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 $β$ and a potential in $γ$ with a minimum in $\fracπ{6}$, 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 $β$ and $γ$ variables respectively, show up in a quite natural way which contrasts their ad-hoc choice when SMA emerges from LDM.

13 figures, 13 pages