Shell-model calculations of the spectroscopic properties of neutron-rich calcium isotopes around 40,48Ca cores

Abstract

With the aim of predicting the possible existence of new magic numbers, we theoretically studied the recently available experimental data for spectroscopic properties of the neutron rich even-even calcium isotopes around Ca 40,48 doubly magic cores. The calculations were performed with the phenomenological interactions for fppn and HO model spaces using the nuclear structure code Nushell. The two-body matrix elements (TBMEs) of the new effective interaction KB3G48 were derived from the microscopic Kuo-Brown’s G-matrix interaction KB3GPN for Ca 40 core. The calculated energies 𝐸(21 +) of the first excited state, the ratio 𝑅4/2 of the excitation energies, the reduced electric transition probabilities 𝐵(𝐸2; 21 + → 01 +) and the ratio 𝐵4/2 of reduced transition probabilities are compared with the available experimental data. The results of this study are an attempt to demonstrate that 𝑁 = 32 or 𝑁 = 34 are new magic numbers for Ca isotopes.