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

TL;DR

This paper introduces the Sextic and Mathieu Approach (SMA), a new analytical model for describing triaxial nuclei by supplementing the Liquid Drop Model with specific potentials, and compares its results with the Coherent State Model.

Contribution

It derives SMA equations analytically from a semi-classical treatment of the CSM Hamiltonian, providing a more natural potential formulation for triaxial nuclei.

Findings

SMA applied successfully to $^{180}$Hf and $^{182}$W.

SMA results are compared with those from the Coherent State Model.

Analytical derivation of SMA from CSM enhances understanding of nuclear shape modeling.

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 $\beta$ and a potential in $\gamma$ with a minimum in $\frac{\pi}{6}$, the Sch\"{o}dinger 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 $\beta$ and $\gamma$ variables respectively, show up in a quite natural way which contrasts their ad-hoc choice when SMA emerges from LDM.