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In this web page we provide detailed (e,2e) studies of electron impact ionization of noble gases including helium, neon, argon, krypton and xenon from near threshold to intermediate energies, where the outgoing electrons carry equal energy from the interaction. The experiments were conducted in the perpendicular plane, where the outgoing electrons are detected orthogonal to the incident electron beam.
The data show the cross sections undergo complex variations as a function of incident energy, and in particular ionization of the heaviest target is at variance to all others that have been studied here. The (e,2e) process provides the most precise experimental data for the study of the ionization of atomic and molecular targets by electron impact. By determining the momenta of the scattered and ejected electrons in a time correlated coincidence measurement, the differential ionization cross section (DCS) is derived for comparison with theoretical models. Since the scattered and ejected electrons may emerge over a wide range of different angles, experiments usually define a specific scattering geometry in which to carry out the measurements. In the present work, we have constrained the spectrometer to measure the DCS only in the perpendicular geometry, where psi = 90A°.
For both electrons to emerge in this geometry it is necessary for an interaction with the target nucleus to occur, and this provides a stringent test of current ionization models.
We have taken measurements with the incident electron energy E0 ranging from near the ionization threshold of the selected target, through to energies up to 80eV above the ionization potential (IP). Understanding these processes is hence important in areas ranging from the production of plasmas in stellar and planetary atmospheres, through to electron impact ionization in lasers and in nuclear reactors. In all cases results are presented for the outgoing electrons having equal energies at the analysers.
The apparatus can measure the DCS from the coplanar to the perpendicular plane geometry by moving the electron gun, gas jet and Faraday cup together around the interaction region (figure 2). The electron analysers consist of a 3-element electrostatic lens that focuses electrons from the interaction region into a hemispherical energy selector.
The data were taken over a period of several months, and the electron gun current was varied for each of the data sets so as to ensure linearity of the detection system. The energy of the incident electron beam was determined by observing the negative ion elastic scattering resonance in helium at ~19eV, so as to determine the offset in the gun due to contact potentials. The energies of the outgoing electrons were determined by observing inelastic scattering from the excited targets, and by considering the location of Fano resonances in the ionization continuum.
The experimental data for helium are taken from previous work carried out in Manchester re-presented here normalised to unity at the peak of the DCS to allow comparison with other noble gases.
The ground state of helium is 1S0, with an electronic configuration 1s2, and so both bound electrons occupy s-shell orbitals prior to the interaction. For helium, neon and argon targets, the bound electrons occupy either s-orbitals or p-orbitals in their ground state. It was not possible to resolve these individual channels in our experiment (due to the limited energy resolution of the spectrometer) apart from for xenon, where results were taken for production of the different ion states at incident electron energies from 10eV to 30eV above the IP.
Figure 3 presents results for ionization of helium in the perpendicular plane for ten different incident energies ranging from 3eV to 80eV above the IP. As the incident electron energy increases, additional peaks are seen at angles around 90A° & 270A°. By 20eV above the IP three distinct peaks are clearly visible, the relative strength of the central peak to outer lobes decreasing monotonically as the energy increases. The physical reasons behind these structures has been described by several models, ranging from DWBA calculations through to TDCC models. There is only one process that can produce a peak at 180A? in the perpendicular plane without interaction with the target nucleus.
The peaks at around 90A° & 270A° are found to result from elastic scattering of the incident electron from the core, followed by a single binary collision between the incident electron and a bound electron.
It should be noted that although agreement between theory and experiment in the perpendicular plane has proven to be very good, the results in a coplanar geometry are not as satisfactory, particularly for non-equal outgoing electron energies. The results at the lowest energy are similar in shape to that for helium, with a single broad peak observed centred around 180A°. As the incident energy increases, the DCS for neon shows a very different character to that for helium.
The mechanisms that produce these structures in neon must be quite different to that proposed for helium, apart from at the lowest energy where PCI is expected to dominate for all targets.
Al-Hagan and co-workers recently considered the low energy regime for both He and H2 from threshold to ~10eV above threshold, and concluded that for these targets PCI dominates at energies <2eV, which is also consistent with the observations for neon presented here. The results in figure 4 indicate that the interaction is clearly more complex, and may be due to the momentum distribution of the ionized p-electron and polarizability of the atom (which is 1.9 times greater for neon than for helium). A similar study was carried out for argon, whose outer electronic structure ([Ne]3s23p6) is similar to neon ([He]2s22p6). In the frozen-core approximation as used in many theories, the inner electrons are considered as spectators during the interaction, and so in this approximation the structure of the DCS should be similar for neon and argon. For argon, nine separate energies were chosen for study, so as to reveal the complex variation in the DCS as a function of energy. Once again the results for argon are not consistent with the simple models found successful for helium. Figure 6 shows the results for krypton, which unlike helium, argon and neon also has bound electrons occupying the 3d-shell. Once again results were taken for a lowest energy 2eV above the IP, with the data having much better statistical significance compared to those for argon at the same energy. As the energy increases, the results for krypton show a similar trend to that for argon, with the central minimum deepening until around 10eV above the IP where a central peak starts to emerge. The similarity between argon and krypton data tends to indicate that the d-shell electrons in the heavier target are not playing a significant role in the ionization process. As the heaviest isotopically stable noble gas target, xenon has the largest calculated size (108 pm) due to full occupation of the 4d, 5s and 5p shells. The ionic ground states of Xe+ are sufficiently separated that it was possible to resolve ionization to individual states during the experiments, for energies up to 30eV above the IP. The data are particularly surprising since they do not follow the general trend seen for all other noble gas targets at higher energies. The minimum at 180A° is significantly deeper than for krypton under the same outgoing energy conditions, and unlike krypton this minimum then becomes shallower as the incident energy increases.
These results show that the mechanism for ionization of xenon must once again be different to all other targets that have been studied.
As far as we are aware this phenomenon has never been observed for any other target, and it remains to be seen why this should occur for xenon. Only three energies were selected for these experiments, due to the difficulty of obtaining good statistical data.
The set of data presented here for isotopically stable noble gases shows there is a large variation in the probability of ionization in the perpendicular plane. The perpendicular plane is particularly poignant for testing the most sophisticated electron impact ionization models, since multiple scattering must occur for electrons to emerge in this plane. The perpendicular plane has proven to be a fertile ground to test recent theoretical models, which have found success for simple targets such as helium and molecular hydrogen. It appears that PCI plays a role at the lowest measured energy for each target, although the significance of this process reduces as the target weight increases.
The most surprising result is for the heaviest target xenon, since the relative magnitude of the central peak continues to increase as the incident energy increases, and the side lobes reduce to insignificance. It is worth noting that the resolved data for ionization to the different Xe+ states indicate there is little variation to the measured cross section due to fine structure effects.
KLN thanks the Royal Society for an International Newton Research Fellowship held at the University of Manchester. The following information pertains to experiments presently being conducted in the laser collisions lab of the above laboratory. In these experiments atoms and molecules excited by electron impact are studied when they are in a metastable state following the collision. Many different processes can occur in this reaction, depending upon the energetics and kinetics of the reaction. The experiments described here look at the process of inelastic scattering, where the target is left in a metastable state. The experiments are precursors to measuring stepwise laser excitation of metastable atoms and molecules. An electron which has well defined energy Einc, and momentum Pei is incident on either an atom or a molecular target which is in its ground state. The velocity of the gas is constrained to a narrow distribution by the supersonically expanding shock wave.
The target beam enters a second vacuum chamber where it travels ~ 100mm prior to interacting with a well defined beam of electrons.
These electrons are produced in an electron gun that controls both the direction and energy of the electrons.
Only a very small number of these electrons will interact with the target beam, the majority passing through the interaction region and being collected by a Faraday cup 200mm downstream. The majority of the target beam is also unaffected during the reaction, and passes through the interaction region. The majority undergo an elastic collision where only the direction of the incident electron may change and the target remains in its ground state.
A small number of targets will be excited, and depending upon the energy that can be exchanged between the electrons and the target, excitation to various states can occur. Depending upon the cross section for the state, which is a function of both the energy and the angle through which the electron is scattered, a small number of these targets will be excited to the metastable state. Since these metastable excited targets cannot decay by photon emission, and since there are very few collisions between targets in the gas beam (their relative velocity is close to zero in the beam and therefore their relative position to each other does not change markedly), most of these will remain in the excited state as they pass out of the interaction region.
