  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_o (or, equivalently, the energy E_{FG} of the free Fermi gas).
This paper investigates Bose and Fermi systems with non-vanishing 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 a
l-dependent length scale \xi_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.
