Polarised beams and polarised targets

Abstract

For the complete description of any nuclear reaction involving particles with nonzero spin, measurements of the degree of spin alignment, or change in degree of spin alignment, produced by the reaction are necessary before a complete reaction matrix can be formulated and tested. In the most general case of spin aligned particles with spin = 1/2, all that is implied is that the spins are aligned relative to a preferred direction in space, often determined by some external field. This alignment can be either parallel or antiparallel to the preferred direction and, provided no external perturbing influences are present, the relative populations of these two states may be equal, the differences being due only to factors such as thermodynamic equilibrium or the presence of rapidly varying internal fields. Normally the differences in the energies of the parallel and antiparallel states will be small compared with their total energies and so the populations will be nearly equal. In such a system the nuclear polarisation will be effectively zero because the fractional number of nuclear spins parallel to the preferred direction, N⁺, and the fractional number antiparallel to this direction,N^- ,are approximately equal and thus the polarisation P = N⁺ − N ^- ≈ 0, and further N⁺ + N^- = 1. For polarisation to be present in the aligned beam the populations of the two states must be different. In a nuclear reaction only polarisation can be observed and not alignment.