  Thirty years ago, H.Schwarz has attempted to modulate an electron beam with
optical frequency. When a 50-keV electron beam crossed a thin crystalline
dielectric film illuminated with laser light, electrons produced the
electron-diffraction pattern not only at a fluorescent target but also at a
nonfluorescent target. In the latter case the pattern was of the same color as
the laser light (the Schwarz-Hora effect). This effect was discussed
extensively in the early 1970s. However, since 1972 no reports on the results
of further attempts to repeat those experiments in other groups have appeared,
while the failures of the initial such attempts have been explained by Schwarz.
The analysis of the literature shows there are several unresolved up to now
contradictions between the theory and the Schwarz experiments. In this work we
consider the interpretation of the long-wavelength spatial beating of the
Schwarz-Hora radiation. A more accurate expression for the spatial period has
been obtained, taking into account the mode structure of the laser field within
the dielectric film. It is shown that the discrepancy of more than 10% between
the experimental and theoretical results for the spatial period cannot be
reduced by using the existing quantum models that consider a collimated
electron beam.
