A Simple Systematical Law of E_²1⁺ Values for Heavy Nuclei in the N_pN_n Scheme and the Evolution of the Z=64 Shell Gap

A systematics of excitation energy of the first 2⁺ state E_²1⁺ in even--even heavy nuclei (A≥120) is studied in the N_pN_n scheme. It is found that a simple exponential function describes the dependence of E_²1⁺ values on N_pN_n values very well. In addition, the Z=64 shell gap is reexamined by investigating the systematics of the 52≤Z≤66 region. It is found that the
Z=64 shell gap is largest at N=82 and becomes smaller with either
increasing or decreasing of neutron numbers. The effects of this shell gap become negligible for counting the valence proton numbers when N≥92 or N≤72.