Investigation of electron densities of states of superconducting transition metals with nonmagnetic impurity

The densities of electron states of superconducting transition metals with nonmagnetic impurity are calculated in the whole range of frequencies in the limiting cases $\alpha_2\ll1$, $\alpha_1\sim 1$ and $\alpha_1\gg 1$, $\alpha_2\sim 1$ for $\zeta=\Gamma_1/\Gamma_2<1$. Under these assumptions concerning the parameters $\alpha_n$ and $\zeta$, expressions are obtained for the energy gap $\omega_g$ and a detailed investigation is made of the densities of electron states $n_n(\omega)$ of both bands as functions of the frequency and impurity concentration. It is shown that the density of states $n_1(\omega)$ in the case $\alpha_2\ll1$, $\alpha_1\sim 1$ has two maxima of the same order, one near $\omega_g$ and the other near $\Gamma_2$. The density of states $n_2(\omega)$ has a maximum that is an order of magnitude greater than that of $n_1(\omega)$ in the neighborhood of $\Gamma_2$. In the case of a high impurity concentration ($\alpha_1\gg 1$, $\alpha_2\sim 1$) the energy gap comes close to the order parameter $\Gamma_2$. It is assumed here that $\zeta=\Gamma_1/\Gamma_2<1$. The maxima of the densities of electron states of both bands, $n_n(\omega)$, are obtained at frequencies near the parameter $\Gamma_2$.