The resolution function in neutron time-of-flight experiments

In the high resolution time-of-flight facility GELINA of the Joint Research Centre IRMM short bursts of neutrons are produced by (γ, η) and (γ, f) reactions induced via Bremsstrahlung from 140 MeV electrons impinging on a rotating uranium target. The moderation of the fast neutrons takes place mainly by scattering from hydrogen in the water contained in beryllium cans above and below the uranium target. The neutron energy may be determined from the time difference between the neutron creation and its detection at a given distance from the source (TOF technique). The flight time of a neutron has a distribution in time or its equivalent in distance called the resolution function, which together with the Doppler effect, broadens the natural width (Γ_tot) and attenuates the amplitude of the nuclear resonances. Several processes, like the neutron producing electron pulse, the size of the uranium target and of the moderator assembly, the detector, the acquisition electronics, contribute to the resolution and are assumed to be non correlated to obtain the total shape of the resolution as a function of the neutron energy. For each component the time distribution should be normalized to unit area before the convolution with the theoretical cross section: this will preserve the integral of the neutron interaction probability. Moreover, the time energy relation cannot be seen independently from the resolution since the value of the mean equivalent distance of the resolution function is changing with energy.