Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using N2LO Skyrme pseudo-potential in spherical symmetry

TL;DR

This paper develops an extended N2LO Skyrme pseudo-potential for spherical nuclei, deriving mean-field equations, implementing a numerical solution, and providing a new parametrization that matches experimental data.

Contribution

It introduces a new N2LO Skyrme pseudo-potential, derives the associated mean-field equations, and offers a first parametrization with comparison to experimental data.

Findings

Derived mean-field equations for N2LO pseudo-potential

Implemented numerical solutions for differential equations

Provided a parametrization fitting experimental observables

Abstract

We present the development of the extended Skyrme N2LO pseudo-potential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behaviour of the solutions at the origin. Finally, a fitting procedure for such a N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.