  The effective field theory (EFT) for a toy model of nucleons interacting via
a short range and a long range Yukawa potential is presented. The scattering
amplitude in the 1S0 channel is calculated up to NNLO using KSW power counting
scheme. A particular expansion of the amplitude about the pole at low
(imaginary) momentum is used to derive matching conditions for the EFT
couplings. In addition, after imposing constraints from a Renormalization Group
analysis, there are no new free parameters in the amplitude at NNLO. Comparing
the NNLO phase shifts to the full model we show that the EFT expansion is
converging.
