Particle-Hole Symmetry in Generalized Seniority, Microscopic Interacting Boson (Fermion) Model, Nucleon-Pair Approximation, and Others

TL;DR

This paper demonstrates that particle-hole symmetry is preserved in truncated shell-model subspaces based on generalized seniority and explores its implications in various nuclear models.

Contribution

It provides an explicit transformation between particle and hole representations within generalized seniority truncations and analyzes symmetry preservation in related nuclear models.

Findings

Particle-hole symmetry holds in generalized seniority truncated spaces.

Explicit transformation between particle and hole states is derived.

Symmetry is preserved in models like the interacting boson and nucleon-pair approximation.

Abstract

The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work we show that this symmetry is preserved in the subspace truncated at a certain generalized seniority, and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, we study the particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nucleon-pair approximation, and others.