Determination of the Nucleon-Nucleon Scattering Matrix. IX. (n,p) Analysis from 7 to 750 MeV

Abstract

Papers VII and VIII in this series contained phase-shift analyses of ($p,p$) data from 0-400 MeV and from 0-750 MeV, respectively. The present paper gives the corresponding ($n,p$) analyses. In the energy region below 400 MeV, six single-energy analyses were carried out, as well as an energy-dependent analysis. The combined ($p,p$) plus ($n,p$) energy-dependent analysis below 400 MeV includes 839 ($p,p$) data and 912 ($n,p$) data. With 45 phenomenological parameters representing 14 free isovector phases and 11 free isoscalar phases, we obtain a solution that yields an average ${\chi }^2$ per datum of 1.08 for the 1751 data. This solution gives a precision fit to the data from 400 down to 4 MeV, and it extrapolates well above 400 MeV. At energies below 50 MeV, we find that the existing ($n,p$) data are not yet complete enough to permit a unique determination of the isoscalar phases. Single-energy analyses were also carried out at 425 and 630 MeV, as well as a combined ($p,p$) plus ($n,p$) energy-dependent analysis from 0 to 750 MeV. The energy-dependent solution, which includes 53 phenomenological parameters that represent 25 free phases, was obtained by fitting 1147 ($p,p$) data from 23 to 736 MeV and 901 ($n,p$) data from 14 to 730 MeV. It has an average ${\chi }^2$ per datum of 1.34 for the 2048 data. However, at energies above 450 MeV, where, as shown in Paper VIII, the isovector amplitudes are not well known, we cannot uniquely define the isoscalar amplitudes. Nevertheless, the restriction on the phases imposed by fitting to experiments near 425 and 630 MeV enables us to sharpen our knowledge of the phase shifts at lower energies. We find that the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}D_3^{}{}_{}{}^{}$ phases exhibit maxima in the magnitudes near 300 MeV, and that the ${}_{}{}^1{}_{}{}^{}F_3^{}{}_{}{}^{}$ phase is monotonic. Second-derivative and error matrices are tabulated for the single-energy solutions at 25, 50, 95, 142, 210, 330, and 425 MeV. These matrices, which represent our phase-shift solutions fitted to 683 ($p,p$) data and 572 ($n,p$) data, contain most of the physical content of the entire elastic nucleon-nucleon data collection. Fitting potential models to these matrices is essentially equivalent to fitting directly to the data. Computationally, using the matrices is vastly simpler.