  In this paper we introduce a current-current type interaction term in the
Lagrangian density of gravity coupled to complex scalar fields, in the presence
of a degenerated Fermi gas. For low transferred momenta such a term, which
might account for the interaction among boson and fermion constituents of
compact stellar objects, is subsequently reduced to a quadratic one in the
scalar sector. This procedure enforces the use of a complex radial field
counterpart in the equations of motion. The real and the imaginary components
of the scalar field exhibit different behaviour as the interaction increases.
The results also suggest that the Bose-Fermi system undergoes a BCS-like phase
transition for a suitable choice of the coupling constant.

General Relativity and Quantum Cosmology