The coherence volume of neutron beams and its implication on the description of neutron scattering

The problem of using the shape and size of the neutron coherence or correlation volume for description of the neutron beam devices such as collimators, monochromators or choppers is considered. It is revealed that the wave function within the correlation volume shows partial coherence, i.e. the relative phase between the amplitudes of the wave function evaluated at two separated points within the correlation volume is well defined. If the separation exceeds the coherence volume their average relative phase becomes arbitrary and the coherence will vanish. The van Cittert-Zernike theorem used in light optics for description of partial coherence is applied to matter waves and expanded to non-stationary cases. The neutron scattering and its instrumentation are discussed in the light of coherence functions. The case of small angle neutron scattering is considered as a simple example. It is shown that the coherence volume corresponds to the Fourier transformation of the instrument resolution function. The conclusion is made that the concept a coherence volume allows a description of the scattering process in a space-time frame. This space-time picture may be seen as complementary to the usual van Hove description operating in the Fourier space