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

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 + ^7Li and $ n + $ 7 Be channels which couple to a J P = 2 - state of 8 Be very close to the n + ^7Be threshold . Atnext - to - leadingorder , weareabletogetagooddescriptionofthe $ 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.