Metastable Target Deflection by Electron Impact

This Page has been prepared & edited by

Andrew James Murray

INTRODUCTION

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. 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.

Many different processes can occur in this reaction, depending upon the energetics and kinetics of the reaction. These include:

Elastic scattering of the electrons from the target gas beam. Here the electrons do not lose any energy in the reaction, however the momentum of the electrons may change. 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.


Inelastic scattering of the electrons from the target gas beam. Here the incident electron loses energy in the reaction to the target, which is subsequently excited to one of its (usually discrete) states. 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 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.


Superelastic scattering of the electrons from the target gas beam. In these experiments the target is prepared in some way so that it has internal energy prior to interaction with the electron beam. 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. 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. 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 experiments described here look at the process of inelastic scattering, where the target is left in a metastable state. 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. 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. 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 experiments are precursors to measuring stepwise laser excitation of metastable atoms and molecules. State selectivity is obtainable by exploiting momentum transferred to the atom by the electron impact. For light atoms and molecules (He & H2 for example) the metastable targets are deflected through angles from ~5° for forward electron scattering to in excess of 30° for backward scattering depending upon the impact energy. 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.

It is these deflection experiments and their results that are discussed here.

DIRECT ELECTRON EXCITATION SCHEMES


Figure 1. Direct electron-Target excitation. 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. The target is excited to a metastable state, the electron losing energy Eexc during the reaction. The final momentum of the inelastically scattered electron is given by Pef, whereas the final momentum of the target is given by Paf.


Consider the excitation scheme described in figure 1. Here:

  1. 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.

  2. The target possesses a well defined momentum Pai. 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.


Thus :

  1. The direction of the gas is defined by the spacing and size of the aperture in the gas nozzle together with the skimmer, whereas

  2. 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.

  1. These electrons are produced in an electron gun that controls both the direction and energy of the electrons.

  2. 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.

  3. The majority of the target beam is also unaffected during the reaction, and passes through the interaction region. These ground state targets eventually enter the high vacuum pump located at the top of the interaction chamber from where they are ejected.


Out of the small number of electrons and targets that interact:

  1. The majority undergo an elastic collision where only the direction of the incident electron may change and the target remains in its ground state.

  2. 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. 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.


Hence, the collision yields :

  1. Scattered Electrons with energy Efinal = Einc - Eexc, which have momentum given by Pef

  2. Scattered Atoms (Molecules) in a Metastable State with internal energy Eexc and which carry momentum Paf away from the reaction. Note that if the targets are molecules they may share this internal energy between rotational & vibrational states in the metastable electronic manifold.


In the experiments considered here, measurements of the interaction between the targets and the electrons can be made by :

  1. Studying the momentum of the electrons which have excited the targets. This can be achieved using conventional electron energy analysers that select electrons of a specific energy and scattering angle for measurement. 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.


Alternatively, measurements of the interaction between the targets and the electrons can be made by :

  1. 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. 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 0° through to 180° in space), in principle the cross section for excitation of the state can be completely mapped out over all possible electron scattering angles.

It should be noted that in conventional electron scattering experiments which measure excitation cross sections, the target momentum is not usually considered. 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. 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. Any variation in cross section due to variations in the target momentum is therefore averaged out in the signal that is collected.

There are a number of complications that can arise in these experiments where the target momentum is exploited for measurement.

Principal amongst these difficulties is that of :

Cascades.

  1. 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.


Insufficient State Selection of the Metastable targets.

  1. 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. The signal will then be an incoherent summation of the contributions fom these excited states.

  2. 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.


Overcoming the Measurement difficulties due to Cascades

The difficulties associated with cascading can be overcome by confining the study to the region close to threshold for excitation of the metastable state. Of particular interest in this region is the study of temporary negative ion states that show up as resonances. 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.

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. 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.

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.

Overcoming the difficulties of State Selection of the targets

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. 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.

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.


THE STEPWISE ELECTRON/LASER EXCITATION SCHEME

A brief outline of the stepwise electron/laser experiment is given here. Further information on these experiments can be found by linking to the appropriate page.


