Nonstatistical Theory of Multiple Vacancy Production in Atomic Collisions

Till now interpretation of x-ray satellite data has been limited to the use of models in which the emissions of electrons are treated as statistically independent. This assumption leads to a product of binomial distributions, one for each shell. However, even in the independent Fermi particle model of the target atom, collision theory predicts that the holes are correlated. At a given impact parameter the independent-Fermi-particle probability for producing several holes in a given shell can be written as a term containing only probabilities for the individual vacancies, which reduces for "average holes" to the binomial distribution, plus a correlation term which involves interference among amplitudes for the single-electron transitions. Expressions for the general case are given. To evaluate such expressions, one needs calculations in which the single-electron amplitudes are obtained with consistent relative phases. These have now begun by employing coupled-channels theory.