In terms of the nn center-of-mass coordinates defined in equation we can rewrite equation as

The polarization observables defined by equation can not be easily related to the separate tensor components of the scattering matrix, . Therefore, it is convenient to define a new set of spin observables each of which depend on individual components of the scattering matrix [BBW82].

The new set of observables can be expressed as linear combinations of the polarization transfer observables defined above:

These observables are not independent quantities and are subject to the constraint

and are all non-negative: , where .
Using the definition of the polarization transfer coefficients (eqn.
) and the standard expression for the scattering matrix (eqn.
) one can derive expressions for the nn partial differential
cross sections which relate the spin observables, , to the
amplitudes of the **M-**matrix [IcK92]:

where **I** is the unpolarized differential cross section in the
center-of-mass frame. By inspection one can see that is related
solely to the piece of the interaction in the direction, or the
piece in which the spin is parallel to the direction of the momentum
transfer (referred to as
the longitudinal direction). is related exclusively to a piece of
the interaction in the spin-transverse direction. is also dependent
on a spin-transverse part of the reaction but not as simply as is the case
with . The result is that a comparison of the spin-longitudinal and
spin-transverse parts of the nn interaction will come down to a comparison
of and .

Tue Apr 1 08:52:10 EST 1997