Ultrafast Electron Pulse (e,2e) Processes*

Techniques for producing ultrafast electron pulses have been proposed\footnote{P.~Baum and A.H.~Zewail, Proc.~Natl.~Acad.~Sci.~U.S.A.~\textbf{104}, 18409 (2007); S.A.~Hilbert, C.~Ulterwaal, B.~Barwick, H.~Betalaan, and A.H.~Zewail, \textit{ibid}.~\textbf{106}, 10558 (2009).} and prospects for using such pulses to image electron dynamics in the H atom and the hydrogen molecular ion have been theoretically demonstrated.\footnote{H.-C.~Shao and A.F.~Starace, Phys.~Rev.~Lett.~\textbf{105}, 263201 (2010).} The (e,2e) process provides a means to directly image the momentum distribution of the target.\footnote{M.A.~Coplan, J.H.~Moore, and J.P.~Doering, Rev.~Mod.~Phys.~\textbf{66}, 985 (1994).} We explore here the possibility of observing the time dependence of a coherent superposition of target orbitals by means of the (e,2e) process with ultrafast incident electron pulses. Using scattering theory for a longitudinally coherent beam,\footnote{F.~Robicheaux, Phys.~Rev.~A \textbf{62}, 062706 (2000).} we find that the momentum distribution of a coherent state of the H atom can be retrieved.