Scattered Atoms (Molecules) in a Metastable State with internal energy Eexc and which carry momentum Paf away from the reaction. Studying the momentum of the targets that have been deflected by the electron collision, since these are related to the electron momentum by conservation of momentum. It should be noted that in conventional electron scattering experiments which measure excitation cross sections, the target momentum is not usually considered. There are a number of complications that can arise in these experiments where the target momentum is exploited for measurement. If the incident electron is of sufficient energy to excite not only the metastable state but also higher lying states which through photon emission can decay to the metastable state, there will be a contribution to the target signal due to these cascades. For a significant number of targets there is more than one metastable state, and these may be sufficiently close in excitation energy to be unresolvable when exploiting their individual momentum transfer contributions.
This effect is particularly significant when the target is a molecule since the metastable vibrational and rotational states will be much closer together than can be resolved by even the highest resolution electron impact studies. The difficulties associated with cascading can be overcome by confining the study to the region close to threshold for excitation of the metastable state.
For studies of excitation at energies where contributions from cascading become significant, a time resolved coincidence experiment between the scattered electrons and the deflected targets becomes necessary. Unlike conventional coincidence studies, the direction of the coincident scattered electron is known since the momentum of the excited target is known, and hence the collection rate of the experiments can be enhanced by placing the electron detector at the appropriate point in space. The difficulties associated with state selectivity can be overcome by employing a further stepwise laser excitation step from the metastable state to an upper state using a high resolution laser probe. Since the laser radiation transfers information about the metastable state to this upper state, measurement of the upper state can in principal yield information about the lower state once the laser excitation mechanism is well understood. Allows the electron excitation mechanism to be studied by analysing the stepwise excited state. Field Ionisation if the laser excited state has sufficiently high principal quantum number (high yields, in principal 100% efficient). The latter Field Ionisation technique is adopted in these experiments, although photon detection can be easily installed into the vacuum system if this proves advantageous to measurement of the signal. Molecular Vibrational & Rotational states can be studied in detail for a wide range of targets. A detailed analysis of the laser excitation process is required to fully characterise the electron excited state. The processes where the linear momentum transferred from the electron to the target is exploited to determine cross sections for excitation of the state are now considered.
The square root in the above expression shows the origin of the two different momenta at any given deflection angle of the targets as described in figure 4. Note that for each atom detection angle qa there are 2 contributing momenta Paf1, Paf2 excepting the case of Forward & Backward scattered electrons, as shown in figure 5. Hence with sufficient time resolution and detection angle resolution the experiments should reveal 2 distinct peaks at any given detection angle.
It should be noted that the lifetimes of the low l highly excited helium Rydberg targets, typically only a few microseconds, exclude them from being detected in the present experiments where the targets drift for around 300 microseconds from the interaction region to the metastable detector.
The chamber is lined with a double layer of m-metal which reduces external magnetic fields to < 5mG at the interaction region. Fast output deflector circuit only allows electrons to exit electron gun, preventing any ions created in field free region or other high potential region from reaching interaction region. Angle selectivity is achieved using 1mm apertures 1 & 2 spaced 60mm apart prior to a 719BL CEM metastable detector at end of detector (LHS).
Electrostatic deflection plates remove unwanted electrons and ions from entering the detector and possibly reaching the detectors.
Visible Laser Diodes (VLD's) align the detector to the interaction region formed by electron beam, gas beam and rotation axis of detector.
A control pulse (0 - 150Hz) drives the gas nozzle HT pulse & the electron gun Grid following an appropriate delay. The Turbo-MCS is gated to either sweep over ~100ms for each gas pulse or is set to count events for a set number of gas pulses at each detection angle.
The following graphs show the metastable angular distribution when the target gas is excited using a continuous electron beam, rather than a pulsed electron beam for four different excitation energies from 20eV to 50eV.
As the incident energy increases forward scattering starts to dominate over backscattering as a collision mechanism as might be expected. The evolution from single atom momentum at q'a = 4A°through double momentum peaks at intermediate energies then back to a single peak at the highest scattering angles can clearly be seen as is discussed in figure 4.
Gaussian profiles have been fitted to the peaks to establish the amplitude, width and position of each peak as a function of the deflection angle.
Note that a 4ms electron excitation peak is visible at higher detection angles, which is thought to be due to either photon or stray electron contributions. This accurately yields the time difference between excitation of the target and collection of the metastables. For these experiments the atoms excited by the incident electrons are counted and fitted to a Gaussian of width w and height h as shown in figure 14. Figure 15 shows the results of these least squares fit calculations at 40eV Incident Energy, showing the amplitude h and width w together with the associated peak positions.
Note that this method allows the DCS to be determined over the complete set of scattering angles from forward to 180A° backward scattering of the electrons. Note that some discrepancies exist between the calculations from the fast and the slow atoms.
This effectively acts as a high resolution timing probe of the target gas beam which for helium has a time spread of the order of 6ms from the interaction region to the detector. Electron-electron angular correlation experiments, or so-called (e,2e) coincidence experiments, provide the most detailed test of theories which attempt to describe the ionisation of a target atom by an incoming electron. The parameters (Ea,qa,fa,Eb,qb,fb) are freely selectable experimentally within the constraints that energy and momentum must be conserved during the collision. In the experiments described here the DCS has been measured in the perpendicular plane using a helium target with incident electron energies ranging from 10eV to 80eV above the ionisation threshold. The electron coincidence spectrometer was designed to measure angular and energy correlations between low energy electrons emerging from near-threshold electron impact ionisation of helium and is capable of accessing all geometries from the perpendicular plane to coplanar geometry. A number of modifications to the original spectrometer as described in Hawley-Jones et al (1992) have been implemented and are detailed elsewhere. Unique to this (e,2e) electron spectrometer is the computer interface which controls and optimises the spectrometer during normal operation.
Figure 2 is a block diagram of the hardware interface between the computer and the spectrometer. At the heart of the operation is an IBM 80286 PC which controls the spectrometer and receives information about the system status from monitors around the spectrometer.
The electrostatic lens and deflector voltages in the system are supplied by separate optically isolated active supplies controlled by 12A bit digital to analogue converter (DAC) cards, while a digital monitor measures the voltages and currents on the various lens and deflector elements around the system. The analyser positions are measured by potentiometers located in the drive shafts external to the spectrometer, and are monitored by a datalogger located on the main PC bus, which also monitors the EHT supplies and the vacuum pressure in the system. Count rates from the channel electron multipliers and photomultiplier tube are monitored by a 32 bit counter board, and the TAC output is sent directly to an MCA card installed in the main PC. The software controlling the electron coincidence spectrometer is written to address specific tasks unique to the coincidence experiment.
The main PC controls the spectrometer lens and deflector tuning during operation, optimising these voltages using a Simplex method. Following input of relevant control information, the system is switched to computer control. The electron gun is then optimised to the counts detected by the photomultiplier tube, thus ensuring that the electron current is focussed to a beam of diameter approximately 1mm at the gas jet. The analyser input lenses and deflectors are then adjusted by the computer to optimise the non-coincidence counting rate of each analyser. A coincidence correlation spectrum is then acquired for a predetermined time, after which the analysers are moved to a new position and the optimisation procedure repeated in the inner loop. Once the analysers have moved around the detection plane, the whole system is reoptimised and the process of data collection repeated. A correlation function between the scattered and ejected electrons is therefore accumulated over many sweeps of the detection plane until the results are statistically significant. During operation the running conditions are monitored every 50 seconds by the data logger, allowing any anomalies in the data to be accounted for when final results are considered. Results from experiment for the symmetric case, where the outgoing electrons following the collision have equal energy, are shown in the figures 4a - 4h.
In the perpendicular plane, the symmetry about the incident electron beam direction requires that the DCS must be symmetric about f = 180A° and this is evident in the data. Inspection of the 94.6eV data (35eV scattered and ejected electron energies) indicates that this result does not follow the trends of the other data in the set.
