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Nucleosynthesis of elements above helium is less efficient so that each successive reaction produces less energy per unit mass of fuel. You must have JavaScript enabled in your browser to utilize the functionality of this website. We are very happy to celebrate our new store with you with FREE shipping on orders over $150*.
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Electron-electron angular correlation experiments, or so-called (e,2e) coincidence experiments, provide the most detailed test of theories which attempt to describe the ionisation of a target atom by an incoming electron. The parameters (Ea,qa,fa,Eb,qb,fb) are freely selectable experimentally within the constraints that energy and momentum must be conserved during the collision.
In the experiments described here the DCS has been measured in the perpendicular plane using a helium target with incident electron energies ranging from 10eV to 80eV above the ionisation threshold. The electron coincidence spectrometer was designed to measure angular and energy correlations between low energy electrons emerging from near-threshold electron impact ionisation of helium and is capable of accessing all geometries from the perpendicular plane to coplanar geometry. A number of modifications to the original spectrometer as described in Hawley-Jones et al (1992) have been implemented and are detailed elsewhere. Unique to this (e,2e) electron spectrometer is the computer interface which controls and optimises the spectrometer during normal operation. Figure 2 is a block diagram of the hardware interface between the computer and the spectrometer.
At the heart of the operation is an IBM 80286 PC which controls the spectrometer and receives information about the system status from monitors around the spectrometer.
The electrostatic lens and deflector voltages in the system are supplied by separate optically isolated active supplies controlled by 12A bit digital to analogue converter (DAC) cards, while a digital monitor measures the voltages and currents on the various lens and deflector elements around the system. The analyser positions are measured by potentiometers located in the drive shafts external to the spectrometer, and are monitored by a datalogger located on the main PC bus, which also monitors the EHT supplies and the vacuum pressure in the system. Count rates from the channel electron multipliers and photomultiplier tube are monitored by a 32 bit counter board, and the TAC output is sent directly to an MCA card installed in the main PC.
The software controlling the electron coincidence spectrometer is written to address specific tasks unique to the coincidence experiment. The main PC controls the spectrometer lens and deflector tuning during operation, optimising these voltages using a Simplex method.
Following input of relevant control information, the system is switched to computer control. The electron gun is then optimised to the counts detected by the photomultiplier tube, thus ensuring that the electron current is focussed to a beam of diameter approximately 1mm at the gas jet. The analyser input lenses and deflectors are then adjusted by the computer to optimise the non-coincidence counting rate of each analyser. A coincidence correlation spectrum is then acquired for a predetermined time, after which the analysers are moved to a new position and the optimisation procedure repeated in the inner loop.
Once the analysers have moved around the detection plane, the whole system is reoptimised and the process of data collection repeated. A correlation function between the scattered and ejected electrons is therefore accumulated over many sweeps of the detection plane until the results are statistically significant.
During operation the running conditions are monitored every 50 seconds by the data logger, allowing any anomalies in the data to be accounted for when final results are considered. Results from experiment for the symmetric case, where the outgoing electrons following the collision have equal energy, are shown in the figures 4a - 4h. In the perpendicular plane, the symmetry about the incident electron beam direction requires that the DCS must be symmetric about f = 180A° and this is evident in the data.
Inspection of the 94.6eV data (35eV scattered and ejected electron energies) indicates that this result does not follow the trends of the other data in the set.
The resolution of the spectrometer (~ 1eV) does not allow these contributions to be excluded, and so the 94.6eV data set cannot strictly be considered as part of the overall set of data which is presented here. The first result in this data set therefore is the same as the first result in the previous set, allowing a convenient point for common normalisation of the data sets.
Above 54.6eV incident energy the results differ markedly, the angular correlation evolving into a single broad peak instead of the three distinct peaks observed in the symmetric case. This is most clearly evident at 74.6eV incident energy, where the symmetric case shows three distinct peaks of approximately equal intensity, whereas the non-symmetric case shows only a broad featureless structure centred about 180A°. The sets of data shown in figures 4 and 5 were each normalised relative to the result obtained at 34.6eV incident energy, where both the electrons emerge from the interaction region with an energy of 5eV. The relative angular data presented at any particular energy is normalised by consideration of the electron singles counting rate, which depends on the Double Differential Cross Section at 90A° but is independent of the azimuthal angle f. The procedure adopted here allows an upper and lower bound to be estimated, as no facility exists to allow these overlap volumes to be accurately determined experimentally as is implemented by other electron scattering groups.
The DDCS gives the probability of obtaining an electron from the scattering event at an angle q1 in a solid angle dW1 at an energy E1 A± dE1. The solid angle of detection depends upon the geometry and operating potentials of the electrostatic lenses, and is therefore also a function of the detected electron energy.
