On a New Theory of Nuclear Forces

Abstract

A new theory of nuclear forces is based on the result established in an earlier paper that if the matrix ${\alpha }^0$ in the field equations $({\alpha }^k{p}_k+\chi )\psi =0\mathrm{}$ satisfies the minimal equation ${\{{\left({\alpha }^0\right)}^2-1\}}^2{\left({\alpha }^0\right)}^s=0\mathrm{}$, any integer, then every component of the field $\psi$ satisfies the iterated generalized wave equation ${(\square +{\chi }^2)}^2\psi =0\mathrm{}$ of the fourth order. The static potential between two nucleons is then a sum of the interaction (29) between two point charges and the dipole-dipole interaction (30) multiplied by numerical coefficients and isotopic spin factors. This interaction, unlike the usual one based on the Yukawa theory, allows an exact solution of the deuteron problem. The potentials based on more complicated fields satisfying the $n$ times iterated generalized wave equation are also given.