Nuclear Forces (Scattering of Nucleons by Nucleons)

Abstract

As we have already indicated, experimental knowledge on the proton-neutron system is acquired by studying the scattering of neutrons by protons and by investigations of the properties of the deuteron. An analysis of these data, the goal of which is the determination of phase shifts, requires, first of all, a resolution of the scattered waves in terms of spherical functions. Because of the spins of the proton and neutron this procedure turns out to be somewhat more complicated than in the case of spinless particles which have been described. First of all we must introduce a system for classifying the possible states of the system. In the case of spinless particles the state was determined by the azimuthal quantum number L. In the presence of spin the state of the system is also determined by the spin quantum number S. If the spin and coordinates are independent, the orbital angular momentum and the spin angular momentum are conserved individually. Any coupling between the spin and orbital motion means that the vectors L and S are not conserved individually; rather the total angular momentum J is conserved;* this is the sum of the orbital and spin angular momenta.