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