On the Interaction of Mesotrons and Nuclei

~ 'HE formalism of mesotron field theories was first developed in analogy either with the method of classical electrodynamics that involves the determination of fields produced by pregiven sources, or with the perturbation technique of quantum electrodynamics. This program not only has led to predictions in contradiction with experiment (the singular nature of nuclear forces, and large cross sections for mesotron scattering by nuclei) but is intrinsically inconsistent, for the methods of electrodynamics, involving the neglect of the reaction of field on source, and based on the small magnitude of the coupling between charges and the electromagnetic field, are here quite unjustified. This inconsistency is rendered far sharper by the chargeand spin-dependent couplings of the mesotron theory. These difficulties have led to two apparently unrelated suggestions for modifying the formal treatment of mesotron theory. Thus Heisenberg has attempted a more complete solution of the mesotron equations by including, within the framework of a classical theory, the large reaction of the field on the emitting source. He treated the problem of a neutral vector field interacting with a fixed, spatially extended source to which is attached a classical spin. His calculations showed that the inertia of the spin, arising from the reaction of its proper field, would greatly reduce the spindependent mesotron scat tering. A relativistic variant of this procedure has been elaborated by Bhabha, who based his work on Dirac's classical electron model. Those terms in the field reaction on the source which become singular as a, the spatial extension of the source, vanishes, are discarded and the finite terms are evaluated in the limit of point coupling. However, it is precisely these singular terms that are essential for Heisenberg's explanation of the small mesotron scattering. Furthermore, quite apart from the serious question of whether this method affords a classical description of elementary particles, it is so essentially restricted to the classical domain