SHORT-RANGE INTERACTIONS IN AN EFFECTIVE-FIELD THEORY APPROACH FOR NUCLEON-NUCLEON-SCATTERING

We investigate in detail the effect of making the range of the ''conta ct'' interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective held theory wi th explicit pions, and one where the pions have been integrated out. I n both cases we calculate NN scattering in the S-1(0) channel using po tentials which are second order in the EFT expansion. The contact inte ractions present in the EFT Lagrangian are made finite by use of a squ are-well regulator. We find that there is an optimal radius for this r egulator, at which second-order corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small . The cutoff EFT's which result from this procedure appear to be valid for momenta up to about 100-150 MeV/c. We also find that the radius o f the square well cannot be reduced to zero if the theory is to reprod uce both the experimental scattering length and effective range. Indee d, we show that, if the NN potential is the sum of a one-pion-exchange piece and a short-range interaction, then the short-range piece must extend out beyond 1.05 fm, regardless of its particular form.