Density profile of a harmonically trapped ideal Fermi gas in arbitrary dimension

Abstract

Closed form analytic expressions are derived for the density profile of a harmonically trapped noninteracting Fermi gas in $d$ dimensions. Shell structure effects are included to leading order in 1/N, where $N$ is the number of particles. These corrections to the local density approximation scale as $δn/n\sim N^{-α}$, where $α=(1+1/d)/2$.