Collision of Neutron and Proton

An exact solution is found for the bound and free states of a neutron-proton pair under the influence of a potential field $-D\left[2\mathrm{}\exp \right(\frac{2}{r_0}\left)\right(r_i-r)-\exp (\frac{4}{r_0}\left)\right(r_1-r\left)\right]$, where the field can be of the Majorana type and may depend on the spin coupling. Values of binding energy (for the deuteron), of elastic cross section, of capture cross section and of cross section for the photoelectric disintegration of the bound state are computed for a wide range of the parameters used. Curves of the results are shown. In order to correspond to the experimental values of binding energy and of elastic cross section for slow neutrons, the value of $D$ for the singlet state, $D_s$, must be made about one-half that for the triplet state, $D_t$. Separate calculations are made, assuming a bound singlet state, and assuming no bound singlet state. When this is done, the capture and photoelectric cross sections check the experimental values fairly well, the computed results being practically independent of $r_0$ and $r_1$ as long as these parameters are less than 6×${10}^{-13\mathrm{}}$ cm. Thus a proper choice of two relations between the four parameters $D_s$, $D_t$, $r_0$, $r_1$ gives agreement with four different experimental values; the other two relations needed to determine all four parameters will require further experimental data for their determination.