Nucleon distribution in nuclei beyond theβ-stability line

Abstract

The radii of nucleon distribution, bulk density, and neutron skin in nuclei beyond the β-stability line are studied within the direct variational method. We evaluate the partial equation of state of finite nuclei and demonstrate that the bulk density decreases beyond the beta stability line. We show that the growth of the neutron skin in unstable nuclei does not obey the saturation condition because of the polarization effect. The value of the neutron-skin thickness ∆r np = r 2 n − r 2 p is caused by the different radii (skin effect) and only slightly by the different shapes (halo effect) of neutron and proton distributions. The relative contribution of both effects depends on the competition between the symmetry energy, and the spin-orbit and Coulomb interactions. The calculations of the isovector shift of the nuclear radius ∆r np show its primarily linear dependence on the asymmetry parameter X = (N − Z)/A.

Self-consistent mean-field approach to the statistical level density in spherical nuclei

“…An advantage of our ETF approach is that it provides description for the liquid drop properties, including nuclear mass, deformation energy, fission barrier etc., see Refs, [36][37][38][39], the nuclear mean field V ETF (r) and correspondingly the smooth behavior of the statistical level density. This fact allows one to evaluate the quantum shell corrections consistently with the liquid-drop mass formula within Strutinsky shell-correction method avoiding the introducing of the phenomelogical shell-model mean field.…”

Equation of state and radii of finite nuclei in the presence of a diffuse surface layer

“…The averaged characteristic of nucleon distribution is given by the root mean square (rms) radii for neutron and proton, respectively. Evaluating the values of rms radii and the corresponding neutron-skin thickness, we adopt the extended Thomas-Fermi (ETF) and the direct variational method [5,6]. The nucleon densities and are generated by the profile functions which are determined by the requirement that the energy of the nucleus should be stationary with respect to variations of these profiles.…”

“…Following the direct variational method, we choose a trial function for as a power of the Fermi function for given by, see also Ref. [6],…”

“…Here, the experimental data were taken from Refs. [23,24,25,26,27,28,29], the results obtained using the Gibbs-Tolman-Widom approach are shown by the open circles and the solid line is obtained within the extended Thomas-Fermi approximation with Skyrme interactions [6]. [24], the open circles (connected by dotted line) have been obtained using the Gibbs-Tolman approach described in text and the solid line is obtained using the extended Thomas-Fermi approximation with the Skyrme interaction [15], see Ref.…”

“…[24], the open circles (connected by dotted line) have been obtained using the Gibbs-Tolman approach described in text and the solid line is obtained using the extended Thomas-Fermi approximation with the Skyrme interaction [15], see Ref. [6].…”