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The purpose of this page is to detail the Atom trapping and Cooling experiments being conducted at Manchester. The new apparatus which has been developed is aimed at providing a high density source of atoms for several different experiments in cold atoms.
In the first of these experiments, new types of collision processes are to be studied, including electron collisions from cold atoms, BEC's and from slow atomic beams. The Cold Atom Facility which has been developed in Manchester is a bright source of cold atoms, and is shown in Figure 1. Atoms emitted from the source can be laser collimated in the second stage of the experiment, which consists of a 6-way 200mm 316LN cross attached to the source chamber. Laser collimation can be accomplished either using an optical molasses, through a 2D MOT or by exploiting the transverse momentum transferred to the atomic beam as it traverses this region using angled mirrors. Atoms from the collimated source that enter the Zeeman slower (figure 5) are longitudinally cooled and compressed in phase space using a blue detuned laser which passes along the axis of the Zeeman slower. The design of the apparatus in Manchester allows atoms to be cooled, trapped and accumulated very rapidly from the source, which operates continuously. It has been demonstrated that the trap density reaches saturation (where no more atoms can be trapped due to radiation trapping and other restrictions) within 1 second. The MOT1 chamber has been designed with numerous CF-70 ports to allow additional experiments to be connected to the chamber.
Since the ratio of accumulation time to trapping time is 400:1, the apparatus will be able to continuously load different cold atom experiments from the main source while maintaining the maximum trapping density which can be achieved in each of these experiments. One of the goals in the design of this apparatus was to produce a well-collimated beam of atoms from the atomic beam source prior to laser collimation (see figure 1). There are several different types of atomic beam oven that can be used in these types of experiments, ranging from a simple crucible that directs atoms through a hypodermic needle (and hence produces a beam that is quite divergent) through capillary array sources (which are unsuitable for metal vapour targets as needed here), on through passively collimated sources as is used in Manchester for super-elastic scattering experiments from calcium and finally on to the most sophisticated (and most complex) sources which use a recirculating arrangement for collimation and recycling of the material under study. Recirculating oven sources have several advantages over other sources (if they are suitable). Firstly, since the source only produces atoms which enter the atomic beam, there is very little waste of material.
As an example, the potassium source used in these cold atom experiments in Manchester has been operating for over 2 years without the need to refill the crucible. Secondly, the use of a condensation chamber surrounding the emitting nozzle means that vapour from the oven is re-condensed onto the inner walls of this chamber, to be fed back to the crucible.
Figure 2 shows the recirculating oven that has been designed and commissioned in Manchester.
The condensation chamber is held at a temperature ~340K so that the potassium on the walls is in a liquid form. Potassium vapour that is directed through the output aperture of the condensation chamber becomes the atomic beam which is used in the experiments. Close control of the recirculating oven temperature is achieved by using several constant current supplies which feed the tungsten heaters as shown in figure 2. Although not yet tested with Rb, it is fully expected that this atomic beam oven can be used with equal success using Rubidium (melting temperature 312K) as the chosen source. Rubidium will be used for the production of Bose Einstein Condensates (BEC's) and for other experiments in the near future.
Details of this recirculating beam source are currently being written as a paper for submission to an appropriate journal. Following laser collimation using an optical molasses (figure 1), the atomic beam enters the Zeeman slower. The effective way to slow atoms down using lasers is to adopt the process of laser cooling where the spontaneous emission process is used as a mechanism to provide a dissipative force. An atom initially travelling with momentum pA = MAv is subjected to laser radiation directed in the opposite direction, where MA is the mass of the atom and v is the velocity of the atom.
Since linear momentum must be conserved, absorption of a photon from the field means that the atom must slow down. Firstly it is possible for a second photon from the laser field to stimulate the atom to decay back to the ground state. Secondly, the atom may relax back to the ground state spontaneously (spontaneous emission process). IF the photon is emitted in the same direction as the incident photon, then the momentum of the atom will return back to it's initial value prior to the interaction pA = MAv, and so the atom velocity does not change.
