Eur. Phys. J. D 42, 113-124 (2007)
https://doi.org/10.1140/epjd/e2007-00012-2

Cluster states of fermions in the single l-shell model

¹ Research Group for Statistical Physics of the Hungarian Academy of Sciences, Pázmány P. Sétány 1/A, 1117 Budapest, Hungary
² Department of Physics of Complex Systems, Eötvös University, Pázmány P. Sétány 1/A, 1117 Budapest, Hungary
³ Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences, P.O. Box 49, 1525 Budapest, Hungary

Corresponding author: ^a csordas@tristan.elte.hu

Received: 28 September 2006
Revised: 14 December 2006
Published online: 19 January 2007

Abstract

The paper deals with 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 and applied also to create multi cluster states. Ground state energy expressions are derived for the n-cluster states at different l, s values and interpreted in simple terms.