Multiple echoes in beam spin-echo spectroscopy and their effect on measurements of ultra-fast dynamics.

Helium ( 3 He) spin-echo is a powerful experimental technique used to probe ultra-fast atomic scale surface dynamics. The analysis of these measurements is typically performed assuming there is only a single spin-echo condition, expected to produce a constant signal for pure elastic scattering, a monotonically decaying signal for quasi-elastic scattering and oscillations from inelastic scattering events. In the present work, we show that there are in fact four spin-echoes which must be correctly accounted for, and that even in the case of elastic scattering these additional echoes lead to oscillations which could mistakenly be interpreted as being due to inelastic scattering. We demonstrate that it is possible to accurately simulate the experimental data by propagating the 3 He through the measured magnetic field profile of the apparatus and considering the geometry of the machine, allowing the effect of these additional echoes to be disentangled from inelastic scattering events in future 3 He spin-echo measurements.