Semi-analytic equations to the Cox-Thompson inverse scattering method at fixed energy for special cases

TL;DR

This paper introduces semi-analytic equations for the Cox-Thompson inverse scattering method at fixed energy, simplifying calculations by avoiding matrix inversions and focusing on specific particle parity cases, thus enhancing numerical efficiency.

Contribution

It presents a reformulation of the Cox-Thompson inverse scattering problem resulting in matrix-inversion-free semi-analytic equations for specific particle parity cases.

Findings

Equations are free of matrix inversions.

Method is applicable to identical bosonic and certain fermionic scattering.

Proposed approximate method extends to arbitrary parity partial waves.

Abstract

Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered.