Mass Splitting In Neutron-rich Matter Research Articles

Neutron-proton effective mass splitting in neutron-rich matter

Neutron-proton effective mass splitting in neutron-rich matter

Neutron–proton effective mass splitting in neutron-rich matter and its impacts on nuclear reactions

The neutron–proton effective mass splitting in neutron-rich nucleonic matter reflects the spacetime nonlocality of the isovector nuclear interaction. It affects the neutron/proton ratio during the earlier evolution of the Universe, cooling of proto-neutron stars, structure of rare isotopes and dynamics of heavy-ion collisions. While there is still no consensus on whether the neutron–proton effective mass splitting is negative, zero or positive and how it depends on the density as well as the isospin-asymmetry of the medium, significant progress has been made in recent years in addressing these issues. There are different kinds of nucleon effective masses. In this mini-review, we focus on the total effective masses often used in the non-relativistic description of nuclear dynamics. We first recall the connections among the neutron–proton effective mass splitting, the momentum dependence of the isovector potential and the density dependence of the symmetry energy. We then make a few observations about the progress in calculating the neutron–proton effective mass splitting using various nuclear many-body theories and its effects on the isospin-dependence of in-medium nucleon–nucleon cross-sections. Perhaps, our most reliable knowledge so far about the neutron–proton effective mass splitting at saturation density of nuclear matter comes from optical model analyses of huge sets of nucleon–nucleus scattering data accumulated over the last five decades. The momentum dependence of the symmetry potential from these analyses provide a useful boundary condition at saturation density for calibrating nuclear many-body calculations. Several observables in heavy-ion collisions have been identified as sensitive probes of the neutron–proton effective mass splitting in dense neutron-rich matter based on transport model simulations. We review these observables and comment on the latest experimental findings.

Neutron–proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon–nucleus scattering data within an isospin dependent optical model

The neutron–proton effective mass splitting in asymmetric nucleonic matter of isospin asymmetry δ and normal density is found to be mn−p⁎≡(mn⁎−mp⁎)/m=(0.41±0.15)δ from analyzing globally 1088 sets of reaction and angular differential cross sections of proton elastic scattering on 130 targets with beam energies from 0.783 MeV to 200 MeV, and 1161 sets of data of neutron elastic scattering on 104 targets with beam energies from 0.05 MeV to 200 MeV within an isospin dependent non-relativistic optical potential model. It sets a useful reference for testing model predictions on the momentum dependence of the nucleon isovector potential necessary for understanding novel structures and reactions of rare isotopes.

Symmetry energy, its density slope, and neutron-proton effective mass splitting at normal density extracted from global nucleon optical potentials

Based on the Hugenholtz--Van Hove theorem, it is shown that both the symmetry energy $E$${}_{\mathrm{sym}}(\ensuremath{\rho})$ and its density slope $L(\ensuremath{\rho})$ at normal density ${\ensuremath{\rho}}_{0}$ are completely determined by the nucleon global optical potentials. The latter can be extracted directly from nucleon-nucleus scatterings, ($p,n$) charge-exchange reactions, and single-particle energy levels of bound states. Averaging all phenomenological isovector nucleon potentials constrained by world data available in the literature since 1969, the best estimates of ${E}_{\mathrm{sym}}({\ensuremath{\rho}}_{0})=31.3$ MeV and $L({\ensuremath{\rho}}_{0})=52.7$ MeV are simultaneously obtained. Moreover, the corresponding neutron-proton effective mass splitting in neutron-rich matter of isospin asymmetry $\ensuremath{\delta}$ is estimated to be $({m}_{n}^{*}\ensuremath{-}{m}_{p}^{*})/m=0.32\ensuremath{\delta}$.

Self-Consistent Green Function Calculations for Isospin Asymmetric Nuclear Matter

(Received September 1, 2009; Revised February 2, 2010)The one-body potentials for protons and neutrons are obtained from the self-consistentGreen-function calculations of asymmetric nuclear matter, in particular their dependence onthe degree of proton/neutron asymmetry. Results of the binding energy per nucleon as afunction of the density and asymmetry parameter are presented for the self-consistent Greenfunction approach using the CD-Bonn potential. For the sake of comparison, the same cal-culations are performed using the Brueckner-Hartree-Fock approximation. The contributionof the hole-hole terms leads to a repulsive contribution to the energy per nucleon whichincreases with the nuclear density. The incompressibility for asymmetric nuclear matter hasbeen also investigated in the framework of the self-consistent Green-function approach usingthe CD-Bonn potential. The behavior of the incompressibility is studied for different valuesof the nuclear density and the neutron excess parameter. The nuclear symmetry potentialat fixed nuclear density is also calculated and its value decreases with increasing the nu-cleon energy. In particular, the nuclear symmetry potential at saturation density changesfrom positive to negative values at nucleon kinetic energy of about 200 MeV. For the sakeof comparison, the same calculations are performed using the Brueckner-Hartree-Fock ap-proximation. The proton/neutron effective mass splitting in neutron-rich matter has beenstudied. The predicted isospin splitting of the proton/neutron effective mass splitting inneutron-rich matter is such that

Isospin dependence of three-body force rearrangement contribution

Within the isospin-dependent Brueckner framework, we investigate the contribution of three-body force (TBF) rearrangement to isospin symmetry potential as well as its momentum and density dependence.In particular, we investigate the TBF rearrangement effects on the isospin splitting of neutron and proton effective masses in neutron-rich nuclear matter. We show that the rearrangement contribution of TBF to neutron and proton single-particle potentials is repulsive and increases rapidly with increasing density and momentum. At low densities, the influence of the TBF rearrangement on symmetry potential is rather small, and the TBF rearrangement effect becomes more and more pronounced as the density rises. At high densities, the contribution of TBF rearrangement increases considerably the symmetry potential and modifies remarkably the momentum dependence of the symmetry potential. In both cases with and without including the TBF rearrangement contribution, the predicted neutron effective mass in neutron-rich matter is greater than the proton effective mass. The TBF rearrangement effect is to decrease remarkably both the proton and neutron effective masses, and reduce the magnitude of neutron-proton effective mass splitting in neutron-rich matter at high densities.

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

Within Bombaci's phenomenological single-nucleon potential model we study the neutron-proton effective mass splitting ${m}_{n}^{*}\text{\ensuremath{-}}{m}_{p}^{*}$ in neutron-rich matter. It is shown that an effective mass splitting of ${m}_{n}^{*}<{m}_{p}^{*}$ leads to a symmetry potential that is inconsistent with the energy dependence of the Lane potential constrained by the nucleon-nucleus scattering experimental data.