Elastic collisions of mesons with electrons and protons

Abstract

The cross-sections for the elastic scattering of mesons by protons and electrons are calculated by analogy with Møller's theory of collisions between electrons, and the results are compared with those of Bhabha for the collisions with protons and electrons of Fermi-Dirac particles with the same mass as the meson. For collisions with electrons, the difference is inappreciable for energies of the meson less than 100 times its rest energy, but for collisions with protons the difference is important at much lower energies. The ratio of the corresponding cross-sections for scattering by a Coulomb field is found to tend to infinity as the square of the energy of the incident particle, giving a finite cross-section for the scattering of a meson of infinite energy by such a field. It is pointed out that, if an exact solution of this problem is possible for the meson case, the question of the validity of meson theory for high energies would be considerably clarified.