Symmetric, Lorentz invariant NN amplitude: Yukawa representation

Publisher Website
Google Scholar
Abstract
Previous work on the general representation of NN scattering amplitudes in the full Dirac space of two nucleons is extended to allow a simple realization of the generalized Pauli principle. New kinematic covariants are found which are linearly independent and which have simple particle exchange symmetries. This permits a representation in which all invariant amplitudes are even or odd with respect to interchange of initial state four-momenta or interchange of final state four-momenta for on-mass-shell kinematics. When parity invariance, charge symmetry, and time-reversal invariance are taken into consideration, it is found that for each isospin state there are 56 independent amplitudes for off-mass-shell kinematics, 50 independent amplitudes for quasipotential kinematics, and 44 independent amplitudes for on-mass-shell kinematics. A relativistic meson exchange model is used to calculate the invariant amplitudes for on-mass-shell kinematics, and the resulting amplitudes are fit by sums of Yukawa terms. The analysis provides complete sets of Feynman invariant amplitudes for 200, 500, and 800 MeV NN scattering.