Experimental collision studies of the interactions between low energy electrons, atoms and molecules test the fundamental quantum theories that are now being developed to describe these interactions. In this project, an electron spectrometer will be used to study excitation and ionisation of different targets using a combination of high resolution lasers and electron beams. Ionization studies will be carried out using an e,2e spectrometer that allows measurements to be performed over a wide range of scattering geometries at low incident electron energies, where the cross section for ionisation is largest. Combined excitation and ionisation studies will also be carried out using laser radiation within an optical enhancement cavity, so that both super elastic and laser photo-ionisation measurements can be obtained for alkali and alkali-earth targets. These measurements will then be used in the development of a new cold electron source that is currently being built in Manchester.

The purpose of this particular research project at the University of Manchester is twofold: modernisation of the current (e,2e) coincidence experiment and conducting experimental collision studies of the interactions between low energy electrons, and atoms and molecules to test the fundamental quantum theories to describe these interactions.

The modernisation the current Manchester (e,2e) coincidence experiment will require the development of new power supplies for the electron gun and analysers, and computer applications for power supply control, optimisation, monitoring, data acquisition, and data analysis. The developmental process includes the design of the power supply circuitry and front-panel mockups, building of the power supplies, creating the algorithms and writing the code for the Arduino-controlled power supplies, designing and developing the LabVIEW interfaces for system control and monitoring, optimisation, and data acquisition and analysis. As mentioned, an electron spectrometer will be used to study excitation and ionisation of different targets using a combination of high resolution lasers and electron beams. During the developmental stage, ionisation studies will be carried out using an e,2e spectrometer that allows measurements to be performed over a wide range of scattering geometries at low incident electron energies, where the cross section for ionisation is largest. Studies on molecular Nitrogen have already be conducted and published.



The analysis of the single event processes that take place in the ionisation of atoms and molecules by electron impact are very subtle and quite challenging to understand. The difficulty lies in dealing with the physics of a many-body problem as well as infinite range of Coulomb interactions that arise from the particles involved in the collision.


Understanding the kinematics of (e,2e) reactions begins by concentrating on the most basic process of ionisation by electron impact. Let us first consider the (e,2e) reaction seen in the figure below.

In the initial phase of the interaction, a beam of electrons of energy E0 and momentum k0 is incident on an atomic or molecular target. Following the collision at the interaction region is the second phase, in which two emerging electrons with momenta kA and kB and corresponding energies EA and EB are detected in coincidence by energy analysers at angles θA and θB. Through ionisation, the target shifts from the ground state to an ionic state by a separation energy ε.

ε = E0 − EA − EB = E0 − E

which meets the energy conservation condition. Since the energy of the incident electron must be high enough to ionise the target, then EA ≥ EB. The recoil momentum Q of the ion can be found by conservation of momentum:

k0 = kA + kB + Q


Q = k0 – kA – kB

where kA ≥ kB. We must note that the recoil momentum is separate from the momentum transferred by the incident electron to the atomic or molecular target. The momentum transferred by electron A is simply

q = k0 – kA

As we can see from the figure above, the scattering plane is the plane formed by the trajectories of the scattered and ejected electrons, where Φ measures the deviation from the coplanar geometry.


The kind of information one can extract from such ionisation processes is done through the measurement of the probability that an incident electron of energy E0 and momentum k0, will produce a scattered electron and an ejected electron of respective energies EA and EB, and momenta kA and kB; outgoing electrons that are emitted into their respective solid angles and detected in coincidence with each other. Such a measurement produces triple differential cross sections (TDCS), from which one can obtain single and double differential cross sections, as well as ionisation cross sections that depend only on the energy of the incident electron, E0.

It is clear by now that (e,2e) coincidence experiments yield several arrangements, or geometries in which the collisions occur. For example, one such collision could be of coplanar geometry; an occurrence on the same plane between the momenta k0, kA, and kB. Another important arrangement is when the collision occurs in a perpendicular geometry, where the gun is placed at 90o with respect to the plane at which the outgoing electrons are being detected. Finally there are symmetric and asymmetric geometries; asymmetric is where a fast scattered electron eA is detected in coincidence with a slow ejected electron eB, and symmetric geometries is where the angles θA and θB of the outgoing electrons eA and eB are equal as well their respective energies EA and EB.


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