Normalisation of the resolution function in TOF technique

Abstract

The normalisation factors of the resolution function are the basic components for the conversion of measured neutron scattering spectra to the scattering function S(Q, ω). The instrumental resolution function and its normalisation factors are derived independently of any sample and its S(Q, ω). As shown earlier for Three-Axis Spectrometer, these factors, also in time of flight (TOF) technique, are symmetric for the incoming beam, with p(k_I)k⁴_I, and the scattered beam, with p(k_F)k⁴_F, Here k_I and k_F are the wave vectors of the incoming and scattered neutrons; p(k_I) describes the spectrum of the source in phase-space and p(k_F) the detector efficiency. In direct TOF the conversion factor is [p(k_F)k⁴_F]⁻¹. In inverse TOF it is [p(k_F)k⁴_I]⁻¹ The latter depends on the neutron source. For thermal neutrons (gas in thermal equilibrium) the conversion factor is [k⁴_I exp(−k²_I/k²_T)]⁻¹, where the wave vector k_T corresponds to temperature. For epithermal neutrons, in the eV range, the conversion factor is constant.