The Fermionic Density-functional at Feshbach Resonance

Abstract

We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature.The atoms interact via a short range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second order perturbation theory, has the same density dependence as the first order exchange energy, and the two almost exactly cancel each other at Feshbach resonance irrespective of the shape of the potential, provided $(\mu r_s)>>1$. Here $(\mu {)}^{-1}$ is the range of the two-body potential, and $r_s$ is defined through the number density $n=3/(4\pi r_s^3)$. The implications of this result for universality is discussed.

Five pages, one table. accepted for publication in PRA

References in corpus (6)

• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Observation of Bose-Einstein Condensation of Molecules
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Density-functional theory for fermions in the unitary regime
• Density functional theory for fermions close to the unitary regime