Nonrelativistic nucleon effective masses in nuclear matter: Brueckner-Hartree-Fock model versus relativistic Hartree-Fock model

The density and isospin dependencies of nonrelativistic nucleon effective mass (m(N)*) are studied, which is a measure of the nonlocality of the single particle (s.p.) potential. It can be decoupled as 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 k mass andE mass are determined and compared by using the latest versions of the nonrelativistic Brueckner-Hartree-Fock (BHF) model and the relativistic Hartree-Fock (RHF) model. The latter is achieved based on the corresponding Schrodinger 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 dependencies at the densities considered; 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 dependencies in these two models because they could be dominated either by the k mass (then we have m(n)* > m(p)* in the BHF model), or by the E mass (then we have m(p)* > m(n)* in the RHF model). The isospin splitting in the BHF model is more consistent with the recent analysis from the nucleon-nucleus-scattering data, while the small E mass m(E)* in the RHF case as a result of the missing ladder summation finally leads to an opposite splitting behavior.