Clustering of Fermi particles with arbitrary spin

TL;DR

This paper analyzes a model of fermions with arbitrary spin in a single l-shell, exactly solving for spectra and eigenvectors, revealing cluster formations of (2s+1) particles in the ground state.

Contribution

It provides an exact solution for a fermionic system with arbitrary spin and demonstrates cluster formation in the ground state, extending the understanding of pairing beyond traditional models.

Findings

Exact spectra and eigenvectors for various l, s, N values.

Ground state clusters of (2s+1) particles when N=mu(2s+1).

Relevance to more general and homogeneous systems.

Abstract

A single l-shell model is investigated for a system of fermions of spin s and an attractive s-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different l, s values and particle numbers N. As a generalization of Cooper pairing it is shown that when N=mu(2s+1), mu=1,2,...,2l+1, the ground state consists of clusters of (2s+1) particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.