The resolution function of triple-axis neutron spectrometers in the limit of small scattering angles

The Cooper-Nathans formulation of the resolution function of a triple-axis crystal spectrometer for neutron-scattering experiments gives a singular resolution matrix when the scattering angle is small. The origin of this singularity is discussed and an alternative derivation, of the resolution matrix given which avoids this difficulty. The results are illustrated by numerical calculations for several typical experiments showing that resolution corrections may be large and very significant for experiments at small scattering angles.