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We develop a model for predicting fine- and hyperfine intensities in thedirect photoionization of molecules based on the separability of electron andnuclear spin states from vibrational-electronic states. Using spherical tensoralgebra, we derive highly symmetrized forms of the squared photoionizationdipole matrix elements from which which we derive the salient selection andpropensity rules for fine- and hyperfine resolved photoionizing transitions.Our theoretical results are validated by the analysis of the fine-structureresolved photoelectron spectrum of O$_2$ (reported by H. Palm and F. Merkt,Phys. Rev. Lett. 81, 1385 (1998)) and are used for predicting hyperfinepopulations of molecular ions produced by photoionization.

Fine- and hyperfine-structure effects in molecular photoionization: I. General theory and direct photoionization