Extrapolation of scattering data to the negative-energy region

TL;DR

This paper derives explicit analytic formulas for the effective-range function combining short-range and Coulomb potentials, facilitating extrapolation to negative energies to study bound states in scattering theory.

Contribution

It introduces new analytic expressions for the effective-range function that are suitable for extrapolation to negative energies, enhancing the analysis of bound-state properties.

Findings

Derived explicit formulas for the effective-range function.

Discussed alternative extrapolation methods.

Investigated analytic properties of scattering terms.

Abstract

Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.