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

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.

22 pages, 2 figures, RevTeX4, typos corrected, accepted for publication in European Physical Journal A

References in corpus (6)

• A Bitter Pill: The Primordial Lithium Problem Worsens
• alpha-alpha Scattering in Halo Effective Field Theory
• Radiative Neutron Capture on Lithium-7
• Low energy proton-proton scattering in effective field theory
• Renormalization-group analysis for low-energy scattering of charged particles
• Narrow resonances and short-range interactions

Cited by in corpus (20)

• Nuclear effective field theory: status and perspectives
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules
• Effective Field Theory and the Gamow Shell Model: The 6He Halo Nucleus
• Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO
• Charge form factors of two-neutron halo nuclei in halo EFT
• Marrying {\it ab initio} calculations and Halo-EFT: the case of ${}^7\mathrm{Li}+n\to {}^8\mathrm{Li}+\gamma$
• Resonance Contribution to Radiative Neutron Capture on Lithium-7
• Radiative Neutron Capture on Carbon-14 in Effective Field Theory
• Zero-Range Effective Field Theory for Resonant Wino Dark Matter I. Framework
• Zero-Range Effective Field Theory for Resonant Wino Dark Matter II. Coulomb Resummation
• Zero-Range Effective Field Theory for Resonant Wino Dark Matter III. Annihilation Effects
• Coupled-channels treatment of ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ in effective field theory
• Classification of Coupled-Channel Near-Threshold Structures
• Coupled-channel treatment of ${}^7\mathrm{Li}(n,\gamma {)}^8\mathrm{Li}$ in effective field theory
• Effective range expansion with a long-range force
• Finite-Size Effects in Heavy Halo Nuclei from Effective Field Theory
• An Effective Field Theory Approach to the Stabilization of ${}^8$Be in a QED Plasma
• Low-Energy Deuteron-Alpha Elastic Scattering in Cluster Effective Field Theory
• Effective field theory for resonant wino dark matter