Production of Charged Pions inN−PCollisions

Abstract

The differential cross section and energy spectra for the production of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ mesons by the 400-Mev neutron beam of the Chicago synchrocyclotron on liquid hydrogen has been measured at 90\ifmmode^\circ\else\textdegree\fi{} and 65\ifmmode^\circ\else\textdegree\fi{} in the laboratory, using photographic emulsions as detectors. At 65\ifmmode^\circ\else\textdegree\fi{} (corresponding to 90\ifmmode^\circ\else\textdegree\fi{} in the center-of-mass system), roughly equal numbers of positive and negative pions were observed, while at 90\ifmmode^\circ\else\textdegree\fi{} the ratio of positive to negative pions was found to be 2.01\ifmmode\pm\else\textpm\fi{}0.24. The laboratory integrated cross sections ${(\frac{d{\ensuremath{\sigma}}_{\mathrm{Av}}}{d\ensuremath{\Omega}})}_{\mathrm{Av}}$, in ${\mathrm{cm}}^{2}$/sterad, are: for ${\ensuremath{\pi}}^{+}$ at 90\ifmmode^\circ\else\textdegree\fi{} (2.296\ifmmode\pm\else\textpm\fi{}0.363)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}29}$, for $Tg14$ Mev; for ${\ensuremath{\pi}}^{\ensuremath{-}}$ at 90\ifmmode^\circ\else\textdegree\fi{}, (1.56\ifmmode\pm\else\textpm\fi{}0.357) \ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}29}$ for $Tg14$ Mev; for ${\ensuremath{\pi}}^{+}$ at 65\ifmmode^\circ\else\textdegree\fi{}, (1.22\ifmmode\pm\else\textpm\fi{}0.30)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}29}$, for $Tg41$ Mev; and for ${\ensuremath{\pi}}^{\ensuremath{-}}$ at 65\ifmmode^\circ\else\textdegree\fi{}, (1.31\ifmmode\pm\else\textpm\fi{}0.63)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}29}$. These experimental cross sections are the result of production due to neutrons of all energies above the threshold for pion production in the neutron beam.A phenomenological analysis is made for the reaction $N+P\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ under the hypothesis of charge independence and the energy and angular distributions of the pions at a single neutron energy are deduced from the experimental cross sections. The total cross section for ${\ensuremath{\pi}}^{+}$ or ${\ensuremath{\pi}}^{\ensuremath{-}}$ production, at neutron energy 409 Mev, is determined to be $\ensuremath{\sigma}({\ensuremath{\pi}}^{+})=\ensuremath{\sigma}({\ensuremath{\pi}}^{\ensuremath{-}})=0.16\ifmmode\pm\else\textpm\fi{}0.04 \mathrm{millibarn},$ and the differential cross section for the same neutron energy is calculated to be ${{(\frac{d\ensuremath{\sigma}}{d\ensuremath{\omega}})}^{\ifmmode\pm\else\textpm\fi{}}=(1.07\ifmmode\pm\else\textpm\fi{}0.39)\ensuremath{\mp},(1.38\ifmmode\pm\else\textpm\fi{}0.78)cos\ensuremath{\theta}}{+(0.57\ifmmode\pm\else\textpm\fi{}1.14){cos}^{2}\ensuremath{\theta}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}29} {\mathrm{cm}}^{2}/\mathrm{sterad}.}$