  We consider a cosmic ray spectrum that is a power law in momentum down to a
cutoff and derive a lower cutoff corresponding to $E_{kin} \sim (30-60)$ MeV
from the observed ionization rates in nearby diffuse clouds. While the real
spectra of cosmic rays may not be so simple, we argue that one expects a
substantial change in the spectra at such energies and that, at first
approximation, a power law spectra with a lower cutoff is appropriate. Such a
description of the cosmic rays in the interstellar medium is not only
theoretically more attractive than the spectra used in the literature, but is
also supported by recent observations.
