Superconductivity in systems with a low particle density

A regular procedure for going over from the Fermi picture to the Bose picture of elementary excitations is proposed for Fermi systems with a low density of charge carriers. The residual interaction between bosons can be taken into account. The possibility of describing a low-density system in the mean-field approximation is analyzed. Systems which are equivalent from the standpoint of the mean-field approach may differ substantially in the strength of the residual interactions and thus in the nature of the transition to the condensed state. When a system contains localized impurity states, the interaction of the carriers with impurities can be described through renormalization of the binding energy of the two-particle state. This energy is increased by virtual transitions of particles from the band to impurity levels. 10 refs., 1 fig