To elucidate the permeation of cosmic ultraviolet (UV) background radiation into a pregalactic cloud and the subsequent ionization, the frequency-dependent radiative transfer equation is solved, coupled with the ionization process, for a spherical top-hat cloud composed of pure hydrogen. The calculations properly involve scattering processes of ionizing photons that originate from radiative recombination. As a result, it is shown that the self-shielding, although it is often disregarded in cosmological hydrodynamic simulations, could start to emerge shortly after the maximum expansion stages of density fluctuations. Quantitatively, the self-shielding is prominent above a critical number density of hydrogen, which is given by ncrit = 1.4 × 10-2 cm-3 (M/108 M)?1/5I3/521 for 104 K gas, where M is the cloud mass and the UV background intensity is assumed to be Iν = 10-21I21(ν/νL)-1 ergs cm-2 s-1 sr-1 Hz-1, with νL being the Lyman limit frequency. The weak dependence of ncrit upon the mass is worth noting. The corresponding critical optical depth (τcrit) turns out to be independent of either M or I21, which is τcrit = 2.4 for 104 K gas. The present analysis reveals that the Str?mgren approximation leads to overestimation of the photoionization effects. Also, the self-shielded neutral core is no longer sharply separated from surrounding ionized regions; a low but noticeable degree of ionization is caused by high-energy photons even in the self-shielded core. The present results may be substantial when one considers the biasing by photoionization against low-mass galaxy formation.
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