Bohr Hamiltonian for gamma=0 with Davidson Potential

TL;DR

This paper derives an analytical gamma-rigid solution of the Bohr Hamiltonian with Davidson potential, called X(3)-D, providing energy spectra, wave functions, and transition rates, and investigates its critical point status.

Contribution

It introduces the X(3)-D model, a new analytical solution for gamma=0 using Davidson potential, and applies a variational method to identify its critical point characteristics.

Findings

Derived energy eigenvalues and wave functions for X(3)-D

Calculated B(E2) transition rates

Identified the model's position at the critical point between spherical and deformed nuclei

Abstract

A gamma-rigid solution of the Bohr Hamiltonian is derived for gamma=0 utilizing the Davidson potential in the beta variable. This solution is going to be called X(3)-D. The energy eigenvalues and wave functions are obtained by using an analytic method which has been developed by Nikiforov and Uvarov. BE(2) transition rates are calculated. A variational procedure is applied to energy ratios to determine whether or not the X(3) model is located at the critical point between spherical and deformed nuclei.