The resolution of the spectrometer (~ 1eV) does not allow these contributions to be excluded, and so the 94.6eV data set cannot strictly be considered as part of the overall set of data which is presented here. The first result in this data set therefore is the same as the first result in the previous set, allowing a convenient point for common normalisation of the data sets. Above 54.6eV incident energy the results differ markedly, the angular correlation evolving into a single broad peak instead of the three distinct peaks observed in the symmetric case. This is most clearly evident at 74.6eV incident energy, where the symmetric case shows three distinct peaks of approximately equal intensity, whereas the non-symmetric case shows only a broad featureless structure centred about 180A°.
The sets of data shown in figures 4 and 5 were each normalised relative to the result obtained at 34.6eV incident energy, where both the electrons emerge from the interaction region with an energy of 5eV. The relative angular data presented at any particular energy is normalised by consideration of the electron singles counting rate, which depends on the Double Differential Cross Section at 90A° but is independent of the azimuthal angle f.
The procedure adopted here allows an upper and lower bound to be estimated, as no facility exists to allow these overlap volumes to be accurately determined experimentally as is implemented by other electron scattering groups. The DDCS gives the probability of obtaining an electron from the scattering event at an angle q1 in a solid angle dW1 at an energy E1 A± dE1. The solid angle of detection depends upon the geometry and operating potentials of the electrostatic lenses, and is therefore also a function of the detected electron energy. VA(E1) is given by the three way overlap of the gas beam, electron beam and volume as seen by the analyser. The DDCS varies only slowly over the energy range dE accepted by the analyser (Jones et al 1991) as does the efficiency and solid angle of detection of the analyser as determined from electrostatic lens studies.
The energy resolution DEA is independent of E1 because the pass energy of the hemispherical deflector is kept constant. This expression can be rearranged to yield the ratios of analyser efficiency and solid angle in terms of the DDCS, singles count rates and overlap volumes at the two energies E1 and E2 for an incident energy Einc.. The ratios on the left-hand side of this equation were obtained from the DDCS data of MA?ller-Fiedler et al (1986) at an incident energy of 200eV for each analyser at the selected energies of interest. The first three terms in this expression are evaluated directly from the experiment, while the fourth and fifth terms are taken from the data of MA?ller-Fiedler et al (1986).
As no experimental facilities existed to measure these parameters, a SIMION ray-tracing model was set-up to allow a computational determination of these volumetric terms.
The analyser input electrostatic lenses were also modelled to determine the volume viewed at the interaction point for the varying energies of electrons selected. Figure 6 indicates the experimental geometry as viewed by the analysers in the perpendicular plane, where the atomic beam direction is at 45A° to the incident electron beam trajectory.
Table 1 indicates the calculated relationship GV as determined from the SIMION ray tracing model, and these values have been used to calculate the normalisations as given in figure 4. The dominant error in the expression is given by the double differential cross sections as measured by MA?ller-Fiedler et al (1986), since these terms arise four times in the expression, and typically have measurement errors of A± 15%.
This is possible since the q = 90A° coplanar symmetric energy-sharing result is identical to the perpendicular plane f = 180A° energy-sharing result. Since data was not obtained at an incident energy of 100eV in these experiments, an interpolation between the energy normalised symmetric results yields a relative value. The uncertainty in the normalisations of the relative energy is approximately A±30%, as discussed in the previous section.
The absolute differential cross sections as presented in figures 4 and 5 therefore have uncertainties of approximately A±44%. These latter calculations, normalised to one energy, produced results that were close to those of the experiment.
A simple descriptive model for the symmetric case illuminates a possible scattering processes involved. On the other hand the peak that is observed at 180A° can be explained in terms of either single or multiple scattering. In terms of single scattering it is due to the incident electron selecting a bound electron whose momentum is equal in magnitude but opposite in direction to its own momentum. In terms of multiple scattering, particularly at the lower incident energies, the peak at 180A° has additional contributions that may be described by outgoing electron correlations as in the Wannier model. The mass equivalence of the scattered and ejected electrons requires that a quasi-free collision results in electrons emerging at approximately 90A° to each other irrespective of their resulting energies, and so application of this model would once again yield three peaks, although the relative peak intensities might be expected to change. These results predict a single peak at 180A° due to a mechanism following elastic scattering of the incident electron from the nucleus that is more delicate and complex than the quasi-free collision, however the wings at the lower energies in the experiment are not predicted by this model.
This may not be entirely unexpected as the DWBA model gives better results at higher energies. The central peak predicted by the theory also differs in width and height from the results presented here, when normalised to the 34.6eV data. A channeltron is a horn-shaped continuous dynode structure that is coated on the inside with a electron emissive material. A Daly detector consists of a metal knob that emits secondary electrons when struck by an ion.
A microchannel plate consists of an array of glass capillaries (10-25 um inner diameter) that are coated on the inside with a electron-emissive material.
Microchannel plates (MCP) are also used as an intensifier for low-intensity light detection with array detectors. The (e,2e) spectrometer vacuum chamber (figure 1) is manufactured from 304 grade stainless steel, the construction being carried out by Vacuum Generators using a design of Jones, Read and Cvejanovic, full details of which may be found in T. 3mm thick mu-metal magnetic shielding is placed both internally and externally to decrease extraneous external magnetic fields to less than 5mG at the interaction region.
All inputs and outputs to the spectrometer pass through the vacuum chamber via feedthroughs on the top flange.
The top flange of the vacuum system is a 25mm stainless steel flange with 11 conflat CF70 flanges arranged around a central 200mm flange designed for locating a hydrogen source. Two flanges are used for the high voltage channeltron and photomultiplier tube inputs and pulse outputs. Three rotary motion feedthroughs allow the analysers and electron gun angles to be changed externally via stepper motors for both analysers and for the electron gun.
The ionisation gauge is placed at right angles to the main flange to prevent light from the thoriated iridium filament entering the vacuum system, which would increase noise on the photomultiplier tube.
The ionisation gauge feedthrough is sooted, and a loose cover is placed over the entrance in the chamber flange to prevent stray light from the ion gauge entering the vacuum system.


The target gas enters the system via a CF70 flange which has two 6mm stainless steel tubes welded into the flange. The other gas feed is connected to a hypodermic needle set at 90A° to the incident beam for measurements in other geometries. The gas jet which is not currently used in the interaction region can be used to non-locally fill the chamber with gas for background counting measurements.
The final CF70 flange is used when the photomultiplier tube is cooled, usually during baking of the system following exposure to atmosphere. The tube is cooled by passing vapour from a liquid nitrogen source through expansion coils wrapped around the photomultiplier tube housing. The electron gun is a two stage non-selected gun designed by Woolf (Ph.D thesis, University of Manchester) (see figure 3). The gun consists of a filament, grid and anode source which is focussed using a triple aperture lens through two 1mm defining apertures in the centre of the gun.
The apertures define the electron beam pencil and beam angles, and are focussed onto the interaction region using a second triple aperture lens located between the apertures and interaction region. The electron gun is shielded using advance (constantin) sheet which is grounded to the body of the gun mounting. The gun is mounted onto an x-y translation table to allow placement of the electron beam as accurately as possible to the centre of rotation of the analysers and electron gun rotation axis. The gas jet is mounted from the electron gun using a narrow support of 310 stainless steel, and the Faraday cup can be attached to this support. The original unselected electron gun built by Woolf was completely rewired and a custom built PTFE 25 way inline wire-wrap plug and socket was placed between the 52 way vacuum electrical feedthrough and the electron gun. The wiring from the 52 way feedthrough to the inline plug is shielded colour coded 30 awg PTFE coated advance wire, and the inline plug and socket connectors are non-magnetic gold plated wire wrap pins. The electron analysers are constructed from molybdenum and are mounted from two rotating gear plates controlled externally via the rotation feedthroughs on the top flange (see figure 2).
The input electrostatic lenses for each analyser are three element cylindrical lenses as shown in figure 4. The interaction region is focussed onto the entrance aperture of the hemispherical energy analysers with a beam angle of around zero degrees, the image of the analyser entrance aperture being larger than the size of the interaction region. Field gradients around the input and exit apertures are corrected using standard Jost correctors.
The energy selected electrons passing through the exit apertures are finally collected by Mullard X919BL channel electron multipliers which amplify the single electron to produce a current pulse at their output.
