The total and partial photodissociation cross sections of the molecular ion HeH + are computed by timedependent methods for fragmentation into the excited shells n =1,2,3 up to a photon energy of 40 eV. 1 ⌺ + and 1 ⌸ states are considered for parallel and perpendicular transitions for different initial rotational or vibrational excitations. Nonadiabatic radial and rotational couplings are taken into account. The results from coupledchannel equations are compared with the Born-Oppenheimer approximation. A time-dependent calculation with a femtosecond laser pulse is carried out to simulate a recent crossed beam photodissociation imaging experiment with vacuum ultraviolet free-electron laser ͓H. B. Pedersen et al., Phys. Rev. Lett. 98, 223202 ͑2007͔͒. The dominance of photodissociation perpendicular to the photon polarization is confirmed.
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