Sextic potential for γ-rigid prolate nuclei
Abstract
The equation of the Bohr-Mottelson Hamiltonian with a sextic oscillator potential is solved for γ-rigid prolate nuclei. The associated shape phase space is reduced to three variables which are exactly separated. The angular equation has the spherical harmonic functions as solutions, while the β equation is brought to the quasi-exactly solvable case of the sextic oscillator potential with a centrifugal barrier. The energies and the corresponding wave functions are given in closed form and depend, up to a scaling factor, on a single parameter. The 0+ and 2+ states are exactly determined, having an important role in the assignment of some ambiguous states for the experimental β bands. Due to the special properties of the sextic potential, the model can simulate, by varying the free parameter, a shape phase transition from a harmonic to an anharmonic prolate β-soft rotor crossing through a critical point. Numerical applications are performed for 39 nuclei: 98-108Ru, 100,102Mo, 116-130Xe, 132,134Ce, 146-150Nd, 150,152Sm, 152,154Gd, 154,156Dy, 172Os, 180-196Pt, 190Hg and 222Ra. The best candidates for the critical point are found to be 104Ru and 120,126Xe, followed closely by 128Xe, 172Os, 196Pt and 148Nd.
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