On the binding energy of the deuteron

The binding energy of the deuteron is written in terms of dispersion integrals of the mass-energy form factors of the neutron, proton, and deuteron. These form factors are found by studying the particle-graviton vertex interaction. The vertices are expanded in terms of various intermediate states and the required form factors are extracted from these expansions by the use of projection operators. The threshold region is assumed to dominate and accordingly a cutoff is introduced into the dispersion integrals. The cutoff is, however, related to the neutron-proton mass difference so that no free parameter exists in the work. The binding energy, 2.2MeV, was obtained for a cutoff that corresponded to a neutron-proton mass difference of 1.7MeV. It was found that the strong interaction effects dominated the electromagnetic effects on the binding energy. The strong interaction contribution, introduced through the two nucleon intermediate state expansion of the deuteron-graviton vertex, was found to be sensitive to the cutoff parameter. An indication was made as to the reason for the non-existence of a bound, singlet, S-state neutron-proton system. (author)