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Nonthermal radiation is observed from clusters of galaxies in the radio, hardX-rays, and possibly in the soft X-ray/UV bands. While it is known thatradiative processes related to nonthermal electrons are responsible for thisradiation, the sites and nature of particle acceleration are not known. Weinvestigate here the acceleration of protons and electrons in the shocksoriginated during mergers of clusters of galaxies, where the Fermi accelerationmay work. We propose a semi-analytical model to evaluate the Mach number of theshocks generated during clusters mergers and we use this procedure to determinethe spectrum of the accelerated particles for each one of the shocks producedduring the merger history of a cluster. We follow the proton component,accumulated over cosmological time scales, and the short lived electroncomponent. We conclude that efficient particle acceleration, resulting innonthermal spectra that compare to observations, occurs mainly in minormergers, namely mergers between clusters with very different masses. Majormergers, 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 inappreciable nonthermal activity.Comment: Version accepted for publication in the Astrophysical Journa

Nonthermal Radiation from Clusters of Galaxies: The Role of Merger Shocks in Particle Acceleration