By repeating this process many thousands of times, the atoms will slow down until they are stopped. The process of compression of the velocity distribution occurs since atoms with different velocities will only come into resonance with the laser beam at certain times during the cycling process. The method adopted here changes the internal states of the atoms by application of a magnetic field, which perturbs the atomic transitions which are coupled together by the laser radiation field. Figure 4 shows the type of magnetic field that is required to ensure the atoms can be effectively slowed and cooled. Figure 5 and figure 1 shows Zeeman slower that has been designed for the experiments in Manchester. 3,500m of rectangular section aluminium wire is used to provide the field, wound onto the flight tube as 5 individual coils. These coils are operated by 5 x 20A constant current supplies whose current can be tailored so as to produce the required field profile along the flight tube. Four additional coils are located at the exit of the Zeeman slower which disrupt the field so as to release atoms into the MOT chamber. The Zeeman slower dissipates ~5,000W when operated at full current, and cooling of the slower is implemented by the external copper coils and by an internal water jacket next to the flight tube.
Six laser beams of appropriate polarization are directed at the centre of the coils (the trapping region) which act as an OPTICAL MOLASSES to the atoms which enter this region, as shown in Figure 7. The laser interaction acts as the velocity dependent frictional force that slows the atoms down, in the same way as inside the Zeeman Slower.
Since the molasses component is velocity dependent, as the atoms slow down they will gradually stop moving (within these approximations).
The magnetic field from the anti-Helmholtz coils in combination with the laser beams ensures that the force acting on the atoms also has a restoring component that drives the atoms back to the centre of the trapping region (this force depends on the distance from the centre of the trap). Since the restoring component is distance dependent, atoms subjected to this component will perform simple Harmonic motion (within these approximations).
This does not happen, as the atoms may still absorb and emit photons from the laser field, leading to a minimum velocity that is given by the recoil momentum of the atoms undergoing these absorption and emission processes (the quantum limit). For potassium atoms in the experiment in Manchester, the temperature of the atoms in the trap has been measured to be ~250 micro-Kelvin.
The success of the apparatus in producing a bright rapidly accumulating source of cold atoms means that new experiments now become possible. The first experiments to be attempted will scatter low energy electrons from the cold atoms either produced from the Zeeman slower, or as inside the MOT. For these experiments, a pulsed electron gun has been constructed and installed in the MOT chamber to produce a low energy electron beam of up to 10 microamps current at energies from 2eV to 100eV.
Electrons from this source are directed at the trapped or slow atoms, so that they are ionized by the electron collision as shown in figure 11.
In this case, momentum of incident electron beam is known, as is momentum of cooled or trapped atoms. By measuring the recoiling ions, it is then possible to measure differential cross sections for ionization of these cold targets over the complete scattering geometry as shown in Figure 12. The graph shows the momentum which is transferred from the electron to the ionized potassium target as a function of the momentum of the neutral target, where both outgoing electrons are scattered symmetrically wrt the incident beam direction. By detecting one electron in coincidence with the ion momentum, it is possible to completely determine the cross section for all scattering geometries. This technique is also used in COLTRIMS experiments which exploit supersonically prepared target atoms, however by using cold atoms the sensitivity of the technique is enhanced many times. Further, since the momentum of the initial target can be controlled by the Zeeman slower, it is possible to take sensitive measurements at different angles so as to ensure accuracy in the data.
Other experiments being considered include super-elastic scattering of electrons from trapped atoms, study of interaction of electrons with BEC's, and interaction of fermions with ultra-cold ensembles. Watch this space for new results and developments in these collision experiments, including details of the AC-MOT!
The Cold Atom Facility developed in Manchester has potential to deliver a high density of cold atoms to different experiments so as to allow multiple experiments to be performed from the one source.
