Natural and unnatural parity states of small trapped equal-mass   two-component Fermi gases at unitarity and fourth-order virial coefficient
  Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large s-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the (2,2) and (3,1) systems at unitarity as a function of the range $r_0$ of the underlying two-body potential and extrapolate to the $r_0 \rightarrow 0$ limit. Our calculations include all states with vanishing and finite angular momentum $L$ (and natural and unnatural parity $\Pi$) with relative energy up to $10.5 \hbar \Omega$, where $\Omega$ denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1% or smaller. The (2,2) and (3,1) energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the (3,2) and (4,1) systems at unitarity. 
D. Rakshit, K. M. Daily, D. Blume
cond-mat.quant-gas