  A many-flavor electron gas (MFEG) is analyzed, such as could be found in a
multi-valley semiconductor or semimetal. Using the re-derived polarizability
for the MFEG an exact expression for the total energy of a uniform MFEG in the
many-flavor approximation is found; the interacting energy per particle is
shown to be -0.574447E_h a_0^3/4 m*^3/4 n^1/4 with E_h being the Hartree
energy, a_0 Bohr radius, and m^* particle effective mass. The short
characteristic length-scale of the MFEG motivates a local density
approximation, allowing a gradient expansion in the energy density, and the
expansion scheme is applied to electron-hole drops, finding a new form for the
density profile and its surface scaling properties.