This page describes the atom trapping and cooling experiments currently being conducted in Manchester. Experimental results are shown for three energies in a coplanar symmetric geometry, and for three energies in an asymmetric geometry. Ionization of atomic and molecular targets is one of the most complex and fundamental collision processes that can be studied in detail. To fully characterize these interactions, it is necessary to perform sophisticated measurements where an incident electron of well controlled momentum scatters and ionizes the target.
In these (e,2e) experiments, information about the collision is obtained by measuring the outgoing momenta of the collision products. For molecular targets, it is difficult to know the orientation and alignment of the molecule prior to the interaction occurring, unless this can be defined prior to the collision or can be measured following the collision.
The interaction of low to intermediate energy electrons with molecular targets has been much less studied compared with high energy electron collisions. Experiments on molecular targets often employ effusive beams produced at room temperature, and so the targets may have internal rotational and vibrational energy. Results are presented here for an H2O target at significantly lower energies than has been studied before. Figure 1.1 Representation of the 1b1 state of H2O, showing an incident electron ionizing the molecule.
The experiments described here were carried out in the fully computer controlled and computer optimized (e,2e) spectrometer that operates in Manchester. For the coplanar symmetric experiments described here, the electron detectors were moved so that their angles with respect to the incident beam direction were equal to each other throughout measurement (see figure 1.2).
For coplanar asymmetric experiments, analyzer 1 was fixed at a scattering angle thetaa = 22A°, while analyzer 2 was swept around the scattering plane.
The fixed scattering angle thetaa = 22A° was chosen as this was the smallest angle that could be used without the incident electron beam from the gun striking the side of the analyzer (and so producing unacceptable levels of noise on the coincidence signal). The energy resolution of the spectrometer is set by the resolution of the electron gun and the pass energy of the analyzers. Production of a high quality molecular beam of H2O required careful monitoring of the experiment as it progressed.
The de-gassed water was then transferred to a 150mm long tubular stainless steel flask which was connected to the main vacuum system using a swagelok fitting.
An AD590 sensor was secured to the aluminium block surrounding the flask, so that the temperature of the insulated assembly could be monitored and controlled. To monitor the molecular beam inside the vacuum chamber produced from the water, a quadrupole mass spectrometer was installed onto the spectrometer.
Figure 1.3 shows a typical coincidence energy spectrum obtained from the experiment during operation.
The experiments were carried out over a period of several months, using electron beam currents ~200nA for all data runs. As the incident energy increases, the ratio of forward to backward scattering cross section increases, as has been seen for most atomic targets in this geometry. The measured coplanar asymmetric data is shown in figure 4, again normalized to unity at thetab = 45A°.
As the incident energy is increased to 55eV above threshold, the forward lobe splits into two clear peaks of approximately equal magnitude, as seen in figure 1.5(b). Results from the 1b1 state of water have been presented for coplanar symmetric and asymmetric energies. These results have been compared to a DWBA theory in the paper J Phys B, however the averaging used in this theory was not a good approximation, and so is not expected to yield accurate results for this state.
Experimental results are presented for electron impact ionization of water in the energy regime from near threshold to intermediate energies. Results of a sophisticated model which approximates the random orientation of the target using a spherical averaging of the wave-function prior to the collision, using sophisticated distorted wave Born calculations that include post-collisional interactions in first order and to all orders of perturbation theory are also shown for comparison (see J.
The calculations predict the data most accurately at the lowest energy studied (4eV above threshold) in a coplanar symmetric geometry, whereas the comparison between theory and experiment is generally poor for higher energies and for non-coplanar geometries.
Energy deposition and angular distributions resulting from electron collisions with water are used in charged particle track structure analyses to model radiation damage in biological samples.
