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. 
).
