On the Heavy-Electron Pair Theory in the Limit of Strong Coupling

The pair theory of Marshak and Weisskopf was investigated assuming strong coupling. The strong coupling criterion is $A=\left(\frac{\mathrm{Nf}}{\mu }\right)>\mathrm{}5\mathrm{}$ where $f=\mathrm{coupling} \mathrm{constant}$, $\mu =\mathrm{heavy} \mathrm{electron} \mathrm{mass}$, $N=\int U^2\mathrm{}\left(x\right)\mathrm{}{d}^{3}x$, $U\left(x\right)=\mathrm{source} \mathrm{function} \mathrm{of} \mathrm{the} \mathrm{nucleon}$. $\frac{N\cong 1}{\pi a^3}$, where $a=\mathrm{source} \mathrm{radius}$ (all in units where $\hslash =c=1\mathrm{}$). With this condition, the magnetic moment turns out to be of order $A^{-1\mathrm{}}$, and of magnitude too small to account for the observed anomalies. The leading term in the potential of the force between two nucleons (for $r_{\mathrm{AB}}>2a$) is independent of the spin orientations, of the coupling constants, and of the type of coupling (as long as no derivatives of the heavy-electron field quantities occur in the coupling term). This potential is identical with the one calculated by Jauch and Houriet, but was not considered by Nelson and Oppenheimer. The next term in the potential is of order $A^{-3\mathrm{}}$. It corresponds to a superposition of a (${\Sigma }_A·{\Sigma }_B$) term, a tensor force term, and an ordinary force. Being of order $A^{-3\mathrm{}}$ it is too small, however, to fit the experimental results.