Analytical method to correct the neutron polarisation for triple-axis data

Polarised neutron scattering is the method of choice to study magnetism in condensed matter. Polarised neutrons are yet typically very low in flux and complex experimental configurations further reduce the count rate, neutron polarisation corrections would therefore be needed. Here we analytically derive formulae of the corrected partial differential scattering cross sections. The analytical method is designed for the longitudinal polarisation analysis, and the correction generally holds for time-independent polarised neutrons with a triple-axis spectrometer. We then applied the correction to recent results of our $P_x$ experiment on Y$_3$Fe$_5$O$_{12}$. Although there is a difficulty with experimental determination of inefficiency parameters of neutron spin polarisers and flippers, the correction appears to work properly.