Spherical nuclei near the stability line and far from it
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CLEI Theory
Spherical Nuclei Near the Stability Line and Far From It V. I. Isakov* Petersburg Nuclear Physics Institute, National Research Centre Kurchatov Institute, Gatchina, 188300 Russia Received January 14, 2016
Abstract—Results of microscopic and semiphenomenological calculations of features of spherical nuclei lying near the stability line and far from it are presented. The reason why the nuclei being considered are spherical is that they are magic at least in one nucleon sort. The present analysis is performed for Z = 50 and Z = 28 isotopes and for N = 50 isotones, the region extending from neutron-rich to neutron-deficient nuclei being covered. The isotopic dependence of the mean-field spin–orbit nuclear potential is revealed; systematics of energies of levels and probabilities for electromagnetic transitions is examined; and rootmean-square radii of nuclei are calculated, along with the proton- and neutron-density distributions in them. Nuclei in the vicinity of closed shells are considered in detail, and the axial-vector weak coupling constant in nuclei is evaluated. A systematic comparison of the results of calculations with experimental data is performed. DOI: 10.1134/S1063778816060119
INTRODUCTION
At the present time, experimental investigations in the realms of nuclear physics focus primarily on exploring nuclei that lie far from the stability region. Available experimental data cover wide ranges of nuclei from neutron-rich to neutron-deficient ones and contain information about nuclides both in the vicinity of and far from closed shells, including nuclei from new regions of magic numbers. This brings about the problem of describing, within a unified conceptual framework, the properties of nuclei over the whole accessible range of mass numbers A, as well as of N and Z. Here, we examine basic properties of nuclei, such as single-particle energies, binding energies, neutron-separation energies, and root-mean square radii by employing self-consistent calculations based on the HF + BCS method. At the same time, semiphenomenological calculations based on a phenomenological mean-field nuclear potential and a finite-range effective two-particle interaction determined earlier from a fit to the spectra of nuclei in the vicinities of magic numbers are performed in order to describe single-particle energies, root-mean-square radii of nuclei, their spectra, and probabilities for beta and gamma transitions in them. The spectra and transition probabilities are calculated in the randomphase approximation (RPA). *
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1. EVALUATION OF THE MASS SHELL AND SINGLE-PARTICLE FEATURES The binding energies and single-particle features were determined by the Hartree–Fock–Bogolyubov method used with Skyrme forces and supplemented with the assumption of Bardeen–Cooper–Schrieffer (BCS) contact pairing (HF + BCS method), the respective pairing constants being denoted by Gp and Gn . The total energy of the nucleus can be represented in the form (see [1–3]) Δ2p Δ2 . (1) E = −B = HHF + BCS (r)dr − n − Gn Gp
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