Structure of 12B from measurement and R-matrix analysis of σ(θ) for 11B(n, n)11B and 11B(n, n')11B∗(2.12 MeV), and shell-model calculations

doi:10.1016/0375-9474(83)90170-7

Nuclear Physics A

Volume 394, Issues 1–2, 14–21 February 1983, Pages 221-244

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Abstract

Differential cross sections for neutrons elastically scattered from ¹¹B and inelastically scattered to the first excited state ¹¹B∗ (2.12 MeV) have been measured at 13 incident energies for 4.8 ≦ E_n ≦ 7.6 MeV corresponding to excitation energies in ¹²B of 7.8 to 10.3 MeV. The cross sections were measured at nine laboratory angles per energy from 20° to 160° and show considerable resonance structure. Differential inelastic cross sections were also measured for the 4.45 and 5.02 MeV levels of ¹¹B for 2 to 9 angles at several incident energies. These new elastic and inelastic 2.12 MeV level data have been analyzed together with previously published cross sections for 2 ≦ E_n ≦ 7.5 MeV using a multilevel-multichannel R-matrix program to determine J, π, E_λ and γ_λc for states in ¹²B. The shell model was used to calculate states in ¹²B as well as spectroscopic amplitudes for reactions leading to these states. The results of this model calculation are compared to those of the R-matrix analysis. Much of the structure observed in the experimental work is predicted by the model for E_x ≲ 7 MeV. For levels of higher excitation the agreement is not as good. The experimental data are also compared to continuum shell-model calculations.

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Resonance states in ¹²N were studied by using the resonance elastic scattering of $^{11} C + p$ with a low-energy radioactive ion beam of ¹¹C at 3.5 MeV/nucleon and a thick (CH₂)_n target. The ¹¹C beam was separated by a newly installed CNS radioactive ion beam separator (CRIB). The energy spectrum of recoil protons was measured at laboratory scattering angles around θ_LAB=0° to identify resonance states in ¹²N. The spin-parity values of J^π=3⁻ and (2)⁺ have been determined for the levels at the excitation energies of E_x=3.1 and 3.6 MeV in ¹²N, respectively, suggesting a small contribution of the 3.1-MeV level to the ¹¹C(p, $γ$ )¹²N stellar reaction.
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We generalize the two-cluster generator coordinate method by improving the internal wave functions of the colliding nuclei. These wave functions are described in the shell model (currently restricted to the p shell), with all configurations allowed by the Pauli principle. The model is applied to the ⁸Li(α,n)¹¹B reaction, including $^{11} B^{∗} +n$ exit channels. The total S-factor, as well as the ¹¹B ground-state contribution are in fair agreement with available data. We find that the ¹¹B_g.s.+n channel represents about 25% of the total cross section. We test the microscopic wave functions on the ¹²B energy spectrum, and on ¹¹B(n,n)¹¹B and ¹¹B(n,n′)¹¹B^∗ scattering cross sections; α+⁸Li elastic phase shifts are also presented.
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The generator coordinate method is used to study the ¹²B and ¹²N nuclei, with the n + ¹¹B and $α +^{8} Li$ configurations and their mirrors. The spectroscopic properties are in good agreement with the experiment. The ¹¹C(p, γ)¹²N, ⁸Li(α, n)¹¹B and ⁸B(α, p)¹¹C reactions are investigated at stellar energies. The ¹¹C(p, γ)¹²N cross section is dominated by the 2⁻ resonance (E_c.m. = 0.59 MeV) for which we find Γ_γ = 0.14eV and Γ_p = 130keV. The ⁸Li(α, n)¹¹B and ⁸B(α, p)¹¹C theoretical cross sections are affected by resonances presenting a marked α-structure. We analyze the influence of the present reaction rates in the evolution of zero-metal stars, where a hot pp chain may compete with the triple-α process for ¹²C production.
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Level energies and reduced width amplitudes obtained from shell model calculations for ⁷Li and ⁸Li are incorporated into multilevel, multichannel R-matrix calculations of cross sections for reactions leading to these compound systems. With changes to a very few of the large number of parameters obtained from the model calculations, cross sections for eight reactions leading to the ⁷Li system and for five reactions leading to the ⁸Li system are calculated. For reactions where data are available, the calculated cross sections are in good agreement with experimental measurements. Comparisons of the present work to other structure studies are made and suggestions as to possible improvements in the model calculations are given. The applicability of the technique used here to other nuclear structure studies is discussed.

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^☆: Work supported by US Department of Energy.

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Nuclear Physics A

Abstract

References (21)

Nucl. Phys.

Ohio University Report COO-2490-6

Nucl. Phys.

Study of structure of nuclei with neutrons and nuclear data measurements for MFE

Continuum shell model calculation for neutron scattering from ¹¹B (Diplomarbeit)

Phys. Rev.

Nucl. Phys.

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Cited by (17)

Energy levels of light nuclei A = 12

Study of resonance states in <sup>12</sup>N using a radioactive ion beam of <sup>11</sup>C

Application of an extended cluster model to the <sup>8</sup>Li(α,n)<sup>11</sup>B reaction

Microscopic cluster study of the <sup>12</sup>B and <sup>12</sup>N systems and application to a hot pp chain in zero-metal stars

Energy levels of light nuclei A = 11-12

Reactions leading to the <sup>7</sup>Li and <sup>8</sup>Li systems: Shell model and R-matrix calculations

Structure of 12B from measurement and R-matrix analysis of σ(θ) for 11B(n, n)11B and 11B(n, n')11B∗(2.12 MeV), and shell-model calculations☆

Abstract

Nucl. Phys.

Ohio University Report COO-2490-6

Nucl. Phys.

Phys. Rev.

Nucl. Phys.

Phys. Rev.

Phys. Rev.

Nucl. Phys.

Structure of ¹²B from measurement and R-matrix analysis of σ(θ) for ¹¹B(n, n)¹¹B and ¹¹B(n, n')¹¹B^∗(2.12 MeV), and shell-model calculations☆