VA(E1) is given by the three way overlap of the gas beam, electron beam and volume as seen by the analyser. The DDCS varies only slowly over the energy range dE accepted by the analyser (Jones et al 1991) as does the efficiency and solid angle of detection of the analyser as determined from electrostatic lens studies. The energy resolution DEA is independent of E1 because the pass energy of the hemispherical deflector is kept constant. This expression can be rearranged to yield the ratios of analyser efficiency and solid angle in terms of the DDCS, singles count rates and overlap volumes at the two energies E1 and E2 for an incident energy Einc..
The ratios on the left-hand side of this equation were obtained from the DDCS data of MA?ller-Fiedler et al (1986) at an incident energy of 200eV for each analyser at the selected energies of interest. The first three terms in this expression are evaluated directly from the experiment, while the fourth and fifth terms are taken from the data of MA?ller-Fiedler et al (1986). As no experimental facilities existed to measure these parameters, a SIMION ray-tracing model was set-up to allow a computational determination of these volumetric terms. The analyser input electrostatic lenses were also modelled to determine the volume viewed at the interaction point for the varying energies of electrons selected. Figure 6 indicates the experimental geometry as viewed by the analysers in the perpendicular plane, where the atomic beam direction is at 45A° to the incident electron beam trajectory. Table 1 indicates the calculated relationship GV as determined from the SIMION ray tracing model, and these values have been used to calculate the normalisations as given in figure 4.
The dominant error in the expression is given by the double differential cross sections as measured by MA?ller-Fiedler et al (1986), since these terms arise four times in the expression, and typically have measurement errors of A± 15%.
This is possible since the q = 90A° coplanar symmetric energy-sharing result is identical to the perpendicular plane f = 180A° energy-sharing result. Since data was not obtained at an incident energy of 100eV in these experiments, an interpolation between the energy normalised symmetric results yields a relative value. The uncertainty in the normalisations of the relative energy is approximately A±30%, as discussed in the previous section.
The absolute differential cross sections as presented in figures 4 and 5 therefore have uncertainties of approximately A±44%. These latter calculations, normalised to one energy, produced results that were close to those of the experiment. A simple descriptive model for the symmetric case illuminates a possible scattering processes involved.
On the other hand the peak that is observed at 180A° can be explained in terms of either single or multiple scattering. In terms of single scattering it is due to the incident electron selecting a bound electron whose momentum is equal in magnitude but opposite in direction to its own momentum. In terms of multiple scattering, particularly at the lower incident energies, the peak at 180A° has additional contributions that may be described by outgoing electron correlations as in the Wannier model. The mass equivalence of the scattered and ejected electrons requires that a quasi-free collision results in electrons emerging at approximately 90A° to each other irrespective of their resulting energies, and so application of this model would once again yield three peaks, although the relative peak intensities might be expected to change.
These results predict a single peak at 180A° due to a mechanism following elastic scattering of the incident electron from the nucleus that is more delicate and complex than the quasi-free collision, however the wings at the lower energies in the experiment are not predicted by this model. This may not be entirely unexpected as the DWBA model gives better results at higher energies. The central peak predicted by the theory also differs in width and height from the results presented here, when normalised to the 34.6eV data.
The (e,2e) spectrometer vacuum chamber (figure 1) is manufactured from 304 grade stainless steel, the construction being carried out by Vacuum Generators using a design of Jones, Read and Cvejanovic, full details of which may be found in T.
3mm thick mu-metal magnetic shielding is placed both internally and externally to decrease extraneous external magnetic fields to less than 5mG at the interaction region. All inputs and outputs to the spectrometer pass through the vacuum chamber via feedthroughs on the top flange. The top flange of the vacuum system is a 25mm stainless steel flange with 11 conflat CF70 flanges arranged around a central 200mm flange designed for locating a hydrogen source. Two flanges are used for the high voltage channeltron and photomultiplier tube inputs and pulse outputs.
Three rotary motion feedthroughs allow the analysers and electron gun angles to be changed externally via stepper motors for both analysers and for the electron gun. The ionisation gauge is placed at right angles to the main flange to prevent light from the thoriated iridium filament entering the vacuum system, which would increase noise on the photomultiplier tube. The ionisation gauge feedthrough is sooted, and a loose cover is placed over the entrance in the chamber flange to prevent stray light from the ion gauge entering the vacuum system.
The target gas enters the system via a CF70 flange which has two 6mm stainless steel tubes welded into the flange. The other gas feed is connected to a hypodermic needle set at 90A° to the incident beam for measurements in other geometries. The gas jet which is not currently used in the interaction region can be used to non-locally fill the chamber with gas for background counting measurements. The final CF70 flange is used when the photomultiplier tube is cooled, usually during baking of the system following exposure to atmosphere.
The tube is cooled by passing vapour from a liquid nitrogen source through expansion coils wrapped around the photomultiplier tube housing. The electron gun is a two stage non-selected gun designed by Woolf (Ph.D thesis, University of Manchester) (see figure 3).
