Introduction

The energy-density-functional (EDF) methods are recently intensely studied in nuclear physics to gain more precise and predictive description of stable and exotic nuclei within a unified framework. Such methods can be considered as realizations of the nuclear effective theory at low energies [1] and are motivated by successful applications of the density functional theory in electronic systems, see, e.g., Ref. [2]. In nuclear physics, they have been studied since early 1970s under the names of Hartree-Fock or Hartree-Fock-Bogolyubov methods [3], but in fact they rather correspond to the Kohn-Sham [4] type of approaches, aiming at describing correlated fermion systems by their one-body (local or non-local) densities only.

In the present study we focus on the Skyrme-type EDFs, by which one assumes that the ground-state energy of a given nucleus is given by an integral of a local energy density. As discussed in Ref. [5], our main goal is to look for the spectroscopic-quality EDF, which would correctly describe positions of single-particle (s.p.) energies across the nuclear mass table. To this end, here we analyze dependence of the s.p. energies on the EDF coupling constants and attempt answering the question on whether the current parametrizations of the EDF are rich enough to describe experimental data with reasonable precision. In the present work we look only at bare s.p. energies in doubly magic nuclei, because the polarization effects, which may affect detailed values of s.p. energies, are estimated to be significantly smaller than discrepancies with experimental data [5].

The paper is organized in the following way. In Sec. 2 we briefly introduce necessary definitions and present our method of analysis. Three subsections of Sec. 3 present our results on s.p. energies in function of coupling constants, regression coefficients, and fits to experimental data. Conclusions of our work are presented in Sec. 4.