Isospin-dependent properties of asymmetric nuclear matter in relativistic mean field models

Abstract

Using various relativistic mean-field models, including the nonlinear ones with meson field selfinteractions, those with density-dependent meson-nucleon couplings, and the point-coupling models without meson fields, we have studied the isospin-dependent bulk and single-particle properties of asymmetric nuclear matter. In particular, we have determined the density dependence of nuclear symmetry energy from these different relativistic mean-field models and compare the results with the constraints recently extracted from analyses of experimental data on isospin diffusion and isotopic scaling in intermediate-energy heavy ion collisions as well as from measured isotopic dependence of the giant monopole resonances in even-A Sn isotopes. Among the 23 parameter sets in the relativistic mean-filed model that are commonly used for nuclear structure studies, only a few are found to give symmetry energies that are consistent with the empirical constraints. We have also studied the nuclear symmetry potential and the isospin-splitting of the nucleon effective mass in isospin asymmetric nuclear matter. We find that both the momentum dependence of the nuclear symmetry potential at fixed baryon density and the isospin-splitting of the nucleon effective mass in neutron-rich nuclear matter depend not only on the nuclear interactions but also on the definition of the nucleon optical potential.

Incompressibility of neutron-rich matter

“…In some works, the coefficient K τ is denoted by K asy [19,22,48] or K vs [50,51]. To add to the confusion in notation, in the original contributions by Blaizot and collaborators [1,2,49] the term K sym was used instead of K τ in Eq.…”

“…First, we note that no uniform terminology exists even to denote the neutron-proton asymmetry coefficient. Indeed, the symbols I [46], α [22,47,48], β [32], and δ [9,19,49] are all used in the literature to denote the neutron-proton asymmetry coefficient (N − Z)/A of asymmetric nuclear matter. Second, and perhaps even more confusing, is the myriad of different symbols used to refer to the same bulk properties.…”

“…It is also common practice to express the finite nucleus incompressibility coefficient (K A ) by means of a liquid-droplike mass formula [2,6,9,[48][49][50][51], which highlights the physical meaning of the various contributions to K A . That is,…”

Neutron skin thickness in the droplet model with surface width dependence: Indications of softness of the nuclear symmetry energy

“…Actually, c sym (ρ) provides with excellent accuracy the difference between the binding energies of pure neutron matter (δ = 1) and symmetric matter (δ = 0). It is customary, and insightful, to characterize the behavior of an EOS around the saturation density ρ 0 by means of a few bulk parameters calculated at the saturation point, as in the formula [10,[13][14][15][16]56,[61][62][63] …”

“…This is the case of precision tests of the standard model through atomic parity nonconservation observables [6], and even of studies on constraining a possible time variation of the gravitational constant [7]. In terrestrial laboratories, the available tools to delineate the density dependence of the symmetry energy at saturation and subsaturation densities include the interaction potential between neutron-rich nuclei [8], observables like isospin diffusion and isoscaling in heavy-ion reactions at intermediate energies [9][10][11][12][13][14][15][16][17][18][19][20][21], different modes of collective excitations of nuclei [22][23][24][25][26], and, of course, data on the binding and structure of neutron-rich nuclei and on their neutron skin thickness.…”