Density profile of a harmonically trapped ideal Fermi gas in arbitrary   dimension
  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 $\delta n/n\sim N^{-\alpha}$, where $\alpha=(1+1/d)/2$. 
Erich J. Mueller (Cornell)