https://doi.org/10.1140/epjp/s13360-021-02276-0
Regular Article
X(5) Critical symmetry with inverse square potential via a variational procedure
Department of Physics, University of Ilorin, Ilorin, Kwara State, Nigeria
Received:
22
July
2021
Accepted:
7
December
2021
Published online:
5
January
2022
In the regime of the inverse square potential, the 
transition symmetry solutions of the Bohr Hamiltonian via the variational procedure are presented: the solutions for the energies, the wave functions and the B(E2) transitional rates are obtained. The forward variation of the ‘control parameter’, 
, associated with the inverse square potential shifts the solutions from X(5) to SU(3): the energies increase with the increase in . In the theoretical prediction of 
, 
yields X(5) solutions of the Bohr Hamiltonian with 
and 
. As increases, the solutions leave X(5) and tend to SU(3) solutions with a ‘signature’, 
at 
. With the 
and the 
distributions, some X(5) candidates are mapped in the region. The solutions of the X(5) and the SU(3) symmetry candidates are fitted and compared with the available experimental data.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
