Equation of state of cold atoms: A lowest-order-constrained variational study of systems with large non- s-wave scattering lengths

Dilute Fermi systems with large s-wave scattering length a_s exhibit universal properties if the interparticle spacing r₀ greatly exceeds the range of the underlying two-body interaction potential. In this regime, r₀ is the only relevant length scale and observables such as the energy per particle depend only on r₀ (or, equivalently, the energy E_FG of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum l using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an l-dependent length scale ξ_l, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite l. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.