  Nonthermal radiation is observed from clusters of galaxies in the radio, hard
X-rays, and possibly in the soft X-ray/UV bands. While it is known that
radiative processes related to nonthermal electrons are responsible for this
radiation, the sites and nature of particle acceleration are not known. We
investigate here the acceleration of protons and electrons in the shocks
originated during mergers of clusters of galaxies, where the Fermi acceleration
may work. We propose a semi-analytical model to evaluate the Mach number of the
shocks generated during clusters mergers and we use this procedure to determine
the spectrum of the accelerated particles for each one of the shocks produced
during the merger history of a cluster. We follow the proton component,
accumulated over cosmological time scales, and the short lived electron
component. We conclude that efficient particle acceleration, resulting in
nonthermal spectra that compare to observations, occurs mainly in minor
mergers, namely mergers between clusters with very different masses. Major
mergers, often invoked to be sites for the production of extended radio halos,
are found to have on average too weak shocks and are unlikely to result in
appreciable nonthermal activity.
