Importance of electron time-of-flight measurements in momentum imaging of saddle-point electron emission

Over the past several years, another type of spectrometer has been developed that proves to be superior to conventional spectrometers. In this “momentum imaging” spectrometer, electrons and target-recoil ions produced in ionizing collisions are accelerated to opposing position-sensitive detectors by an external electric field. The momentum imaging spectrometer essentially projects (or images) the initial three-dimensional (3D) electron and recoil-ion momentum vectors onto the 2D plane of each corresponding detector. Because the spread in electron arrival time is quite small in comparison with the spread in recoil-ion arrival time, one can utilize the electron signal as a timing marker to extract the full 3D momentum vector of the recoiling ion. This technique has proven to be quite successful in cold-target recoil-ion momentum spectroscopy. Momentum imaging methods have also been recently utilized in the search for evidence of saddle-point electron emission. Experimental studies of ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{2+}$ incident on He were carried out by Abdallah et al. [Phys. Rev. A 56, 2000 (1997)]. Rather surprisingly, their results exhibited projectile-charge dependent shifts in the opposite direction than that implied by the saddle-point mechanism. However, as we shall demonstrate, proper saddle-point shifts may be observed if one takes into account the time of flight of the electron.