Resolution and intensity considerations of an ideal He atom time-of-flight spectrometer for measurements of surface phonon dispersion curves

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Abstract
Analytic expressions are derived to calculate the instrumental width of the phonon energy‐loss peaks obtained in a helium atom inelastic scattering apparatus used in the measurement of surface phonon dispersion curves at single crystals. The formulas take into account all the kinematic effects arising from the velocity distribution of the incident beam, the angular resolution of the instrument, as well as the finite time resolution of the time‐of‐flight detection system. Implications for the optimal design parameters are discussed.