A convenient expression of the Green function in LL neutron interferometry

The operation of a two-thick-crystal LL neutron interferometer is strongly dependent on the size of the entrance slit as compared to the “Pendellösung length”. In the case of a narrow slit, the ray-optics formalism breaks down and the intensity profile around the center of the Borrmann fan of the second crystal, where focussing occurs, has to be calculated from the Green function which is the wave function in the observation plane for a point-source of the entrance slit, the different points of this slit being considered as incoherent. This Green function, which takes into account the presence of a test object on the beam path between the crystals, is normally a complicated integral expression. This leads to lengthy numerical calculations. It is shown that for a phase gradient φ between the crsytals, the Green function can be expressed by an expansion in terms of the Bessel functions J_2n(&φ;).