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

TL;DR

This paper presents a theoretical model for predicting fine- and hyperfine-structure effects in molecular photoionization, utilizing tensor algebra to derive selection rules and validate predictions with experimental spectra.

Contribution

It introduces a general theoretical framework for analyzing fine- and hyperfine-resolved photoionization in molecules, emphasizing the separability of electron and nuclear spin states.

Findings

Validated model with O₂ photoelectron spectrum

Derived selection and propensity rules for transitions

Predicted hyperfine populations of molecular ions

Abstract

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.