  Radio observations at metre-centimetre wavelengths shed light on the nature
of the emission of HII regions. Usually this category of objects is dominated
by thermal radiation produced by ionised hydrogen, namely protons and
electrons. However, a number of observational studies have revealed the
existence of HII regions with a mixture of thermal and non-thermal radiation.
The latter represents a clue as to the presence of relativistic electrons.
However, neither the interstellar cosmic-ray electron flux nor the flux of
secondary electrons, produced by primary cosmic rays through ionisation
processes, is high enough to explain the observed flux densities. We
investigate the possibility of accelerating local thermal electrons up to
relativistic energies in HII region shocks. We assumed that relativistic
electrons can be accelerated through the first-order Fermi acceleration
mechanism and we estimated the emerging electron fluxes, the corresponding flux
densities, and the spectral indexes. We find flux densities of the same order
of magnitude of those observed. In particular, we applied our model to the
"deep south" (DS) region of Sagittarius B2 and we succeeded in reproducing the
observed flux densities with an accuracy of less than 20% as well as the
spectral indexes. The model also gives constraints on magnetic field strength
($0.3-4$ mG), density ($1-9\times10^4$ cm$^{-3}$), and flow velocity in the
shock reference frame ($33-50$ km s$^{-1}$) expected in DS. We suggest a
mechanism able to accelerate thermal electrons inside HII regions through the
first-order Fermi acceleration. The existence of a local source of relativistic
electrons can explain the origin of both the observed non-thermal emission and
the corresponding spectral indexes.
