  Low-energy cosmic rays are a fundamental source of ionization for molecular
clouds, influencing their chemical, thermal and dynamical evolution. The
purpose of this work is to explore the possibility that a low-energy component
of cosmic-rays, not directly measurable from the Earth, can account for the
discrepancy between the ionization rate measured in diffuse and dense
interstellar clouds. We collect the most recent experimental and theoretical
data on the cross sections for the production of H2+ and He+ by electron and
proton impact, and we discuss the available constraints on the cosmic-ray
fluxes in the local interstellar medium. Starting from different extrapolations
at low energies of the demodulated cosmic-ray proton and electron spectra, we
compute the propagated spectra in molecular clouds in the continuous
slowing-down approximation taking into account all the relevant energy loss
processes. The theoretical value of the cosmic-ray ionization rate as a
function of the column density of traversed matter is in agreement with the
observational data only if either the flux of cosmic-ray electrons or of
protons increases at low energies. The most successful models are characterized
by a significant (or even dominant) contribution of the electron component to
the ionization rate, in agreement with previous suggestions. However, the large
spread of cosmic-ray ionization rates inferred from chemical models of
molecular cloud cores remains to be explained. Available data combined with
simple propagation models support the existence of a low-energy component
(below about 100 MeV) of cosmic-ray electrons or protons responsible for the
ionization of molecular cloud cores and dense protostellar envelopes.
