The determination of errors in polarized neutron diffractometry

Abstract

The polarized neutron method of determining the magnetic form factor of magnetic materials is examined in detail with special attention given to the way in which statistical errors are propagated. Because of the nonlinear relation between the polarizing efficiency of a crystal and the magnetic scattering length, the usual methods of linear error theory will not work. However, this difficulty can be circumvented by using the nonlinear formulas directly. The statistical error analysis is applied to the practical problem of how long one should count on a particular Bragg peak. This time will depend on the ratio of the magnetic to the nuclear scattering lengths, p/b, and on the accuracy with which the beam polarizations and flipping efficiencies have been determined.