Introduction

The nuclear mean-field methods constitute principal tools of a description of nuclear states in heavy nuclei [1]. Their applicability to nuclei is interpreted within the Hohenberg-Kohn [2] and Kohn-Sham theorems [3] involving the nuclear energy density functional (EDF). Recently, we formulated the N$^3$LO nuclear EDF with gradient corrections up to sixth order [4]. The present study presents practical formulation of the method, allowing for a solution of the corresponding self-consistent equations. We also present the computer program HOSPHE (v1.00), which solves the self-consistent equations by using the expansion of single-particle wave functions on the spherical harmonic oscillator (HO) basis.

The paper is organized as follows. In Section 2, we present concise review of the method. In Section 3, we give general forms of the N$^3$LO potentials, fields, and densities, which are then in Section 4 specified to the case of spherical symmetry. Sections 5-10 describe the structure, installation, and test runs of the code HOSPHE (v1.00), and Section 11 concludes our study.