A Study of Nuclear Shape Coexistence Near the Fifth Island of Inversion Using the Hartree–Fock plus Bardeen–Cooper–Schrieffer Method
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The evolution of shell structure and nuclear deformation in neutron-rich nuclei remains one of the major challenges in nuclear structure physics, particularly near regions associated with shell erosion and shape coexistence. In the present work, neutron-rich isotones with neutron numbers N=50 and N=34 are investigated within the Hartree–Fock (HF) plus Bardeen–Cooper–Schrieffer (BCS) framework using the Skyrme SLy5 parameterization. The potential energy surfaces (PES) are calculated as functions of the quadrupole deformation parameter β2 in order to determine the equilibrium nuclear shapes and examine the evolution of shell stability in neutron-rich systems. The calculated results for 70Ca show a nearly spherical minimum at β2 = 0.001 together with a weak oblate configuration, while 72Ti and 74Cr exhibit multiple competing minima corresponding to spherical, oblate, and prolate shapes, indicating pronounced shape coexistence and weakening of the traditional N=50 shell closure. For the N=34 isotones, 54Ca displays weak deformation with β2 = −0.052, supporting enhanced spherical stability, whereas 56Ti and 58Cr exhibit increasing prolate deformation with β2 = 0.101 and β2 = 0.151, respectively, reflecting stronger collective effects and shell evolution. These results indicate that proton-neutron correlations, pairing interactions, and deformation-driving orbitals play a significant role in the evolution of shell structure and the emergence of shape coexistence phenomena in neutron-rich nuclei.
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