The gun consists of a filament, grid and anode source which is focussed using a triple aperture lens through two 1mm defining apertures in the centre of the gun. The apertures define the electron beam pencil and beam angles, and are focussed onto the interaction region using a second triple aperture lens located between the apertures and interaction region. The electron gun is shielded using advance (constantin) sheet which is grounded to the body of the gun mounting.
The gun is mounted onto an x-y translation table to allow placement of the electron beam as accurately as possible to the centre of rotation of the analysers and electron gun rotation axis. The gas jet is mounted from the electron gun using a narrow support of 310 stainless steel, and the Faraday cup can be attached to this support. The original unselected electron gun built by Woolf was completely rewired and a custom built PTFE 25 way inline wire-wrap plug and socket was placed between the 52 way vacuum electrical feedthrough and the electron gun. The wiring from the 52 way feedthrough to the inline plug is shielded colour coded 30 awg PTFE coated advance wire, and the inline plug and socket connectors are non-magnetic gold plated wire wrap pins. The electron analysers are constructed from molybdenum and are mounted from two rotating gear plates controlled externally via the rotation feedthroughs on the top flange (see figure 2).
The input electrostatic lenses for each analyser are three element cylindrical lenses as shown in figure 4.
The interaction region is focussed onto the entrance aperture of the hemispherical energy analysers with a beam angle of around zero degrees, the image of the analyser entrance aperture being larger than the size of the interaction region. Field gradients around the input and exit apertures are corrected using standard Jost correctors. The energy selected electrons passing through the exit apertures are finally collected by Mullard X919BL channel electron multipliers which amplify the single electron to produce a current pulse at their output. A principle source of noise on the signal pulses arises from the turbo-molecular pump motor. The noise from the turbo pump is reduced to ~ 5mV using these techniques, and as the average pulse height from the saturated multiplier is around 20-40 mV, this allows adequate discrimination following amplification. The pre-amplifiers located external to the vacuum system are commercial 100X preamplifiers with 400pS rise-times, manufactured by Phillips Scientific. The NIM signals produced by the discriminators drive two ORTEC 437 Time to Amplitude Converter's via appropriate delay cables and an ORTEC pulse delay unit. The main TAC output feeds an ORTEC Multichannel Analyser card located in the PC controlling the experiment, whereas the second monitor TAC drives an external MCA, allowing convenient monitoring of the coincidence signal as the experiment progresses. The high voltage supplies to the electron multipliers are two Brandenberg 5kV supplies controlled by the main PC via serial DAC's. Principally the filter is used to reduce pickup noise from entering via the HT cable onto the multiplier output.
Secondly, the filter has a slow response time for high voltage spikes, and reduces the probability of damage to the pulse electronics should the EHT supply suddenly turn on or off. Capacitor C2 decouples the 1kW load resistor to earth for high frequency pulses from the CEM's, and the voltage appearing across this load is connected via the capacitor C3 to the input of the 6954 preamplifier. Since the input impedance of the preamplifier is 50W and the CEM is effectively an ideal constant current supply, most of the current passes through to the preamplifier. Finally, the 10M resistor prevents the output to the preamp from rising above ground when the preamp is disconnected from the circuit and is therefore a safety device for the preamplifier when initially connected.
The original design placed the atomic beam nozzle and Faraday cup on the same support structure fixed to the body of the electron gun, with the atomic beam direction being in the detection plane when the perpendicular plane geometry is chosen (see figure 2).
A second configuration is adopted for exclusively perpendicular plane coincidence experiments, the atomic beam nozzle being oriented at an angle of 45A° to the detection plane so that the gas effusing from the nozzle does not fill the analysers when they oppose the nozzle (see figure 6). In this configuration the support strut for the atomic beam nozzle is terminated lower than the detection plane, as is the nozzle itself. For non-perpendicular plane measurements the Faraday cup is once mounted from the support strut and the gas effuses perpendicular to the electron beam direction. One difficulty when aligning an (e,2e) coincidence experiment lies in the focussing the incident electron beam and analysers onto the interaction region. The throughput of electron current as detected by the Faraday cup is insensitive to both position and focusing of the electron beam, since the cup opening is usually made quite large (in this case 6 - 10mm) and the bias voltage applied to the cup to prevent electrons returning to the interaction region allows all electron trajectories within this opening to be detected. Conventionally, following maximisation of the Faraday cup current, the beam is steered and focussed onto the gas jet as detected by counts in the analysers. This has the disadvantage that the overlap volume is maximised for both atomic and electron beam density, which tends to place the interaction volume as close as possible to the output of the atomic beam nozzle, which is almost certainly not in the centre of the detection plane. To eliminate the need for time consuming iterative techniques and the associated errors due to detection geometry, a separate method for tuning the electron gun is adopted that does not depend upon the analysers. The interaction between the target and the electron beam not only produces ionisation, but the valence states of the target also are excited with various probabilities depending upon the incident energy of the electron beam.
