Parametrization of a spin-polarized [Formula Presented] experiment

We use the density-matrix formalism to parametrize a spin-polarized [Formula Presented] experiment where a [Formula Presented] electron is ejected from a closed-shell system and the fine structure of the ion is resolved experimentally. This formulation allows a definition from general principles of the recently observed spin up-down asymmetry [X. Guo and co-workers, Phys. Rev. Lett. 76, 1228 (1996); J. Phys. B 30, 4097 (1997)] due to the fine-structure effect [S. Jones et al., Phys. Rev. Lett. 72, 2554 (1994); G. F. Hanne, in Abstracts of Contributed Papers, XVIIth International Conference on the Physics of Electronic and Atomic Collisions, edited by W. R. MacGillivray, I. E. McCarthy, and M. C. Standage (Hilger, Bristol, 1992), p. 199] and the complete definition of potentially observable quantities such as the polarization of the fast- and slow-emitted-electron beams and the orientation of the ion beam after the collision. These parameters are defined for the general case where the incoming-electron beam has an arbitrary polarization [Formula Presented] and calculated in an asymmetric kinematic for the case where the initial-electron beam is, respectively, unpolarized and polarized perpendicular to the scattering plane.