Fluctuations of energy losses of charged particles colliding with an oscillator

Abstract

Fluctuations of energy losses of fast charged particles colliding with an oscillator have been con sidered in the dipole approximation. In this approximation, the problem has been solved exactly, and fluctu ations of energy losses of the oscillator from the initial state |m〉 = |0〉 have been found in the form of the sum of single integrals. It has been shown that the Bohr formulas for fluctuations can be obtained in the passage to the classical limit, whereas analogs of the Fano formula in perturbation theory and the Titeica formula in the nonperturbative case can be obtained when the velocities of an ion are much higher than atomic velocities.