Nonrelativistic nucleon effective masses in nuclear matter: BHF versus RHF

TL;DR

This study compares nonrelativistic nucleon effective masses derived from BHF and RHF models, analyzing their density, isospin dependences, and neutron-proton splitting to understand their different physical origins.

Contribution

It provides a detailed comparison of effective masses and their components in BHF and RHF models, highlighting the different mechanisms affecting neutron-proton mass splitting.

Findings

Neutron-proton effective mass splittings have similar asymmetry dependences in both models.

Splittings can be dominated by either k-mass or E-mass, leading to different mass ordering.

The models predict different asymmetry dependences for the effective masses due to their underlying physics.

Abstract

The density and isospin dependences of the nonrelativistic nucleon effective mass ($m^*$) are studied, which is a measure of the nonlocality of the single particle (s.p.) potential. We decouple it further into the so called k-mass ($m^*_k$, i.e., the nonlocality in space) and E-mass ($m^*_E$, i.e., the nonlocality in time). Both masses are determined and compared from the latest versions of the nonrelativistic Brueckner-Hartree Fock (BHF) model and the relativistic Hartree-Fock (RHF) model. The latter are achieved based on the corresponding Schr\"{o}dinger equivalent s.p. potential in a relativistic framework. We demonstrate the origins of different effective masses and discuss also their neutron-proton splitting in the asymmetric matter in different models. We find that the neutron-proton splittings of both the k-mass and the E-mass have the same asymmetry dependences at considered densities, namely $m^*_{k,n} > m^*_{k,p}$ and $m^*_{E,p} > m^*_{E,n}$. However, the resulting splittings of nucleon effective masses could have different asymmetry dependences in the two models, because they could be dominated either by that of the k-mass (then we have $m^*_n > m^*_p$ in the BHF model) or by that of the E-mass (then we have $m^*_p > m^*_n$ in the RHF model).