Coherent excitation with a train of electron pulses

The Coulomb field of an electron passing an atom generates a transverse electric field corresponding to a half cycle of electromagnetic radiation and a longitudinal field corresponding to a single cycle pulse. These fields induce transitions within the atom. The power spectrum of the radiation of a single-cycle pulse is very broad. The field of the passing electron can induce transitions in the atom to all states for which the energy difference to the initial state, /spl Delta/E, is within the generated power spectrum. As a result, collisional excitation lacks selectivity in the population of the excited states. We investigate how, in such a collisional process, the transfer to an excited state can be enhanced. In our search for a scheme to control the excited state population we are inspired by the success of controlled photoexcitation using narrow-band lasers, having many oscillations of the e.m. radiation field. We investigated if enhanced excitation of a selected state is also possible for electron collisions and thus turn the (inefficient) broadband excitation into controlled excitation to a selected final state. To this end we consider the impact of a train of electron pulses with a repetition frequency /spl nu/. As in the optical case, this will induce a series of N broadband bursts of radiation spectrum. As can be seen in the figure the analogy with photons holds and N electron bursts spaced with time /spl tau//sub r/ will also favour transitions with frequency /spl nu/=1//spl tau//sub t/.