Ground state of isotopic fermion-boson mixtures

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Abstract
An investigation of the ground-state configuration of isotopic fermion-boson mixtures is reported for both two and three dimensions. A detailed numerical study of systems interacting with Lennard-Jones-type potentials is presented, enabling one to interpert these results in terms of a picture of the fermion-boson mixture as being built up from an "underlying" boson-boson mixture. It is thus possible to argue that the presence of Fermi-Dirac statistics in one of the constituents is a necessary condition for miscibility in the ground state of an isotopic mixture. Further a criterion is presented for the fermion chemical potentials which is used to distinguish those mixture systems whose ground state is complete separation from those systems whose ground state is at least partially mixed. Finally the analysis is applied to the helium and spin-polarized hydrogen isotopic mixtures (in two and three dimensions) and, wherever possible, the calculated numbers are compared to experiment.