Deconstructing 1S0 nucleon-nucleon scattering

TL;DR

This paper analyzes nucleon-nucleon scattering in the 1S0 channel using a distorted-wave method, revealing rapid energy dependence above 100 MeV and suggesting the inclusion of the Delta resonance for accurate modeling.

Contribution

It introduces a modified effective-range expansion to remove one-pion exchange effects and assesses the impact of two-pion exchange and short-range interactions in nucleon scattering.

Findings

Residual short-range interaction varies rapidly above 100 MeV

Breakdown scale of effective theory is about 270 MeV

Including the Delta resonance may improve scattering descriptions

Abstract

A distorted-wave method is used to analyse nucleon-nucleon scattering in the 1S0 channel. Effects of one-pion exchange are removed from the empirical phase shift to all orders by using a modified effective-range expansion. Two-pion exchange is then subtracted in the distorted-wave Born approximation, with matrix elements taken between scattering waves for the one-pion exchange potential. The residual short-range interaction shows a very rapid energy dependence for kinetic energies above about 100 MeV, suggesting that the breakdown scale of the corresponding effective theory is only 270MeV. This may signal the need to include the Delta resonance as an explicit degree of freedom in order to describe scattering at these energies. An alternative strategy of keeping the cutoff finite to reduce large, but finite, contributions from the long-range forces is also discussed.