These photons are detected by the photomultiplier tube, by placing a 450nm A± 50nm optical filter in front of the photocathode. The interaction region is therefore defined where an aperture in front of the photocathode is focused by the lens. The plano-convex focussing glass lens is covered by a grounded fine tungsten mesh to eliminate surface charging.
The photomultiplier tube may be cooled by circulating nitrogen gas boiled off LN2 through copper coils encircling the photomultiplier tube housing.
The photomultiplier tube used in the experiment is a 9789QB EMI photomultiplier tube with a bi-alkali photocathode peaking in the blue region of the optical spectrum. As with the electron multiplier circuitry, it is important to optimise the load of the photomultiplier tube so that reflections along the feeder line to the counting electronics are minimised. The 1nF 6kV capacitors across the dynodes close to the output stage are used as charge storage pumps that quickly refurbish the surface charge on the dynodes, allowing increased counting rates. The dynode resistors are 1% tolerance metal film resistors as these are more stable with temperature. The EHT supply to the photomultiplier tube is a Brandenberg 2kV supply operating at 1500V for this tube. The negative going output pulses from the tube measure typically 200-500mV in height, and therefore are able to directly drive an ORTEC 473A constant fraction discriminator located in one of the NIM crates. All resistors and capacitors for the dynode chain are soldered to the photomultiplier tube base internal to the vacuum system, using standard 5-core solder. Typical pulse heights from the electron multipliers in saturation mode are 25-40mV, whereas the typical height of the photomultiplier tube pulses is of the order of 250mV.
The electron multiplier pulses are obtained from the multiplier supply circuitry as explained above.
The amplified pulses from the 6954 amplifiers pass along doubly shielded RG-58 cable to the input of the ORTEC 473A discriminators. The two analyser discriminators are located in separate NIM crates to increase isolation and reduce common mode pickup.
The slow rise-time positive outputs from the 473A discriminators pass to three ORTEC 441 rate-meters which allow counting and monitoring of the pulses.
The fast NIM pulses from the analyser 473A CFD's pass through appropriate delay lines to two 437 TAC's. This second multichannel analyser allows the operator to monitor the total accumulated coincidence signal during operation.
The lens supplies that control the voltages impressed onto the lens elements and deflectors in the experiment were developed over a number of years, and therefore take different forms.
Three of these supplies feed the deflectors in the electron gun, the other two supply the input deflectors in the analysers. In a second 19" crate is located the gun lens high voltage supplies together with the high voltage supplies for the Faraday cup. In a third 19" crate is located the analyser voltage supplies together with a set of serial loading supplies that control the electron multiplier EHT supplies. A further supply controls the current boost circuitry located in the filament constant current supply unit (see below). The outputs of each computer controlled supply that drives an individual lens element or deflector are connected to a 70 relay switching board. The Digital voltmeter is in turn accessed via an IEEE-488 interface which is addressed by an 8086 slave PC which converses with the central PC which controls the experiment.

The outputs from the relay board connect to the spectrometer via shielded multicore cables which take the gun voltages to the 52 way feedthrough and the analyser voltages to the two 19 way feedthroughs located on the vacuum flange. The gun supply multicore also carries the filament supply current to the 52 way feedthrough. The Faraday cup current is measured by the Keithley Digital voltmeter when under computer control but this can also be measured by an external pico-ammeter. In addition to the analyser electrostatic lens and deflector voltage connections, the 19 way CF70 feedthroughs are used to control signals from internal sensing opto-isolators which control the stepper motor interlocks. The stepper motors that drive the analysers and electron gun around the detection plane are five phase motors with integral 10X reduction gearboxes driving the rotary motion feedthroughs. The intelligent stepper motor drivers are addressed via a serial port located on the controlling PC bus.
An additional interference problem was traced to the RS232 serial line from the controlling PC. The PC bus was found to be poorly earthed due to very little copper being used for the bus earth.
This was cured by decoupling the 0V RS232 line from the main 0V line for the stepper motors, as is shown in figure 10.
The analyser stepper motor supplies have a facility for halting the motors using limit switches which are optically coupled to the internal 68000 logic circuits driving the supplies.
The SD5443-3 phototransistor normally illuminated by the TEMT88PD photodiode during operation ensured a fail-safe mechanism should any of these components fail (this automatically prevent the motors from running). Should the analysers move into a position as defined by the four criteria (a) - (d) above, a shutter located on the analyser turntables moves between the appropriate photodiode and phototransistor, shutting off the light and thereby shutting down the stepper motor current. Only motion in the opposite direction is allowed by controlling logic, allowing the analyser to move away from the point of imminent collision but no closer.
The six pairs of optocouplers that prevent the analysers moving into the Faraday cup, electron gun and gas jet support are located on the mounting struts supporting the main body of the spectrometer.
