  Based on self-consistent T-matrix approximation (SCTMA), the Mott insulator -
Bose-glass phase transition of one-dimensional noninteracting bosons subject to
binary disorder is considered. The results obtained differ essentially from the
conventional case of box distribution of the disorder. The Mott insulator -
Bose-glass transition is found to exist at arbitrary strength of the
impurities. The single particle density of states is calculated within the
frame of SCTMA, numerically, and (for infinite disorder strength) analytically.
A good agreement is reported between all three methods. We speculate that
certain types of the interaction may lead to the Bose-glass - superfluid
transition absent in our theory.
