Accurate photodissociation cross sections have been obtained for the A-X electronic transition of HeH+ using ab initio potential curves and dipole transition moments. Partial cross sections have been evaluated for all rotational transitions from the vibrational levels v"=0-11 and over the entire accessible wavelength range 100-1129 Angstrom. Assuming a Boltzmann distribution of the rovibrational levels of the X state, photodissociation cross sections are presented for temperatures between 500 and 12,000 K. A similar set of calculations was performed for the pure rovibrational photodissociation in the X-X electronic ground state, but covering photon wavelengths into the far infrared. Applications of the cross sections to the destruction of HeH+in the early Universe and in UV-irradiated environments such as primordial halos and protoplanetary disks are briefly discussed
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