Figure 2. The Stepwise Electron/Laser Excitation scheme. 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. The target is then further excited using resonant laser radiation to a higher lying state which is then studied. 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.


ADVANTAGES AFFORDED BY THESE EXPERIMENTS

  1. Offers Spectroscopic Advantages presented by electron excitation (wide range of excitation energies, absence of any angular momentum restrictions) together with very high resolution of laser source

  2. Allows the electron excitation mechanism to be studied by analysing the stepwise excited state. This laser excited state can be studied either by looking at either :

    1. Photon emission to a lower lying state (difficult, as the selected photon yield is very low), or by

    2. 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.

  1. Molecular Vibrational & Rotational states can be studied in detail for a wide range of targets.


DISADVANTAGES OF THE STEPWISE EXCITATION SCHEME

  1. Requires expensive tunable laser source. Difficult to get funding as the funding bodies seem not to like these hybrid experiments that employ more than one speciality (ie laser & electron spectroscopy expertise)

  2. The experiments are often very difficult and time consuming.

  3. A detailed analysis of the laser excitation process is required to fully characterise the electron excited state.


ELECTRON-ATOM MOMENTUM TRANSFER THEORY

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.

ENERGY CONSERVATION

The system defined by the target and the electron must obey the Energy Conservation Equation:


where

  1. Pei, Pai are the momenta of the incident electron and target respectively

  2. Pef, Paf are the momenta of the scattered electron and target respectively

  3. me is the electron mass

  4. ma is the mass of the target and

  5. Eexc is the metastable state excitation energy


MOMENTUM CONSERVATION

Figure 3a shows the general momentum transfer scheme :


Figure 3a. The general momentum transfer scheme. Electrons incident along the z-axis have a well defined energy Einc and thus a well defined momentum Pei. 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. The electrons excite the target which carry internal energy Eexc away from the reaction. 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). Both energy and momentum must be conserved during the reaction.


The system defined by the target and the electron must obey momentum conservation. Hence, for the general geometry as shown in figure 3a :


Solving these energy & momentum equations simultaneously yields for the general case :



For planar geometry (see figure 3b) as used in this experiment these equations reduce to:


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.


Figure 3b. The coplanar momentum transfer scheme. Electrons incident along the z-axis have a well defined energy Einc and a well defined momentum Pei. 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. The electrons excite the target which carry internal energy Eexc away from the reaction. The scattered electrons are confined to the xz plane and leave the interaction region with momentum Pef at a scattering angles thetae. The deflected excited targets therefore must also leave the interaction region in the xz-plane and are deflected to the angle thetaa. Both energy and momentum are conserved during the reaction.



Figure 4. 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. Electrons incident along the z-axis with well defined energy Einc and well defined momentum Pei can scatter throughout the range of angles from 0° (forward scattering) through to 180° (backward scattering) as shown in figures (a) and (b). 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. No momentum can be transferred along the x-axis for either of these extreme cases. 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. In the example shown, electrons scattered in the lower xz-plane experience a momentum change larger than electrons scattered into the upper xz-plane. Observation of the targets at any intermediate deflection angle will therefore display two different momenta for these targets.


Figure 5 graphs the results of calculations where electrons excite the singlet 2S metastable state of Helium where the atom velocity is 1800 m/s (typical for supersonic expansions as in these experiments) and the incident electron energy is 40eV. The graphs show the effects as a function of the momentum, velocity and deflection angle of the target helium atoms.


Figure 5a. Target deflection as a function of the scattered electron direction where electrons excite the singlet 2S metastable state of a Helium target and where the initial velocity is 1800 m/s. The incident electron energy is 40eV.


Figure 5b. Deflected target momentum and velocity as a function of the scattered electron direction where electrons excite the singlet 2S metastable state of a Helium target and where the initial velocity is 1800 m/s. The incident electron energy is 40eV.


Figure 5c. Target deflection as a function of the deflected target momentum and velocity where electrons excite the singlet 2S metastable state of a Helium target and where the initial velocity is 1800 m/s. The incident electron energy is 40eV. 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.

  1. 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.