These low energy electrons have an effect over a much wider volume than the targeted cancer site. At incident energies less than ~200eV, the collision dynamics are strongly influenced by effects including post-collision interactions, target polarization, distortions in the wave-functions for the participating electrons and multiple collisions. Current models now yield reasonable agreement with experimental data for a range of atoms, implying a good understanding of the collision dynamics under the conditions used in the experiments, and these models are now being extended to low energy (e,2e) collisions from molecules. Recent experiments studying simple diatomic targets including H2 and N2 have provided benchmark data.
The apparatus at Manchester can also access non-coplanar geometries, and so has provided additional data to further test these models.
In a previous study the groups at Manchester and Missouri investigated the 1b1 (HOMO) state of H2O in coplanar kinematics. By contrast, the 3a1 orbital of interest here is involved in the O-H bonding and has a charge density distribution distorted from that of a symmetric atomic like orbital. The experimental triple differential cross sections (TDCS) presented here were measured in the (e,2e) apparatus at the University of Manchester. The spectrometer can be operated in a standard coplanar geometry where the momenta of all three electrons (the incident and two outgoing electrons) are within the same detection plane (psi = 0A°, figure 2.1).
The power supplies for the electrostatic lenses in the electron gun and the electron analyzers are fully computer controlled and computer optimized, allowing for automated tuning at regular intervals, with the analyzers being re-optimized each time they move to a new angle.
The energy of the spectrometer was re-calibrated at the start of each new kinematic arrangement, by measuring the coincidence binding energy spectrum.
Over the course of this study the binding energy spectra were recorded for various energies and geometries, and it is estimated that contamination from neighbouring orbitals was always less than 10%, and is more typically in the range of 0.5%. The distilled water sample used to provide the molecular target beam was contained within a 50mm diameter 100mm long stainless steel vessel sealed by a CF-70 flange to a 6.35mm swagelok fitting. The sample vessel and gas handling line were held at a constant temperature of 50A?C throughout data collection, so as to create sufficient driving pressure for the target beam. The purity of the target beam was verified with a Spectra VacScan mass spectrometer fitted to the scattering chamber.
The background pressure within the scattering chamber was set to 1.1 x 10-5 torr during operation, and was found to remain constant throughout all data runs. During these experiments we observed an unusual behaviour of the tungsten hairpin filament used as the incident electron source. To facilitate this, the current measured by the Faraday cup located on the opposite side of the interaction region to the electron gun was monitored by the computer control software, and the current through the filament adjusted to maintain a beam current of 300nA throughout data collection. In the present study we also measured the coincidence energy resolution from ionization of helium, and found this did not change, indicating that the temperature of emission remained approximately constant.
The data presented in figures 3-5 were then averaged over these angular sweeps, and the uncertainties in the measurements determined from the complete set of data for each scattering angle.
The experimental data are not measured on an absolute scale and so experiment and theory are normalized to a maximum of unity at each energy, as shown in figure 2.2. As the energy of the outgoing electrons is lowered, it would be expected that the Coulomb repulsion between the outgoing electrons should play an increasingly important role, driving the electrons apart. The best agreement between experimental data and theory is at the lowest energy, where the experimental data and MDW model are in excellent agreement for the binary peak. A key advantage of the spectrometer in Manchester is the ability to measure data for kinematics in non-coplanar geometries. Non-coplanar measurements were hence taken here with both outgoing electrons having an energy of 10eV. As shown in figure 1, the geometry adopted in this spectrometer provides a common normalization point (xi1 = xi2 = 90A°) for all gun angles psi, which allows ALL data at a given energy to be referenced to a common point. For the current measurements, the coplanar data have been normalized to a maximum of unity, as before. The data in figure 2.3 show a clear trend indicating the binary and recoil peaks diminish in magnitude as the angle of the electron gun angle increases. The data contrasts strongly with the theoretical models for the larger gun angles y, where the theories predict significantly more structure than is seen in the data.
The final kinematic configuration used symmetric geometries and 20eV excess energy as above, however in this case the data are for unequal energy sharing between the outgoing electrons.
