Dynamical theory of molecular photoionization: electron ejection kinematics and angular distributions from molecules fixed in space

Abstract

Photoionization of molecules and other atomic aggregates fixed in space is studied from a dynamical perspective employing solutions of the time-dependent Schrödinger equation. The wave functions and associated kinematical behaviors of excited and ejected electrons are determined explicitly in short- and long-time limits, generalizing early results of Bethe for central potentials to anisotropic targets. Ehrenfest’s theorem is employed to clarify the origins of the transient forces and consequent kinematical behaviors of excited and ionized K-shell electrons obtained from explicit solutions of the time-dependent Schrödinger equation, revealing hybrid classical-quantal behaviors in wave functions and expectation values of position and momentum operators. In addition to providing pedagogical insights into time-resolved aspects of these fundamental photoprocesses, and a corresponding basis for theoretical studies of dynamical target relaxation, associated photoelectron-ion correlation, and other specifically time-dependent post-collision interaction phenomena, the new development resolves technical issues associated with the irreducibly infinite degeneracy of the scattering continuum for the anisotropic potentials characteristic of polyatomic molecules. Photoionization cross sections differential in electron ejection angles are derived from the formalism for fixed-in-space molecules of arbitrary complexity which are applicable in both time-resolved and steady-state situations, and an invariant subspace of excitation and ionization functions required in computational applications of the approach is constructed employing Lanczos–Krylov sequences of L 2 vectors and previously devised Stieltjes–Akhiezer methods, without reference to or calculations of the underlying individual discrete or continuum eigenstates. Electron angular-distribution data for fixed-in-space molecules measured over the full (4 π) range of emission angles for all molecular orientations are shown to be highly redundant, and to provide invariant physical information in the form of no more than three irreducible-tensor body-frame complex angular emission amplitudes at a given photon energy. These issues are illustrated with applications to ionization of fixed-in-space diatomic molecules for linear and circularly polarized incident radiation, in which cases the minimal set of molecular configurations and polarizations required to determine the invariant body-frame emission amplitudes is described in detail.