Ground state of electron-hole droplets

The free-particle state corresponding to the ground state of a plasma in a band structure composed of (a) $\nu$ valleys, (b) two valleys of different masses, (c) one "anisotropic" valley is studied. The Hartree-Fock approximation leads, for (a) and (b), to only one filled valley. Only intervalley correlations restore the unperturbed ground state (a), or a state close to (b), and make the droplets stable. For (c), the state is slightly more spherical than the free-particle ground state, but, in the three cases, the energy is not significantly changed.