Collision of Proton and Deuteron

Abstract

The present calculation is similar to that of Schiff on neutron-deuteron collisions, and is based on the suggestion of Morse that the function $sin(kr+\delta )-e^{-\epsilon r} sin\delta cos\mathrm{kr}$ will be a good approximation to the actual wave function if the parameters are properly adjusted. By joining this function smoothly with the Coulombian field wave function, we obtain the scattering formula for proton-deuteron collisions, while, by extending this function to infinity, we get the neutron-deuteron scattering. The coordinate system, in which the Hamiltonian is separable, was used, and this is the main difference from Schiff's calculation. The cross section for neutron-deuteron scattering was found to be 3.2×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ at vanishing neutron energy, in good agreement with experiments. For proton-deuteron scattering, no good agreement was obtained. In the range of angle of scattering less than about 70°, the calculation gives still a tolerable result, but, for larger angles, the experimental scattering increases very rapidly. Such a rapid increase does not seem to be explained without some other important improvement of the theory.