The **M-**matrix, or scattering matrix, gives all the necessary information
about the nucleon-nucleon interaction. In order to define the form of the
**M-**matrix first one must choose the frame of reference for the reaction.
The nucleon-nucleon (nn) center-of-mass frame is the most convenient.
In terms of the ingoing and outgoing momenta we can define the nn
center-of-mass coordinates:

Invariance arguments (i.e. parity, time reversal, rotation, )
reduce the possible number of independent terms in the **M-**matrix
to five [Wol56]. In the nn center-of-mass coordinates the **M-**matrix
has the standard form [KMT59]:

where and are the Pauli spin matrices for the
incident and target nucleons, respectively. The scattering coefficients
**A**, **B**, **C**, **E**, and **F** are functions of energy, momentum transfer
, and isospin. In fact, for a given coefficient

where and are the isospin of the incident and target
nucleons, respectively, and and are linear combinations of the
coefficients of the isospin triplet and singlet states. For the
charge-exchange reaction only the will contribute,
and
the coefficients in equation (e.g. **A**) will be understood to
refer to the isospin **=** 1 piece (e.g. ).

Tue Apr 1 08:52:10 EST 1997