Separable Expansions of V_{low} for 2- and 3-Nucleon Systems

TL;DR

This paper introduces a systematic and efficient method for developing effective theories of two- and three-nucleon systems using separable expansions of potentials, which converge rapidly and improve computational accuracy.

Contribution

It presents a novel approach combining separable potentials with renormalization group evolution to achieve accurate, controlled approximations for few-nucleon systems.

Findings

Rapid convergence of the separable expansion with only two terms.

Accurate bound state and scattering results for 2- and 3-nucleon systems.

Enhanced computational efficiency in few-body nuclear calculations.

Abstract

We present an alternative organizational scheme for developing effective theories of 2- and 3-body systems that is systematic, accurate, and efficient with controlled errors. To illustrate our approach we consider the bound state and scattering properties of the 2- and 3-nucleon systems. Our approach combines the computational benefits of using separable potentials with the improved convergence properties of potentials evolved with a renormalization group procedure. Long ago Harms showed that any potential can be expanded in a series of separable terms, but this fact is only useful if the expansion can be truncated at low order. The separable expansion provides an attractive organizational scheme that incorporates the two body bound state in the leading term while allowing for systematic corrections thereafter. We show that when applied to a renormalization group-evolved potential, the separable expansion converges rapidly, with accurate results for both 2- and 3-body scattering processes using only two separable terms.