Toward a new description of triaxial nuclei

Abstract

The liquid drop Hamiltonian is amended with a potential which allows us to separate, in the intrinsic frame, the equations for $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ coordinates. The Schr\"odinger equation for $\ensuremath{\beta}$ is that for a sextic oscillator plus a centrifugal term, while that for $\ensuremath{\gamma}$ is just the equation for the Mathieu function. The total energy has a compact form. The operator for the electric quadrupole transitions is considered in the intrinsic frame and involves two parameters accompanying the harmonic and anharmonic components. The parameters determining the energies as well as those defining the transition operator are to be determined by a fitting procedure. Applications refer to five isotopes: $^{188}\mathrm{Os}$, $^{190}\mathrm{Os}$, $^{192}\mathrm{Os}$, $^{228}\mathrm{Th}$, and $^{230}\mathrm{Th}$. Results are in good agreement with the corresponding experimental data. Results are also compared with those obtained within the coherent state model. A possible connection between the two formalisms is pointed out.