A superconductor with 4-fermion attraction, considered by Ma\'{c}kowiak and
Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic
interaction V between conduction fermions and localized distinguishable spin
1/2 magnetic impurities. V has the form of a reduced s-d interaction. An
upper and lower bound to the system's free energy density f(H,β) is
derived and the two bounds are shown to coalesce in the thermodynamic limit.
The resulting mean-field equations for the gap Δ and a parameter y,
characterizing the impurity subsystem are solved and the solution minimizing
f is found for various values of magnetic coupling constant g and impurity
concentration. The phase diagrams of the system are depicted with five distinct
phases: the normal phase, unperturbed superconducting phase, perturbed
superconducting phase with nonzero gap in the excitation spectrum, perturbed
gapless superconducting phase and impurity phase with completely suppressed
superconductivity.Comment: 21 pages, 3 figure