  Mean-field theory of non-interacting disordered electron systems is widely
and successfully used to describe equilibrium properties of alloys in the whole
range of disorder strengths. It, however, fails to take into account effects of
quantum coherence and localizing back-scattering effects when applied to
transport phenomena. We present an approximate scheme extending the mean-field
theory for one-electron properties in that it offers a formula for the
two-particle vertex and the electrical conductivity non-perturbatively
including the leading-order vertex corrections in a way that the approximation
remains consistent and the conductivity non-negative in all disorder regimes.
