Partial dynamical symmetry in Bose-Fermi systems

TL;DR

This paper extends the concept of partial dynamical symmetry to Bose-Fermi systems, demonstrating that certain states can preserve symmetry exactly while others are mixed, with an application to the nucleus $^{195}$Pt.

Contribution

It introduces a generalized framework for partial dynamical symmetry in systems with interacting bosons and fermions, providing a new approach to analyze nuclear spectral features.

Findings

Spectral analysis of $^{195}$Pt shows partial symmetry preservation.

Selected states in the model are exactly solvable with preserved symmetry.

The approach offers insights into symmetry breaking in mixed systems.

Abstract

We generalize the notion of partial dynamical symmetry (PDS) to a system of interacting bosons and fermions. In a PDS, selected states of the Hamiltonian are solvable and preserve the symmetry exactly, while other states are mixed. As a first example of such novel symmetry construction, spectral features of the odd-mass nucleus $^{195}$Pt are analyzed.