  In this paper, we consider smooth shot noise processes and their expected
number of level crossings. When the kernel response function is sufficiently
smooth, the mean number of crossings function is obtained through an integral
formula. Moreover, as the intensity increases, or equivalently, as the number
of shots becomes larger, a normal convergence to the classical Rice's formula
for Gaussian processes is obtained. The Gaussian kernel function, that
corresponds to many applications in physics, is studied in detail and two
different regimes are exhibited.
