Inverse scattering J-matrix approach to nucleon-nucleus scattering and the shell model

TL;DR

This paper presents an extension of the $J$-matrix inverse scattering method for analyzing nucleon-nucleus scattering, linking scattering data with shell model eigenstates, and compares results with No-core Shell Model calculations.

Contribution

It introduces an extended $J$-matrix inverse scattering approach for charged particles and demonstrates its application to $n ext{-} ext{alpha}$ and $p ext{-} ext{alpha}$ scattering, connecting scattering analysis with shell model states.

Findings

The extended method effectively analyzes $n ext{-} ext{alpha}$ and $p ext{-} ext{alpha}$ scattering.

Results show good agreement with No-core Shell Model calculations.

The approach provides direct access to eigenstates related to the shell model.

Abstract

The $J$-matrix inverse scattering approach can be used as an alternative to a conventional $R$-matrix in analyzing scattering phase shifts and extracting resonance energies and widths from experimental data. A great advantage of the $J$-matrix is that it provides eigenstates directly related to the ones obtained in the shell model in a given model space and with a given value of the oscillator spacing $\hbar\Omega$. This relationship is of a particular interest in the cases when a many-body system does not have a resonant state or the resonance is broad and its energy can differ significantly from the shell model eigenstate. We discuss the $J$-matrix inverse scattering technique, extend it for the case of charged colliding particles and apply it to the analysis of $n\alpha$ and $p\alpha$ scattering. The results are compared with the No-core Shell Model calculations of $^5$He and $^5$Li.