(p, γ) Resonance-Curve Shapes and Measurements of Resonance Energies withH1+Beams

Abstract

During the preparation of a new precise absolute energy scale for nuclear reaction accelerators, some were observed in the behavior of ($p, \ensuremath{\gamma}$) resonances. These observations led to an exhaustive investigation of ($p, \ensuremath{\gamma}$) yield-curve shapes and detailed interpretation of these shapes in terms of physically significant quantities such as resonance energy and resonance width. Most of the measurements have been made with respect to the 992-keV resonance in the ${\mathrm{Al}}^{27}(p, \ensuremath{\gamma})$ reaction, but other reactions have also been used. A list of the anomalies observed includes (1) the failure of the peaks of thin-target resonance yield curves to be shifted from resonance energy by as much as half the target thickness, (2) the displacement of the midpoint of the rise of thick-target yield curves to bombarding energies below the resonance energy, (3) the of the yield curve for thick targets forming a hump above the thick-target plateau, (4) the obtaining of apparently different intrinsic resonance widths for the same resonance and from the same thick target at different times separated by a few weeks, and (5) the obtaining of significantly different thick-target yield-curve shapes from the same target in two different orientations with respect to the beam. The anomalies are all satisfactorily explained on the basis of fluctuations in energy loss of the bombarding protons as they penetrate the target. The theory used was chiefly developed by Symon. Detailed numerical integrations of the formal yield equation have been made, and in most cases very good fits have been made with the experimental data. The information gained from this investigation is applied to energy calibrations resulting in precise best values for the following narrow ($p, \ensuremath{\gamma}$) resonances: ${\mathrm{Al}}^{27}(p, \ensuremath{\gamma}){\mathrm{Si}}^{28}$ reaction, 991.91\ifmmode\pm\else\textpm\fi{}0.30 and 1317.19\ifmmode\pm\else\textpm\fi{}0.40 keV; ${\mathrm{C}}^{13}(p, \ensuremath{\gamma}){\mathrm{N}}^{14}$ reaction, 1747.06\ifmmode\pm\else\textpm\fi{}0.53 keV; ${\mathrm{Ni}}^{58}(p, \ensuremath{\gamma}){\mathrm{Cu}}^{59}$ reaction, 1423.64\ifmmode\pm\else\textpm\fi{}0.43 and 1843.45\ifmmode\pm\else\textpm\fi{}0.56 keV. The displacement of the midpoint of the rise of a thick-target yield curve from the resonance energy ${E}_{r}$ as a function of the resonance width $\ensuremath{\Gamma}$ is discussed, and a typical curve of this relationship is shown. The overshoot or hump height for a thick target as a function of $\ensuremath{\Gamma}$ is also discussed, and a curve is shown.