We study the spectral properties of the Schrodinger operator with a constan
t electric field perturbed by a bounded potential. It is shown that if the
derivative of the potential in the direction of the electric field is small
er at infinity than the electric field, then the spectrum of the correspond
ing Stark operator is purely absolutely continuous. In one dimension, the a
bsolute continuity of the spectrum is implied by just the boundedness of th
e derivative of the potential. The sharpness of our criterion for higher di
mensions is illustrated by constructing smooth potentials with bounded part
ial derivatives for which the corresponding Stark operators have a dense po
int spectrum. (C) 2000 American Institute of Physics. [S0022-2488(00)03809-
3].