Proposed experimental study of wave-particle duality in $p,p$ scattering

Of all nuclear physics experiments none are more fundamental than ``elastic'' $p,p$ and, secondarily, $p,d$ or $d,d$ scattering. Recognizing that these particles are themselves composite, ``elastic'' scattering may be accompanied by temporary internal rearrangement with undetectably small energy loss. % This paper argues that correct calculation of the spin dependence of $p,p$ elastic scattering must account for a previously-neglected relativistic effect of ``$G$'', the anomalous magnetic dipole moment (MDM) of the scattering particles and proceeds to describe storage ring $p,p$ scattering configurations capable of confirming this contention. % Especially important experimentally for protons is the existence of ``near perfect'' proton-carbon scattering polarimetric analyzing power $A$ near $K=183.1$\,MeV laboratory kinetic energy. % Possibilities: (i) With counter-circulating $K=200\,$MeV energy proton beams the final spin states of coincident scattered protons can be determined with high probability for a significantly large fraction of all scatters. For comparison with current descriptions this corresponds roughly to proton kinetic energy $K=400\,$MeV in the laboratory frame, close to the pion production threshold. % (ii) In a ``DERBENEV-style'' figure-8 storage ring, independently polarized, diametrically opposite bunches on orthogonal orbits can collide at the beam crossover point with symmetric $K''\approx200$ MeV energies in a slow, transversely moving frame. % (iii) $p$ and $d$ beams can counter-circulate at the same time in a small racetrack shaped ring with superimposed electric and magnetic bending. In this case the scattering would be ``WOLFENSTEIN-style'' with collinear incident orbits. % To investigate the consistency of quantum mechanics and special relativity it is proposed to implement options (ii) and (iii) in the COSY beam hall.