Effect of impurity modes with quasilocal and local frequencies on the superconducting transition temperature

An anisotropic irregular semiconductor is under consideration. It is believed that the effective parameter of the interaction-lambda-which determines electron coupling is less or about 0.5. The Eliashberg integral equation system is solved for T→Tsub(c). A simple analytic expression is obtained for Tsub(c). The character of a varying critical temperature in superconductors with impurity atoms is analyzed in detail. The dependence of the critical temperature on parameters describing the phonon spectrum of an impurity system is investigated. The existence of impurity modes with quasilocal and local frequencies in the phonon spectra can lead both to relatively small and to rather noticeable variations in Tsub(c). The first case is typical of the situation when an impurity atom is practically an isotopic defect. If an impurity atom is very heavy (Msub(I)<>γ0) coupled with matrix atoms. A sharp decrease in the effective force constant γ1 for an impurity atom results in the growth of delta Tsub(c): delta Tsub(c) approximately cγ0/γ1(lambda - μsup((0)). On the contrary a rise in the γ1 value requires a negative correction to Tsub(c), and delta Tsub(c) approximately c/(lambda - μsup((0)), where c - an impurity concentration, μ - matrix element of the Coulomb screened interaction averaged over the Fermi surface and multiplied for the density of normal electron states on the Fermi level. Comparison with experimental data is made. A qualitative description of the Tsub(c) change due to the impurity presence is given for a set of solutions. There is a satisfactory quantitative agreement between calculated and experimental values of delta Tsub(c)