Water ice is abundant both astrophysically, for example in molecular clouds, and in planetary systems. The Kuiper belt objects, many satellites of the outer solar system, the nuclei of comets and some planetary rings are all known to be water-rich. Processing of water ice by energetic particles and ultraviolet photons plays an important role in astrochemistry. To explore the detailed nature of this processing, we have conducted a systematic laboratory study of the irradiation of crystalline water ice in an ultrahigh vacuum setup by energetic electrons holding a linear energy transfer of 4.3 +/- 0.1 keV mm-1. The irradiated samples were monitored during the experiment both on line and in situ via mass spectrometry (gas phase) and Fourier transform infrared spectroscopy (solid state). We observed the production of hydrogen and oxygen, both molecular and atomic, and of hydrogen peroxide. The likely reaction mechanisms responsible for these species are discussed. Additional formation routes were derived from the sublimation profiles of molecular hydrogen (90-140 K), molecular oxygen (147 -151 K) and hydrogen peroxide (170 K). We also present evidence on the involvement of hydroxyl radicals and possibly oxygen atoms as building blocks to yield hydrogen peroxide at low temperatures (12 K) and via a diffusion-controlled mechanism in the warming up phase of the irradiated sample.