Two optocouplers are located on the side of analyser 2, and two shutters are located on the sides of analyser 1 to prevent the analysers colliding with each other. Finally a ninth optocoupler is located over the electron gun counterweight which monitors when the gun is at an angle less than 65A°, where the sweep angle around the detection plane is reduced.
The current boost circuit operates from a serial driven supply card as detailed previously. The main filament drive is through six power diodes that feed the current from the constant current supply to the filament. The Darlington transistor T1 feeds additional current to the filament via three parallel 10 turn 100W trim resistors through a 1N4007 diode. As the constant current supply acts as an infinite resistance source, the boost circuit supplies additional current only when the voltage at the anode of the feed 1N4007 exceeds the output voltage of the constant current supply.
Finally, the filament bias voltage (and hence energy of the electrons) is set to the midpoint of the filament by two 100W balancing resistors located across the terminals.
In addition to the ADC buffer card, three independent isolated regulated supplies drive REF01 voltage reference sources for measurement of the positions of 10 turn potentiometers located on the analyser and electron gun rotary drive shafts. The angular position of the electron gun and analysers is calibrated when the system is opened using visible laser diodes that define these angles to an accuracy of A±0.2A°.
Figure 13 shows an overall block diagram detailing the computer control and high speed pulse interfacing to the spectrometer. 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. In this work, we present results on the formation of vertical molecule structures formed by two vertically aligned InAs quantum dots (QD) in which a deliberate control of energy emission is achieved. The simplest interacting quantum dot (QD) system is a QD molecule (QDM) composed of two closely spaced QD [1a€“3]]. In this sense, here, we present a process that optimizes the growth of coupled structures in vertical arrangement by the use of a low-density nanoholes template fabricated by droplet epitaxy [11].
Thus, the growth procedure starts with the filling of previously formed nanoholes with InAs material.
Once formed the first layer of QD (QD1 hereinafter), a GaAs intermediate barrier with a thickness of 4 nm is subsequently grown to guarantee a large tunneling effect [5]. With the aim of studying the optical emission of the resulting QD molecule structures, a 155-nm-thick GaAs layer is finally grown.
Transmission electron microscopy images have been obtained to know the structural configuration of the resulting molecules. Table 1 lists the different values of the emission energies ascribed to QD1 and QD2 in the molecule structures. More experimental work is needed to demonstrate if these paired QD structures show electronic coupling as corresponding to QD molecules. Altogether, these results show that by varying the amount of InAs material deposited at a nanoholes template formed by droplet epitaxy, the emission of a first layer of QD can be tuned to obtain either a symmetric or an asymmetric vertically coupled QDM. This means that the reactions occur at greater rates so that radiation pressure balances gravity.
To get this score, a product normally has to be in a high priority section of the house and possibly contribute to a large percentage of an average home’s energy spending. She has more than 12 years of experience in clinical and corporate settings, and has extensive experience in one-on-one diet counseling and meal planning.
In many cases, low energy density or low-calorie foods are whole, unprocessed foods, such as fruits, vegetables, very lean proteins and low-fat dairy products without added sugars. Department of Agriculture's National Nutrition Database, a 1 ounce serving of a very lean protein food provides 35 calories; far less calories than medium-fat protein foods, which provide 75 calories per ounce. For example, an 8 fluid ounce cup of non-fat cow's milk or non-fat plain yogurt provides approximately 80 calories. These experiments measure the angular correlation between a projectile electron which is scattered from a target and a resulting electron which is ionised from the target. For an unpolarised target and unpolarised incident electron beam the only azimuthal angle of significance is given by f = fa - fb.
When the electrons are detected in the perpendicular plane, the two angles qa and qb are both equal to 90A°.
The perpendicular plane is accessed mainly through double collision processes (Hawley-Jones et al (1992), which represent only part of the full dynamical picture.
The computer loads all the voltage supplies from either a manually selected set of voltages or from the results of a previous optimisation run. This decouples the tuning of the electron gun from any tuning requirements of the electron analysers.
This should be compared with the data obtained near threshold by Hawley-Jones et al (1992), which also shows a single peak with an approximately Gaussian structure.
This is considered to be due to the contribution to the cross section of a number of resonances in helium for scattered and ejected electron energies around 35eV.
The model indicated that the electron gun operating at the voltages determined by the optimisation routines produced an electron beam of diameter approximately 1.0mm at the interaction region, consistent with the tuning of the electron beam onto counts from the photomultiplier which views a 1mm3 volume. For the non-symmetric data no compensation is required for volume effects since GV = 1.0 at all values of Ei.
The electrons are then able to emerge at approximately 90A° with respect to each other in the perpendicular plane, as is observed.
As the momentum distribution of the bound electron peaks at zero for helium, the peak at 180A° diminishes with increased incident electron energy as the probability of finding a bound electron with the required momentum decreases.
