On the Angular Distributions of Electrons Photoejected from Fixed-in-Space and Randomly Oriented Molecules

New theoretical expressions are devised from a dynamical perspective for molecular photoionization cross sections differential in electron ejection angles which facilitate comparisons between theory and experiment and provide a convenient basis for ab initio calculations. The cross sections obtained for fixed-in-space molecules, including the lowest-order (nondipole) effects of retardation, are given in terms of invariant molecular body-frame transition moments and related normalized angular-distribution amplitudes which can be calculated employing interaction-prepared states without reference to specific scattering boundary conditions. Corresponding expressions for molecular dipole and nondipole anisotropy factors appropriate for randomly oriented molecules are obtained in closed forms involving expectation values of harmonic polynomials over the fixed-in-space body-frame angular-distribution amplitudes. The expressions are seen to be in the spirit of corresponding results for atomic photoionization anisotropy factors, to which they reduce in appropriate limits. Interpretations of recently measured angular distributions of photoelectrons from the K-shell of molecular nitrogen illustrate how the development relates measurements on randomly oriented molecules to those performed on fixed-in-space molecules. The theoretical formalism provides results in excellent accord with measurements of the molecular nitrogen K-shell dipole anisotropy factor, and accounts for the origins of large nondipole effects observed at relatively low photon energies (ℏω≤500 eV) in the measured angular distributions