Nonrelativistic nucleon effective masses in nuclear matter: BHF versus RHF

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).