performed. The deduced deformation lengths for the 2⁺ state agreed with those extracted in other studies but the deformation length for the 3^? state was smaller. The ⁹⁰Zr(⁷Li, ⁶Li)⁹¹Zr angular distributions were measured for the 1.21 and 2.03 MeV states and the 2.19 MeV doublet in ⁹¹Zr. Also, ⁹⁰Zr(⁷Li, ⁶He)⁹¹Nb angular distributions were measured for the ground states, 0.10, 3.41 and 4.82 MeV states in ⁹¹Nb. The transitions well matched in angular momentum were described by finite-range DWBA calculations, while other transitions displayed the same phase problems seen with heavier ions. The extracted spectroscopic information was consistent with the results of other reaction studies. At the present energy, it was not possible to determine whether the l = 1 phase problem that occurs for heavy-ion single-nucleon transfer reactions on 2s-1d shell nuclei occurs in ⁹¹Zr also.