Self-Consistent Calculation of the Charge Radii in a Long ${}^{\mathbf{58{-}82}}$Cu Isotopic Chain

Abstract

The charge radii are calculated in long chain of copper isotopes that includes the ${}^{58,79}$Cu exotic nuclei, which are close to the doubly magic nuclei of ${}^{58,78}$Ni, and the nuclei featuring the $N=32$, $34$, and $40$ magic subshells. Use is made of the self-consistent theory of finite Fermi systems and the family of energy density functionals proposed by Fayans and his coauthors (DF3, DF3-a, …). The results are compared with experimental data and with the results of the calculations based on self-consistent models that employ new versions of the Fayans functional—Fy(std) and Fy(HFB, $\nabla r$), whose parameters were obtained by means of an extended optimization protocol—as well as with the results of ab-initio calculations performed on the basis of the renormalization-group model and with the results of the calculation with a density-dependent spin–orbit interaction stemming from three-nucleon forces. The weakening of odd–even staggering of radii of nuclei in the ISOLDE-CERN experiments as the nuclei approach the $N=50$ closed neutron shell is analyzed, and the possible mechanisms behind this weakening are considered. It is shown that the isotopic dependences of the charge radii and the total beta-decay energies are correlated.