Algebraic Solutions for $U^{BF}(5)-O^{BF}(6)$ Quantum Phase Transition in Odd Mass Number Nuclei

TL;DR

This paper develops algebraic solutions within the interacting boson-fermion model to describe the $U^{BF}(5)-O^{BF}(6)$ quantum phase transition in odd-mass nuclei, supported by experimental data on Ba and Rh isotopes.

Contribution

It introduces a new algebraic solution for odd-A nuclei using dual algebraic structures and affine $SU(1,1)$ Lie algebra, extending the interacting boson-fermion model.

Findings

Energy spectra match experimental data

Calculated B(E2) transition rates agree with observations

Identified signatures of the phase transition in specific isotopes

Abstract

The spherical to deformed $\gamma -unstable$ shape- phase transition in odd-A nuclei is investigated by using the Dual algebraic structures and the affine $SU(1,1)$ Lie Algebra within the framework of the interacting boson - fermion model. The new algebraic solution for A-odd nuclei is introduced. In this model, Single $j = 1/2 $ and $ 3/2 $ fermions are coupled with an even-even boson core. Energy spectra, quadruple electromagnetic transitions and an expectation value of the d-boson number operator are presented. Experimental evidence for the $U^{BF} (5)-O^{BF} (6)$ transition in odd -A $Ba$ and $Rh$ isotopes is presented. The low-states energy spectra and $B(E2)$values for these nuclei have been also calculated and compared with the experimental data.