Exact solution of the Brueckner-Bethe-Goldstone equation with three-body forces in nuclear matter

TL;DR

This paper presents an exact solution to the Brueckner-Bethe-Goldstone equation incorporating three-body forces in nuclear matter, providing insights into the accuracy of common approximations used in such calculations.

Contribution

It introduces an exact method for solving the equation with three-body forces, comparing it to approximate methods to evaluate their accuracy.

Findings

The angle-average approximation is fairly accurate.

The total momentum approximation is quite inaccurate.

Exact solutions reveal significant differences from approximations.

Abstract

An exact treatment of the operators Q/e(\omega) and the total momentum is adopted to solve the nuclear matter Bruecker-Bethe-Goldstone equation with two- and three-body forces. The single-particle potential, equation of state and nucleon effective mass are calculated from the exact G-matrix. The results are compared with those obtained under the angle-average approximation and the angle-average approximation with total momentum approximation. It is found that the angle-average procedure, whereas preventing huge calculations of coupled channels, nevertheless provides a fairly accurate approximation. On the contrary, the total momentum approximation turns out to be quite inaccurate compared to its exact counterpart.