Meson Production by Mesons

Abstract

A calculation of meson production in a meson-nucleon collision has been carried out for the processes ${\pi }^{+}+p\to {\pi }^{+}+{\pi }^{+}+n$ and ${\pi }^{+}+p\to {\pi }^{+}+{\pi }^0+p$, 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 ${\pi }^{+}$ production is 0.86 mb and that for ${\pi }^0$ production is 5.5 mb. The angular distribution of each final state meson is of the form $A+{cos}^2\theta$. For ${\pi }^{+}$ production, at 250-Mev incident-meson kinetic energy, $A=0.64\mathrm{}$. 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.