One of these is internally connected to a gas jet which can be set at 45A° to the incident electron beam and is used in the perpendicular plane experiments. These stainless steel feeder tubes are connected to the nozzle using grounded shielded PTFE hose. One follows the anode, another corrects the beam direction between the apertures and a third steers the beam onto the interaction region. This shield is coated with aerodag colloidal graphite to reduce patch fields on the surface of the metal, and is made as small as possible to allow the analysers to approach the gun as close as is feasible when non-perpendicular plane geometries are selected (see figure 2). The XY translation table is mounted from the rotating yoke, to which is attached the photomultiplier tube. This allows the gun to be dismounted from the system without the need for rewiring of the feedthrough when the need arises (filament changes, cleaning etc). The wiring between the gun and inline socket is also shielded colour coded PTFE coated advance wire facilitating spot welding to the electrostatic lens elements of the gun. The analysers are mounted onto x-z translation tables that allow them to view the interaction region accurately over the full range of angles accessible. These lenses have a capability for energy zooming of around 10 : 1, and have a maximum entrance acceptance angle of A±3A° as defined by the entrance apertures. This ensures that the overlap volume accepted by each analyser encompasses the interaction volume for all detection angles as the analysers move in the detection plane. These devices use an activated lead glass internal surface which has a high coefficient of secondary electron emission when a high voltage (around 3000V) is applied across the multiplier. This noise may be picked up by the channel electron multiplier and the high voltage feed to the multiplier, and is generated internally in the vacuum system.
The CFD's are operated in NaI mode as this has a 2ms dead time following the initial pulse, thus reducing the possibility of false triggering due to any mismatching impedance reflections along the delay cable. These EHT supplies are connected via VERO 200 high voltage couplings to high voltage cable connecting to the pickoff circuitry located on the high voltage feedthroughs. This allowed the analysers to roam the detection plane over a complete 360A° angular range. The configuration of the target source hypodermic when perpendicular plane measurements are conducted. The common procedure is to initially maximise the current from the gun onto the Faraday cup, then onto analyser counts as the electron beam is moved through the gas jet. Maximising the Faraday cup current is therefore only a crude preliminary alignment of the incident electron gun beam.
This therefore assumes that the analysers are initially focused onto the interaction region, and a slow iterative technique must be adopted where the analysers and electron gun are tuned so as to maximise the signal from both analysers. In this case a true differential cross section is not obtained, since the scattered and ejected electron trajectories lie in a different plane than defined in the initial experimental alignment.

An EMI 9789QB reduced photocathode photomultiplier tube is installed in the vacuum system together with optical focussing and defining elements (figure 2).
A group of these excited states decay back to lower valence states with the emission of visible photons at wavelengths around 450nm for both helium and argon targets.
Tuning of the electron gun to PMT counts therefore guarantees that the electron gun is steered and focussed to the point at the centre of the detection plane independent of the analysers or gas beam density. This is mainly used when the vacuum system is baked at temperatures above 55A°C, since the photocathode is rapidly damaged by temperatures exceeding this. The tube is a venetian blind dynode construction, and has a reduced photocathode to decrease the noise on the output of the tube to less than 20Hz. The photomultiplier tube base was thoroughly cleaned in an ultrasound following location of these components, to displace any flux residue from the solder joints. It is therefore necessary to amplify the channeltron pulses prior to transmission to the discriminators, whereas the photomultiplier tube pulses are sufficiently large to not require further amplification. These pulses are amplified by Phillips Scientific 6954 100X amplifiers located external to the EHT feedthroughs connected by 10cm lengths of RG-58 cable. These crates are further decoupled from the AC mains supply using filter circuitry on each supply line. Internal to these rate-meters buffer 7400 TTL chips have been added to send to 32 bit counters located in the main PC via RG-58 cable. These supplies are fully floating, their mid-point voltage being equal to the lens element voltage in which the deflectors are housed. All these supplies are fully computer controlled isolated units with low output impedance to reduce noise and eliminate current loops. This relay switching unit allows either the voltage or the current on each lens element to be measured by a Keithley Digital voltmeter. This drive is further reduced internally by 10X reduction gears, resulting in a reduction ratio of 100:1.
This led to the ground line of the RS232 serial line moving around with respect to the 0V stepper motor reference as drive current to the motors returned along the ground line. The optocoupler logic circuit circuit that controls the stepper motors and avoids collisions between the analysers, the electron gun, the Faraday cup and the hypodermic support.
Added to this filament supply is a computer controlled current boost circuit that can be used to increase the filament current during electron gun tuning. The additional current then returns to the 12V DC regulated supply via a second 1N4007 diode. This therefore depends upon both the current driving the filament, as well as the resistance of the filament when hot (typically 4W - 6W). This supply feeds current to the filament without changing the characteristics of the main constant current supply used while operating the spectrometer. These high stability reference sources ensure that the analyser and electron gun positions are accurately measured with time. A datalogger internal to the controlling PC establishes a cubic spline relationship between the measured angles and the corresponding ADC conversion from the potentiometers. This PC also controls the selection of the relay motherboard for measurement of the required lens element either in voltage or current mode when a request is sent from the controlling computer via an RS232 serial line. 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.
