Neutron-Proton Scattering below 20 MeV

Critical examination and analysis of existing $n-p$ scattering data below 20 MeV reveal that they provide quantitative information only about the $S$-wave scattering lengths and effective ranges, which are found to be $a_t=5.396\mathrm{}\pm 0.011$ F; $a_s=-23.678\mathrm{}\pm 0.028$ F; $r_t=1.726\mathrm{}\pm 0.014$ F; $r_s=2.51\mathrm{}\pm 0.11\pm 0.043$ F; where the second error quoted for $r_s$ is a conservative estimate of the uncertainty due to departures from the shape-independent approximation. The correlations in error are $〈\delta a_t\delta a_s〉=-0.7828\mathrm{}\delta a_t\delta a_s$; $〈\delta a_t\delta r_s〉=-0.8547\mathrm{}\delta a_t\delta r_s$; $〈\delta a_s\delta r_s〉=0.7029\mathrm{}\delta a_s\delta r_s$. An estimate of the contribution to the total cross section from scattering in higher angular momentum states, based on model calculations, $p-p$ phases, and the $cos\theta$ term in the differential cross section, allows the deviation from the shape-independent approximation to be computed at 14.1 and 19.665 MeV from total cross-section measurements. It is shown on theoretical grounds that this must come almost entirely from the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state, and extreme limits to this variation are established. The value found is close to zero at both energies, in accord with theoretical expectations, but the uncertainty is so large that it barely excludes the extreme limits. Some qualitative evidence for or against the existence of the long-range one pion exchange interaction in this state could be obtained by improving the experiments below 5 MeV, but the uncertainty arising from the non-$S$ wave scattering precludes any but qualitative results. It is shown that this uncertainty cannot be removed by improved measurement of the differential cross section because 8 independent pieces of experimental information are required. We conclude that the energy variation of the $S$ waves below 20 MeV cannot be measured without recourse to experiments which separate the spin states of the particles, such as spin-correlation, triple scattering, polarized-beam polarized-target, etc. If some information is taken from $p-p$ scattering and some from theory, a single such measurement in each system might suffice; this minimal program is briefly discussed.