An exponential gap relation for vibrational energy transfer in a dissipative medium

The dynamic description of a collision in a medium is reformulated using an interaction picture. This transformation can be used both as a computational device and as a basis for analytical approximations. Numerical results for the problem of a collinear atom-oscillator collision including friction are generated as an example. An adiabaticity parameter is derived via a saddle point approximation and the exact numerical results are shown to scale exponentially with this parameter. In the adiabatic limit the gap law is exp (-π???L/ν) where L is the range of the potential and ??? is the renormalized oscillator frequency, which is always lower than that of the isolated molecule.