The data were only taken for coplanar and perpendicular plane geometries, so as to contrast differences in these two extremes. The key differences that can be seen in these data for the coplanar geometry are that the binary peak moves to a smaller angle as the energy asymmetry increases, as might be expected from post collisional interactions. Agreement is mixed, and rather surprisingly gives best results at low energies, where it might be expected that the approximations are least accurate.
The experimental results for both equal and non-equal energy sharing in the perpendicular plane show almost no structure, whereas the theoretical calculations predict that three clearly defined lobes should be seen. This work was supported by the University of Manchester and the US National Science Foundation under Grant. 12.A A  Naja A, Staicu-Casagrande E M, Lahmam-Bennani A, Nekkab M, Mezdari F, Joulakian B, Chuluunbaatar O and Madison D H 2007 J. 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.
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The apparatus produces a bright, cold atom source which competes with the best in the world for speed of accumulation of cold atoms into a Magneto-Optical Trap (MOT), and for the lifetime of atoms that are subsequently cooled and trapped. These experiments will exploit the momentum transferred in the collision process to ascertain new information about the target interactions, and to study collisions with cold and ultra-cold targets for the first time.
The apparatus consists of a recirculating oven source, which produces a quasi-collimated beam of atoms into the laser collimation stage. The cold atom facility that has been developed at Manchester, showing the various components of the apparatus and the laser beams which are used to cool and trap the atoms emitted from the source.
Large windows are attached to the cross to allow the collimating laser beams to enter this region. In the present setup, optical molasses has been used to increase the collimation of the atomic beam prior to the Zeeman slower. The aim of this design is to facilitate rapid trapping of the cold atoms, then transfer of these cold atoms to different experiments that are connected to the MOT1 chamber via these ports. In this way, experiments which have low cross sections (such as collisions experiments with electrons, neutrals or ions) will be possible in the near future.
By ensuring this criteria is met, the vacuum chambers are far less polluted by unwanted atoms that are emitted from the source. This means that the source can be operated for very long periods of time without the need to refill the crucible. The physical size of the condensation crucible and the output aperture then defines the collimation of the atomic beam that exits and therefore becomes the emerging atomic beam. The crucible is loaded with potassium (melting temperature ~337K) and the temperature of different components of the source are closely controlled. Surface tension ensures that the liquid potassium runs down the walls of the condensation chamber and is gravity fed back to the crucible (which operates at a temperature of ~650K).
The temperature of the condensation chamber is accurately controlled by passing a heated high temperature silicon oil through a sealed chamber within the walls of the chamber as shown. Since atoms emerging from the oven have a wide range of different velocities (as dictated by the Maxwell Boltzmann distribution), it is necessary to slow these atoms down so that they can be captured by the MOT. The laser frequency (wavelength) is set to be resonant with the atomic transition so that there is a high probability of absorption of a photon from the laser field by the atom, which is then promoted to an excited state.
In this case (stimulated emission process) the photon from the atom emerges in the same direction as the photon in the laser field.
In this case, the atom has no 'memory' of how it was excited, and so does not know the direction of the incident photon.
By ensuring that either the laser frequency or the atomic transition frequency is time (or space) dependent, compression can occur.
One method that is used is to 'chirp' the slowing laser beam (figure 1) so that as the atoms slow down they remain in resonance with the laser beam. As the atoms slow down, the magnetic field is then adjusted so that the atoms remain in resonance with the laser beam (or they will Doppler shift out of resonance).
A set of 'disruption coils' are used at the exit of the slower to ensure atoms can escape into the MOT chamber. Picture of the Zeeman slower shown with the cooling coils surrounding the current carrying coils. Inside this chamber is a twin set of coils setup to produce zero field at the centre of the coils (anti-Helmholtz configuration), as shown in figure 6.