A principle source of noise on the signal pulses arises from the turbo-molecular pump motor. The noise from the turbo pump is reduced to ~ 5mV using these techniques, and as the average pulse height from the saturated multiplier is around 20-40 mV, this allows adequate discrimination following amplification.
The pre-amplifiers located external to the vacuum system are commercial 100X preamplifiers with 400pS rise-times, manufactured by Phillips Scientific.
The NIM signals produced by the discriminators drive two ORTEC 437 Time to Amplitude Converter's via appropriate delay cables and an ORTEC pulse delay unit. The main TAC output feeds an ORTEC Multichannel Analyser card located in the PC controlling the experiment, whereas the second monitor TAC drives an external MCA, allowing convenient monitoring of the coincidence signal as the experiment progresses. The high voltage supplies to the electron multipliers are two Brandenberg 5kV supplies controlled by the main PC via serial DAC's.
Principally the filter is used to reduce pickup noise from entering via the HT cable onto the multiplier output. Secondly, the filter has a slow response time for high voltage spikes, and reduces the probability of damage to the pulse electronics should the EHT supply suddenly turn on or off. Capacitor C2 decouples the 1kW load resistor to earth for high frequency pulses from the CEM's, and the voltage appearing across this load is connected via the capacitor C3 to the input of the 6954 preamplifier. Since the input impedance of the preamplifier is 50W and the CEM is effectively an ideal constant current supply, most of the current passes through to the preamplifier.
Finally, the 10M resistor prevents the output to the preamp from rising above ground when the preamp is disconnected from the circuit and is therefore a safety device for the preamplifier when initially connected.
The original design placed the atomic beam nozzle and Faraday cup on the same support structure fixed to the body of the electron gun, with the atomic beam direction being in the detection plane when the perpendicular plane geometry is chosen (see figure 2). A second configuration is adopted for exclusively perpendicular plane coincidence experiments, the atomic beam nozzle being oriented at an angle of 45A° to the detection plane so that the gas effusing from the nozzle does not fill the analysers when they oppose the nozzle (see figure 6).
In this configuration the support strut for the atomic beam nozzle is terminated lower than the detection plane, as is the nozzle itself. For non-perpendicular plane measurements the Faraday cup is once mounted from the support strut and the gas effuses perpendicular to the electron beam direction. One difficulty when aligning an (e,2e) coincidence experiment lies in the focussing the incident electron beam and analysers onto the interaction region.
The throughput of electron current as detected by the Faraday cup is insensitive to both position and focusing of the electron beam, since the cup opening is usually made quite large (in this case 6 - 10mm) and the bias voltage applied to the cup to prevent electrons returning to the interaction region allows all electron trajectories within this opening to be detected.
Conventionally, following maximisation of the Faraday cup current, the beam is steered and focussed onto the gas jet as detected by counts in the analysers. This has the disadvantage that the overlap volume is maximised for both atomic and electron beam density, which tends to place the interaction volume as close as possible to the output of the atomic beam nozzle, which is almost certainly not in the centre of the detection plane. To eliminate the need for time consuming iterative techniques and the associated errors due to detection geometry, a separate method for tuning the electron gun is adopted that does not depend upon the analysers.
The interaction between the target and the electron beam not only produces ionisation, but the valence states of the target also are excited with various probabilities depending upon the incident energy of the electron beam. These photons are detected by the photomultiplier tube, by placing a 450nm A± 50nm optical filter in front of the photocathode.
The interaction region is therefore defined where an aperture in front of the photocathode is focused by the lens. The plano-convex focussing glass lens is covered by a grounded fine tungsten mesh to eliminate surface charging. The photomultiplier tube may be cooled by circulating nitrogen gas boiled off LN2 through copper coils encircling the photomultiplier tube housing. The photomultiplier tube used in the experiment is a 9789QB EMI photomultiplier tube with a bi-alkali photocathode peaking in the blue region of the optical spectrum.
As with the electron multiplier circuitry, it is important to optimise the load of the photomultiplier tube so that reflections along the feeder line to the counting electronics are minimised. The 1nF 6kV capacitors across the dynodes close to the output stage are used as charge storage pumps that quickly refurbish the surface charge on the dynodes, allowing increased counting rates. The dynode resistors are 1% tolerance metal film resistors as these are more stable with temperature.
The EHT supply to the photomultiplier tube is a Brandenberg 2kV supply operating at 1500V for this tube. The negative going output pulses from the tube measure typically 200-500mV in height, and therefore are able to directly drive an ORTEC 473A constant fraction discriminator located in one of the NIM crates. All resistors and capacitors for the dynode chain are soldered to the photomultiplier tube base internal to the vacuum system, using standard 5-core solder.
Typical pulse heights from the electron multipliers in saturation mode are 25-40mV, whereas the typical height of the photomultiplier tube pulses is of the order of 250mV. The electron multiplier pulses are obtained from the multiplier supply circuitry as explained above. The amplified pulses from the 6954 amplifiers pass along doubly shielded RG-58 cable to the input of the ORTEC 473A discriminators. The two analyser discriminators are located in separate NIM crates to increase isolation and reduce common mode pickup. The slow rise-time positive outputs from the 473A discriminators pass to three ORTEC 441 rate-meters which allow counting and monitoring of the pulses.
The fast NIM pulses from the analyser 473A CFD's pass through appropriate delay lines to two 437 TAC's.
This second multichannel analyser allows the operator to monitor the total accumulated coincidence signal during operation. The lens supplies that control the voltages impressed onto the lens elements and deflectors in the experiment were developed over a number of years, and therefore take different forms. Three of these supplies feed the deflectors in the electron gun, the other two supply the input deflectors in the analysers. In a second 19" crate is located the gun lens high voltage supplies together with the high voltage supplies for the Faraday cup.
In a third 19" crate is located the analyser voltage supplies together with a set of serial loading supplies that control the electron multiplier EHT supplies. A further supply controls the current boost circuitry located in the filament constant current supply unit (see below). The outputs of each computer controlled supply that drives an individual lens element or deflector are connected to a 70 relay switching board. The Digital voltmeter is in turn accessed via an IEEE-488 interface which is addressed by an 8086 slave PC which converses with the central PC which controls the experiment. The outputs from the relay board connect to the spectrometer via shielded multicore cables which take the gun voltages to the 52 way feedthrough and the analyser voltages to the two 19 way feedthroughs located on the vacuum flange. The gun supply multicore also carries the filament supply current to the 52 way feedthrough. The Faraday cup current is measured by the Keithley Digital voltmeter when under computer control but this can also be measured by an external pico-ammeter.
In addition to the analyser electrostatic lens and deflector voltage connections, the 19 way CF70 feedthroughs are used to control signals from internal sensing opto-isolators which control the stepper motor interlocks. The stepper motors that drive the analysers and electron gun around the detection plane are five phase motors with integral 10X reduction gearboxes driving the rotary motion feedthroughs. The intelligent stepper motor drivers are addressed via a serial port located on the controlling PC bus. An additional interference problem was traced to the RS232 serial line from the controlling PC. The PC bus was found to be poorly earthed due to very little copper being used for the bus earth. This was cured by decoupling the 0V RS232 line from the main 0V line for the stepper motors, as is shown in figure 10. The analyser stepper motor supplies have a facility for halting the motors using limit switches which are optically coupled to the internal 68000 logic circuits driving the supplies.
The SD5443-3 phototransistor normally illuminated by the TEMT88PD photodiode during operation ensured a fail-safe mechanism should any of these components fail (this automatically prevent the motors from running).
Should the analysers move into a position as defined by the four criteria (a) - (d) above, a shutter located on the analyser turntables moves between the appropriate photodiode and phototransistor, shutting off the light and thereby shutting down the stepper motor current. Only motion in the opposite direction is allowed by controlling logic, allowing the analyser to move away from the point of imminent collision but no closer. The six pairs of optocouplers that prevent the analysers moving into the Faraday cup, electron gun and gas jet support are located on the mounting struts supporting the main body of the spectrometer. Two optocouplers are located on the side of analyser 2, and two shutters are located on the sides of analyser 1 to prevent the analysers colliding with each other. Finally a ninth optocoupler is located over the electron gun counterweight which monitors when the gun is at an angle less than 65A°, where the sweep angle around the detection plane is reduced. The current boost circuit operates from a serial driven supply card as detailed previously. The main filament drive is through six power diodes that feed the current from the constant current supply to the filament.
