Molecular-orbital decomposition of the ionization continuum for a diatomic molecule by angle- and energy-resolved photoelectron spectroscopy. I. Formalism

Abstract

A theoretical formalism is developed for the quantum-state-specific photoelectron angular distributions (PADs) from the direct photoionization of a diatomic molecule in which both the ionizing state and the state of the ion follow Hund’s case (b) coupling. The formalism is based on the molecular-orbital decomposition of the ionization continuum and therefore fully incorporates the molecular nature of the photoelectron–ion scattering within the independent electron approximation. The resulting expression for the quantum-state-specific PADs is dependent on two distinct types of dynamical quantities, one that pertains only to the ionization continuum and the other that depends both on the ionizing state and the ionization continuum. Specifically, the electronic dipole-moment matrix element rlλ exp(iηlλ) for the ejection of a photoelectron with orbital angular momentum quantum number l making a projection λ on the internuclear axis is expressed as ΣαλŪlαλλ exp (iπτ̄αλλ) Mαλλ, where Ūλ is the electronic transformation matrix, τ̄αλλ is the scattering phase shift associated with the αλth continuum molecular orbital, and Mαλλ is the real electronic dipole-moment matrix element that connects the ionizing orbital to the αλth continuum molecular orbital. Because Ūλ and τ̄αλλ depend only on the dynamics in the ionization continuum, this formalism allows maximal exploitation of the commonality between photoionization processes from different ionizing states. It also makes possible the direct experimental investigation of scattering matrices for the photoelectron–ion scattering and thus the dynamics in the ionization continuum by studying the quantum-state-specific PADs, as illustrated in the companion article on the photoionization of NO.