Theory of angular distribution and spin polarization of photoelectrons

General formulas of the angular distribution and spin polarization of photoelectrons are derived for arbitrarily polarized incident photons including all multipole effects of the photon fields. Dynamical parameters are given in terms of reduced matrix elements suitable for a general multichannel theory in both the relativistic and nonrelativistic formulations. Low-energy photoionization processes, where the electric-dipole approximation is valid, are dealt with in detail. Simple explicit formulas of the angular distribution and spin polarization of photoelectrons are given for closed-shell atoms. Applications of the present formulation using various relativistic multichannel theories are discussed briefly. A relativistic version of the $K$-matrix method, by which both closed- and open-shell atoms can be treated, is also given.