Unitary Fermi gas in a harmonic trap

We present an ab initio calculation of small numbers of trapped, strongly interacting fermions using the Green’s function Monte Carlo method. The ground-state energy, density profile, and pairing gap are calculated for particle numbers N=2–22 using the parameter-free “unitary” interaction. Trial wave functions are taken in the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that the energies can be well fitted by the expression a_TFE_TF+Δ mod(N,2) where E_TF is the Thomas-Fermi energy of a noninteracting gas in the trap and Δ is the pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value Δ=0.7±0.2ω for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.