  (Abridged) The propagation of ionizing radiation through model atmospheres of
terrestrial-like exoplanets is studied for a large range of column densities
and incident photon energies using a Monte Carlo code we have developed to
treat Compton scattering and photoabsorption. Incident spectra from parent star
flares, supernovae, and gamma-ray bursts are modeled and compared to energetic
particles in importance. We find that terrestrial-like exoplanets with
atmospheres thinner than about 100 g cm^-2 transmit and reprocess a significant
fraction of incident gamma-rays, producing a characteristic, flat surficial
spectrum. Thick atmospheres (>~ 100 g cm^-2) efficiently block even gamma-rays,
but nearly all incident energy is redistributed into diffuse UV and visible
aurora-like emission, increasing the effective atmospheric transmission by many
orders of magnitude. Depending on the presence of molecular UV absorbers and
atmospheric thickness, up to 10% of the incident energy can reach the surface
as UV reemission. For the Earth, between 2 x 10^-3 and 4 x 10^-2 of the
incident flux reaches the ground in the biologically effective 200--320 nm
range, depending on O_2/O_3 shielding. Finally, we suggest that transient
atmospheric ionization layers can be frequently created at low altitudes. We
conclude that these events can produce frequent fluctuations in atmospheric
ionization levels and surficial UV fluxes on terrestrial-like planets.
