General Classical Theory of Spinning Particles in a Meson Field

H. J. Bhabha
1941 Proceedings of the Royal Society A  
An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant y - of the dimensions of a reciprocal length, y being the meson theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical
more » ... trary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 109 eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p4/F 2 (p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E ~ 3-5 its value at this point being 3 x 10~26 cm.2, after which it decreases rapidly, becoming proportional to E~2 at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E > The scattering of longitudinally polarized mesons is due to the translational but not therotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2e and -e may occur in nature, the above results on July 19, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from t Bhabha and Corben (1941), referred to in this paper as C. Classical theory of spinning particles in a meson field 315 on July 19, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from This differs completely from the quantum cross-section for the scattering of mesons by neutrons (or protons) due to the appearance of the constant K , Vol 178 A.
doi:10.1098/rspa.1941.0057 fatcat:u4dpxqdptjahzmtsugdoaqkohi