The Darlington transistor T1 feeds additional current to the filament via three parallel 10 turn 100W trim resistors through a 1N4007 diode.
As the constant current supply acts as an infinite resistance source, the boost circuit supplies additional current only when the voltage at the anode of the feed 1N4007 exceeds the output voltage of the constant current supply. Finally, the filament bias voltage (and hence energy of the electrons) is set to the midpoint of the filament by two 100W balancing resistors located across the terminals. In addition to the ADC buffer card, three independent isolated regulated supplies drive REF01 voltage reference sources for measurement of the positions of 10 turn potentiometers located on the analyser and electron gun rotary drive shafts. The angular position of the electron gun and analysers is calibrated when the system is opened using visible laser diodes that define these angles to an accuracy of A±0.2A°. Figure 13 shows an overall block diagram detailing the computer control and high speed pulse interfacing to the spectrometer. A blog on the repair, operation and calibration of surface analysis systems and components including electron spectrometers, sputter ion guns and vacuum related hardware. Print PDFUsing Ta2O5 or SiO2 works well for aligning an ion beam to the focal point of an X-ray photoelectron or scanning Auger electron spectrometer.
Because the current measured into the Faraday cup is in the low nA range, a picoammeter (such as the RBD Instruments Inc.
Another benefit of using a Faraday cup is that you can also determine the electric current density using a multiplication factor.
While observing the picoammeter, adjust the focus (objective) and condenser on the ion gun control and the mechanical offsets (thumbscrews) on the ion gun for maximum current into the Faraday cup. This entry was posted in Ion Sources and tagged faraday cup, ion beam alignment, picoammeter by Randy. For electrons to emerge in this geometry they must undergo multiple scattering including scattering from the nucleus of the target, and so this provides a highly sensitive test for scattering theories. In these experiments a single electron of well defined momentum impacts with a target in the interaction region, resulting in target ionization and a scattered and ejected electron which emerge after the interaction has taken place. Our (e,2e) apparatus can access a wide range of geometries from a coplanar geometry, where the incident, scattered and ejected electrons all occupy the same plane, through to the perpendicular geometry, where the scattered and ejected electrons emerge in a plane orthogonal to the incident electron trajectory (figure 1). In this regime the probability of single ionization is a maximum, and so it is here that most ionizing collisions with electrons occur in nature.
Low energy electron ionization has also been attributed to the production of DNA damage in biological tissue, and so it is important to understand these collisions at a fundamental level to describe the physics of these processes.
The helium results are reproduced from previous studies carried out in Manchester, re-presented here for completeness. By choosing the analyser residual energy to pass electrons around the selector, a channel electron multiplier detects electrons of the specified energy for subsequent amplification and counting. In the perpendicular plane, only the mutual angle phi = xi1 + xi2 is relevant, where xi1, xi2 are as shown in figure 1. The orbital angular momentum of each electron is hence zero, with a momentum distribution that peaks around zero a.u. The configuration of the 10 electrons in neon is 1s22s22p6, whereas argon has 18 electrons occupying a configuration [Ne]3s23p6. The data files for these results can be downloaded as a TAB deliminated text file Helium.txt.
Experimental results for the ionization of helium in the perpendicular plane, with incident energies ranging from 3eV to 80eV above the ionization potential for this target. This is considered to be due to the dominance of post-collisional interactions (PCI) between the outgoing electrons, which drives electrons emerging with equal energies from the interaction region asymptotically towards opposite directions.
At ~50eV excess energy the three lobes have equal amplitudes, whereas at higher energies the outer lobes dominate. The DWBA theory most easily allows the different processes involved in the interaction to be switched on and off, and this has explained the origin of these lobes. This process requires the momentum of the incident electron to be exactly matched by the momentum of the bound electron, with both electrons moving in opposite directions prior to the interaction. In this case, since the particles have equal mass and energy, they emerge from the interaction region at a mutual angle of 90A° & 270A° as observed.
It is therefore clear that further work is needed to fully describe the ionization reaction, even for a simple target like helium. The lowest energy studied was 5eV above the IP, with six measurements being taken up to 50eV above the IP as shown.
Experimental results for the ionization of neon in the perpendicular plane, with incident energies ranging from 5eV to 50eV above the ionization potential for this target. The width for this peak in neon is ~120A°, which is broader than ~80A° for the same outgoing electron energy in helium. As the energy is raised to 10eV above the IP, the broad single peak seen at the lowest energy increases in width, and develops a flat structure at the peak.
However, at higher energies the mechanisms proposed for helium ionization described above would be expected to produce similar structures in all targets that have a central ionic core. The calculated atomic radius of argon (71pm) is however significantly larger than that for helium (31pm) or neon (38pm) due to the n=3 shell being occupied. Experimental results for the ionization of argon in the perpendicular plane, with incident energies ranging from 2eV to 50eV above the ionization potential for this target. The lowest energy studied was 2eV above the IP, the data at this energy having poor statistics due to experimental difficulties working with argon at this energy.
This minimum flattens at 10eV above the IP and rapidly evolves into a clear peak 15eV above the IP. The results further indicate that the use of a A”frozen-coreA• approximation is unlikely to be accurate in any theory attempting to emulate these data.
The physical size of krypton (88pm) is slightly larger than argon due to occupation of this shell, and due to closed occupation of the 4s and 4p shells. Experimental results for the ionization of krypton in the perpendicular plane, with incident energies ranging from 2eV to 50eV above the ionization potential for this target. Ionization of krypton no longer shows the dominance of PCI as predicted by Wannier, since there is now a central minimum at 180A°. This central peak is not as significant in krypton compared to the side lobes, and by 30eV above the IP is once again diminishing. It also appears that the variation in cross section as a function of energy follows a similar pattern for each of these targets.
A coincidence energy loss spectrum is shown in figure 7 to illustrate this separation at an incident electron energy 10eV above the IP for this target.
The results were taken from 2eV above the IP to 70eV above the IP for this target, so as to establish the variation in the cross section that is observed. At the lowest energy 2eV above the IP, a clear two-peak structure is observed which is similar to that observed from krypton. The results at higher energies are surprising, as the mechanism that produces the central peak with the electrons moving opposite each other is clearly dominating all other scattering processes.
The data files for these results can be downloaded as a TAB deliminated text file Xenon2.txt.
These data indicate that fine structure in the final ion state does not play a significant role in the ionization process, since the comparison between this data and that reproduced from figure 8 shows that the shapes of the cross section for each energy are very similar.
This contrasts to the coplanar geometry most often adopted, where the dominant scattering mechanism is usually a single binary scattering between electrons, resulting in a high probability that forward scattering occurs. The results presented here will hence further test these models for heavier targets, so as to elucidate the scattering mechanisms that result in the observations.
Argon, krypton and xenon also all evolve a central peak as the incident electron energy increases from near threshold, which cannot be due to PCI. The side lobes observed previously in the perpendicular plane have been attributed to a binary collision between the incident electron elastically scattered into this plane and a bound electron.
It is hence likely that the results for neon, argon and krypton are also not significantly altered by these effects, even though the spectrometer was not capable of resolving their individual ion states. CK would like to thank the University of Manchester for providing a PhD scholarship while carrying out this work. The electron impact occurs when a well controlled electron beam interacts with a well defined gas beam comprising ground state atoms or molecules under investigation. Here the electrons do not lose any energy in the reaction, however the momentum of the electrons may change. Here the incident electron loses energy in the reaction to the target, which is subsequently excited to one of its (usually discrete) states.
In these experiments the target is prepared in some way so that it has internal energy prior to interaction with the electron beam.
This is here defined as a state that cannot decay to a lower state of the target via a single photon emission (dipole allowed) transition. State selectivity is obtainable by exploiting momentum transferred to the atom by the electron impact.
This is brought about in these experiments by employing a supersonically expanded jet of target gas which is skimmed by an expontially flared aperture in a source chamber.
