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Physical Review Letters

Universal Shapes of Small Fermion Clusters

Hannu Häkkinen, J. Kolehmainen, M. Koskinen, P.O. Lipas, M. Manninen

Published Feb 10, 1997• 52 citations
Publisher

Abstract

Small atomic nuclei and clusters of alkali-metal atoms have similar shapes. We show that this similarity is a universal result of the density-functional theory. The shapes and the odd-even staggering of the total energy are nearly independent of the interactions between the fermions.
DOI
10.1103/physrevlett.78.1034

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In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the energy density of the free Fermi gas with a proportionality constant $\ensuremath{\xi}$. The author uses a simple density functional parametrized by an effective mass and the universal constant $\ensuremath{\xi}$, and employs Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\ensuremath{\xi}=0.42$ and a rather large effective mass. The form of the density functional is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.
Abstract We select a couple of density functional formalisms suitable for the computation of the highest spin clusters composed of a small number of heavy alkali-metal atoms such as Rb and Cs. Using B3P86 and PW91PW91 density functional methods with Lanl2dz basis set, we analyze the geometry, the binding energy, and the bond length of Rbn and Csn with n = 2–14 in the highest spin state. The exchange energy of the highest spin clusters increases the binding energy with the number of the constituent atoms.
We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density functional and determines the corrections from the analyical results for the harmonically trapped two-body system. The corrections due to the finite scattering length compare well with the result of Monte Carlo simulations. We also apply our results to symmetric neutron matter.