Theory of Inelastic Proton-Deuteron Scattering

Abstract

Calculations are made of the small-angle inelastic proton-deuteron cross section near threshold. The theory assumes impulse approximation to relate the interaction of the incident proton with the target nucleons to the free nucleon-nucleon scattering amplitude. Effective-range theory is used to describe the final-state interaction of the target nucleons in the $S$ state. The cross section at small angles is dominated by events which leave the target nucleons in the singlet $S$ state. The cross section depends on three nucleon-nucleon parameters: the coefficients of the singlet $S$ and triplet $S$ terms in the cross section, ${\ensuremath{\Sigma}}_{s}$ and ${\ensuremath{\Sigma}}_{t}$ and the sum of the proton-neutron and proton-proton differential cross sections, ${\ensuremath{\sigma}}_{\mathrm{np}}+{\ensuremath{\sigma}}_{\mathrm{pp}}$. These parameters are determined at the laboratory angles of 5\ifmmode^\circ\else\textdegree\fi{}, 10\ifmmode^\circ\else\textdegree\fi{}, 15\ifmmode^\circ\else\textdegree\fi{}, and 20\ifmmode^\circ\else\textdegree\fi{} by making a least-squares fit to the experimental measurements of Stairs, Wilson, and Cooper in the preceding paper. This fit mainly determines ${\ensuremath{\Sigma}}_{s}$. This parameter is particularly sensitive to the isotopic spin zero nucleon-nucleon amplitudes and thus these values of ${\ensuremath{\Sigma}}_{s}$ may be of use in future phase-shift analyses.