Meson Production by Mesons

Abstract

A calculation of meson production in a meson-nucleon collision has been carried out for the processes ${\ensuremath{\pi}}^{+}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{+}+n$ and ${\ensuremath{\pi}}^{+}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{0}+p$, by means of the method of Low. Use has been made of an approximate from of the Chew-Low transition matrix for scattering off the energy shell. This matrix exhibits explicity the resonance behavior of the isotopic spin $\frac{3}{2}$, angular momentum $\frac{3}{2}$ scattering state. At 350-Mev incident-meson kinetic energy, the cross section for ${\ensuremath{\pi}}^{+}$ production is 0.86 mb and that for ${\ensuremath{\pi}}^{0}$ production is 5.5 mb. The angular distribution of each final state meson is of the form $A+{cos}^{2}\ensuremath{\theta}$. For ${\ensuremath{\pi}}^{+}$ production, at 250-Mev incident-meson kinetic energy, $A=0.64$. The two final-state pions seem to share the available kinetic energy. The probability for a spin flip of the nucleon in the process is about 1.5 times the probability for no spin flip.