The existing theory gives the cross section for the process of scattering of mesons by heavy particles (i.e., the protons and the neutrons), which increases with energy and is thus contradictory to experimental data as well as to a number of general principles. This increase must be explained as a result of the neglect of the reaction of the proper field of the particle's quasi-magnetic moment on the motion of this moment. If the proper field is taken into account in a quantum mechanical case, we are naturally led to the necessity of supposing that the proton and the neutron possess excited states of spin $\frac{3}{2}$ and even greater. In the present paper, the relativistic theory for the particle capable of being in the state with spin ½ and the rest mass $m_1$, as well as in the state with spin $\frac{3}{2}$ and the rest mass $m_2>m_1$ is developed. It is shown that the cross section for the scattering of light (of mesons) by the magnetic (by the quasi-magnetic) moment of such a particle increases at first with energy, as in the usual theory. However, for photons with energies $\hslash \nu \gg (m_2-m_1)c^2$ the cross section becomes constant (the recoil for the heavy particle being neglected). Therefore, the introduction of the higher spin states, which is adequate to account for the proper field of the particle's moment, offers the possibility of treating consistently the interaction of the magnetic moment with radiation by the usual perturbation theory methods.

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