  2. Hence with sufficient time resolution and detection angle resolution the experiments should reveal 2 distinct peaks at any given detection angle.


Figure 6. Variation of the maximum and minimum target deflection angle as a function of the incident energy of the electrons. The variation between electrons exciting the singlet and triplet 2S metastable states of a Helium target with initial velocity of 1800 m/s is shown, together with the variation in deflection angle for highly excited Rydberg states.


Figure 6 shows the maximum & minimum atomic deflection angles over a range of incident electron energies exciting helium metastable states & high Rydberg states from threshold to 40eV incident energy.

  1. 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.



EXPERIMENTAL SETUP FOR METASTABLE ANGULAR DETECTION.

THE ATOMIC (MOLECULAR) SOURCE


Figure 7. The Source chamber. For details see text.

  1. Source Chamber pumped by 2500l/s oil diffusion pump. Ensures minimal stalling during high repetition rate gas pulses.

  2. Supersonic Expansion in source chamber is used to reduce beam velocity distribution

  3. 1mm orifice skimmer at exit of source chamber/ entrance to interaction chamber is used to define the target beam direction. This aperture together with the 1mm exit orifice of the nozzle are aligned using visible laser diodes.

  4. Piezoelectric Nozzle ensures stable pulse repetition - Typical pulse widths are 500ms (quasi-Gaussian profile) at repetition rates up to 150Hz.

THE INTERACTION CHAMBER


Figure 8. The Source and Interaction chambers. See text for details.

  1. The Interaction Chamber is pumped by a 500 l/s turbo-molecular pump on top of the chamber which is placed directly over the skimmer aperture

  2. The electron gun,

  3. Faraday cup, and

  4. metastable detector are installed in this chamber as shown. All are aligned using Visible Laser Diodes apertured to accurately define their individual axes.

  5. The chamber is lined with a double layer of m-metal which reduces external magnetic fields to < 5mG at the interaction region.


  1. All internal components are manufactured from non-magnetic materials including :

    1. PTFE

    2. 310 grade non-magnetic Stainless Steel

    3. Molybdenum (used for all electrostatic lens elements)

    4. Aluminium

    5. Advance (constantin) electrostatic shielding which is Dagged (Coloidal graphite) to create a uniform conductive surface

  2. Details of the individual components in the interaction chamber are as follows:

THE UNSELECTED ELECTRON GUN


Figure 9. The unselected electron gun. A standard commercial tungsten filament provides a source of thermal electrons. These are normally pinched off from exiting the region of the filament using a -15V grid potential wrt the tip of the filament. 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. 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. 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.

The electron gun consists of :

  1. A conventional hot tungsten filament which is used for the electron source

  2. An electron extraction region which consists of a pulsed retardation Pierce grid with extraction anode (quasi-collimates electrons from filament)

  3. 2 stages of electron optics are used to focus electrons from 5eV to 100eV energy with zero beam angle and a 3 degree pencil angle (1mm diameter beam at interaction region)

  4. Fast Grid pulsing circuit can produce electron beam pulses of high brightness (average 5mA) for periods of less than 1ms with rise/fall times of approximately 50ns.

  5. 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. This is important as the detector may measure ions created as the electron beam interacts with the gas beam.


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.

THE METASTABLE & HIGH RYDBERG DETECTOR


Figure 10. The Metastable and high Rydberg detector

  1. Angle selectivity is achieved using 1mm apertures 1 & 2 spaced 60mm apart prior to a 719BL CEM metastable detector at end of detector (LHS).

  2. Electrostatic deflection plates remove unwanted electrons and ions from entering the detector and possibly reaching the detectors.

  3. Field Ionisation Plates can select highly excited Rydberg atoms (detected as Ions on side CEM) - This is difficult in practice due to relatively short lifetimes of HR atoms directly excited by electron impact

  4. Accurate calibration of deflection angle is achieved using a CNC machined angle calibration plate - 0.5mm apertures pass light from photodiode/phototransistor optocoupler as shown in figure 11.




Figure 11. The calibrated angle plate which accurately measures the deflection angle of the target beam.

