Application of the sextic oscillator potential together with Mathieu and spheroidal functions for triaxial and X(5) type nuclei

In this paper, we present new interesting solutions for the Bohr-Mottelson Hamiltonian. The Bohr-Mottelson Hamiltonian is amended with a potential which depends on both β and γ deformation variables and which allows us to separate the β variable from the other variables. The equation for the β variable is quasi-exactly solved for a sextic oscillator with centrifugal barrier potential. Concerning the γ equation, its solutions are the angular spheroidal and Mathieu functions for X(5) type and triaxial nuclei, respectively. The models developed in this way are conventionally called the Sextic and Spheroidal Approach (SSA) and the Sextic and Mathieu Approach (SMA). SSA and SMA have been successfully applied for several nuclei. Results are detailed for ¹⁹²Os, for which the best agreement with experimental data, for both energy spectrum and E2 transition probabilities, is obtained with SSA