Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model

TL;DR

This paper extends the Interacting Vector Boson Model to include fermions via supersymmetry, successfully describing odd-mass nuclei spectra and transition probabilities, demonstrating the model's enhanced applicability to nuclear structure analysis.

Contribution

The paper develops a supersymmetric extension of IVBM using orthosymplectic groups to incorporate fermion degrees of freedom for odd-mass nuclei.

Findings

Accurately describes collective spectra of odd-mass nuclei

Predicts B(E2) transition probabilities consistent with experiments

Highlights the importance of symplectic structure in modeling transitions

Abstract

A supersymmetric extension of the dynamical symmetry group $Sp^{B}(12,R)$ of the Interacting Vector Boson Model (IVBM), to the orthosymplectic group $OSp(2\Omega/12,R)$ is developed in order to incorporate fermion degrees of freedom into the nuclear dynamics and to encompass the treatment of odd mass nuclei. The bosonic sector of the supergroup is used to describe the complex collective spectra of the neighboring even-even nuclei and is considered as a core structure of the odd nucleus. The fermionic sector is represented by the fermion spin group $SO^{F}(2\Omega)\supset SU^{F}(2)$. The so obtained, new exactly solvable limiting case is applied for the description of the nuclear collective spectra of odd mass nuclei. The theoretical predictions for different collective bands in three odd mass nuclei, namely $^{157}Gd$, $^{173}Yb$ and $^{163}Dy$ from rare earth region are compared with the experiment. The $B(E2)$ transition probabilities for the $^{157}Gd$ and $^{163}Dy$ between the states of the ground band are also studied. The important role of the symplectic structure of the model for the proper reproduction of the $B(E2)$ behavior is revealed. The obtained results reveal the applicability of the models extension.