Photo-Disintegration of the Deuteron at High Energies

Abstract

Total cross sections and angular distributions for the photo-disintegration of the deuteron for energies between 10 and 150 Mev are computed for various types of central neutron-proton interactions. Most of the explicit computations are carried out for the case of 50 percent ordinary and 50 percent exchange interaction. Neutron-proton interactions considered are of the square well, Yukawa, and exponential type with two effective ranges. Theoretical analysis of the experimental data on high energy neutron-proton scattering excludes the square well, but is compatible with both Yukawa and exponential types of potentials. The Yukawa potential is replaced by an equivalent Hulthén potential. For the square-well and exponential potentials explicit analytic solutions were obtained. Our treatment of the case of the exponential potential is rigorous and at the same time almost as simple as that of the Hulthén potential. A qualitative discussion of the photoelectric dipole transition is given on the basis of the $f$-sum rule. This shows how exchange forces greatly increase the cross section at high energies. The discussion can be carried out for any exchange ratio. It is pointed out that only the photo-electric dipole and quadrupole cross sections can be obtained independently of specific meson theories of nuclear forces. The results for photo-disintegration show a pattern similar to those on neutron-proton scattering: very little difference between Yukawa and exponential potentials, somewhat larger difference between these two and the square-well potential. There is a pronounced dependence on effective range. In the Appendix a simple derivation of the dipole cross section for the ordinary square well potential is given, based on a transformation involving the equations of motion.