These ground state targets eventually enter the high vacuum pump located at the top of the interaction chamber from where they are ejected. They can then drift for many hundreds of microseconds before a collisional de-excitation occurs either with each other or with a surface or stray molecule inside the vacuum chamber. Note that if the targets are molecules they may share this internal energy between rotational & vibrational states in the metastable electronic manifold.
This can be achieved using conventional electron energy analysers that select electrons of a specific energy and scattering angle for measurement.
As the possible target deflection angles following the collision is confined to a much smaller range than the possible scattering angles of the electrons (which range from 0A° through to 180A° in space), in principle the cross section for excitation of the state can be completely mapped out over all possible electron scattering angles. In these experiments only the momentum of the electron is measured, both for the incident beam and for the scattered electrons using energy and angle selective analysers. The signal will then be an incoherent summation of the contributions fom these excited states. Of particular interest in this region is the study of temporary negative ion states that show up as resonances. Measurements of energy selected scattered electrons in coincidence with measurement of the excited targets then exclude any contribution from upper states, since the electrons which excite these states are excluded from the coincidence measurement. Tunable laser radiation has an energy resolution typically 1,000 to 1,000,000 times better than is possible using electron spectrometers, and so resonant excitation can individually select the metastable state for further excitation following electron impact excitation.
The coplanar momentum transfer scheme, showing the relationship between the extrema of the electron scattering angles together with the corresponding extrema of the target deflaction angles. The graphs show the effects as a function of the momentum, velocity and deflection angle of the target helium atoms. Variation of the maximum and minimum target deflection angle as a function of the incident energy of the electrons. This aperture together with the 1mm exit orifice of the nozzle are aligned using visible laser diodes.
All are aligned using Visible Laser Diodes apertured to accurately define their individual axes. This is important as the detector may measure ions created as the electron beam interacts with the gas beam. The calibrated angle plate which accurately measures the deflection angle of the target beam. This additionally allows the zero angle to be calibrated wrt the apertures in the source chamber which define the ground state target beam direction.
Since the interaction region to detector distance is accurately known, this immediately yields the value of final atom momentum Paf(qa) to substitute into the appropriate equations. Gaussian fitting parameters as a function of the Detection Angle for the time resolved metastable atom deflections at 40eV Incident Energy.
It can be seen that the DCS is forward peaked as expected, and that the DCS has been determined at the complete set of scattering angles from forward to backward scattering.
This may be attributable to errors associated with the solid angle of detection of the analyser which has not been considered in the above calculation. These experiments measure the angular correlation between a projectile electron which is scattered from a target and a resulting electron which is ionised from the target.
For an unpolarised target and unpolarised incident electron beam the only azimuthal angle of significance is given by f = fa - fb. When the electrons are detected in the perpendicular plane, the two angles qa and qb are both equal to 90A°. The perpendicular plane is accessed mainly through double collision processes (Hawley-Jones et al (1992), which represent only part of the full dynamical picture. The computer loads all the voltage supplies from either a manually selected set of voltages or from the results of a previous optimisation run.
This decouples the tuning of the electron gun from any tuning requirements of the electron analysers. This should be compared with the data obtained near threshold by Hawley-Jones et al (1992), which also shows a single peak with an approximately Gaussian structure. This is considered to be due to the contribution to the cross section of a number of resonances in helium for scattered and ejected electron energies around 35eV.
The model indicated that the electron gun operating at the voltages determined by the optimisation routines produced an electron beam of diameter approximately 1.0mm at the interaction region, consistent with the tuning of the electron beam onto counts from the photomultiplier which views a 1mm3 volume.


For the non-symmetric data no compensation is required for volume effects since GV = 1.0 at all values of Ei.
The electrons are then able to emerge at approximately 90A° with respect to each other in the perpendicular plane, as is observed. As the momentum distribution of the bound electron peaks at zero for helium, the peak at 180A° diminishes with increased incident electron energy as the probability of finding a bound electron with the required momentum decreases.
An ion striking the channeltron creates secondary electrons that have an avalanche effect to create more secondary electrons and finally a current pulse.
The secondary electrons are accelerated onto a scintillator that produces light that is then detected by a photomultiplier tube. The capillaries are biased at a high voltage and like the channeltron, an ion that strikes the inside wall one of the capillaries creates an avalanche of secondary electrons. One of these is internally connected to a gas jet which can be set at 45A° to the incident electron beam and is used in the perpendicular plane experiments. These stainless steel feeder tubes are connected to the nozzle using grounded shielded PTFE hose.
One follows the anode, another corrects the beam direction between the apertures and a third steers the beam onto the interaction region. This shield is coated with aerodag colloidal graphite to reduce patch fields on the surface of the metal, and is made as small as possible to allow the analysers to approach the gun as close as is feasible when non-perpendicular plane geometries are selected (see figure 2). The XY translation table is mounted from the rotating yoke, to which is attached the photomultiplier tube. This allows the gun to be dismounted from the system without the need for rewiring of the feedthrough when the need arises (filament changes, cleaning etc). The wiring between the gun and inline socket is also shielded colour coded PTFE coated advance wire facilitating spot welding to the electrostatic lens elements of the gun.
The analysers are mounted onto x-z translation tables that allow them to view the interaction region accurately over the full range of angles accessible. These lenses have a capability for energy zooming of around 10 : 1, and have a maximum entrance acceptance angle of A±3A° as defined by the entrance apertures. This ensures that the overlap volume accepted by each analyser encompasses the interaction volume for all detection angles as the analysers move in the detection plane. These devices use an activated lead glass internal surface which has a high coefficient of secondary electron emission when a high voltage (around 3000V) is applied across the multiplier. This noise may be picked up by the channel electron multiplier and the high voltage feed to the multiplier, and is generated internally in the vacuum system. The CFD's are operated in NaI mode as this has a 2ms dead time following the initial pulse, thus reducing the possibility of false triggering due to any mismatching impedance reflections along the delay cable.
These EHT supplies are connected via VERO 200 high voltage couplings to high voltage cable connecting to the pickoff circuitry located on the high voltage feedthroughs. This allowed the analysers to roam the detection plane over a complete 360A° angular range. The configuration of the target source hypodermic when perpendicular plane measurements are conducted.
The common procedure is to initially maximise the current from the gun onto the Faraday cup, then onto analyser counts as the electron beam is moved through the gas jet.
Maximising the Faraday cup current is therefore only a crude preliminary alignment of the incident electron gun beam. This therefore assumes that the analysers are initially focused onto the interaction region, and a slow iterative technique must be adopted where the analysers and electron gun are tuned so as to maximise the signal from both analysers.
In this case a true differential cross section is not obtained, since the scattered and ejected electron trajectories lie in a different plane than defined in the initial experimental alignment. An EMI 9789QB reduced photocathode photomultiplier tube is installed in the vacuum system together with optical focussing and defining elements (figure 2). A group of these excited states decay back to lower valence states with the emission of visible photons at wavelengths around 450nm for both helium and argon targets. Tuning of the electron gun to PMT counts therefore guarantees that the electron gun is steered and focussed to the point at the centre of the detection plane independent of the analysers or gas beam density. This is mainly used when the vacuum system is baked at temperatures above 55A°C, since the photocathode is rapidly damaged by temperatures exceeding this. The tube is a venetian blind dynode construction, and has a reduced photocathode to decrease the noise on the output of the tube to less than 20Hz. The photomultiplier tube base was thoroughly cleaned in an ultrasound following location of these components, to displace any flux residue from the solder joints. It is therefore necessary to amplify the channeltron pulses prior to transmission to the discriminators, whereas the photomultiplier tube pulses are sufficiently large to not require further amplification. These pulses are amplified by Phillips Scientific 6954 100X amplifiers located external to the EHT feedthroughs connected by 10cm lengths of RG-58 cable. These crates are further decoupled from the AC mains supply using filter circuitry on each supply line.
Internal to these rate-meters buffer 7400 TTL chips have been added to send to 32 bit counters located in the main PC via RG-58 cable.
These supplies are fully floating, their mid-point voltage being equal to the lens element voltage in which the deflectors are housed. All these supplies are fully computer controlled isolated units with low output impedance to reduce noise and eliminate current loops. This relay switching unit allows either the voltage or the current on each lens element to be measured by a Keithley Digital voltmeter.
