Relativistic Brueckner-Hartree-Fock in nuclear matter without the average momentum approximation

TL;DR

This paper derives exact angular integration expressions for the center of mass momentum in relativistic Brueckner-Hartree-Fock theory and assesses the impact of the common approximation on nuclear matter properties.

Contribution

It provides the first detailed derivation of exact momentum integrals in RBHF theory, evaluating the approximation's effect on nuclear matter saturation and symmetry energy parameters.

Findings

Exact treatment affects higher order physical quantities.

Approximation introduces non-negligible errors in binding energy.

Results align with experimental constraints on nuclear matter properties.

Abstract

Brueckner-Hartree-Fock theory allows to derive the $G$-matrix as an effective interaction between nucleons in the nuclear medium. It depends on the center of mass momentum $\bm{P}$ of the two particles and on the two relative momenta $\bm{q}$ and $\bm{q'}$ before and after the scattering process. In the evaluation of the total energy per particle in nuclear matter usually the angle averaged center of mass momentum approximation has been used. We derive in detail the exact expressions of the angular integrations of the momentum $\bm{P}$ within relativistic Brueckner-Hartree-Fock (RBHF) theory, especially for the case of asymmetric nuclear matter. In order to assess the reliability of the conventional average momentum approximation for the binding energy, the saturation properties of symmetric and asymmetric nuclear matter are systematically investigated based on the realistic Bonn nucleon-nucleon potential. It is found that the exact treatment of the center of mass momentum leads to non-negligible contributions to the higher order physical quantities. The correlation between the symmetry energy $E_{\mathrm{sym}}$, the slope parameter $L$, and the curvature $K_{\mathrm{sym}}$ of the symmetry energy are investigated. The results of our RBHF calculations for the bulk parameters characterizing the equation of state are compared with recent constraints extracted from giant monopole resonance and isospin diffusion experiments.