Absolutely continuous spectrum of a typical Schr\"odinger operator with a slowly decaying potential

We consider a family of multi-dimensional Schr"odinger operators $-\Delta+t V$withareal$t$\mathrm{.}Thepotential$V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the absolutely continuous spectrum of this operator covers the interval $[0,\mathrm{\infty })$ for almost every $t$.