What causes the ionization rates observed in molecular clouds? The role of cosmic ray protons and electrons

Cosmic rays are usually assumed to be the main ionization agent for the interior of molecular clouds where UV and X-ray photons cannot penetrate. Here we test this hypothesis by limiting ourselves to the case of diffuse clouds and assuming that the average cosmic ray spectrum inside the Galaxy is equal to the one at the position of the Sun as measured by Voyager 1 and AMS-02. To calculate the cosmic ray spectrum inside the clouds, we solve the one-dimensional transport equation taking into account advection, diffusion and energy losses. While outside the cloud particles diffuse, in its interior they are assumed to gyrate along magnetic field lines because ion-neutral friction is effective in damping all the magnetic turbulence. We show that ionization losses effectively reduce the CR flux in the cloud interior for energies below $\approx 100$ MeV, especially for electrons, in such a way that the ionization rate decreases by roughly 2 order of magnitude with respect to the case where losses are neglected. As a consequence, the predicted ionization rate is more than 10 times smaller than the one inferred from the detection of molecular lines. We discuss the implication of our finding in terms of spatial fluctuation of the Galactic cosmic ray spectra and possible additional sources of low energy cosmic rays.