Cluster states of fermions in the single l-shell model

Gour, Jeffrey R.

András Csordás, Szoke, Eva, P. Szépfalusy

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.

Dieter Ihle

Sarai Dery Folkestad, Kristine Lauvstad Kruken, Henrik Koch A

We present a spin-adapted coupled cluster singles and doubles model for the excitation energies of molecular doublets. The entanglement coupled cluster approach represents an unconventional take on the notorious problem of spin adaptation for open-shell species. In this approach, the high-spin open-shell molecular system is coupled to non-interacting bath orbitals to form a total closed-shell system. In entanglement coupled cluster theory, many of the attractive features of the spin-adapted closed-shell coupled cluster are retained: an unambiguous definition of the cluster operator and a terminating Baker-Campbell-Hausdorff expansion. The model produces excitation energies of a quality comparable to that of the closed-shell counterpart. Additionally, some ionized states that cannot be modeled accurately with the alternative equation-of-motion approach for ionized states can be described with the entanglement coupled cluster singles and doubles model.

András Csordás, P. Szépfalusy, Éva Szőke

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.