Semiclassical treatment of asymmetric semi-infinite nuclear matter: surface and curvature properties in relativistic and non-relativistic models

Abstract

Surface and curvature properties of asymmetric semi-infinite nuclear matter are studied to beyond the proton drip. Using the semiclassical extended Thomas-Fermi method, the calculations are performed in the non-relativistic and relativistic mean field theories (Skyrme forces and non-linear σ−ω parametrizations). First we discuss the bulk equilibrium between the nuclear and drip phases. Next we analyze the asymmetric surface as a function of the bulk neutron excess. We examine local quantities related to the density profiles and, for two definitions of the bulk reference energy, the surface and curvature energy coefficients. The calculation of the curvature energy is carefully treated. The sensitivity of the nuclear surface to the relativistic effects is investigated. Mass formulae useful for arbitrary neutron excess are discussed, and their limit at small asymmetries is compared with the liquid droplet model mass formula.

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

“…When δ 0 is not very large, so that occurrence of drip nucleons does not take place (which is the situation in all cases considered in the present work), the constrained energy per unit area reads [53,59,72] …”

“…In the relativistic model the variational equations (A2) are supplemented with additional field equations for the meson fields; the calculational details for the relativistic problem can be found in Refs. [53][54][55].…”

“…The second definition of the reference energy is based on taking the value of the energy per particle in bulk asymmetric nuclear matter. Accordingly, on the bulk reference energy chosen, there exist two forms of the surface energy in ASINM, which are called E surf,µ and E surf,e [53,72]. In the small asymmetry limit, it can be shown that the difference between these two quantities behaves as E surf,e − E surf,µ = 9J 2 2Q δ 2 0 .…”

“…Here, we will show that the ratio of the DM parameters J and Q, which drives the value of the neutron skin thickness in heavy nuclei, is correlated with the slopes in density of the nuclear symmetry energy and of the EOS of neutron matter. We compare the DM values for the neutron skin thickness with the results obtained in self-consistent extended Thomas-Fermi (ETF) calculations of finite nuclei [52][53][54][55], because both methods are free of shell effects. A non-negligible role of the contribution of the difference in the surface widths of the neutron and proton density profiles is noticed.…”

Wigner–Kirkwood expansion for semi-infinite quantum fluids

“…Surface properties of quantum particle systems have been investigated only in the presence of some smooth confining external-potential barriers (see, e.g., [10,11]). The sole exceptions are represented by semiclassical studies of 3D quantum Coulomb fluids in the high-temperature Debye-Hückel limit for which one has the explicit results for the density profile near a plain hard wall [12] and for the largedistance tail of charge correlations along a plain hard wall or a conducting wall [13].…”