Cosmic ray penetration in diffuse clouds

Cosmic rays are a fundamental source of ionization for molecular and diffuse clouds, influencing their chemical, thermal, and dynamical evolution. The amount of cosmic rays inside a cloud also determines the $\gamma$-ray flux produced by hadronic collisions between cosmic rays and cloud material. We study the spectrum of cosmic rays inside and outside of a diffuse cloud, by solving the stationary transport equation for cosmic rays including diffusion, advection and energy losses due to ionization of neutral hydrogen atoms. We found that the cosmic ray spectrum inside a diffuse cloud differs from the one in the interstellar medium (ISM) for energies smaller than $E_{br}\approx 100$ MeV, irrespective of the model details. Below $E_{br}$, the spectrum is harder (softer) than that in the ISM if the latter is a power law $\propto p^{-s}$ with $s$ larger (smaller) than $\sim0.42$. As a consequence also the ionization rate due to CRs is strongly affected. Assuming an average Galactic spectrum similar to the one inferred from AMS-2 and Voyager 1 data, we discuss the resulting ionization rate in a typical diffuse cloud.