The tensor force between two protons at long range

The interaction energy due to long range tensor forces between two protons as accurately measured in molecular H ₂ agrees fully with that expected from the interaction of the measured magnetic moments of the two protons. This agreement sets an upper limit on the maximum possible long range tensor force which might be mediated by the exchange of an intermediate particle of mass less than 0.2 electron mass. A general expression is given for the limit as a function of the parameters assumed for the radial dependence of the interaction energy and the mass of the mediating particle provided the effects of molecular vibration are neglected; typical limits are tabulated. In a few specific cases the effects of molecular vibration are calculated and more severe limits are then obtained.