### Abstract

Recent developments in the physics of low-density trapped gases make it worthwhile to verify old, well-known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground-state energy of a dilute gas of N fermions interacting with a short-range, positive potential of scattering length a. For spin-12 fermions, this is E∼E0+(22m)2πNa, where E0 is the energy of the noninteracting system and is the density. A similar formula holds in two dimensions (2D), with a replaced by ln(a2). Obviously this 2D energy is not the expectation value of a density-independent pseudopotential.

Original language | English (US) |
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Article number | 053605 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 71 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2005 |

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*71*(5), [053605]. https://doi.org/10.1103/PhysRevA.71.053605