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Dilute Fermi systems with large s-wave scattering length a_s exhibituniversal properties if the interparticle spacing r_o greatly exceeds the rangeof the underlying two-body interaction potential. In this regime, r_o is theonly relevant length scale and observables such as the energy per particledepend only on r_o (or, equivalently, the energy E_{FG} of the free Fermi gas).This paper investigates Bose and Fermi systems with non-vanishing angularmomentum l using the lowest order constrained variational method. We focus onthe regime where the generalized scattering length becomes large and determinethe relevant length scales. For Bose gases with large generalized scatteringlengths, we obtain simple expressions for the energy per particle in terms of al-dependent length scale \xi_l, which depends on the range of the underlyingtwo-body potential and the average interparticle spacing. We discuss possibleimplications for dilute two-component Fermi systems with finite l. Furthermore,we determine the equation of state of liquid and gaseous bosonic helium.

Equation of state of atomic systems beyond s-wave determined by the lowest order constrained variational method: Large scattering length limit