Beam Velocity Analysis

The measurement of the velocity distribution in (low-energy) ion beams is conventionally performed using electrostatic analyzers or the time-of-flight technique which also works with neutral beams. Similarly to the time of flight, the Doppler shift essentially measures the beam velocity v. However, the measured time interval decreases, whereas the Doppler shift increases 

A more quantitative comparison is easily performed by use of Eq. (4). For time-of-flight measurements we assume that a fixed time interval St can be resolved at the detector placed at a distance L from a chopper slit. Sufficiently fast choppers consist of electric defiection plates for the initial ion beam and a slit defining the entrance of the drift space, e.g., after a collision chamber where neutral products may arise from specific reactions. Then the energy resolution is given by 

If the chopper (instead of the detector) determines the time resolution, it can be shown that for an optimized electric field amplitude of the deflector 

Coming back to our comparison we find that beyond mass A 40 (with all other parameters unchanged) the time-of-flight resolution will become superior to the optical resolution. But the energy dependence shows that for beam energies above a few keV the Doppler shift measurement becomes definitely more favorable. Moreover, the choice of a weak transition 

With increasing vapor pressure these peaks become stronger, and additional equidistant peaks become observable. This is ascribed to secondary excitations, according to 

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The intensity of signal transmitted to the detector is greatly improved by using time-of-flight methods instead of mechanical velocity selectors. The beam of product molecules is chopped into a sequence of short pulses and the molecules then travel a known distance before being detected. The time-of-arrival spectrum at the detector gives the velocity distribution of the products [30]. This method of velocity analysis is now widely used in studies of crossed-beam reactions [111]. 

Figure B2.3.3. Crossed-molecular beam apparatus employed for the study of the F + D2 -> DF + D reaction. Indicated in the figure are (1) the effusive F atom source (2) slotted-disk velocity selector (3) liquid-nitrogen-cooled trap (4) D2 beam source (7) skimmer (8) chopper (9) cross-correlation chopper for product velocity analysis and (11) rotatable, ultrahigh-vacuum, triply differentially pumped, mass spectrometer detector chamber. Reprinted with permission from Lee [29]. Copyright 1987 American Association for the Advancement of Scienee. 

Shortly after these results were published, Bernstein and coworkers (10,11) completed a crossed beam study of the reaction of K atoms with HBr and DBr, with velocity selection of the incident K-atom beam and velocity analysis of the KBr product. Analysis of the data showed that the product KBr c.m. angular distributions are broadly backward-peaked for K + HBr and nearly isotropic for K + DBr and that the recoil velocity distributions are broad and extend to the maximum value allowed energetically. These results differ considerably from the results for K + TBr since (i) when taken together, the angular distributions imply that the KBr product shifts nonmonotonically from broadly backward-peaked to nearly isotropic to sharply backward-peaked with the isotopic substitutions HBr DBr TBr and (ii) the mean recoil energy is much lower (and therefore the product excitation much higher) for K + TBr. These differences are still unresolved at this writing. 

Single-Beam Technique with Velocity Analysis Only... 

A single-beam technique with Wien filter velocity analysis and quad-rupole filter mass analysis of the products was used by Fink and King in experiments in the energy region from 5 to 30 eV. Details of this machine have not been published. 

SB, single beam with velocity analysis only SBA, single beam with velocity and angular analysis CB, crossed beams MB, merging beams MS, mass spectrometric MSP, mass spectrometric pulsed. ... 

Single-beam experiments, with velocity analysis only, have been performed in the low-energy regions by Fink and King and by Henglein. Results are consistent with those described above. 

Single-beam studies with velocity analysis only have been made of the reactions... 

A large number of polyatomic halides H- alkali and alkaline earth metal atom reactions have been studied by angular and velocity analysis in molecular-beam experiments and by laser-induced fluorescence analysis of the vibrational and rotational distributions in beam-gas experiments. In the beam studies of and + CH3I, K + + CH3NO2,... 

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