  In the present paper we propose a doubly orbitally degenerate narrow-band
model with correlated hopping. The peculiarity of the model is taking into
account the matrix element of electron-electron interaction which describes
intersite hoppings of electrons. In particular, this leads to the concentration
dependence of the effective hopping integral. The cases of the strong and weak
Hund's coupling are considered. By means of a generalized mean-field
approximation the single-particle Green function and quasiparticle energy
spectrum are calculated. Metal-insulator transition is studied in the model at
different integer values of the electron concentration. With the help of the
obtained energy spectrum we find energy gap width and criteria of
metal-insulator transition.
