Neutron-proton effective mass splitting in neutron-rich matter

Nucleon effective masses in neutron-rich matter are studied with the relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space. The neutron and proton effective masses for symmetric nuclear matter are 0.80 times rest mass, which agrees well with the empirical values. In neutron-rich matter, the effective mass of the neutron is found to be larger than that of the proton, and the neutron-proton effective mass splittings at the empirical saturation density are predicted as $0.187\alpha$ with $\alpha$ being the isospin asymmetry parameter. The result is compared to other ab initio calculations and is consistent with the constraints from the nuclear reaction and structure measurements, such as the nucleon-nucleus scattering, the giant resonances of ${}^{208}\mathrm{Pb}$, and the Hugenholtz–Van Hove theorem with systematics of nuclear symmetry energy and its slope. The predictions of the neutron-proton effective mass splitting from the RBHF theory in the full Dirac space might be helpful to constrain the isovector parameters in phenomenological density functionals.

Figure 1

The effective masses at Fermi momentum $M_{NR,\tau }^{*}\left(k_F^{\tau }\right)$ as functions of the asymmetry parameter $\alpha$ at the density $\rho =0.16{\text{fm}}^{-3}$ calculated by the RBHF theory in the full Dirac space [41] (a), in comparison with the results obtained by the RBHF theory with the projection method [45] (b), and the momentum-independence approximation method [38] (c). The results from the BHF theory are also shown for comparison [29] (d).

Figure 2

The neutron-proton effective mass splitting as a function of the asymmetry parameter $\alpha$ at the density $\rho =0.16{\text{fm}}^{-3}$ calculated by the RBHF theory in the full Dirac space (solid and empty squares). The line represents the linear fitting for data in solid squares.

Figure 3

The neutron-proton effective mass splitting as a function of the density $\rho$ calculated by the RBHF theory in the full Dirac space with the $NN$ interactions Bonn A, B, and C [58]. The solid lines with solid symbols denote the full calculation with tensor force, while the short-dotted lines with empty symbols denote the self-consistent calculations without tensor force.

Figure 4

The neutron-proton effective mass splitting at the density $\rho =0.16{\text{fm}}^{-3}$ calculated by the RBHF theory in the full Dirac space (red solid star), in comparison with the constraints from analyzing nuclear structure and reaction experiments [12, 20, 60, 62] (shaded regions), and the theoretical results obtained by the RBHF theory with the projection method (red empty star), the nonrelativistic BHF [29] and extended BHF theory [27] (blue semifilled squares), the SCGF approach [63] (cyan dot), the MBPT calculation with chiral effective forces [35] (orange arrows), the Skyrme-Hartree-Fock theory (black error bar), and the covariant density functional theory [64] (gray and purple error bars).