A New Method for Determining the Relative Phase with Which Slow Neutrons Are Scattered by Nuclei

Abstract

To determine the relative phase with which neutrons are scattered by an element $A$, cross-section measurements are obtained for $A$, for a reference element $B$, and for a substitutional solid solution of $A$ and $B$. The experimental value of the effective coherent scattering cross section, $\sigma _{\mathrm{coh}}^{}{}_{}{}^{\prime }$, for the solid solution, when compared with the values calculated from the data for pure $A$ and $B$, shows whether the two constituent elements scatter neutrons in the same or in opposite phases. Measurements made with the Columbia neutron velocity spectrometer show that copper and nickel scatter with the same phase, and manganese and nickel with opposite phases, in agreement with other methods of phase determination. The following more accurate values of the free scattering cross sections, ${\sigma }_{\mathrm{f}}$, and new values of the effective coherent scattering cross sections, $\sigma _{\mathrm{coh}}^{}{}_{}{}^{\prime }$, were obtained: copper, ${\sigma }_{\mathrm{f}}=8.2\mathrm{}$ barns, $\sigma _{\mathrm{coh}}^{}{}_{}{}^{\prime }=6.6\mathrm{}$ barns; nickel, ${\sigma }_{\mathrm{f}}=17.4\mathrm{}$ barns, $\sigma _{\mathrm{coh}}^{}{}_{}{}^{\prime }=13.9\mathrm{}$ barns; manganese, ${\sigma }_{\mathrm{f}}=1.80\mathrm{}$ barns. $\sigma _{\mathrm{coh}}^{}{}_{}{}^{\prime }=\sim 1.9$ barns.