Neutron monochromator response based on the secondary extinction Green's function for Bragg geometry

A theoretical expression is derived for the differential output rate of a neutron monochromator system when used in the Bragg geometry. The derivation of this expression starts from the Green's function solution to the secondary extinction power equations for a thick mosaic slab. The combined effect of collimator and crystal positioning, beam divergence, total internal reflection off the collimator walls, and order contribution is included in the final expression. This expression has been programmed for numerical integration to yield a value for the absolute output counting rate in each order for arbitrary values of the two dozen or so independent parameters necessary to specify the system. The calculated output rate is compared with some preliminary experiments done with a single axis spectrometer equipped with a 2:1 half angling device. These experiments include rocking curves, tracking curves (movement of the crystal perpendicular to the diffracting planes), and 2:1 Bragg response curves, all of which can be generated for comparison within the program by proper choice of looped parameters. In addition, an example of a typical calculated radiation transfer matrix between sets of Soller slits is given. It is proposed that these calculations may prove useful in allowing the measurement of neutron cross sections in the sub-thermal energy range without a mechanical filter even though several orders are simultaneously present.