Scattering phase shifts from overlap relations in the $J$-matrix method

TL;DR

This paper introduces a new formula for calculating scattering phase shifts within the $J$-matrix method using overlap relations, facilitating potential applications in many-body nuclear physics calculations.

Contribution

The paper presents a novel overlap relation-based formula for phase shifts in the $J$-matrix method, extending its applicability to many-body scattering problems.

Findings

Demonstrated the method in single-channel potential scattering

First step towards general many-body scattering and reactions

Potential integration with configuration-interaction shell model

Abstract

The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable bases analogous to existing integral relations or overlap integrals in a (continuous) position basis. We demonstrate the method in single-channel potential scattering. Such a result is the first step towards a more general approach to scattering and reactions in popular many-body methods such as the configuration-interaction shell model.