Properties of nonadiabatic superconducting systems with paramagnetic impurity

We present the basic system of equations for a theory of superconductivity for systems with chaotically distributed paramagnetic impurities of substitution in which the Migdal theorem is violated (it cannot be supposed ω₀ ≪ E_F ). We take into account electron–phonon and impurity diagrams as well as supplementary ones corresponding to the intersection of electron–phonon and electron–impurity lines. Decrease of the quantity T_C with increase of impurity concentration is shown to weaken in comparison with the case of the usual superconductors. The degree of this decrease is determined by quantities m and q_c. The coefficient of the isotope effect α, energy gap and order parameter at T = 0 are also calculated. The behaviour of these quantities as a function of impurity concentration depends on the Migdal parameter m = ω₀ /E_F and transferred momentum q_c.