Scattering of Polarized Nucleon Beams

Abstract

The polarization formulas for the general reaction $a+b\ensuremath{\rightarrow}c+d$ are given in a compact form and specialized for the scattering of polarized nucleon beams at unpolarized targets. These targets may have arbitrary spin, possibly being different before and after collision. An interesting quantity in this problem is the polarization of the scattered nucleon beam. On the basis of general invariance properties of the transition matrix, this polarization is expressed by the polarization of the incoming nucleon beam and the relative momenta before and after collision. The invariant coefficients in this relation are functions of energy and scattering angle only; they are given in terms of the parameters of the transition matrix.By using these formulas, it is shown that with triple scattering experiments one can obtain two new relations between the parameters of the transition matrix at fixed energy and angle. Quadruple scattering leads to two further relations. These relations represent information in addition to the differential cross section and the polarization resulting from unpolarized beams. The results are specialized for targets of spin zero and spin one-half, where in the latter case also the scattering of identical particles is discussed briefly.