Low-energy $p-d$ scattering: High-precision data, comparisons with theory, and phase-shift analyses

Angular distributions of $\sigma \left(\theta \right),$ $A_y,$ ${\mathrm{iT}}_{11},$ $T_{20},$ $T_{21},$ and $T_{22}$ have been measured for $d-p$ scattering at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=667\mathrm{}\mathrm{keV}.$ This set of high-precision data is compared to variational calculations with the nucleon-nucleon potential alone and also to calculations including a three-nucleon $\mathrm{}\left(3N\right)\mathrm{}$ potential. Agreement with cross section and tensor analyzing power data is excellent when a $3N$ potential is used. However, a comparison between the vector analyzing powers reveals differences of approximately 40% in the maxima of the angular distributions which is larger than reported at higher energies for both $p-d$ and $n-d$ scattering. The inclusion of phenomenological spin-orbit forces in a $3N$ potential improves the comparison with vector analyzing powers substantially. Single-energy phase-shift analyses were performed on this data set and a similar data set at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=431.3\mathrm{}\mathrm{keV}.$ The role of the different phase-shift parameters in fitting these data is discussed.