Precise determination of the effective-range parameters up to an arbitrary order

TL;DR

This paper introduces a recurrence relation-based method to accurately compute arbitrary order effective-range parameters for nuclear potentials, applicable to neutral and charged systems, enhancing precision in low-energy scattering analysis.

Contribution

The paper presents a novel recurrence relation approach combined with the Lagrange mesh technique to compute effective-range parameters to any order with high precision.

Findings

Method achieves high accuracy in calculating effective-range parameters.

Applicable to both neutral and charged nuclear systems.

Demonstrated effectiveness with potential models for nuclear systems.

Abstract

We propose a method to compute, for a given potential model, an arbitrary coefficient of the effective-range function expanded as a power series in energy. The method is based on a set of recurrence relations at low energy, that allows a compact and general description to any order in energy for neutral and charged cases. By using the Lagrange mesh technique to compute the R-matrix at zero energy, this proposal permits to compute, with a very good precision, the effective-range parameters. We use a potential model for some nuclear systems to illustrate the effectiveness of this method and to discuss its numerical limitations.