Movie of the atoms being trapped in the MOT from the Zeeman slower (first successful trapping with an accumulation time ~1sec, and aA  lifetime ~10 seconds). Collisional ionization of atoms from the Zeeman slower or within the MOT trap, showing the setup of the experiment which detects the recoiling ions from the interaction. The collision for ionization of cold atoms from Zeeman slower and those trapped in the MOT. The incident energy is 30eV, and the curves show the effect of the ionization process on the final ion momenta (velocity and angle) as a function of the scattering angle. These experiments may be far ranging, depending on the apparatus that is connected to the source. Coplanar symmetric and asymmetric electron impact ionization studies from the 1b1 state of H2O at low to intermediate impact energies. The experimental data show a wide variation in the cross section over this range of energies. These ionizing collisions are important in a wide range of different areas, ranging from plasma physics, astrophysics, atmospheric physics, medical and biological processes involving low energy electrons through to the study of high voltage discharges.
The scattered electron is then detected in time correlated coincidence with either the electron ejected during ionization, or with the resulting ion. This is usually accomplished by determining a cross section that is five fold differential in angle and energy. In most cases, this means that an averaging over the orientation of the target must be included for theory to compare with experimental results.
This energy region (from threshold to ~200eV) is important as it is here that the cross section for ionization is largest. The ionization potential from these ground ro-vibrational states is usually less defined than for atomic targets, due to the associated Franck-Condon overlap between the potential energy curves of the neutral molecules and the resulting ions. This apparatus is described in detail on other web pages on this fileserver, and has been designed to operate in the energy regime from ~10eV to ~300eV. In this configuration, the energies selected for the scattered and ejected electrons were equal. The inner diameter of this flask was 9mm, and the outside diameter was 12.7mm, so that a standard swaged fitting could be used.
This was accomplished using a Newport model 325 temperature controller, which supplied drive current to the TEC.
This proved invaluable, as it was then possible to continuously monitor the background gases in the chamber during operation. In this example, the analyzers were set to pass electrons of energy 20eV, and a symmetric geometry was chosen with thetaa = thetab = 45A°. Over this period of time, the filament current driving the cathode had to be steadily decreased, probably since the water vapour within the vacuum chamber slowly reduced the diameter of the filament. The data is normalized to unity at thetaa = thetab = theta = 45A°, since the results have not been placed on an absolute scale. Results were taken in symmetric coplanar and non-coplanar geometries, with both equal and non-equal outgoing electron energies. The human body, and other biological material comprise of ~80% water, which makes it an ideal test case to investigate processes occurring in the body. These models are an active area of research since the observation that high energy radiation that is used to treat cancers also liberates many low energy electrons, causing additional damage to cell DNA.
Knowledge of the collision dynamics of low energy electrons with biological systems is hence needed, so as to develop robust models of these processes. In such experiments the energy and momenta of the outgoing electrons are measured, giving a five fold differential cross section.
In this regime these processes must be considered on an equal basis, and so the complexity of the interactions means that theoretical studies have mainly been limited to atomic targets.
This contrasts to atoms which have a single nuclear scattering centre, and which can hence be described using a spherical basis. A further challenge arises since the experiments cannot, at present, align the molecules prior to the collision, so the models must consider the random orientation of the targets for accurate comparison.
The majority of data is recorded in a coplanar geometry, where the incident and two outgoing electrons are in the same plane, and were conducted at a higher incident energy than the studies presented here. The symmetry of the 2py oxygen atomic orbital, representing the lone pair of electrons on the oxygen atoms, prevents it from hybridizing with the H atomic orbital, leaving the molecular 1b1 HOMO orbital essentially atomic like, and therefore symmetric. However, the orientation averaged molecular orbital used in the theoretical calculation is a bad approximation for that state given the cancellations due to the orbital symmetry. The molecular orbital used in the model therefore should not suffer from the same cancellation problem during the orientational averaging procedure. This apparatus is fully computer controlled and computer optimized, allowing it to operate continuously without user intervention.
A coplanar geometry (psi = 0A?) is defined when all three electrons are in the detection plane.
