The Meson Theory of Nuclear Forces I. General Theory

Abstract

In this paper, the meson theory of nuclear forces is presented in a simplified way. As in Yukawa's first paper, the forces between two nuclear particles are derived directly from the field equations and the Hamiltonian of the meson field (\textsection{}2,3), without quantization of the field. The charge dependence of the forces is discussed (\textsection{}4) and it is found that only two assumptions are in agreement with experimental facts, notably the equality of the forces between two like and two unlike nuclear particles in the singlet state. These assumptions are either (1) that nuclear particles interact only with neutral mesons (neutral theory) or (2) that they interact equally strongly with neutral, positive and negative mesons (symmetrical theory). It is then shown (\textsection{}5) that the part of the force which does not depend on the spin of the nuclear particle does not fulfill any useful function in the theory. Accordingly, the hypothesis is made that this part is absent so that there is only a spin-dependent interaction (single force hypothesis). Finally (\textsection{}6), it is pointed out that the interaction must be cut off at small distances in order to obtain finite eigenvalues for the deuteron. Such a cutting off is to be expected from the general theory, particularly because of the possibility of the simultaneous emission of two or more mesons. The cut-off is to be expected at a distance ${r}_{0}$ of about one-third the range of the nuclear forces.