  The photodissociation cross section of the molecular ion HeH$^+$ was
calculated within the Born-Oppenheimer approximation for a parallel, a
perpendicular, and an isotropic orientation of the molecular axis with respect
to the field, considering also different initial vibrational and rotational
states. The results were compared to recent data from a free-electron laser
experiment performed at the FLASH facility [H.B. Pedersen {\it et al.}, Phys.
Rev. Lett. 98, 223202, (2007)]. Within the experimental uncertainties
theoretical and experimental results are compatible with each other.
