Cluster states of Fermions in the single l-shell model

TL;DR

This paper investigates the ground state structures of fermionic gases in a single l-shell, revealing cluster formations of (2s+1) atoms and deriving energy expressions for these multi-cluster states.

Contribution

It introduces a cluster-based framework for understanding the ground states of fermionic gases in a single l-shell, including explicit energy formulas.

Findings

Clusters of (2s+1) atoms form in the ground state.

Explicit energy expressions for multi-cluster states are derived.

Cluster states depend on particle number and shell parameters.

Abstract

The paper concerns the ground state structure of the partly filled l-shell of a fermionic gas of atoms of spin s in a spherically symmetric spin independent trap potential. At particle numbers N=n(2s+1), n=1,2,...,2l+1 the basic building blocks are clusters consisting of (2s+1) atoms, whose wave functions are completely symmetric and antisymmetric in space and spin variables, respectively. The creation operator of a cluster is constructed whose repeated application to the vacuum leads to the multi-cluster state. Ground state energy expressions are derived for the n-cluster states at different l,s values and interpreted in simple terms.