We present a theoretical calculation of the influence of ultraviolet radiative pumping on the excitation of the rotational levels of the ground vibrational state for HD molecules under conditions of the cold diffuse interstellar medium (ISM). Two main excitation mechanisms have been taken into account in our analysis: (i) collisions with atoms and molecules and (ii) radiative pumping by the interstellar ultraviolet (UV) radiation field. The calculation of the radiative pumping rate coefficients $Gamma_{rm ij}$ corresponding to Dranes model of the field of interstellar UV radiation, taking into account the self-shielding of HD molecules, is performed. We found that the population of the first HD rotational level ($J = 1$) is determined mainly by radiative pumping rather than by collisions if the thermal gas pressure $p_{rm th}le10^4left(frac{I_{rm{UV}}}{1}right),mbox{K,cm}^{-3}$ and the column density of HD is lower than $log N({rm{HD}})<15$. Under this constraint the populations of rotational levels of HD turns out to be as well a more sensitive indicator of the UV radiation intensity than the fine-structure levels of atomic carbon. We suggest that taking into account radiative pumping of HD rotational levels may be important for the problem of the cooling of primordial gas at high redshift: ultraviolet radiation from first stars can increase the rate of HD cooling of the primordial gas in the early Universe.
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