Critical Point of the 152Sm, 154Gd, and 156Dy Isotones

Abstract

The even—even rare-earth nuclei in U(5)—SU(3) region at neutron number (N) = 90, have been systematically studied using the Bohr—Mottelson Model (BM), Interacting Vector Boson Model (IVBM), and Interacting Boson Model (IBM). The positive ground-state band (GSB) of ¹⁵²Sm, ¹⁵⁴Gd, and ¹⁵⁶Dy nuclei has been calculated by using BM, IVBM, and IBM, while the negative-parity band (NPB) of those nuclei are calculated by BM and IVBM only. To determine the intermediate structure, the ratio (r(I + 2)/I) and E-GOS curve (E-Gamma Over Spin) as a function of the spin (I) have been drawn. In the IBM, the calculated reduced B(E2) transition probabilities of the GSB in the ¹⁵²Sm, ¹⁵⁴Gd, and ¹⁵⁶Dy nuclei are analyzed and compared to the prediction of vibrational U(5) and rotational SU(3) limits. In the Sm—Dy nuclei with N = 90, the U(5)—SU(3) IBM potential energy surfaces (PES’s) are analyzed and evolve from spherical to deformed shapes with increasing the boson number. The critical phase transition points are identified in the space of model parameters and ¹⁵²Sm,¹⁵⁴Gd, and ¹⁵⁶Dy nuclei have been found to be close to critical points.