Study Effect of Majorana Coefficient on the Energy Levels of 138-144,148Gd Even-Even Isotopes Using IBM-2

Abstract

The mixed symmetry state property (MSS) for even-even ^138-144,148Gd isotopes was studied using the IBM-2. This model discovered and emphasized various empirically questionable states and provided good agreement for the excited energy levels for the g-band and acceptable for the β and γ bands. The effect of the Majorana parameter  was studied as a function of changing the mixing symmetry of the levels  using three different values ​​(0.005, 0.02, and 0.04) and the value of the Majorana parameter  was almost constant. By increasing the Majorana parameter to the values ​​(0.02 and 0.04), the mixing levels began to appear clearly, especially the levels . Energy level and energy ratios showed that ¹³⁸Gd, ¹⁴⁰Gd are between rotational SU(3) and gamma-unstable O(6) symmetries and ¹⁴²Gd, ¹⁴⁴Gd, and ¹⁴⁸Gd are transitional nuclei among gamma-unstable O(6) to vibrational SU(5) symmetries. The results of theoretical and practical energy levels were in good agreement.