Neutron-Proton Interaction. Part II. The Scattering of Neutrons by Protons

It may be that also for free particles, as well as in the case of binding, the neutron-proton interaction operator can be represented by a potential $J_1\mathrm{}\left(r\right)\mathrm{}$. Because the conditions of binding and of scattering are so different there is no reason to expect $J_1$ to be identical with $J$, the potential for binding. The inequalities $J_1<J$ and $\frac{\partial J_1}{\partial W}<0\mathrm{}$ ($W$ denotes the kinetic energy) should hold if some part of the potential results from a polarization of each particle in the field of the other or from a high frequency exchange process. For slow neutrons a thirty percent decrease in the magnitude of the interaction in going from binding to free particles yields an increase in the cross section for scattering by protons of several hundred percent over the value given by $J$. This larger value is required by recent measurements. The rapid fall of the experimental cross section with increasing $W$ requires that $J_1$ decrease steadily as $W$ is made larger in accordance with the relation $J_1\mathrm{}(r,v)=e^{-g({\beta }_0+\frac{v}{c})}J\left(r\right)\mathrm{}$. Here $g$ is a positive constant, $v$ is the relative velocity of the colliding particles and ${\beta }_{0}c$ is identified with the average relative velocity of the particles in the deuteron.