Electrostatic Corrections to Nucleon-Nucleon Dispersion Relations

Abstract

BS>Assuming that a nonrelativistic wave-function description of the nucleon-nucleon scattering system is valid at low energy and large distances, analytic properties of nuclear (i.e., total minus Coulomb) partial wave scattering amplitudes are investigated as functions of the c.m. momentum q. For singlet states, the essential singularity at q/sup 2/ = 0 can be treated exactly in the partial wave dispersion relation. The remaining singularities are branch points located at the same position as for the non-Coulomb case. The discontinuity across the 1- pi exchange cut is a simple multiplicative factor (which goes to unity as e/sup 2/ goes to zero) times the discontinuity in the absence of Coulomb scattering. From this structure, an integral equation for the partial wave scattering amplitude is derived. Consequences of these corrections in the /sup 1/S/sub o/ state are investigated. For q/sup 2/ < - mu /sup 2/ there are additional electrodynamic corrections to the interaction produced by multi- pion exchange. These should be, at most, of about the 31/2% mass difference between charged and neutral pions. Any phenomenological treatment of the multi- pion exchange should differ by, at most, 31/2% between n-p and p-p scattering. Representing this interaction by a single pole, but includingmore » exactly, single- pion exchange, and the charged-neutral pion mass difference in that exchange, the low-energy /sup 1/S/sub o/ n-p and p-p scatterings are consistent with charge independence. Assuming exact charge symmetry, an n-n scattering length of -27 plus or minus 1.4 fermi is predicted. Since a departure from charge symmetry of plus or minus 5% would vary this prediction between -18 and -53 fermi, a measurement of this quantity will provide a sensitive quantitative test of charge symmetry. (auth)« less