(Received January 21, 1943)
The mesotron field surrounding the nucleons and the motion of their spins were classically investigated by solving the equations of motion for the field and the spins not taking account of the commutation relations between various quantities. We treated the charged longitudinal, the neutral pseudoscalar and the symmetrical pseudoscalar mesotrons. It was found that the motion consists of the precession of the spins and the simultaneous rotation of the self-field. The angular velocities of the precession of the spins or of the isotopic spins of the nucleons are very small on account of the large inertia of the self-field for the rotation, and, as the result, the nuclear potential can sufficiently be approximated by the static potentials in the sense of Møller and Rosen-field(1) regarding the spin quantities in them as classical vectors. It is to be noted that the singularities of the potentials do not disappear even if we solve the problem rigorously in the classical limit and consequently take the possible effect of the reaction of the field into account.
The quantum-mechanical Hartree approximation was also applied to these problems, and it was shown that, when the coupling is strong, the results of the quantum mechanical treatment agree quite well with the classical, and that they also coincide with the static potential of Moller and Rosenfeld when the coupling is weak.
As we have two sorts of quantities, i.e., (1) self-energy, singularity of the potential, which increase with increasing strength of the coupling and (2) scattering cross-section of the nucleon for slow mesotrons, the isobar separation of the nucleon, which decrease with the increasing coupling parameter, it will be possible in principle to determine the upper and the lower limits of the coupling strength, the constant of the interaction or of the cutting-off, by comparing the theory with the experiments.
URL : http://ptp.ipap.jp/link?PTPS/2/82/
DOI : 10.1143/PTPS.2.82