  For the three-terminal NSN device with single-mode normal terminals and
without Coulomb blockade, we propose the interpretation of charge transfer
process which allows us to consistently characterize the device operation as
that of a Cooper pair splitter in terms of scattering matrix elements as well
as in terms of measurable quantities. The obtained explicit expression for the
splitting probability notably contains the two-particle interference term not
available from conductance measurements. We show that splitting doesn't
necessarily rely on single-particle crossed Andreev reflection amplitude thus
allowing for the unit efficiency at zero energy. Our results imply that the
current cross-correlator generally doesn't provide definite measure of
splitting.
