We have performed an experiment in which a polarized electron beam ionizes
an orbitally oriented and/or spin-polarized valence electron of sodium. The
cross section for this reaction is measured for well-resolved vector momen
ta of the two electrons in the final channel. In order to study the transfe
r of the initial spin and orbital orientation from the electron-atom system
to the final-state correlated electron pair, we develop a tensorial recoup
ling scheme in which the measured quantities are expressed in terms of inde
pendent, irreducible spherical tensor components. By this procedure the cro
ss section is separated into terms characterized by their specific rotation
al transformation properties, decoupling of geometrical effects due to init
ial-state preparation from effects associated with details of the scatterin
g dynamics is achieved, and exchange and orbital angular momentum transfer
effects are disentangled. For a comparison with experiment we performed num
erical ionization-cross section calculations within the distorted wave Born
approximation and the dynamically screened three Coulomb waves theory. For
some tensorial parameters significant discrepancies between theory and exp
eriment are observed that underline the importance of the state-specific me
asurements as stringent tests of scattering theories.