Application of the sextic oscillator with a centrifugal barrier and the spheroidal equation for some X(5) candidate nuclei

Abstract

The eigenvalue equation associated with the Bohr–Mottelson Hamiltonian is considered in the intrinsic reference frame and amended by replacing the harmonic oscillator potential in the β variable with a sextic oscillator potential with centrifugal barrier plus a periodic potential for the γ variable. After the separation of variables, the β equation is quasi-exactly solved, while the solutions for the γ equation are just the angular spheroidal functions. An anharmonic transition operator is used to determine the reduced E2 transition probabilities. The formalism is conventionally called the sextic and spheroidal approach (SSA) and applied for several X(5) candidate nuclei: 176, 178, 180, 188, 190Os, 150Nd, 170W, 156Dy and 166, 168Hf. The SSA predictions are in good agreement with the experimental data of the mentioned nuclei. The comparison of the SSA results with those yielded by other models, such as X(5) (Iachello 2001 Phys. Rev. Lett.87052502), infinite square well (Raduta et al 2009 Nucl. Phys.A 81946) and Davidson like potential (Raduta et al) for the β, otherwise keeping the spheroidal functions for the γ , and the coherent state model (Raduta et al 1981 Phys. Lett. B 99 444, Raduta et al 1982 Nucl. Phys.A 381 253, Raduta et al 1987 Phys. Rev. C 36 2111, Raduta et al 1983 Z. Phys. A 313 69, Raduta et al 1997 Phys. Rev. C 55 1747, Raduta et al 2002 Phys. Rev. C 65 064322, Raduta and Sabac 1983 Ann. Phys., NY 148 1, Raduta 2004 Recent Research Developments in Nuclear Physics vol 1) respectively, suggests that SSA represents a good approach to describe nuclei achieving the critical point of the U(5)→SU(3) shape phase transition.