The emission energy of the first layer of QD forming the molecule can be tuned by the deposition of controlled amounts of InAs at a nanohole template formed by GaAs droplet epitaxy.
QDM are receiving much attention both as playground for studying coupling and energy transfer processes between a€?artificial atomsa€? and as new systems, which substantially extend the range of possible applications of QD [4]. 4b shows the emission of the remaining three PL peaks that would correspond to the QD2 family in the QD paired structures. As a characteristic when using a droplet epitaxy patterning process, the density of QD molecules obtained is low enough (2 A— 108 cma?’2) to permit their integration as active elements in advanced photonic devices where spectroscopic studies at the single nanostructure level are mandatory. Whilst a massive star may spend a few million years on the main sequence, its helium core-burning phase may be a few hundred thousand years. The higher the score is, the more critical, we believe, it is for the energy efficiency of your home. Fruits contain fructose, which is fruit sugar, so they are, in general, higher in calories than vegetables.
One cup of non-fat fruited yogurt, prepared with aspartame or another non-nutritive sweetener, provides, on average, 80 to 100 calories. Further it allows the electron gun to be aligned and focussed accurately onto the interaction region whose centre is located at the intersection of the axes of rotation of the analysers and the electron gun. This type of double collision process must therefore be modelled using higher order scattering terms as is done using the DWBA. The spectrometer is shown configured in the perpendicular plane, the electron gun being placed in the vertical position with respect to the analysers which span the horizontal detection plane. The electron source is a heated tungsten hairpin filament heated by passing around 2A of DC current through the filament. The saturated gain of these devices yields around 1E8 electrons in the output current pulse for a single electron which enters the input cone. This allows the analyser to roam over a complete 360 degrees of the detection plane when in this geometry (apart from the position where the analysers would clash wth each other).
The analysers are then adjusted for maximum signal count and the procedure is iterated until a maximum is found. The dark noise count is also reduced when cooled, however since the reduced cathode PMT only produces dark counts of less than 20Hz at room temperature, this is not necessary during routine operations.
The 1.82M resistor was chosen to optimise the single photon counting efficiency of the tube. It is not found that these solder connections significantly affect the ultimate vacuum pressure in the system. Isolated DC supplies to these amplifiers is obtained from a standard +15V supply, the circuit diagram being given in figure 8.
The power supply to these TTL buffers is derived from the rate-meter supplies via 7805 5V regulators located internally.
This supply boosts the current without changing the main supply, thus ensuring supply stability before and after the electron gun is tuned. 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. The QD of the second layer are formed directly on top of the buried ones by a strain-driven process. In such systems, the coupling involves tunneling of electrons and holes between two adjacent dots separated by a thin intermediate barrier layer. At this moment, for completing the molecule structure, a second layer of QD (QD2 hereinafter), located above the QD1, is grown by the deposition of 0.9 ML of InAs at the same conditions used for the underlying nanostructures.
Contrast in this image is due to changes in composition, dark areas indicating the presence of In in In(Ga)As layers.
It can be observed that the emission energies are similar in all the cases showing that the size of the nanostructures formed in the QD2 layer remains almost invariable despite the different amount of InAs deposited underneath (see PL energy values in Table 1). The carbon burning phase lasts a few hundred years, neon-burning phase a year, oxygen-burning half a year and the silicon-burning only a day.
One serving of fruit is about 1 cup, or one medium-sized piece, and provides, on average, 60 to 80 calories. Department of Agriculture's MyPyramid website, one serving is 1 cup, raw or cooked, for all vegetables except leafy greens. This is essential for experiments where all of these may be varied over 3-Dimensional space.
The electron gun is a two stage non-energy selected gun that produces an incident electron beam current of up to 4 microamps at an incident energy from around 30eV to 300eV. The 470k resistors bias the dynodes to achieve saturation of the current pulse at the output of the tube, hence biasing the tube for single photon counting applications.
This was found to be necessary to eliminate problems associated with current loops from the 20A peak motor current feeding the common point of the logic circuitry. 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. In particular, it has been observed [5] that for a 4-nm-thick intermediate tunneling layer, the coupling strength is optimized for the spectroscopic observation of large electron anti-crossing energy splitting [5]. It can be observed the formation of the double structure that consists of two InAs QD separated by the 4-nm-thick GaAs barrier layer. Examples of fruits that provide the most volume for the least amount of energy in the form of calories include peaches, nectarines, kiwi fruit, melon and berries -- such as raspberries, strawberries or blueberries. The analysers are identical, and consist of a 3-element electrostatic lens focussing the interaction region onto the entrance of a hemispherical electrostatic energy analyser.
