Measurement of the 12C(p, pi 0)13N reaction by recoil detection.

Abstract

Differential cross sections for the neutral pion production reaction $^{12}\mathrm{C}$(p,${\mathrm{\ensuremath{\pi}}}^{0}$${)}^{13}$${\mathrm{N}}_{\mathrm{g}.\mathrm{s}.}$ have been measured at 153.5, 166.1, 186.0, and 204.0 MeV bombarding energy using recoil detection. The shape of the angular distribution agrees well with that of the mirror reaction $^{12}\mathrm{C}$(p,${\mathrm{\ensuremath{\pi}}}^{+}$${)}^{13}$${\mathrm{C}}_{\mathrm{g}.\mathrm{s}.}$. Isospin invariance predicts for the ratio of the cross sections \ensuremath{\sigma}(p,${\mathrm{\ensuremath{\pi}}}^{+}$)/\ensuremath{\sigma}(p,${\mathrm{\ensuremath{\pi}}}^{0}$)=2. At 153.5, 166.1, and 186.0, MeV, where (p,${\mathrm{\ensuremath{\pi}}}^{+}$) cross sections have been reported previously by other groups at the same reduced pion momentum \ensuremath{\eta}=${\mathit{p}}_{\mathrm{\ensuremath{\pi}}}$/${\mathit{m}}_{\mathrm{\ensuremath{\pi}}}$c=0.34,0.55,0.78, the ratio of the total cross sections is 2.02\ifmmode\pm\else\textpm\fi{}0.14, 3.14\ifmmode\pm\else\textpm\fi{}0.12, and 2.12\ifmmode\pm\else\textpm\fi{}0.16, respectively. The (p,${\mathrm{\ensuremath{\pi}}}^{0}$) cross sections at 166 MeV is therefore 1.57\ifmmode\pm\else\textpm\fi{}0.06 times larger than expected. For ${\mathit{T}}_{\mathit{p}}$160 MeV, the experimental cross sections are larger than predicted by a phase space and Coulomb barrier penetration calculation that fits the higher-energy data. Differential cross sections were also obtained for the $^{12}\mathrm{C}$(p,${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$${)}^{13}$O reaction, and upper limits set for differential cross sections for radiative capture to the ground state of $^{13}\mathrm{N}$.