Phase Separation in Isotopic Fermi-Bose Mixtures

An isotopic mixture of fermions and bosons has been investigated at a given pressure, using the hard sphere diameter $a$ as a perturbation parameter. The results agree with those obtained before at a given density. To first order in $a$ it is found that above a critical pressure the mixture separates into two coexisting phases. The phase separation curve has its top on the $\lambda$ curve of the mixture. The phase separation remains incomplete at $T=0\mathrm{}$ for a wide range of densities. The slopes at the top and the behavior near $T=0\mathrm{}$ of the phase separation curve have been computed. Also the osmotic pressure of dilute solutions has been obtained.