The Multiple Production of Mesons

In this paper an attempt is made to treat the impacts of nucleons of very high energy (≫ ${\mathrm{Mc}}^2$). These impacts lead to meson emission, despite the relatively small momentum transfers to be expected, because changes of nuclear charge and spin require a readjustment of the nuclear meson fields. Where the fields are strong (as e.g., in the pseudoscalar case), meson emission is multiple, and the multiplicity increases with energy. For weaker coupling (e.g., scalar fields) this is not true. Two closely related methods are developed for a more quantitative description of these collisions. These methods may be expected to give valid results when the collision time is short compared to the periods of the emitted mesons, and when the emission of mesons into the various modes can be treated as statistically independent. Under these conditions the total cross section may be expected to be about ${10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$, and the multiplicity to approach for high energies $2g^{\frac{2}{3}}{\left(\frac{M{E}_0}{2\pi {\mu }^2{c}^2}\right)}^{\frac{1}{2}}$, with $E_0$ the primary energy and $g$ the dimensionless coupling constant. Some applications to the calculation of positive excess, primary spectrum, angular distribution, and the theory of auger showers, are discussed briefly in the final section.