Lepton-neutron interaction and S-wave low energy parameters

TL;DR

This paper derives a lepton-neutron potential considering electromagnetic interactions, compares form factor parametrizations, and calculates low-energy scattering parameters, highlighting potential divergences in partial wave sums.

Contribution

It introduces a detailed operator form of the lepton-neutron potential including various interaction terms and computes low-energy parameters for S-wave states.

Findings

Computed lepton-neutron low-energy parameters for S-waves.

Compared different neutron electromagnetic form factor parametrizations.

Identified a possible divergence in partial wave summation due to spin-orbit potential.

Abstract

A lepton-neutron potential in configuration space is obtained. It is based on the Coulomb plus hyperfine interaction Hamiltonian integrated over the neutron charge and magnetic densities. Different parametrisations of the neutron electromagnetic form factors are compared. It is given in the operator form with a central, spin-spin, tensor and spin-orbit terms. The potentials for lowest partial waves states are presented. We compute the lepton-neutron lepton ($ln$) low-energy parameters for the S-waves, estimate the zero-energy cross sections for higher angular momentum states, and point out a possible divergence in the partial wave summation due to the spin-orbit potential.