On the theory of the ionization-induced drag of fast charged particles

The moments in the theory of deceleration of fast charged particles colliding with an oscillator have been considered in the dipole approximation. In this approximation, the problem has been solved exactly, and the moment of the oscillator has been determined from the initial state $|m\rangle=|0\rangle$ in the form of the sum of 1D integrals. The method considered here makes it possible to calculate the moments for ion velocities close to atomic velocities ($v\sim v_{a}$).