Photoelectron spectroscopic studies of polyatomic molecules: Theory for spin polarization

A general, nonrelativistic, multichannel theory for angle- and spin-resolved photoelectron spectroscopy of polyatomic molecules in the electric dipole approximation has been developed. Expressions for angular distribution of electrons ejected with defined spin polarization, both in molecule- and laboratory-fixed frames of reference from molecular targets with fixed as well as with random orientation in space, are derived. The transformation properties of the molecular point symmetry group are used to their full advantage to reduce these expressions to their simplest possible forms. The ionization amplitude is thus shown to decompose into a sum of transitions each involving the final-state wave function belonging to an irreducible representation of the point group of the target molecule. The formulas obtained herein can therefore be used to study spin-resolved photoionization in both linear and nonlinear molecules of any symmetry corresponding to one of the 32 point groups, either in their gaseous phase or oriented on liquid and solid surfaces. In order to study both the angular distribution as well as the degree of spin polarization of photoelectrons in terms of alternative contributions of the angular momentum transfer ${(\mathrm{j}}_t$) from photon to the ejected electron, a new set of ionization amplitudes is introduced whose contributions to the angular distribution add incoherently. This new approach not only simplifies the resulting expressions, but also eliminates the interference terms $j_t$≠$j_t^{\mathcal{’}}$ which were present in an earlier expression for angular distribution of spin-polarized atomic photoelectrons. The theory developed in this paper has been used in the accompanying article to analyze photoionization in a nonlinear molecule whose point symmetry group is $T_d$.