Energy staggering in superdeformed bands for isodiaphere nuclei in A ~ 40-60 mass region

Abstract

The properties of superdeformed (SD) bands of isodiaphere nuclei ( 𝐶𝑎 40 , 𝐶𝑢 58 , 𝑍𝑛 60) have been studied in the scope of four and five parameters' formulas of the Bohr-Mottelson collective model. The unknown parameters are obtained by fitting the experimental measurements of the gamma-ray transition energies using MATLAB software. The rotational frequency ℏ𝜔, the kinematic 𝐽 (1) , and dynamic 𝐽 (2) moments of inertia are determined by using the best fitted parameters. The obtained 𝛾-ray transition energies 𝐸𝛾 are in good agreement with the experimental measurements. Also, the theoretical results of the kinematic 𝐽 (1) , and dynamic 𝐽 (2) moments of inertia using both formulas agree well with the experimental data. The staggering Δ𝐼 = 2 phenomenon is represented by using various order derivatives of -ray transition energies 𝐸 𝛾 with respect to spin angular momentum I. We conclude that the five parameters formula of Bohr-Mottelson collective model successes in interpreting the appeared pairing correlations in the experimental measurements for the studied nuclei.