Symmetry properties of the S matrix in a fully relativistic distorted-wave treatment of electron-impact ionization -: art. no. 052701

The symmetry properties of the S matrix in a fully relativistic distorted-wave treatment of electron-impact ionization are investigated. It is shown that the square modulus of the scattering matrix element in which the spin states of all four electrons are determined is not invariant under the reversal of the direction of alignment of all spins. The largest of two contributions to this noninvariance originates from the relativistic modifications of the continuum wave functions induced by the distorting potential of the target atom. A second smaller contribution is manifested on reducing the eight-dimensional matrix elements of the QED covariant propagator to purely spatial two-electron integrals. The triple differential cross section (TDCS) exhibits a spin asymmetry unless the entire scattering process occurs in a single plane. There will be a difference in the TDCS between an (e,2e) event in which the initial beam is polarized parallel or antiparallel with respect to the beam direction even if the target is unpolarized and the final spin states are not determined. The TDCS will remain unchanged if, in addition to reversal of the direction of spin alignment, one appropriate momentum component of one of the two outgoing electrons is reversed.