Nucleon-nucleon scattering near 50 MeV. II. Sensitivity of variousn−pobservables to the phase parameters

In the first paper in this series, we reported on a phase-shift analysis of existing $p-p$ and $n-p$ data in the energy range of 47.5 to 60.9 MeV. Two results were emphasized. The first is that the available $n-p$ data leave ${\epsilon }_1$ undetermined within the range -10° to +3°, resulting in a range of phase-parameter solutions, rather than a single solution. The second result is that while ${\epsilon }_1$ is very poorly determined, $\delta \left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ is rather well determined, but at a value which appears to conflict not only with values obtained at adjacent energies, but also with the value (or narrow range of values) predicted by meson-theoretical models. In that paper it is reported that the Harwell $n-p \frac{d\sigma }{d\Omega }$ data are responsible for this value of $\delta \left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$. The remaining data, consisting only of ${\sigma }_{\mathrm{tot}}$ data, polarization data, and other $\frac{d\sigma }{d\Omega }$ data, are consistent with the theoretical predictions. In this paper we look more closely at the sensitivity of experimental observables to variations in the partial-wave parameters. We extend the number of experimental observables under study to twenty, and consider the effect on these of varying seven different phase parameters: $\delta {\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)}_{\mathrm{np}}$, $\delta \left({}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)$, ${\epsilon }_1$, $\delta \left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, $\delta \left({}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}\right)$, $\delta \left({}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}\right)$, and $\delta \left({}_{}{}^3{}_{}{}^{}D_3^{}{}_{}{}^{}\right)$. We discover that the best observable to fix $\delta \left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ is still the differential cross section, and recommend, as in the first paper, that it be measured both at extreme forward and extreme backward angles. We also discover that the reason ${\epsilon }_1$ is very poorly determined by the present data is that neither ${\sigma }_{\mathrm{tot}}$, $\frac{d\sigma }{d\Omega }$, nor $P$ is sensitive to changes in ${\epsilon }_1$. We find that the experimental observables which are sensitive to ${\epsilon }_1$ and can fix this parameter are, in order of decreasing sensitivity, $A_{\mathrm{zz}}$, $C_{\mathrm{pp}}$, $A_t^{\prime }$, $C_{\mathrm{KK}}$, $A_t$, $D_t$, $C_{\mathrm{nn}}$, and $A_{\mathrm{xx}}$.