Correlation in atomic scattering

Correlation due to the Coulomb interactions between electrons in many-electron targets colliding with charged particles is formulated, and various approximate probability amplitudes are evaluated. In the limit that the electron-electron, 1/$r_{\mathrm{ij}}$, correlation interactions are ignored or approximated by central potentials, the independent-electron approximation is obtained. Two types of correlations, or corrections to the independent-electron approximation due to 1/$r_{\mathrm{ij}}$ terms, are identified: namely, static and scattering correlation. Static correlation is that contained in the asymptotic, e.g., bound-state, wave functions. Scattering correlation, arising from correlation in the scattering operator, is new and is considered in some detail. Expressions for a scattering correlation amplitude, static correlation or rearrangement amplitude, and independent-electron or direct amplitude are derived at high collision velocity and compared. At high velocities the direct and rearrangement amplitudes dominate. At very high velocities, ν, the rearrangement amplitude falls off less rapidly with ν than the direct amplitude which, however, is dominant as electron-electron correlation tends to zero. Comparisons with experimental observations are discussed.