Asymmetry and Spin-Orbit Effects in Binding Energy in the Effective Nuclear Surface Approximation

TL;DR

This paper analytically derives particle densities and surface energy properties of nuclei considering asymmetry and spin-orbit effects within a sharp-edged nucleus approximation, providing insights into nuclear surface characteristics.

Contribution

It introduces analytical expressions for nuclear surface tension coefficients and finite-size corrections, incorporating asymmetry and spin-orbit effects in the effective nuclear surface model.

Findings

Analytical formulas for isoscalar and isovector tension coefficients.

Finite-size corrections to the beta stability line.

Effective nuclear surface shapes derived with higher order corrections.

Abstract

Isoscalar and isovector particle densities are derived analytically by using the approximation of a sharp edged nucleus within the local energy density approach with the proton-neutron asymmetry and spin-orbit effects. Equations for the effective nuclear-surface shapes as collective variables are derived up to the higher order corrections in the form of the macroscopic boundary conditions. The analytical expressions for the isoscalar and isovector tension coefficients of the nuclear surface binding energy and the finite-size corrections to the $\beta $ stability line are obtained.