Proton-Neutron Final-State Interaction

The reactions $p(d,2p)n$ and $d(p,2p)n$ were studied at a proton bombarding energy of 16.0 MeV and deuteron bombarding energies of 16.0 and 10.0 MeV. The protons were detected in coincidence with solid-state detectors at angles that allow strong enhancement of the $p-n$ final-state interaction. The coincidence resolving time was sharpened by using time-energy correlation techniques that utilize an on-line SDS-910 computer. The data were analyzed using the "data-simulation technique." A simple theory, which, apart from normalization, contained three adjustable parameters, was found to produce satisfactory fits. In this theory, the final-state interactions are accounted for by assuming additive enhancements for each pair of final-state particles and each spin state. The primary interaction is approximated by the sum of a constant amplitude plus the spectator-effect amplitude. The widths of the final-state interaction peaks are in good agreement with Watson theory using the known singlet $p-n$ scattering length $a_{\mathrm{np}}^{}{}_{}{}^s$ of —23.69 F. The most accurately determined scattering length was extracted from the 16-MeV $p+d$ data and was $a_{\mathrm{np}}^{}{}_{}{}^s=-23.8\mathrm{}\pm 0.5$ F. This agreement indicates that interference effects are not important in this reaction at center-of-mass energies above a few MeV if coincidence techniques are employed. With similar methods, a comparative study of the $n+d$ reaction in order to measure the singlet $n-n$ scattering length should be fruitful.