Gamow shell model description of the radiative capture reaction Li8(n,γ)Li9

Abstract

Background: The $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ reaction plays a critical role in several reaction chains leading to the nucleosynthesis of $A>12$ nuclei. Due to unstable nature of $^{8}\mathrm{Li}$ and the unavailability of neutron targets, direct measurements of this reaction are exceedingly difficult. Only upper limits of this cross section, provided by the indirect experiments, have been obtained so far.Purpose: In this work, we use the Gamow shell model (GSM) in the coupled-channel representation (GSM-CC) to study the properties of $^{9}\mathrm{Li}$ and the radiative capture reaction $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$.Method: GSM-CC is a theoretical framework allowing for the description of both nuclear structure and reaction cross sections. In GSM-CC calculations, a translationally invariant Hamiltonian is used with a finite-range two-body interaction tuned to reproduce the low-energy spectra of ${}^{8,9}\mathrm{Li}$. The reaction channels are built by coupling wave functions of the ground state ${2}_{1}^{+}$, the first-excited state ${1}_{1}^{+}$, and the first resonance state ${3}_{1}^{+}$ in $^{8}\mathrm{Li}$ with the neutron wave function of the projectile in different partial waves. In the calculation of $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ cross section, all relevant $E1$, $M1$, and $E2$ transitions from the initial continuum states to the final bound states ${3/2}_{1}^{\ensuremath{-}}$, ${1/2}_{1}^{\ensuremath{-}}$ and the resonance ${5/2}_{1}^{\ensuremath{-}}$ of $^{9}\mathrm{Li}$ are included.Results: The GSM-CC approach reproduces the experimental low-energy spectrum, neutron emission threshold, and spectroscopic factors in $^{9}\mathrm{Li}$. The calculated reaction rate is consistent with the experimental upper limit of the reaction rate obtained in the indirect measurements at stellar energies.Conclusion: The GSM-CC calculations suggest that the $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ reaction does not reduce significantly heavy-element production via the main chain $^{7}\mathrm{Li}(n,\ensuremath{\gamma})^{8}\mathrm{Li}(\ensuremath{\alpha},n)^{11}\mathrm{B}(n,\ensuremath{\gamma})^{12}\mathrm{B}({\ensuremath{\beta}}^{+})^{12}\mathrm{C}$. Major contribution to the calculated cross section is given by the direct $E1$ transition to the ground state of $^{8}\mathrm{Li}$. The contribution of excited states to the reaction rate does not exceed $\ensuremath{\approx}20$% of the total reaction rate.