https://doi.org/10.1140/epjp/s13360-021-01451-7
Regular Article
U(5) and O(6) shape phase transitions via E(5) inverse square potential solutions
Department of Physics, University of Ilorin, Ilorin, Kwara State, Nigeria
Received:
13
January
2021
Accepted:
16
April
2021
Published online:
6
May
2021
The inverse square potential is used to provide the ‘pictures’ of the transitions symmetry from U(5) to O(6) via the variational procedure of the E(5) solutions. The variation of the single-parameter 
of the inverse square potential shifts the E(5) solutions: the energy eigenvalues increase when increases. In the theoretical prediction of 
, 
yields solutions that correspond to the U(5) symmetry of the Bohr Hamiltonian with 
. As increases, the solutions of E(5) materialize with 
at 
. The solutions leave E(5) and approach O(6) with 
at 
. The solutions of 
and 
of the E(5) symmetry candidates are fitted and compared with the available experimental values. With the same variational method, the ratios of B(E2) transition rates within the ground state leave O(6) and approach E(5) solution as increases.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
