Nucleon-nucleon scattering at high energy

Abstract

The nucleon-nucleon scattering and polarization experiments cannot be explained by a simple local potential. This method gives good results in the low energy domain. But between 0 and 300 MeV, for example, it is well known that the Schrodinger equation is inadequate. It is necessary, at high energies, to use a completely covariant formulation for two body systems—the-Bethe and Salpeter equation (1,2)—in order to take into account relativistic corrections. With an analytical continuation of the scattering amplitude for the imaginary values of relative time (or relative energy), we can generalize the method of partial waves to a four dimensional euclidian problem. It is shown that, in the simplified case of spinless particles (Klein-Gordon particles), the physical phase shifts corresponding to a given value of the orbital angular momentum are easily obtained. For the more realistic case of spin 1/2 particles (Dirac particles) it is possible to calculate the differential crosssection. Explicit solutions are obtained with an approximate method of resolution for the integral equations. Further, one can determine the value of the coupling constant that gives the correct experimental neutronproton singlet scattering length, in the case of the « ladder approximation ». The1S phase shift, calculated for various values of the energy, exhibits a change of sign in the energy region of 140 MeV. This result is in agreement with the experiments and the «hard core» theory of Levy (3-6).