The Anode deflector pair corrects for any misalignment of the filament emission point with respect to the axis of the electron gun. As a characteristic when using a droplet epitaxy patterning process, the density of quantum dot molecules finally obtained is low enough (2 A— 108 cma?’2) to permit their integration as active elements in advanced photonic devices where spectroscopic studies at the single nanostructure level are required.
It is, however, technologically challenging to obtain resonant quantuma€“mechanical coupling due to size, composition, and strain inhomogeneities inherent in self-assembled QD.
According to these results, the aimed tuning effect on the size of QD1 by the use of nanoholes has been successfully obtained.
The evolution of these two PL peaks with increasing excitation power (not shown) reveals that they correspond to two different QD families, as they do not show any relative saturation effects corresponding to one QD family with ground and excited states. The Chamber is lined internally with 3mm thick mu-metal, and a mu-metal cylinder encloses the chamber externally as shown.
The electrons selected in angle and energy are amplified using Mullard 919BL channel electron multipliers. The defining apertures limit the pencil and beam angles of the electron beam following focussing by lens 2 onto the interaction region. The load is set by the 50W resistor across the anode to the HT feed, the pulse being decoupled to ground via the 1nF capacitor.
In this sense, great efforts have been dedicated to the formation of vertical coupled QD by self-assembling processes [6]. It is noticeable that as a difference to the strain-driven formation of QD2, or in general, in a self-assembling process, QD1 forms at a lower level than the WL, clearly indicating a formation mechanism that involves preferential nucleation of InAs material into previously fabricated GaAs nanoholes by droplet epitaxy [12]. On the other hand, despite this engineered change in size of QD1, the nucleation of QD2 takes place on top of the buried QD1 with same density of QD1 layer and similar dimensions in all cases. Combining these optical emission results with those obtained by TEM structural analysis, it can be established a direct correspondence of the different emission energies to the recombination of carriers at the upper and lower QD layers of the molecule structure. Examples of low energy density vegetables include asparagus, cucumber, green beans, spinach, lettuce, sweet bell peppers, radishes, onions, broccoli, cauliflower and mushrooms.
This reduces the magnetic field at the interaction region to less than 5mG, an acceptable level for the electron energies used in this experiment. The interaction region defined by the interaction of the gas target beam and the electron beam is focussed onto the photocathode of an EMI 9789QB photomultiplier tube via a lens, 450nmA±50nm optical filter and defining aperture. Placement of the apertures ensures that the beam angle is close to zero degrees at the interaction region over a wide range of energies, whereas the aperture opening reduces the pencil angle to around A±2 degrees over this energy range.
The most used fabrication process leading to vertically aligned QD is based on the formation of one layer of self-assembled QD, followed by a thin spacer layer. These results show that the size of the strain driven formed QD2 is controlled by the amount of InAs deposited. Figure 4a shows as filled areas the three different PL emissions that would correspond to the QD1 family for the three different QD paired structures. The target gas effuses from a 0.6mm ID hypodermic needle constructed from platinum iridium alloy.
The 10MW safety resistor prevents the output charging up to a high voltage if the feed is disconnected. The deflectors between the apertures correct for space and surface charge beam variations inside the field free region, whereas the final deflectors allow the beam to be steered onto the interaction region defined by focussing a 1mm aperture in front of the photomultiplier tube onto the gas target beam. Then, upon further InAs deposition, a second layer of QD is formed, on top of the buried QD, by strain-driven processes. Moreover, the strain gradient at the surface is large enough to promote preferential nucleation of InAs just on top of the buried QD1, even for InAs deposited thickness of 0.9 ML, which is much lower than the critical thickness for QD formation in absence of local strain fields [14]. As expected from previous results [12], the effect of the different amount of InAs deposited in the first layer of nanostructures permits the emission energy of the QD1 to be tuned in a wide range.
The electrons passing through the interaction region which are not scattered are collected in a Faraday cup opposite the electron gun. By this growth procedure, tuning of the emission energy of one of the QD at the same time that is maintained unaltered the emission properties of the other, although not impossible, is difficult to achieve due to the lack of control in size for self-assembled QD. The gun, photomultiplier tube, gas hypodermic and Faraday cup all rotate on a common yoke with an axis through the centre of the horizontal detection plane, allowing all geometries from the perpendicular plane to the coplanar geometry to be accessed.
The tuning effect of the emission energy of one of the QD forming the molecule respect to the other would permit to build symmetric vertical QDM, in which the energy emission of both QD forming the molecule matches, and asymmetric vertical QDM, in which the energy emission of one QD is blue-shifted or red-shifted respect to the other [5a€“7]. Apart from this lack of control in size of the QD forming the QDM by a self-assembling process, there is an intrinsic inter-dependent nature between the QD size and density that makes difficult the design of QD of a desired size and with a low enough density for its spectroscopic study at the single nanostructure level [8a€“10].

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