^aInformation Processing and Telecommunication Laboratory, Department of

Electrical Engineering, Faculty of Technology, University TAHRI Mohammed

Bechar, Algeria

^bPhysics of Radiations and their Interaction with Matter Laboratory, Department of Physics, Faculty of Matter Sciences, University of Batna 1, Batna, Algeria

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 40,48Ca 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 40Ca core. The calculated energies E (2) of the first excited

state, the ratio R4/2 of the excitation energies, the reduced electric transition

probabilities B(E2; 2 → 0) 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.