On nonsingular potentials of Cox-Thompson inversion scheme

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.

8 pages, 3 figures

References in corpus (4)

• Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy
• Reconstruction of Rb-Rb inter-atomic potential from ultracold Bose-gas collision
• Semi-analytic equations to the Cox-Thompson inverse scattering method at fixed energy for special cases
• Some Results on Inverse Scattering

Cited by in corpus (2)

• Interlacing of positive real zeros of Bessel functions
• Fixed energy potentials through an auxiliary inverse eigenvalue problem