The exact description of intruder states in ${}^{112}$Cd nucleus by using a mixing formalism based on $SU(1,1)$ transitional Hamiltonian and $O(6)$-Casimir operator

In this paper, we used a transitional Hamiltonian which has $U(5)\leftrightarrow (6)$ transition to improve theoretical predictions for energy spectra and quadrupole transition rates of ${}^{112}$Cd nucleus. To this aim, the transitional Hamiltonian in the affine $SU(1,1)$ algebra has been extended by adding the $O(6)$-Casimir operator and mixing Hamiltonian to increase exactness in the description of 4${}_2^{+}$ and 2${}_3^{+}$ intruder levels of this nucleus. We also considered the wave functions of both regular and intruder states, as a combination in the $N$ and $N+2$ boson spaces. The results confirm the advantages of using such mixing approaches and describing the energy and transition rates with high accuracy