Persistence of the N=50 shell closure over the isotopic chains of Sc, Ti, V and Cr nuclei using relativistic energy density functional

Abstract

The analytical expression of the density-dependent binding energy per nucleon for the relativistic mean field (RMF), the so-called relativistic energy density functional (Relativistic-EDF), is used to obtain the isospin-dependent symmetry energy and its components for the isotopic chain of Sc-, Ti-, V- and Cr-nuclei. The procedure of the coherent density fluctuation model is employed to formulate the Relativistic-EDF and Brüeckner energy density functional (Brüeckner-EDF) at local density. A few signatures of shell and/or sub-shell closure are observed in the symmetry energy and its components, i.e. surface and volume symmetry energy, far from the [Formula: see text]-stable region for odd-[Formula: see text] Sc- and V-, and even–even Ti- and Cr- nuclei with nonlinear NL3 and G3 parameter sets. A comparison is made with the results obtained from Relativistic-EDF and Brüeckner-EDF with both NL3 and G3 for the considered isotopic chains. We find Relativistic-EDF outperforms the Brüeckner-EDF in predicting the shell and/or sub-shell closure of neutron-rich isotopes at [Formula: see text] for these atomic nuclei. Moreover, a relative comparison has been made for the results obtained with the nonlinear NL3 and G3 parameter sets.