The Fully Computer Controlled &   Computer Optimised

(e,2e) Coincidence Spectrometer at Manchester


Page constructed by Andrew Murray

This Page was last updated on the 13th March, 2011.



Link to scientific Papers from the group about (e,2e) processes in Manchester




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1.0 Introduction to ionization by electron impact


The purpose of this page is to detail for the interested reader the fully computer controlled and computer optimised(e,2e) coincidence experiment at


•Atomic & Molecular Physics Group, School of Physics & Astronomy, Schuster Laboratory, Manchester University, Manchester, M13 9PL, United Kingdom.

Although there is an implicit assumption that the reader has a familiarity with coincidence experiments, this is not completely necessary to enjoy this page and the associated pages that accompany this home page.

For those who are interested, many excellent reviews on this subject can be found, including articles by:


•Ian McCarthy & Erich Weigold, Electron-Atom Collisions,Cambridge University Press, UK (1995)

•Azzedine Lahmam-Bennani, J Phys B. 24 p 2401 (1991) and

•Eminyan M, MacAdam K B, Slevin J and Kleinpoppen H J Phys B 7 1519(1973)


1.1 Overview of Atomic Coincidence Experiments


Coincidence experiments are used in atomic physics principally in two ways.


The first way that they are used is as a 'noise' filter, where unwanted signals from events occurring at the interaction region are rejected by carefully timing the detected events so as to exclude those that cannot arise from the reaction. As an example, such experiments may be used to exclude the cascade contributions to lifetime measurements of atomic fluorescence when states lying higher than the state under investigation are excited.

The principle use of coincidence experiments however, is to investigate single event processes that occur when either electrons, ions, atoms or photons interact with the target atoms or molecules. This is usually achieved by detecting the momentum of the scattered particle (in future here described as an electron) and observing the correlated reaction of the atomic system.


Three types of coincidence experiment are briefly described :


The Electron-Photon Coincidence Experiment. Here an electron excites a target atom (molecule) and the fluorescence emanating from the excited state is detected, usually as single photons. The angular distribution of the photon flux may be measured, or the polarisation of the photons may be measured in coincidence with the detected electrons. Either measurement allows information about the electron collision process to be deduced.

The Stepwise Electron-Photon Coincidence Experiment. This is basically a variant on the above experiment, except that the electron excited state is coupled to the fluorescence state via high resolution single modeLaser radiation. This permits the same information to be deduced, with the additional advantage that electron excited metastable states that do not directly decay by single photon emission can be probed using the laser radiation, the information about the electron excited state being coherently transferred to a higher lying state which subsequently decays. Measurement of the polarisation or angular distribution of the upper state fluorescence then yields information about the lower electron excited state, together with information about the laser excitation process. Further, the very high spectral resolution of the laser allows single isotopic species to be selected for the measurement, eliminating the uncertainties accompanying the direct electron-photon coincidence studies that have to sum over these individual contributions.

The (e,2e) Coincidence Experiment. These experiments are used to determine properties of the ionisation process due to electron collision with a target atom or molecule, rather than to look at excitation of the target as in the previous two examples. The most common variation of these experiments is to ionise a target which is in the ground state. The incident electron then ionises the target, thereby producing a second ionised electron. The scattered (incident) electron and the ionised electron from the target are then detected in coincidence. Usually the momenta of these electrons are selected with only a narrow uncertainty, thereby constraining the experiment to obey both Energy and Momentum conservation rules within these uncertainties. Selection of the electron energies therefore allows the ionised target state to be selected (ground state or perhaps excited state), whereas selection of the scattered and ionised electron angles allows the dynamics of the ionisation process to be studied. A vast array of experiments is therefore possible, since the electrons can be scattered or ionised into any direction throughout space, and they can emerge from the reaction zone with any energy from threshold (0eV of Kinetic Energy),through equal energy sharing to a maximum Kinetic Energy given by the energy difference between the incident electron energy and the ionisation energy of the target. The spectrometer described in these pages can access virtually any geometry throughout space over a wide range of energies, and is therefore incredibly versatile for carrying out these measurements.

Further types of coincidence measurements are possible. These include


(gamma-2e)experiments where a high energy photon doubly ionises a target thereby producing 2 electrons from the reaction,

•higher order ionisation studies ((e,3e) etc) and

•laser assisted (e,2e) coincidence studies, to name but a few.

