  An effective field theory treatment of nucleon-nucleon scattering at low
energy shows much promise and could prove a useful tool in the study of nuclear
matter at both ordinary and extreme densities. The analysis is complicated by
the existence a large length scale --- the scattering length --- which arises
due to couplings in the short distance theory being near critical values. I
show how this can be dealt with by introducing an explicit s-channel state in
the effective field theory. The procedure is worked out analytically in a toy
example. I then demonstrate that a simple effective field theory excellently
reproduces the 1S_0 np phase shift up to the pion production threshold.
