Improvement to Generalized Separable Expansion Method in Lippmann-Schwinger Equation

TL;DR

This paper presents an improved generalized separable expansion method for the Lippmann-Schwinger equation, which analytically handles singularities at the two-body bound state threshold, enhancing the conversion of realistic NN potentials into separable forms.

Contribution

The paper introduces a novel GSE approach that accurately treats singularities, improving the conversion process of NN potentials into separable potentials for three-body calculations.

Findings

Enhanced accuracy in representing NN potentials.

Analytical treatment of singularities at bound state thresholds.

Improved convergence in three-body Faddeev equations.

Abstract

Realistic nucleon-nucleon (NN) potentials are generally not in separable form, but there is a way to convert them into separable potentials, called the generalized separable expansion (GSE). When the separable potential is substituted into a three-body Faddeev equation, which generally has two Jacobi momenta, the integral equation is conveniently reduced to a one-variable integral equation. The two-body scattering t-matrix of the conventional GSE does not have an exact singularity at the energy threshold of the two-body bound state. The newly introduced GSE improves this by treating the singularity analytically.