Shape evolution: An insight from the ground state bulk and surface properties of N(Z)=38, 40, and 42 series

The evolution of shape in finite nuclei shows tremendous changes in nuclear structure properties within the nuclear Segre chart. The neutron-rich nuclei around mass A~100 are important due to the changing behavior of nuclear shapes across isotopic chains. We have investigated the ground state bulk properties of nuclei for N(Z)=38, 40 and 42 isotonic(isotopic) series within the covariant density functional theory using the DD-ME2 (finite range) and DD-PC1 (zero range) interactions. A search for the shell closure at and around N(Z)~40 has been done in the chosen isotopic and isotonic series. The impact of shape evolution or deformation on nuclear charge radii and the surface properties has been analyzed in the mass region of about 70~100. The surface properties such as the symmetry energy, neutron pressure, and symmetry energy curvature have been studied using the coherent density fluctuation model. The study gives the correlation of symmetry energy and its coefficients with the nuclear quadrupole deformation. On ignoring the effects of shape evolution, a good correlation of the surface properties can be obtained with the neutron skin-thickness of nuclei. N(Z)=40 is found to behave as a magic number in the Z(N) = 40 and 42 series, and N(Z) = 38 as a deformed magic in Z(N) = 38 series only. In addition, a deformed magic behavior is obtained at N = 58 across all the isotopic series corresponding to both DD-ME2 and DD-PC1 interactions. While the magicity of N = 70 is suggested by DD-ME2 interaction. The symmetry energy of nuclei is changed by an amount of 1-2 MeV on varying the quadrupole deformation.