1.2. Electron-Photon Coincidence experiments


In the case of electron photon coincidence experiments, the atomic system excited by electron impact reacts by emitting a photon, which is subsequently detected either in angular correlation with the scattered electron, or the polarisation of the correlated emitted photon is measured(Figure 1).



Figure 1. The electron-Photon coincidence experiment.An incident electron excites the target to an intermediate excited state,losing energy in the process. This electron scatters through an angle theta with respect to its incident direction, and is subsequently detected using an energy and angle selecting analyser. The excited target relaxes either back to the ground state or to a lower intermediate state, releasing energy as a photon during this process. Detection of this photon either as a function of angle with respect to the incoming electron, or by measuring the polarisation of the photon in coincidence with the scattered electron yields detailed information about the excitation process.


Examples of electron-photon experiments can be found in:


•Standage M.C.and Kleinpoppen H. Phys. Rev. Lett. 36 577 (1976)

•Blum K and Kleinpoppen H Phys. Rep. 96 p 251 (1983)


1.3. Stepwise Electron-Photon Coincidence experiments




Figure 2. The stepwise Laser electron-Photon coincidence experiment. An incident electron excites the target to an intermediate excited state, losing energy in the process. This electron scatters through an angle theta with respect to its incident direction, and is subsequently detected using an energy and angle selecting analyser. The excited target is further excited using single mode CW laser radiation whose power, polarisation and radiation direction is accurately controlled. The upper laser excited state relaxes either back to a lower intermediate state, releasing energy as a photon during this process. Detection of the polarisation of this photon in coincidence with the scattered electron yields detailed information about the electron excitation process. Details of the Laser pumping process can also be determined from these measurements.


Examples, including theoretical and experimental papers which detail this type of electron-photon coincidence experiment can be found in:


•Murray A J, Webb C J, MacGillivray W R & Standage M C, Phys RevLett 62 411 (1989)

•Murray A J, MacGillivray W R & Standage M C, J Phys B 23 3373 (1990)

•Murray A J, MacGillivray W R & Standage M C J Mod Optics 38 961(1991)

•Murray A J, MacGillivray W R & Standage M C, Phys Rev A 44 3162(1991)

•Murray A J, Pascual R, MacGillivray W R & Standage M C, J PhysB 25 1915 (1992)

•Masters A T, Murray A J, Pascual R & Standage M C Phys Rev A 533884 (1996)


2.0. The (e,2e) Ionisation coincidence experiment


An alternate type of experiment to those investigating EXCITATION of the target are those where the incident electron has sufficient energy to IONISE the target. For these so-called (e,2e) experiments the energy lost by the incident electron upon scattering from the target atom is sufficient to promote ionisation of the target, which ejects either a valence electron or an inner shell electron(should the incident energy be sufficiently large). The angular correlation which exists between the electron emitted from the target and the scattered electron is then measured, as shown in figure 3:




Figure 3. The (e,2e) interaction region and scattering geometry. An incident electron of sufficient energy collides with a target at the interaction region. The target is subsequently ionised, the incident electron losing energy in the process and scattering into an angle theta.The target is split into an ion and an ejected electron. This ejected electron leaves the interaction region at some angle, as does the scattered incident electron. Both electrons are detected in coincidence using energy and angle sensitive analysers. The angular correlation between these electrons measured as the detectors roam over various angles then reveals detailed information about the ionisation process.

Examples of (e,2e) experiments can be found in the reviews by


•Ian McCarthy & Erich Weigold, Electron-Atom Collisions,Cambridge University Press, UK (1995) and

•Azzedine Lahmam-Bennani, J Phys B. 24 p 2401 (1991)


It is these ionisation coincidence experiments that are performed using the spectrometer in Manchester.

2.1 The Manchester (e,2e) Experiment (1982-1990)


The Manchester (e,2e) experiment has been designed primarily to study angular correlations arising between the scattered electron and an electron ejected from a valence state of the target. As such, the incident electron energy is adjustable from 20eV to 300eV.


The spectrometer has the advantage that all possible geometries are accessible from coplanar geometry to the perpendicular plane geometry (see figure 4). The original experiments by Hawley-Jones et al, J Phys B 25 2398 (1992) measured ionisation close to threshold to study the so-called Wannier effect. These experiments were carried out in the perpendicular plane using a hemispherical energy selected electron gun.