This drive is further reduced internally by 10X reduction gears, resulting in a reduction ratio of 100:1. This led to the ground line of the RS232 serial line moving around with respect to the 0V stepper motor reference as drive current to the motors returned along the ground line. The optocoupler logic circuit circuit that controls the stepper motors and avoids collisions between the analysers, the electron gun, the Faraday cup and the hypodermic support. Added to this filament supply is a computer controlled current boost circuit that can be used to increase the filament current during electron gun tuning. The additional current then returns to the 12V DC regulated supply via a second 1N4007 diode. This therefore depends upon both the current driving the filament, as well as the resistance of the filament when hot (typically 4W - 6W).
This supply feeds current to the filament without changing the characteristics of the main constant current supply used while operating the spectrometer.
These high stability reference sources ensure that the analyser and electron gun positions are accurately measured with time.
A datalogger internal to the controlling PC establishes a cubic spline relationship between the measured angles and the corresponding ADC conversion from the potentiometers. This PC also controls the selection of the relay motherboard for measurement of the required lens element either in voltage or current mode when a request is sent from the controlling computer via an RS232 serial line. But, in order to optimize the ion beam focus at larger beam sizes, a Faraday cup is required.
For Auger electron spectrometers, acquire an elastic peak just to the side of the Faraday cup hole and then move the Faraday cup hole to the center of the TV image. This will ground the target and apply +90V to the ion lead on the specimen stage (which in turn makes the electrical contact to the Faraday cup). By optimizing a few ranges of current and using those parameters to acquire depth profiles on a standard such as SiO2 or TaO5 (both available from RBD) you can create a matrix of reproducible sputter rates. Hence it is possible to accumulate a full range of DCS measurements over all scattering angles using this spectrometer.
The incident electron can move from the coplanar geometry (psi = 0A°) to the perpendicular plane (psi = 90A°), the outgoing electrons being measured in the detection plane. The shape of the DCS for a given energy and target is then of importance, for comparison with theory. This contrasts with the other noble gas targets whose levels are 1S0, but whose valence electrons occupy closed p-orbitals. By contrast, the bound electrons in both of the heavier targets also occupy d-orbitals, with a correspondingly more complex momentum distribution. As the outgoing electron energy is lowered, the post collisional interaction time increases, resulting in an increased flux in the 180A° direction.
At excess energies over 80eV above the IP the central lobe has virtually disappeared, leaving only the two outer lobes in the DCS. In this case, momentum conservation requires the outgoing electrons to move in opposite directions (180A°) in the perpendicular plane. The data files for these results can be downloaded as a TAB deliminated text file Neon.txt. At 15eV above the IP this flat structure has evolved into two peaks with 180A° now being a local minimum.
The static polarization of argon is eight times larger than for helium, so scattering effects due to polarization of the target are expected to be significantly larger than for neon or helium.
The data files for these results can be downloaded as a TAB deliminated text file Argon.txt.
This central peak is visible for incident energies up to 40eV above the IP, until at the highest energy (50eV above the IP) this has once again disappeared, the side peaks having also moved outwards compared to at the lower energies. The relative magnitude of this minimum compared to the peaks around 110A° & 250A° is however larger than for higher incident energies, so there is probably a contribution to the cross section at this angle due to PCI.
This central peak has virtually disappeared 40eV above the IP and there is no evidence of a peak 50eV above the IP. It might hence be expected that the cross section for the heaviest target (xenon) would follow a similar trend to that of argon and krypton.
The data are fitted to two Gaussians, showing that contamination from each ionic state is <10% when the spectrometer is set to each peak in the cross section.
The data files for these results can be downloaded as a TAB deliminated text file Xenon1.txt.
This indicates that PCI is once again not the dominant mechanism producing the cross section at this energy. The relative magnitude of this peak compared to the lobes at 110A° and 250A° then increases in magnitude as the energy increases, as with krypton and argon.
This result indicates that fine structure does not appear to play a significant role in electron collision processes at these energies. The marked contrast between results for helium and all other noble gas targets demand that these models carefully consider the intricacies of the interaction, since a simple extension of the basic physical ideas presented for helium cannot explain the experimental data.
For argon and krypton the relative magnitude of this peak increases with respect to the side lobes until it reaches a maximum, then decreases to become insignificant at the highest energies measured.
This process has always been considered as the dominant mechanism at higher incident energies, yet the new results presented here indicate these ideas need to be revisited for this heavy target.
Thus the electrons may be scattered throughout space from the reaction zone, the distribution of these electrons then giving information on the elastic differential cross section for the target in question. These states may be below the ionisation limit of the target, in which case the target usually remains neutral, or higher order excitation processes can occur where more than one electron in the target is excited. The interaction then removes energy from the target and so the electrons emerge from the reaction with greater energy than they had prior to the reaction. The excited target therefore has a very long lifetime, since the probability of 2 photon decay is much smaller than for single photon decay processes. For light atoms and molecules (He & H2 for example) the metastable targets are deflected through angles from ~5A° for forward electron scattering to in excess of 30A° for backward scattering depending upon the impact energy. An electron of well defined momentum Pei collides with a target atom or molecule in its ground state that has a well defined initial momentum Pai. These experiments are conventionally limited to a range of scattering angles that does not include either the forward scattering region of the backward scattering region.
These experiments do not have the spatial or temporal resolution to define either the incident or the final target momentum, since they mostly produce a target beam via continuous effusive flow from a capillary.
These resonances occur since the scattered electron following excitation can remain in the region of the excited target for sufficient time to form a pseudo-stable state which has its own unique properties. As before the electron of incident momentum Pei is scattered inelastically from the target of incident momentum Pai, leaving the target in a metastable state. Electrons incident along the z-axis have a well defined energy Einc and thus a well defined momentum Pei. Electrons incident along the z-axis have a well defined energy Einc and a well defined momentum Pei. Electrons incident along the z-axis with well defined energy Einc and well defined momentum Pei can scatter throughout the range of angles from 0A° (forward scattering) through to 180A° (backward scattering) as shown in figures (a) and (b).
Amplitude h, peak position and peak width w are all calculated using a least squares fit to the data, a sample of which is presented in figure 14. Further it allows the electron gun to be aligned and focussed accurately onto the interaction region whose centre is located at the intersection of the axes of rotation of the analysers and the electron gun. This type of double collision process must therefore be modelled using higher order scattering terms as is done using the DWBA. Since a Faraday cup can only be used in an analog mode it is less sensitive than other detectors that are capable of operating in pulse-counting mode.
This cascading effect creates a gain of 103 to 104 and produces a current pulse at the output.
The spectrometer is shown configured in the perpendicular plane, the electron gun being placed in the vertical position with respect to the analysers which span the horizontal detection plane. The electron source is a heated tungsten hairpin filament heated by passing around 2A of DC current through the filament. The saturated gain of these devices yields around 1E8 electrons in the output current pulse for a single electron which enters the input cone. This allows the analyser to roam over a complete 360 degrees of the detection plane when in this geometry (apart from the position where the analysers would clash wth each other). The analysers are then adjusted for maximum signal count and the procedure is iterated until a maximum is found. The dark noise count is also reduced when cooled, however since the reduced cathode PMT only produces dark counts of less than 20Hz at room temperature, this is not necessary during routine operations. The 1.82M resistor was chosen to optimise the single photon counting efficiency of the tube. It is not found that these solder connections significantly affect the ultimate vacuum pressure in the system. Isolated DC supplies to these amplifiers is obtained from a standard +15V supply, the circuit diagram being given in figure 8. The power supply to these TTL buffers is derived from the rate-meter supplies via 7805 5V regulators located internally. This supply boosts the current without changing the main supply, thus ensuring supply stability before and after the electron gun is tuned.
When the bias box is set to the ion input, the target is grounded and the output of the bias box is routed from the ion lead (Faraday cup) on the specimen stage to the input of the picoammeter. For X-ray photoelectron spectroscopy systems, move the Faraday cup hole to the center of the system microscope’s image at the highest possible magnification setting.
