Determination of the effective parameters of proton-$^{3}$He scattering on the basis of the neutron-triton scattering data

TL;DR

This study investigates the relationship between neutron-triton and proton-Helium-3 scattering parameters using a potential model, predicting scattering lengths that support a specific phase analysis set.

Contribution

The paper introduces a potential model with a delta-shell interaction to relate neutron-triton and proton-Helium-3 scattering parameters, accounting for Coulomb effects.

Findings

Coulomb renormalization does not alter the established relation between scattering lengths.

Predicted p--$^{3}$He scattering lengths favor a specific phase analysis set.

The model supports the inequality $A^{1}_{nc} < A^{0}_{nc}$ for scattering lengths.

Abstract

We have studied the relations between the neutron-triton scattering lengths and effective ranges and the corresponding quantities for the p --$^{3}$He scattering in the framework of the potential model with an effective nucleon-nucleus interaction in the form of a $\delta $-shell potential. It is shown that the Coulomb renormalization of the pure nuclear scattering lengths does not change the relation well established for the n + $^{3}$H system between the lengths: $A^{1} < A^{0}$. We have predicted the p--$^{3}$He scattering lengths which give preference to set I of the phase analysis performed by E.A. George et al. (2003), which corresponds to the inequality $A^{1}_{nc} < A^{0}_{nc}$ for the scattering lengths.