The angular resolution of the apparatus is estimated as A±3A°, based on geometric considerations of the electrostatic lenses at those energies. Several freeze-pump-thaw cycles were performed using a salted ice slurry bath, to remove dissolved gas impurities from the water prior to admission into the scattering chamber.
Over time the emission current from the filament dramatically increased, when a constant current was delivered to the filament.
The data were normalized to a collection time of 1000sec for each measurement, and up to 30 sweeps of the detection plane were used to produce statistically significant results. The overall shape of the TDCS measured at corresponding energies in a previous study of the 1b1 state are qualitatively similar, however the 1b1 state shows a second peak in the binary region emerging at higher energies that is not observed in the 3a1 state.
PCI would also be expected to shift the recoil peak towards xi = 90A°, although this cannot be confirmed in the data. This agreement diminishes as the energy increases, which is unexpected since the MDW model is usually more accurate at higher energies. The TDCS measured in the perpendicular plane is almost constant over all analyzer angles, which is very different to what is observed for atomic targets. The progression in both models shows a decrease in cross section from psi = 0A° to 45A°, after which the intensity once again increases. There also appears to be a narrowing in the main binary peak as the asymmetry increases, with a new shoulder appearing around xi = 60A°. This contrasts markedly with the calculations, which predict triple peaks in the perpendicular plane that change magnitude only marginally with the asymmetry. This discrepancy is seen both for equal energy and for non-equal energy data, which have been taken in coplanar and perpendicular geometries. 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. Initial collimation of the atomic beam is achieved in the recirculating oven source through the use of small apertures as is shown in figure 2. The Zeeman slower is shown without the cooling coils which surround the current carrying coils, and the liquid nitrogen trap has yet to be installed onto the source chamber. In this way, atoms accumulated in MOT1 can be transferred to several different experiments where they can be recaptured for further study, or experiments can be directly conducted on the trapped atoms in MOT1. Since no atoms are emitted apart from those in the atomic beam, contamination of the vacuum chamber is virtually eliminated. In this way, atoms are emitted from the nozzle into the condensation chamber, where they are re-condensed onto the walls of this chamber.
In this way, the complex temperature conditions which are essential for correct operation of this source can be maintained. Further, it is important to also compress the velocity distribution of these atoms so that they have a much narrower distribution at the exit of the slowing tube. In this case, the momentum of the atom will return back to its original value pA, and there is NO slowing of the atom by the laser beam. Theoretical approximations accurate at high impact energies can no longer be applied, and so there are stringent demands on theory which must be satisfied for accurate comparison with data. The (e,2e) coincidence signal for molecules may then have a correspondingly lower yield compared to an atomic target where the ionization potential is well defined. A pictorial representation of the water molecule in the 1b1 state is given in figure 1.1 below.
The spectrometer allows measurements to be conducted from a coplanar geometry through to the perpendicular plane, although in the present measurements only a coplanar geometry was used.
The analyzer pass energy was then set to measure electrons so that the overall resolution of the coincidence signal (as measured using a helium atomic target) was 600meV. The pump removed background gas from the flask, and extracted dissolved gases held in the water. The flask was secured to the cold side of a 50mm x 50mm thermo-electric cooler (TEC) using a large aluminium block, and the assembly (flask + block) was insulated from the air using Styrofoam. The 1b1, 3a1 and 1b2 states are clearly resolved in this spectrum, which is fitted to three Gaussian peaks to ascertain the widths of the spectral profiles.
These data were measured in a coplanar geometry with outgoing electron energies of 20eV detected at theta1 = theta2 = 55A°. Figure 1.5(a) shows the lowest energy results, with an incident energy 15eV above the ionization threshold. Molecular wave-functions are generally not spherical, the nuclei within the molecule providing multiple scattering centres.
