The Interaction Between a Neutron and a Proton and the Structure ofH3

Suppose that the interaction between a neutron and a proton depends on their distance apart so as to be negligible above a certain small distance $a$, and yet is responsible for the mass defect of ${\mathrm{H}}^2$. Suppose further that the interaction between two neutrons and a proton may be compounded in the usual way from that between a neutron and a proton, the interaction between two neutrons being neglected, while there is no prohibition of a wave function symmetrical in the positions of two neutrons. Then it is shown that the mass defect of ${\mathrm{H}}^3$ is made arbitrarily large by taking $a$ small enough. The observed mass defect of ${\mathrm{H}}^3$ thus provides, on the above assumptions, a lower limit for $a$; and in particular rules out the possibility that the interaction may be regarded as arising from a singularity in configuration space. We conclude, in effect, that: either two neutrons repel one another by an amount not negligible compared with the attraction between a neutron and a proton; or that the wave function cannot be symmetrical in their positions; or else that the interaction between a neutron and a proton is not confined within a relative distance very small compared with ${10}^{-13\mathrm{}}$ ${\mathrm{cm}}^1$.