Neutron-Proton Scattering with Spin-Orbit Coupling. I. General Expressions

Abstract

Neutron-proton scattering in the triplet spin state is discussed under the following assumptions about the nuclear forces: (1) the forces are conservative, (2) they allow time-reversal, i.e., the reciprocity law is valid, (3) the spin vectors of the neutron and proton enter in a symmetrical way, so that the total spin of of the system is preserved during the collision, and (4) the forces have a finite range. We do not assume that the forces can be derived from a potential function (i.e., that they are velocity-independent).General expressions are given for the scattering matrix and for the differential cross section. The matrix elements of the scattering matrix are expressed in terms of the minimum numbers of real, independent parameters. The energy dependence of these parameters near zero energy can be predicted uniquely on the basis of assumptions (1) to (4) above.