On nonsingular potentials of Cox-Thompson inversion scheme

TL;DR

This paper identifies conditions to generate nonsingular potentials via the Cox-Thompson inverse scattering method with a single phase shift, ensuring unique solutions and avoiding singularities, while also discovering new Bessel function zero inequalities.

Contribution

It establishes a condition for nonsingular potentials in Cox-Thompson inversion with one phase shift and introduces new inequalities for Bessel function zeros.

Findings

Conditions for nonsingular potentials are derived.

Unique solutions of the integral equation are maintained.

New inequalities for zeros of Bessel functions are discovered.

Abstract

We establish a condition for obtaining nonsingular potentials using the Cox-Thompson inverse scattering method with one phase shift. The anomalous singularities of the potentials are avoided by maintaining unique solutions of the underlying Regge-Newton integral equation for the transformation kernel. As a by-product, new inequality sequences of zeros of Bessel functions are discovered.