Constraining the neutron-proton effective mass splitting in neutron-rich matter

One of the most fundamental properties characterizing the propagation of a nucleon in nuclear medium is its effective mass[1, 2, 3]. The latter describes to leading order the effects related to the non-locality of the underlying nuclear effective interactions and the Pauli exchange effects in many-fermion systems. In neutron-rich matter, an interesting new question arises as to whether the effective mass m∗n for neutrons is higher or lower than that for protons m∗p. Microscopic many-body theories, e.g., the Landau-Fermi liquid theory[4] and the BruecknerHartree-Fock (BHF) approach[5], predict that m∗n > m ∗ p in neutron-rich matter. On the other hand, some effective interactions within phenomenological approaches predict the opposite[6]. Unfortunately, up to now almost nothing is known experimentally about the neutron-proton effective mass splitting m∗n−m ∗ p in neutron-rich medium. Knowledge about nucleon effective mass in neutron-rich matter is critically important for understanding several properties of neutron stars[7, 8, 9]. It is also important for the reaction dynamics of nuclear collisions induced by radioactive nuclei, such as, the degree and speed of isospin diffusion, the neutron-proton differential collective flow as well as the isospin equilibrium[6, 10, 11, 12]. Moreover, it influences the magnitude of shell effects and basic properties of nuclei fare from stability[1]. However, even the sign of the neutron-proton effective mass splitting remains rather controversial theoretically. It is thus imperative to constrain the neutron-proton effective mass splitting in neutron-rich matter using experimental data. In a recent study by Rizzo et al.[6], nuclear reactions with radioactive beams were proposed as a means to disentangle the sign of the neutron-proton effective mass splitting in neutron-rich matter. In this note we take a completely different approach for the same purpose. We show that an effective mass splitting ofm∗n < m ∗ p leads to a symmetry potential that is inconsistent with the energy dependence of the Lane potential constrained by existing nucleon-nucleus scattering data. The effective mass splitting of m∗n < m ∗ p is thus ruled out phenomenologically