Coherence approach to neutron polarization propagation in instruments

Abstract

The propagation of the mutual coherence function is a well known method to describe the effects of neutron's propagation through scattering instruments. This method is extended with the description of the coherence matrix to account for neutron polarization effects and its propagation through an instrument. A propagation law for the coherence matrix and the condition under which it can be used is derived. A rigorous description of polarization analysis is given. The phase-object approximation to describe small angle neutron scattering is extended to incorporate scattering in magnetic materials. The developed theory is applied to spin echo small angle neutron scattering and the neutron depolarization technique.

Measurement of gravitation-induced quantum interference for neutrons in a spin-echo spectrometer

“…The measurements consist of determining the polarization of the beam by measuring the spin-up and spin-down eigenstate intensity at the detector [19] as a function of the spin-echo phase difference according to Eq. (1):…”

Coherence approach in neutron, x-ray, and neutron spin-echo reflectometry

“…We will use the formalism of the coherence matrix, ⌫ as developed in Ref. 4 to describe the propagation of the polarized neutron beam trough the instrument. This will be discussed in Sec.…”

“…[13][14][15] Another way to solve the scattering of the neutron-wave function is to use the phase-object approximation. 4 The Lippmann-Schwinger equation can be iterated resulting in an infinite series for ⌿ sc ͑r ជ͒ which can be rewritten in the form…”

“…Rauch et al 2 and Pushin et al 3 applied coherence theory for their measurements with Bonze-Hart interferometers. Moreover, in a recent paper 4 it was shown that by using the coherence matrix formalism it is possible to describe the propagation of both up-and down-spin states of a neutron wave. The principles of this method and the application of coherence theory to the propagation of neutrons through a reflectometer are described in the following section.…”

Dynamical theory: Application to spin-echo resolved grazing incidence scattering from periodic structures

“…Among these theories are the Born approximation, the distortedwave Born approximation, the phase-object approximation and the dynamical theory (DT). Although these theoretical approaches have given good account of data in several cases of electron, x-ray and neutron scattering measurements, [2][3][4][5] one should keep in mind that they do not hold for all scattering regimes. We are investigating the limits of validity of these theories and their applicability in various scattering regimes and will present our findings in a future work.…”