Coupled-channel effective field theory and proton-$^7$Li scattering

TL;DR

This paper uses renormalisation group analysis to develop an effective field theory for coupled-channel scattering involving short-range forces and Coulomb interactions, applied specifically to proton-$^7$Li and related nuclear systems.

Contribution

It introduces a systematic RG-based approach to coupled-channel scattering with Coulomb effects, providing a new EFT framework for low-energy nuclear reactions.

Findings

Identified three fixed points for two S-wave channels with different bound/virtual states.

Derived power countings for the effective field theories in these systems.

Achieved good fits to experimental phase shifts and cross sections with minimal parameters.

Abstract

We apply the renormalisation group (RG) to analyse scattering by short-range forces in systems with coupled channels. For two S-wave channels, we find three fixed points, corresponding to systems with zero, one or two bound or virtual states at threshold. We use the RG to determine the power countings for the resulting effective field theories. In the case of a single low-energy state, the resulting theory takes the form of an effective-range expansion in the strongly interacting channel. We also extend the analysis to include the effects of the Coulomb interaction between charged particles. The approach is then applied to the coupled $p+{^7}$Li and $n+{^7}$Be channels which couple to a $J^P=2^-$ state of $^8$Be very close to the $n+{^7}$Be threshold. At next-to-leading order, we are able to get a good description of the $p+{^7}$Li phase shift and the ${^7}$Be(n,p)${^7}$Li cross section using four parameters. Fits at one order higher are similarly good but the available data are not sufficient to determine all five parameters uniquely.