Bohr Hamiltonian with P\"oschl Teller potential in {\gamma} unstable and {\gamma} stable pictures

TL;DR

This paper analytically solves the Bohr Hamiltonian with P"oschl Teller potential for both {b3} unstable and stable nuclei, deriving energy spectra and transition rates that closely match experimental data.

Contribution

It provides an exact analytical solution using the asymptotic iteration method for the Bohr Hamiltonian with P"oschl Teller potential, improving agreement with experimental transition rates.

Findings

Good agreement with experimental energy spectra and transition rates.

Transition rates are closer to experimental data than previous models.

Analytical solutions are obtained for both {b3} unstable and stable nuclei.

Abstract

In this paper, we present an analytical solution for the Bohr Hamiltonian with the trigonometric P\"oschl Teller (P.T) potential in the cases of {\gamma} unstable nuclei and {\gamma} stable axially symmetric prolate deformed ones with {\gamma} = 0. The energy spectra and corresponding wave functions are derived by means of the asymptotic iteration method. In addition, B(E2) transition rates are calculated and compared with experimental data. Overall good agreement is obtained for inter and intra band transitions within ground state and \b{eta} bands. Our numerical results, particularly for transition rates are much closer to experimental ones in comparison with those obtained by Davidson and Kratzer potentials which are widely used in the literature.