New features of the triaxial nuclei described with a coherent state model

Abstract

Supplementing the Liquid Drop Model (LDM) Hamiltonian, written in the intrinsic reference frame, with a sextic oscillator plus a centrifugal term in the variable ${\hat{I}}^2$ and a potential in ${\hat{I}}^3$ with a minimum in $\frac{\ddot{I}}{€}6$, the Schödinger equation is separated for the two variables which results in having a new description for the triaxial nuclei, called Sextic and Mathieu Approach (SMA). SMA is applied for two non-axial nuclei, ${}^{180}$Hf and ${}^{182}$W and results are compared with those yielded by the Coherent State Model (CSM). As the main result of this paper we derive analytically the equations characterizing SMA from a semi-classical treatment of the CSM Hamiltonian. In this manner the potentials in ${\hat{I}}^2$ and ${\hat{I}}^3$ variables respectively, show up in a quite natural way which contrasts their ad-hoc choice when SMA emerges from LDM.

13 figures, 13 pages