Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1996-07-24
Phys.Lett. B390 (1997) 7-12
Physics
Nuclear Physics
Nuclear Theory
5 pages, RevTeX. Version accepted for publication in Phys. Lett. B. Minor changes to the text have been made in order to clari
Scientific paper
10.1016/S0370-2693(96)01411-6
We discuss a number of constraints on the effects of zero-range potentials in quantum mechanics. We show that for such a potential $p \cot(\delta)$, where $p$ is the momentum of the nucleon in the center of mass frame and $\delta$ is the S-wave phase shift, must be a monotonically decreasing function of energy. This implies that the effective range of the potential is non-positive. We also examine scattering from the sum of two 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 attractive, and the logarithmic derivative of the radial wave function at the origin must be a monotonically decreasing function of energy. If the short-range interaction is not of zero range then a constraint which gives the minimum possible range for it to fit the phase shifts exists. The implications of these results for effective field theory treatments of nucleon-nucleon interactions are discussed.
Cohen Thomas D. .
Phillips Daniel R.
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