Coupled-channel treatment of $^7\mathrm{Li}(n,\gamma)^8\mathrm{Li}$ in effective field theory

TL;DR

This paper develops a coupled-channel effective field theory approach to calculate the low-energy $^7$Li(n,γ)$^8$Li capture reaction, highlighting the role of the excited core and providing a next-to-leading order analysis.

Contribution

It introduces a coupled-channel halo EFT framework for the reaction, including the excited core, and compares its results with previous models, revealing key differences.

Findings

Excited core affects overall cross section normalization.

Momentum dependence is similar with or without excited core at this order.

Kinematical effects of the excited core are negligible below 1 MeV.

Abstract

The E1 contribution to the capture reaction $^7\mathrm{Li}(n,\gamma)^8\mathrm{Li}$ is calculated at low energies. We employ a coupled-channel formalism to account for the $^7\mathrm{Li}^\star$ excited core contribution. We develop a halo effective field theory power counting where capture in the spin $S=2$ channel is enhanced over the $S=1$ channel. A next-to-leading order calculation is presented where the excited core contribution is shown to affect only the overall normalization of the cross section. The momentum dependence of the capture cross section, as a consequence, is the same in a theory with or without the excited $^7\mathrm{Li}^\star$ degree of freedom at this order of the calculation. The kinematical signature of the $^7\mathrm{Li}^\star$ core is negligible at momenta below 1 MeV and significant only beyond the $3^+$ resonance energy, though still compatible with a next-to-next-to-leading order correction. We compare our formalism with a previous halo effective field theory calculation [Zhang, Nollett, and Phillips, Phys. Rev. C 89, 024613 (2014)] that also treated the $^7\mathrm{Li}^\star$ core as an explicit degree of freedom. Our formal expressions and analysis disagree with this earlier work in several aspects.