Multiphoton transitions of a bound electron interacting with an $N$-dimensional oscillator

Multiphoton transitions of a bound electron interacting with an $N$-dimensional oscillator are considered. Allowance is made for excitation of the oscillator by an external electromagnetic field and for the mixing of the molecular normal vibrations when a quantum transition occurs (Dushinsky effect). An exponential dependence of electron transition rate on the parameters of the mixing of the molecular vibrations is established. The theory is compared with experiment for the example of the $\mathrm{SO}_2$ molecule.