Evolution of the moments and transition probability models in energy transfer processes

The evolution of the first and second moments during collisional relaxation of an ensemble of highly vibrationally excited molecules is analysed theoretically and with numerical resolution of the master equation. Single exponential relaxation of the average excitation energy, characterised by a linear dependence on energy of the amount of energy transferred, allows one to obtain the microscopic energy transferred per collision. Also, there is always a set of independent energy transfer functions, P(E', E), which yields the same first moment. In contrast, the evolution of the spread of the energy level populations is quite different, allowing for the characterization of P(E', E) models. For a quadratic energy dependence of [Delta E] on E, the energy loss profiles are sensitive to the energy distribution and the microscopic first moment can be obtained only under certain conditions.