The scattering of neutrons by deuterons and the nature of nuclear forces

Abstract

The theory of the scattering of neutrons by deuterons has been worked out for neutrons with energy in the range 0-11.5 MV. It is assumed that the interaction energy of all fundamental particles is the same, and calculations have been carried out assuming three types of such interaction—an ordinary unsaturated force, an exchange force of Majorana-Heisenberg type, and a ‘mixed’ exchange force involved all exchange operators. The space-dependent part of the interaction is taken to be of the form Ae -2 r/a , with the constants A and a as determined by Present and Rarita from a study of the binding energies and collision properties of the light nuclei. To obtain differential equations for the functions describing the relative motion of neutron and deuteron Wheeler’s method of resonating group structure was employed. The resulting integro-differential equations, which include exchange of particles as well as exchange forces, were solved numerically. An exact solution of the deuteron internal wave equation for the exponential interaction was used throughout. Results for the total elastic cross-section, calculated with exchange forces, agree well with the observed values, but ordinary forces give, for 2.2 MV neutrons, a cross-section 1.5 times too large. The calculated angular distribution, in relative co-ordinates, is very much more uniform for exchange forces than for ordinary forces. For 2.2 MV neutrons this difference is so marked as to be easily detectable by experiment, and it is deduced that the measurements by Barschall and Kanner of the angular distribution for such neutrons are compatible only with the assumption of exchange forces. It is pointed out that the result that ordinary forces lead to a much less uniform angular distribution is likely to be a general one, independent of the detailed accuracy of the theory.