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Supernova remnants interacting with molecular clouds are ideal laboratoriesto study the acceleration of particles at shock waves and their transport andinteractions in the surrounding interstellar medium. In this paper, we focus onthe supernova remnant W28, which over the years has been observed in all energydomains from radio waves to very-high-energy gamma rays. The bright gamma-rayemission detected from molecular clouds located in its vicinity revealed thepresence of accelerated GeV and TeV particles in the region. An enhancedionization rate has also been measured by means of millimetre observations, butsuch observations alone cannot tell us whether the enhancement is due to lowenergy (MeV) cosmic rays (either protons or electrons) or the X-ray photonsemitted by the shocked gas. The goal of this study is to determine the originof the enhanced ionization rate and to infer from multiwavelength observationsthe spectrum of cosmic rays accelerated at the supernova remnant shock in theunprecedented range spanning from MeV to multi-TeV particle energies. Wedeveloped a model to describe the transport of X-ray photons into the molecularcloud, and we fitted the radio, millimeter, and gamma-ray data to derive thespectrum of the radiating particles. The contribution from X-ray photons to theenhanced ionization rate is negligible, and therefore the ionization must bedue to cosmic rays. Even though we cannot exclude a contribution to theionization rate coming from cosmic ray electrons, we show that a scenario wherecosmic ray protons explain both the gamma-ray flux and the enhanced ionizationrate provides the most natural fit to multiwavelength data. This stronglysuggests that the intensity of CR protons is enhanced in the region forparticle energies in a very broad range covering almost 6 orders of magnitude:from $\lesssim 100$ MeV up to several tens of TeV.

Constraining the cosmic ray spectrum in the vicinity of the supernova remnant W28: from sub-GeV to multi-TeV energies