The scattering problem for a long-range periodic in time potential

The multidimensional Schrödinger operator $H=-\Delta+V(x,t)$ with a time-dependent potential is considered. The potential may decrease slowly with respect to space variable but its mean value in time is equal to zero. It is shown that for the pair $H_0=-\Delta$, $H$ wave operators exist and their ranges coincide with the absolute continuous subspace of the corresponding operator of monodromy.