  We present a semiclassical study of level widths for a class of
one-dimensional potentials in the presence of an ohmic environment. Employing
an expression for the dipole matrix element in terms of the Fourier transform
of the classical path we obtain the level widths within the Golden rule
approximation. It is found that for potentials with an asymptotic power-law
behavior, which may in addition be limited by an infinite wall, the width that
an eigenstate of the isolated system acquires due to the coupling to the
environment is proportional to its quantum number.
