Energy-dependent and energy-independent phase-shift analyses are given for ($p,p$) and ($n,p$) experiments from 0.5 to 450 MeV. The 2066 data include 1076 ($p,p$) and 990 ($n,p$) values. The theoretical analysis has been extended to include magnetic-moment corrections, separate ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ phases for ($p,p$) and ($n,p$) scattering, $S$-wave vacuum-polarization effects, and inelastic effects due to pion production with isotopic spin $I=1\mathrm{}$ (down to threshold). Precision fits to the data are obtained over the whole energy range. The least-squares sum ${\chi }^2$ is 1126 for a 26-parameter energy-dependent fit to the ($p,p$) data. The $M$ value is 1.046. The value for the pion-nucleon coupling constant obtained from this solution is $g^2=14.43\mathrm{}\pm 0.41$. The $I=1\mathrm{}$ scattering matrix is quite accurately and uniquely determined over the whole energy range. Two 26-parameter energy-dependent solutions are given for the fit to the ($n,p$) data. The first solution (unconstrained) has somewhat anomalous values for ${\epsilon }_1$ and ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ at low energies. The second solution has a constraint that forces ${\epsilon }_1$ to positive values at low energies. When this is done, the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ phase also changes to values expected from theory. The values of ${\chi }^2 \mathrm{}\left(M\right)\mathrm{}$ from the ($n,p$) data for these two solutions are 1100 (1.11) and 1138 (1.15), respectively; thus both solutions are statistically acceptable. The ($n,p$) solution at 425 MeV has been greatly improved by the addition of precise triple-scattering data from the Chicago-Wisconsin group. Comparison of energy-dependent and energy-independent solutions shows that the $I=0\mathrm{}$ scattering matrix is fairly accurately determined at 142, 210, and 425 MeV, but at 25, 50, 95, and 330 MeV the solution is not definitive, because of a lack of ($n,p$) data. Measurement of the ratio $\frac{\sigma \left({180}^{\circ }\right)}{\sigma \left({90}^{\circ }\right)}$ for ($n,p$) scattering at 25 or 50 MeV to an accuracy of 1% would help to remove the ambiguity in the ${\epsilon }_1$ and ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ phases. The use of a separate ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ phase for ($n,p$) scattering eliminated the difficulty we formerly had in fitting to ($n,p$) total cross sections below 100 MeV, and especially at very low energies. The addition of $S$-wave vacuum-polarization effects permitted a precision fit to the lowest-energy ($p,p$) differential-cross-section data. The combined ($p,p$) plus ($n,p$) 1—450-MeV energy-dependent solution, with 52 parameters representing 27 elastic phases and one inelastic phase, has ${\chi }^2=2226\mathrm{}$ for 2066 data. The $M$ value is 1.077.

• Received 4 November 1968

DOI:https://doi.org/10.1103/PhysRev.182.1714