Relativity and Nuclear Forces

To obtain an estimate of the relativity correction in nuclear problems, the Klein-Gordon theory is applied to the common forms of interaction between the neutron and the proton. Because there is an appreciable region of space in which the zero-point energy is enormous, the relativity effect is larger than would be supposed by mere inspection of binding energies. For the deuteron, it amounts to several times the binding energy if the forces have a range around ${10}^{-13\mathrm{}}$ cm; for ranges about 3 × ${10}^{-13\mathrm{}}$ cm it decreases to a few percent of the binding energy.—The calculations were based on two types of assumed interactions: the rectangular potential hole and the error function potential.