Once the mechanical offsets on the ion gun have been adjusted to where no further increase in current is noted, lock them down securely and also make sure that the ion gun housing is tight. For the data presented here, the perpendicular plane was chosen, so only the mutual angle phi = xi1 + xi2 is relevant. The combined coincidence energy resolution of the unselected energy electron gun and the two analysers is ~1eV. Krypton has 36 electrons and has a ground state configuration [Ar]3d104s24p6, while xenon has 54 electrons with a ground state configuration [Kr]4d105s25p6. This type of threshold behaviour was first predicted by Wannier and was later considered by Peterkop, Rau and others to explain results in this regime.
This mechanism was considered as being the main reason for the peak at 180A° until the work of Madison and co-workers in 2009 showed the probability of this occurring was low. As the energy increases further, the peaks separate in angle, and the minimum at 180A° deepens.
This angular shift of the side lobes is consistent with PCI playing a continuing role in the interaction, since as the energy increases the effects of PCI diminish, and the electrons move away from 180A° as is observed. The data files for these results can be downloaded as a TAB deliminated text file Krypton.txt. However, unlike krypton and argon whose central peak reaches a maximum and then decreases, the central peak in xenon continues to dominate the cross section as the energy rises. Further, the frozen core approximation often adopted in these models which treat all non-ionized electrons as spectators does not appear valid for the heavier targets when compared to neon, even thought the outer valence electrons have the same p-type character. The energy required to excite these processes is usually above the ionisation limit, and so these excitation mechanisms often lead to ionisation via photon emission or through autoionisation.
In these experiments the initial target state is almost always prepared by excitation with a laser beam from the ground state, since very high yields (theoretically up to 50% for CW laser excitation) of target excitation can be achieved prior to electron collision.
This long lifetime (which can be up to seconds if there are no other mechanisms for de-excitation) is exploited in these experiments, which measure the quantity of metastable targets as a function of the target deflection angle following electron collision.
The correspondence (via momentum and energy conservation equations) between the deflection angle and arrival time at the detector of the excited target with the electron scattering angle therefore allows differential cross sections to be measured over the full range of possible scattering geometries from forward to backward scattering.
The target is excited to a metastable state, the electron losing energy Eexc during the reaction. Any variation in cross section due to variations in the target momentum is therefore averaged out in the signal that is collected. The target is then further excited using resonant laser radiation to a higher lying state which is then studied. These electrons interact with a beam of target atoms or molecules prepared with a well defined momentum Pai travelling along the x-axis with an initial thermal energy Eai. These electrons interact with a beam of target atoms or molecules prepared with a well defined momentum Pai travelling along the x-axis with an initial energy Eai.
Since momentum must be conserved in the reaction, the change of electron momentum delta Pe along the z-axis for these cases must be balanced by a corresponding change in momentum Delta Pa of the targets along this axis. The graph shows the effect discussed in figure 4, where for each deflection angle there are two distinct atom momenta corresponding to unique electron scattering directions. These are normally pinched off from exiting the region of the filament using a -15V grid potential wrt the tip of the filament. This is essential for experiments where all of these may be varied over 3-Dimensional space. The electron gun is a two stage non-energy selected gun that produces an incident electron beam current of up to 4 microamps at an incident energy from around 30eV to 300eV. The 470k resistors bias the dynodes to achieve saturation of the current pulse at the output of the tube, hence biasing the tube for single photon counting applications.
This was found to be necessary to eliminate problems associated with current loops from the 20A peak motor current feeding the common point of the logic circuitry. When an ion beam is larger than the 250um Faraday cup aperture, only the portion of the beam that is 250um or smaller is measured.
Do not adjust the mechanical offsets for subsequent focus adjustments at different condenser (COND) or beam voltage settings.
They proposed a triple scattering mechanism to describe this peak, where the incident electron first scatters elastically from the nucleus so as to enter the detection plane, followed by a binary inelastic collision with a bound electron, followed by elastic scattering of one of the electrons back from the nucleus. This trend continues up to the highest energy which was possible to measure (70eV above the IP), where the central peak is seen to be broad with a width ~100A°. It is hence likely that these assumptions will need to be relaxed to accurately model the data. Some experiments have also been conducted where the target beam is prepared in a metastable state using electron bombardment, but these experiments are very preliminary.
The final momentum of the inelastically scattered electron is given by Pef, whereas the final momentum of the target is given by Paf.
The high resolution of the laser excitation allows details of the electron excitation to be studied in higher detail than is possible using electron spectroscopy alone.
When requested the grid potential is rapildly raised so that the positive anode potential field reaches the filament to extract electrons which are accelerated and focussed onto the interaction region using 2 triple aperture electrostatic lenses. The analysers are identical, and consist of a 3-element electrostatic lens focussing the interaction region onto the entrance of a hemispherical electrostatic energy analyser. The Anode deflector pair corrects for any misalignment of the filament emission point with respect to the axis of the electron gun.
By adjusting the ion beam focus and position for maximum current into the Faraday cup, the ion beam can be aligned and the current density can be optimized for any ion beam condition.
In those cases, short out the target and and connect the picoammeter to the ion lead on the specimen stage.
Instead, you can optimize the position of the ion beam into the Faraday cup by using the offset adjustments on the ion gun control if necessary. This complex mechanism was found to emulate the cross section more closely compared to the single scattering process originally envisaged.
As for all measurements in this study, the DCS must be zero for the electrons emerging at the same angle (0A°, 360A°), due to post collisional interactions between outgoing electrons of equal energy. At all energies greater than 40eV above the IP, the outer peaks seen in all other targets have disappeared. The scattered electrons leave the interaction region with momentum Pef at scattering angles (thetae, phie), whereas the deflected excited targets leave the interaction region with linear momentum Paf at polar angles (thetaa, phia). The scattered electrons are confined to the xz plane and leave the interaction region with momentum Pef at a scattering angles thetae. In general as shown in figure (c), for a particular target deflection angle between these two extrema there are two possible electron scattering angles that can result in targets deflected to this angle, as shown.
A further set of output deflectors pulsed simultaneously with the grid allows the final focussed beam to pass through the exit aperture and onto the target beam.
The Chamber is lined internally with 3mm thick mu-metal, and a mu-metal cylinder encloses the chamber externally as shown.
The electrons selected in angle and energy are amplified using Mullard 919BL channel electron multipliers. The defining apertures limit the pencil and beam angles of the electron beam following focussing by lens 2 onto the interaction region. The load is set by the 50W resistor across the anode to the HT feed, the pulse being decoupled to ground via the 1nF capacitor. Typically, though, the 04-303 ion source is operated at 3-to-4kV with 15MPa of argon pressure. The deflected excited targets therefore must also leave the interaction region in the xz-plane and are deflected to the angle thetaa. In the example shown, electrons scattered in the lower xz-plane experience a momentum change larger than electrons scattered into the upper xz-plane. This set of deflectors also removes any ions created inside the electron gun in the high potential regions from reaching the interaction chamber, since their flight times are much slower than the associated electron pulse. This reduces the magnetic field at the interaction region to less than 5mG, an acceptable level for the electron energies used in this experiment. The interaction region defined by the interaction of the gas target beam and the electron beam is focussed onto the photocathode of an EMI 9789QB photomultiplier tube via a lens, 450nmA±50nm optical filter and defining aperture. Placement of the apertures ensures that the beam angle is close to zero degrees at the interaction region over a wide range of energies, whereas the aperture opening reduces the pencil angle to around A±2 degrees over this energy range.
Therefore, the maximum ion current passing into a Faraday cup under those conditions is more in the range of 150 to 200nA. Observation of the targets at any intermediate deflection angle will therefore display two different momenta for these targets.
The target gas effuses from a 0.6mm ID hypodermic needle constructed from platinum iridium alloy. The 10MW safety resistor prevents the output charging up to a high voltage if the feed is disconnected.
The deflectors between the apertures correct for space and surface charge beam variations inside the field free region, whereas the final deflectors allow the beam to be steered onto the interaction region defined by focussing a 1mm aperture in front of the photomultiplier tube onto the gas target beam.
The electrons passing through the interaction region which are not scattered are collected in a Faraday cup opposite the electron gun. The gun, photomultiplier tube, gas hypodermic and Faraday cup all rotate on a common yoke with an axis through the centre of the horizontal detection plane, allowing all geometries from the perpendicular plane to the coplanar geometry to be accessed.



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