HOW SHORT IS TOO SHORT - CONSTRAINING ZERO-RANGE INTERACTIONS IN NUCLEON-NUCLEON-SCATTERING

We discuss a number of constraints on the effects of zero-range potent ials in quantum mechanics. We show that for such a potential p cot(del ta), where p is the momentum of the nucleon in the center of mass fram e and delta is the S-wave phase shift, must be a monotonically decreas ing function of energy. This implies that the effective range of the p otential is non-positive. We also examine scattering from the sum of t wo potentials, one of which is a short-range interaction. We find that if the short-range interaction is of zero-range then it must be attra ctive, and the logarithmic derivative of the radial wave function at t he origin must be a monotonically decreasing function of energy. if th e short-range interaction is not of zero range then a constraint which gives the minimum possible range for it to fit the phase shifts exist s. The implications of these results for effective field theory treatm ents of nucleon-nucleon interactions are discussed.