Coherent excitation of then=3states in hydrogen

This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the $n=3\mathrm{}$ state by electron bombardment. By coherence is meant that the density matrix describing the atom after the collision has off-diagonal matrix elements in the field-free basis. The differential cross section for producing Balmer-$\alpha$ photons at 90° to the electron beam is calculated as a function of an applied longitudinal electric field. The off-diagonal elements show up as a dependence of the observed light on the directions of the electric field. Theoretical results based on the Born approximation are compared with an experiment at 200 and 500 eV. It is pointed out that this method for measuring relative phases of scattering amplitudes can be generally applied and is not restricted to $n=3\mathrm{}$ excitation of hydrogen.