Equation of state of Bose and Fermi systems beyond s-wave determined by the lowest order constrained variational method: large scattering length limit

Dilute Fermi systems with large $s$-wave scattering length $a_s$ exhibit universal properties if the interparticle spacing $r_o$ greatly exceeds the range of the underlying two-body interaction potential. In this regime, $r_o$ is the only relevant length scale and observables such as the energy per particle depend only on $r_0$ (or, equivalently, the energy $E_{FG}$ of the free Fermi gas). We investigate Bose and Fermi systems with non-vanishing angular momentum using the lowest order constrained variational (LOCV) method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales at unitarity. We obtain simple expressions for the energy per particle in terms of a combined $l$-dependent length scale $\xi_l$. For example, within the LOCV framework the energy per particle of $p$-wave and $d$-wave interacting fermions depends not only on $E_{FG}$, as in the case of $s$-wave fermions, but also on an energy scale that depends on the range of the underlying two-body potential. Furthermore, we investigate the behaviors of $s$-wave interacting Bose and Fermi systems in the non-universal, density-dependent regime. *Supported by NSF.