Communication: Photoionization of degenerate orbitals for randomly oriented molecules: The effect of time-reversal...

The photoelectron asymmetry parameter β, which characterizes the direction of electrons ejected from a randomly oriented molecular ensemble by linearly polarized light, is investigated for degenerate orbitals. We show that β is totally symmetric under the symmetry operation of the point group of a molecule, and it has mixed properties under time reversal. Therefore, all degenerate molecular orbitals, except for the case of degeneracy due to time reversal, have the same β (Wigner-Eckart theorem). The exceptions are e-type complex orbitals of the C_n, S_n, C_nh, T, and T_h point groups, and calculations on boric acid (C_3h symmetry) are performed as an example. However, including those point groups, all degenerate orbitals have the same β if those orbitals are real. We discuss the implications of this operator formalism for molecular alignment and photoelectron circular dichroism.