Analytical mass formula and nuclear surface properties in the ETF approximation

TL;DR

This paper develops an analytical model within the ETF approximation to accurately determine nuclear surface properties and energies, explicitly relating them to Skyrme functional parameters with high precision.

Contribution

It introduces an analytical approach for nuclear surface energy and diffuseness, including non-local effects, improving accuracy over previous models.

Findings

Analytical formula for symmetric nuclei surface energy derived.

Explicit relations between energy functional parameters and surface properties.

Achieves better than 200 keV per nucleon accuracy in binding energy predictions.

Abstract

The problem of the determination of the nuclear surface and surface symmetry energy is addressed in the framework of the Extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. For the case of symmetric nuclei, the resulting ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed, which cannot be simply deduced from the local part of the functional. In the case of asymmetric nuclei, we propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves over previous models and leads to a precision better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.