Matrix elements of the Argonne v18 potential

TL;DR

This paper presents two numerical methods for calculating matrix elements of the Argonne v18 potential, validating their accuracy and applicability in nuclear physics models.

Contribution

It introduces a second approach for arbitrary wave functions and compares it with the harmonic-oscillator method, ensuring consistency.

Findings

Both methods produce identical results within numerical accuracy.

Gauss-Hermite quadrature converges with at least 512 points.

The second approach extends applicability to arbitrary wave functions.

Abstract

We discuss two approaches to the calculation of matrix elements of the Argonne v18 potential. The first approach is applicable in the case of a single-particle basis of harmonic-oscillator wave functions. In this case we use the Talmi transformation, implemented numerically using the Moshinsky transformation brackets, to separate the center-of-mass and relative coordinates degrees of freedom. Integrals involving the radial part of the potential are performed using Gauss-Hermite quadrature formulas, and convergence is achieved for sets of at least 512 points. We validate the calculation of matrix elements of the Argonne v18 potential using a second approach suitable for the case of an arbitrary functional form of the single-particle wave functions. When the model space is represented in terms of harmonic-oscillator wave functions, results obtained using these two approaches are shown to to be identical within numerical accuracy.