This becomes a computationally intensive problem, and so approximations are usually made to allow these calculations to become tractable. In this study the analyzers were always kept in a symmetric configuration with xi1 = xi2 = xi. A needle valve at the entrance to the scattering chamber controlled the flow of target H2O vapour into the interaction region. This indicates that an H2O target molecular beam of high purity was created, as confirmed from binding energy spectral studies.
This increase in emission current was often more than a factor of 2 within a 24 hour period. The solid line shows results from the Molecular Distorted Wave Born Approximation (MDW) while the dashed line was generated from the Molecular 3-body Distorted Wave Approximation (M3DW).
This trend is much clearer in the present data compared to that from the 1b1 state measured at higher energies.
For the theoretical model, the coplanar TDCS has also been normalized to unity for both MDW and M3DW models. These measurements were taken in a series of symmetric non-coplanar geometries with outgoing electron energies of 10eV. The M3DW model follows a trend that is closer to the experimental data, although neither model accurately predicts the results that have been obtained.
The theoretical calculations are also shown, where once again the data and theory have been normalized to unity at the peak in the coplanar geometry.
The minimum around 90A° in this geometry does not change substantially as the energy sharing changes. 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. In the first experiments using this Facility, potassium atoms have been cooled and trapped. Once the atoms enter MOT1, they experience frictional force due to the laser interaction and a restoring force due to the magnetic field, so that they rapidly cool to a temperature ~250 micro-Kelvin around the centre of the trap. The angles that could be accessed in this configuration ranged from thetaa = thetab = 25A° through to thetaa = thetab = 135A°. The acceptance angle of the analyzer lenses was A±3A°, as set by input apertures at the entrance to the electrostatic lenses.
This de-gassing procedure was carried out for ~2 hours before the water sample was used in the experiment, to ensure that the proportion of dissolved gases in the water was minimized. The hot side of the TEC was attached using thermal conducting paste to an aluminium heatsink to which a 12VDC boxer fan was secured, so that heat from the TEC could be dissipated efficiently. If this ratio reduced, the experiment was halted and the water changed to a newly de-gassed sample.
In this case, the 1b1 state was found to have a width of 620meV, which is comparable to that for an atomic target. The contrast between the maximum and minimum in the cross section increases as the energy increases.
As the energy increases further to 95eV above threshold (figure 1.5(c)), the double peak in the forward direction is still visible but the magnitudes of the peaks are now different.
The purity of this beam was monitored regularly using the mass spectrometer throughout this study. To ensure constant incident electron beam current throughout the measurements as required, the filament current was hence also placed under computer control. The experimental and theoretical data has been independently normalised to unity at each energy. Dr Kate Nixon thanks the British Council for funding under the research exchange programme, and the Royal Society for a Newton International Fellowship. 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. For asymmetric geometries, thetaa is fixed at 22A° while analyzer 2 is swept around the scattering plane.
A glass flask was used for this procedure as this allowed the process to be visually monitored.
This indicates that the energetic effects of ro-vibrational transitions from the ground state to the ion state are negligible for this state.
Further checks were made regularly on the energy of the incident electron beam by monitoring the coincidence energy spectrum (figure 1.3), and regular monitoring of the partial pressures of the gases in the vacuum chamber. A second peak occurs in the backscatter region, however the maximum of this peak appears to occur at thetab < 225A°. For non-coplanar geometries the electron gun is lifted out of the plane, and is defined by the angle psi. 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. There is an offset of 1eV in the position of the peaks which is due to contact potentials in the spectrometer. The full line represents a three-Gaussian fit, whereas the dotted lines show the individual Gaussians from this fit, illustrating the degree of separation measured with the current energy resolution. The results in the backward direction also have structure, with a minimum occurring when thetab ~ 250A°. 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.
Very little contamination is expected from neighbouring orbitals in the measured TDCS for the 3a1 state. Concept related to the uploaded by khanacademytrends in the firstionization anne hathaway wardrobe malfunction pics car, stores in new york city that sell prom dresses, If you lookpatterns of energy is the periodic table .



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