  Second-order [O(k^2), k=omega/c] nondipole effects in soft-x-ray
photoemission are demonstrated via an experimental and theoretical study of
angular distributions of neon valence photoelectrons in the 100--1200 eV
photon-energy range. A newly derived theoretical expression for nondipolar
angular distributions characterizes the second-order effects using four new
parameters with primary contributions from pure-quadrupole and octupole-dipole
interference terms. Independent-particle calculations of these parameters
account for a significant portion of the existing discrepancy between
experiment and theory for Ne 2p first-order nondipole parameters.
