On the Scattering of Mesons of Spin12ℏby Atomic Nuclei

Abstract

The non-electric scattering of charged mesons by protons and neutrons is calculated as a first-order effect in the heavy electron pair theory of nuclear forces. The latter theory regards the mesons as heavy electrons, that is, as particles with spin $\frac{\hslash }{2}$, obeying the Dirac equation and differing from usual electrons only in their rest mass $\mu$. An upper limit for the scattering cross section of mesons by nuclear particles is derived; it is found that the cross section is less than 4×${10}^{-30\mathrm{}}$ ${\mathrm{cm}}^2$ for mesons of energy $E=\mu c^2$ and less than 1.6×${101}^{-29\mathrm{}}$ for $E=3\mathrm{}\mu c^2$. These values are about 1000 times smaller than the corresponding cross sections obtained on the basis of meson theories of nuclear forces which ascribe to the meson a spin $\hslash$. In contrast to the latter theories the values obtained in the present paper are in agreement with the upper limits of the scattering cross section found experimentally by Wilson and others. For meson energies large compared to the rest energy of the proton or neutron, the scattering cross section increases linearly with the energy; it first attains the value ${10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$ for meson energies of the order of ${10}^{11}$ ev.