Binding Energy of the Deuteron

The binding energy of the deuteron is written in terms of once-subtracted, sidewise dispersion relations for the mass-energy form factors of the neutron, proton, and deuteron. The threshold region is assumed to dominate, and accordingly a cutoff is introduced into the dispersion integrals. This cutoff is, however, related to the proton-neutron mass difference $\delta M$, so that no free parameter exists in the work. The binding energy $B$ is reproduced for a cutoff value corresponding to $\delta M\sim 1.7$ MeV, this being the $\delta M$ calculated by Pagels. Both electromagnetic effects and the deuteron breakup into an $S$-wave, triplet-state nucleon pair are considered for contributions to $B$. No realistic estimate has been made of the effect on the result of $\pi$ mesons in the intermediate-state expansion. The two-nucleon-state contribution dominates the results, accounting for approximately 90% of $B$ at the experimental value of 2.2 MeV.