Coherent excitation of then=3 level of hydrogen in a field free region

The theory of coherent excitation of then=3 level of atomic hydrogen by electron impact is studied using density matrix techniques. A set of multipole parameters is defined which allows to characterise coherently excited states with different angular momenta. Numerical results of these parameters, calculated in first order Born approximation, are tabulated for several energies and angles. Angular distribution and polarization of Balmer-α radiation are expressed in terms of the initial multipole parameters for the case that scattered electrons and emitted photons are detected in coincidence. The theory of cascade effects is briefly considered and applied to the case where scattered electrons and Lyman-α photons are detected in coincidence, generalising earlier formulations. Most of the formulas presented here are quite general and can be applied, for example, to an analysis of light emitted by beam foil excited hydrogenic levels.