  Some astrophysical observations of molecular hydrogen point to a broadening
of the velocity distribution for molecules at excited rotational levels. This
effect is observed in both Galactic and high redshift clouds. Analysis of H_2,
HD, and CI absorption lines has revealed the broadening effect in the
absorption system of QSO 1232+082 (z_{abs}=2.33771). We analyze line broadening
mechanisms by considering in detail the transfer of ultraviolet radiation (in
the resonance lines of the Lyman and Werner H_2 molecular bands) for various
velocity distributions at excited rotational levels. The mechanism we suggest
includes the saturation of the lines that populate excited rotational levels
(radiative pumping) and manifests itself most clearly in the case of
directional radiation in the medium. Based on the calculated structure of a
molecular hydrogen cloud in rotational level populations, we have considered an
additional mechanism that takes into account the presence of a
photodissociation region. Note that disregarding the broadening effects we
investigated can lead to a significant systematic error when the data are
processed.