  1. A combination of photodiode detector output and a stepper motor gearbox reduction by 2000:1 ensures accurate alignment of the analyser to ~0.05° using an interpolation routine between the apertures detected by the photodiode array.

  2. Visible Laser Diodes (VLD's) align the detector to the interaction region formed by electron beam, gas beam and rotation axis of detector. This additionally allows the zero angle to be calibrated wrt the apertures in the source chamber which define the ground state target beam direction.

  3. Ensures high alignment accuracy of the metastable detector over the full range of angles from 0 to 40 degrees


THE DETECTION ELECTRONICS


Figure 12. The Detection electronics for measurement of angle deflected metastable targets.

  1. Metastable electron multiplier negative going pulses are amplified at the source and are then discriminated in an ORTEC 473A Constant Fraction Discriminator which feeds an EG&G ORTEC Turbo Multichannel Scalar (MCS)

  2. The detection angle is controlled & monitored using an 80486 PC which controls the stepper motor & the detection electronics

  3. A control pulse (0 - 150Hz) drives the gas nozzle HT pulse & the electron gun Grid following an appropriate delay.

  4. 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.


EXPERIMENTAL RESULTS

CW Electron Excitation

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.





Figure 13. Results from 20eV to 50eV incident electron energy for excitation of Helium metastable atoms with CW electron excitation of a 400ms gas beam


Figure 13 shows results from 20eV to 50eV incident electron energy for excitation of Helium metastable atoms with CW electron excitation of 400ms gas beam (no timing resolution)

  1. Results show the general features as in figure 6 where atom deflection in the forward and backward electron scattering angles is a function of incident electron energy

As the incident energy increases forward scattering starts to dominate over backscattering as a collision mechanism as might be expected.


Pulsed Electron Excitation.

The following graphs show selected results for excitation of helium using a 40eV incident electron beam emitted for 4 microseconds over the range of detection angles from 4° to 28°.









Figure 14. Examples with a 40eV incident electron beam exciting Helium atoms with a 4ms pulsed electron excitation over the full range of atomic scattering geometries q'a from 4° to 28°.

  1. Figure 14 show examples from 40eV incident electron energy for excitation of Helium metastable atoms with 4ms pulsed electron excitation over the full range of atomic scattering geometries q'a from 4° to 28°.

  2. The evolution from single atom momentum at q'a = 4°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.

  1. 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.

  2. This accurately yields the time difference between excitation of the target and collection of the metastables. 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.


CALCULATION OF DIFFERENTIAL CROSS SECTIONS

For electron impact excitation of metastable Helium Differential Cross Section (DCS) given by :


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.

- The area under the Gaussian Ag is proportional to the productw.h and is therefore proportional to the number of electrons exciting these atoms at a given incident energy for the associated electron scattering angle qe. This angle can be determined from the data since


where xint, tint are the distance from the interaction region to the detector and the associated atomic time of flight respectively as determined from 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.




Figure 15. Gaussian fitting parameters as a function of the Detection Angle for the time resolved metastable atom deflections at 40eV Incident Energy. 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.

Hence the associated electron scattering angle  is calculated by :


where Pai, Pei are determined from the Least Squares fit to the data shown in figure 14.

- For 40eV nominal incident energy, this fitting yields

  1. Pei = 3.55 x 10^-24 Kg.m/s (i.e. 40.8eV - the Actual incident energy)

  2. Pai = 1.31 x 10^-23 Kg.m/s (i.e. 80meV the supersonic atomic beam incident energy)

-The relative Differential Cross Section is therefore given by


Figure 16 shows the DCS calculated from the data of figure 15. 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.

  1. Note that this method allows the DCS to be determined over the complete set of scattering angles from forward to 180° backward scattering of the electrons.

  2. Note that some discrepancies exist between the calculations from the fast and the slow atoms. 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.



Figure 16. Calculated DCS for helium metastable excitation as function of scattering angle at 40eV Incident Energy.

REFERENCES

Murray et al Phys Rev Lett 62 p411 (1989)

Srigengan et al ICPEAC XVII (1991) PD1

Farrell et al Phys Rev A 37 p4240 (1988)