Figure 4. The (e,2e) scattering geometry accessible in the Manchester experiment. The spectrometer allows full access to the coplanar geometry, where the incident, scattered and ejected electrons are all in the same plane, through to the perpendicular plane geometry, where the scattered and ejected electrons emerge perpendicular to the incident electron direction. In these experiments it is convenient to define the detection plane as the plane of spanned by the ejected and scattered electrons, in contrast to the scattering plane defined in figure 1. Clearly the ionisation is independent of the chosen geometry, and so results obtained in one geometry can be defined in the alternate geometry via a simple transformation.

Further work using an unselected electron gun by M.B.J. Woolf (Ph.DThesis, Man. Univ. (1989)) measured the angular correlated differential cross section for electron scattering from a helium target for incident energies from 10 to 80eV above the ionisation threshold in the perpendicular plane, with the scattered and ejected electrons emerging from the scattering region with equal energy.


At the completion of these experiments hardware was installed for testing the computer controlled optimisation routines, allowing a feasibility study to be conducted. The computer controlled hardware and associated software was tested by optimising signal from resonance states in helium. Full details of these experiments may be found in the thesis of B.C.H. Turton (Ph.DThesis University of Manchester (1990)).


2.2 The Manchester (e,2e) Experiment (1990-present)


Following these initial optimisation experiments, the apparatus was modified to allow coincidence experiments to be conducted using the computer control and optimisation hardware. This required considerable modification to the apparatus and the software controlling the experiment. In addition,the efficiency of the experiment was reviewed and significant improvements were made to increase both the analyser efficiency and the timing resolution. Implementation of these improvements occupied most of 1990, and coincidence data collection re-commenced in November 1990, once more in the perpendicular plane.


For full details of the computer control hardware, see


•Murray AJ et al, Rev Sci Inst 63 3349 (1992).

The purpose of the perpendicular plane experiments was twofold.


•Firstly, they allowed the optimisation routines to be tested in a fully operating coincidence experiment while verifying the data obtained by Woolf.

•Secondly, they allowed a comparison of the efficiency and reproducibility of the optimisation technique as compared to manually obtained data.

Results verified that the computer control and optimisation significantly improved the experimental data when compared with data obtained with manual operation, both in statistical accuracy and angular symmetry. This data accumulated in less time than could be obtained manually, since the experiment ran 24 hours a day.


Since these initial measurements data has been obtained in the perpendicular plane for symmetric and non-symmetric energies over the incident energy range from 34.6eV to 104.6eV. For full details, see


•Murray AJ et al, J Phys B 25 3021 (1992)).

Following from these perpendicular plane measurements, results coupling the coplanar symmetric differential cross section to the perpendicular plane differential cross section have been obtained from 44.6eV to 74.6eV incident energy, confirming that rapid changes occur to the differential cross section in this energy regime. See


•Murray AJ and Read FH, Phys Rev Lett 69:2912 (1992), and

•Murray AJ and Read FH, Phys Rev A 47:3724.

These results, together with additional results closer to the ionisation threshold, have been parameterised in terms of a set of orthogonal angular functions defining the correlation between three vectors in space, in this case chosen to be the incident, scattered and ejected momenta of the electrons taking part on the reaction process. For details of this parameterisation, see


•Klar H. and Fehr M. (1992) Z Phys D, 23:295

•Murray AJ et al Phys Rev A 49:R3162 (1994)

•Murray AJ et al J Phys B(1996) in press.


The parameterisation allows the angular and energetic parts of the differential cross section to be separated, and allows a common basis to be defined for all ionisation processes.


Measurements of the cross section for ionisation with excitation of the ion have also been carried out with this spectrometer, these experiments confirming the advantages afforded by computer control which allows the stability of the experiment to be maintained over a period of months.For details, refer to:


•Murray AJ and Read FH J Phys B 25 L579 (1992).

Experiments to obtain the differential cross section for ionisation of Argon ranging from the perpendicular plane to the coplanar geometry have also been conducted, although the results of these experiments have not as yet been published.


Additional measurements at 27.6eV, 29.6eV and 34.6eV incident energy on Helium ranging from the coplanar to the perpendicular plane have recently been completed. These results also have not yet been published.


2.3 (e,2e) Hardware & software control


For a more complete description of the (e,2e) Spectrometer Hardware and results, follow the links given above.