Theory of Mesons and Nuclear Forces

Abstract

As was first pointed out by Yukawa, it is in principle possible to account for the short-range forces between nuclear particles by the assumption of virtual emission and absorption processes involving intermediary particles of integral spin, the so-called mesons¹, the mass of which is determined by the range of the forces. As has been shown by Kemmer², the simplest wave-equations for the mesons which satisfy, besides the claim of relativistic invariance, the condition of giving a positive definite expression for the energy, reduce to four types, characterized by different co-variance properties of the wave-functions, and each allowing the existence of neutral as well as positively and negatively charged mesons. Starting from such wave-equations, including the interaction of the meson field with the heavy nuclear constituents, the estimation of the resulting expressions for the nuclear forces has hitherto been carried out by using the ordinary perturbation method of quantum theory, and taking into consideration only the first non-vanishing approximation, in spite of the well-known lack of convergence of the method. It would thus seem desirable to discuss more closely the reliability of such results, and for this purpose a possible method of attack is suggested by an analogous situation in quantum electrodynamics, where a suitable canonical transformation allows us to separate, from the expression of the total energy of a system consisting of electrons and an electromagnetic field, a term depending only on the coordinates of the electrons and representing the Coulomb potential energy.