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

TL;DR

This paper enhances the theoretical modeling of the $^{112}$Cd nucleus by combining $SU(1,1)$ algebra and $O(6)$-Casimir operators to accurately describe intruder states and energy spectra.

Contribution

It introduces a novel mixing formalism based on an extended $SU(1,1)$ Hamiltonian with $O(6)$-Casimir operator for better intruder state description.

Findings

Improved energy spectrum predictions for $^{112}$Cd.

High-accuracy quadrupole transition rate calculations.

Effective description of intruder states using mixing formalism.

Abstract

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