Independent center, independent electron approximation for dynamics of molecules and clusters

A formalism is developed for evaluating probabilities and cross sections for multiple-electron transitions in scattering of molecules and clusters by charged collision partners. First, the molecule is divided into subclusters each made up of identical centers (atoms). Within each subcluster coherent scattering from identical centers may lead to observable phase terms and a geometrical structure factor. Then, using a mean field approximation to describe the interactions between centers we obtain AI∼∑k∏keiδkIAIk. Second, the independent electron approximation for each center may be obtained by neglecting the correlation between electrons in each center. The probability amplitude for each center is then a product of single electron transition probability amplitudes, aIki, i.e. AIk≊∏iaiki. Finally, the independent subcluster approximation is introduced by neglecting the interactions between different subclusters in the molecule or cluster. The total probability amplitude then reduces to a simple product of amplitudes for each subcluster, A≊∏IAI. Limitations of this simple approximation are discussed.