  The angular momentum (partial wave) reduction of the Lippmann--Schwinger
equation describing the interaction of two spin 1/2 particles is extended to
the case in which the spin singlet and triplet states are coupled. A straight
forward method for obtaining the angular momentum decomposition of the general
potential is indicated. The derived formalism is needed to describe the
interaction between two nonidentical spin--1/2 particles or between two
nucleons when isospin symmetry is violated. The resulting modification of the
Stapp phase--shift analysis is given.
