On the Meson Charge Cloud Around a Proton

Abstract

The calculations of Fröhlich, Heitler, and Kahn for the deviation from the Coulomb law for a proton owing to mesons are re-examined and extended to the scalar meson theory. A perturbation calculation is used up to terms proportional to the square of the coupling constant, including the recoil of the nucleon to first order in $\frac{\mu }{M}$. The recent Dirac theory involving negative energy states of the mesons, in conjunction with the $\lambda$-limiting process due to Wentzel, makes the theory convergent. The dissociation probability $P$ of a proton in this theory is proportional to the square of the coupling constant and to the mass ratio $\frac{\mu }{M}$. $P$ is of the order of 2 percent. The meson charge cloud produces only a slight decrease of the Coulomb force acting on a charged test-particle, not a reversal of this force. No experimentally observable effects can be expected from the processes considered. The results of Fröhlich, Heitler, and Kahn are not reproduced by the convergent theory.