Ionization of water using the (e,2e) technique


from the 1b1 HOMO state & from the 3a1 n-HOMO state

 

 

Researchers involved in this project:

 

 

Kate L Nixon, Christian Kaiser and Andrew James Murray

 

 

 

 

1. Coplanar symmetric and asymmetric electron impact ionization studies from the 1b1 state of H2O at low to intermediate impact energies.

 

1.0 Abstract:

 

(e,2e) ionization differential cross sections are presented for incident electron energies ranging from 15eV to 95eV above the ionization threshold of the 1b1 molecular state of H2O.

 

Experimental results are shown for three energies in a coplanar symmetric geometry, and for three energies in an asymmetric geometry. The experimental data show a wide variation in the cross section over this range of energies.

 

 

1.1 Introduction.

 

Ionization of atomic and molecular targets is one of the most complex and fundamental collision processes that can be studied in detail. 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.

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. The scattered electron is then detected in time correlated coincidence with either the electron ejected during ionization, or with the resulting ion.

In these (e,2e) experiments, information about the collision is obtained by measuring the outgoing momenta of the collision products. This is usually accomplished by determining a cross section that is five fold differential in angle and energy.

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. In most cases, this means that an averaging over the orientation of the target must be included for theory to compare with experimental results. In these cases there is loss of information about the collision process.

The interaction of low to intermediate energy electrons with molecular targets has been much less studied compared with high energy electron collisions. This energy region (from threshold to ~200eV) is important as it is here that the cross section for ionization is largest. 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.

Experiments on molecular targets often employ effusive beams produced at room temperature, and so the targets may have internal rotational and vibrational energy. 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. 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.

Results are presented here for an H2O target at significantly lower energies than has been studied before. A coplanar geometry was chosen, and results are presented for both coplanar symmetric and coplanar asymmetric geometries, with incident energies ranging from 15eV to 95eV above the ionization threshold of the 1b1 state of neutral H2O. A pictorial representation of the water molecule in the 1b1 state is given in figure 1.1 below.


Figure 1.1 Representation of the 1b1 state of H2O, showing an incident electron ionizing the molecule.

 

1.2. Experimental setup.

 

The experiments described here were carried out in the fully computer controlled and computer optimized (e,2e) spectrometer that operates in Manchester. 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. 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 power supplies for the electrostatic lenses that control the electron gun and electron detectors are fully computer controlled, and so the spectrometer can be operated for 24 hours/day without the need for operator intervention.

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). In this configuration, the energies selected for the scattered and ejected electrons were equal. The incident electron energy was set to 20eV, 40eV and 60eV above the ionization potential from the 1b1 state, which is around 12.6eV. The angles that could be accessed in this configuration ranged from thetaa = thetab = 25° through to thetaa = thetab = 135°.



Figure 1.2. The coplanar geometry chosen for the studies detailed here. (q1, q2) are the angles of the electron analysers with respect to the incident beam direction k0. For coplanar symmetric geometries, thetaa = thetab. For asymmetric geometries, thetaa is fixed at 22° while analyzer 2 is swept around the scattering plane.


For coplanar asymmetric experiments, analyzer 1 was fixed at a scattering angle thetaa = 22°, while analyzer 2 was swept around the scattering plane. In this case, analyzer 2 detected electrons with fixed energy of 5eV, whereas analyzer 1 detected electrons with energies of 10eV, 50eV and 90eV so as to cover a range of energies from low to intermediate energies.


The fixed scattering angle thetaa = 22° 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 range of angles which could be accessed in this configuration ranged from thetab = 30° to 140° (forward scattering) and from thetab = 225° to 290° (the backscattering direction).


The energy resolution of the spectrometer is set by the resolution of the electron gun and the pass energy of the analyzers. The electron gun used two electro-static lenses to deliver a quasi-collimated beam with an energy resolution ~0.5eV, a beam angle of 0° and a pencil angle of 2°. 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 acceptance angle of the analyzer lenses was ±3°, as set by input apertures at the entrance to the electrostatic lenses.


1.2.1 Production of the water target.


Production of a high quality molecular beam of H2O required careful monitoring of the experiment as it progressed. Pure liquid water was initially loaded into a spherical glass flask connected to a 12l/s roughing pump. The pump removed background gas from the flask, and extracted dissolved gases held in the water. 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. A glass flask was used for this procedure as this allowed the process to be visually monitored.


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. The inner diameter of this flask was 9mm, and the outside diameter was 12.7mm, so that a standard swaged fitting could be used. 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 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.


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. This was accomplished using a Newport model 325 temperature controller, which supplied drive current to the TEC. The controller held the temperature of the water at a constant value of 23°C ± 0.1°C throughout data collection.

To monitor the molecular beam inside the vacuum chamber produced from the water, a quadrupole mass spectrometer was installed onto the spectrometer. This proved invaluable, as it was then possible to continuously monitor the background gases in the chamber during operation. All experiments were performed with a ratio of H2O to N2 (and other gases) of >30:1. If this ratio reduced, the experiment was halted and the water changed to a newly de-gassed sample. Typical partial pressures in the vacuum chamber during operation were: H2O = 5.2 x 10-6 torr, N2 = 6 x 10-8 torr, O2 = 4.9 x 10-8 torr.


1.2.2 The coincidence energy loss spectrum.


Figure 1.3 shows a typical coincidence energy spectrum obtained from the experiment during operation. In this example, the analyzers were set to pass electrons of energy 20eV, and a symmetric geometry was chosen with thetaa = thetab = 45°. 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. In this case, the 1b1 state was found to have a width of 620meV, which is comparable to that for an atomic target. This indicates that the energetic effects of ro-vibrational transitions from the ground state to the ion state are negligible for this state. There is an offset of 1eV in the position of the peaks which is due to contact potentials in the spectrometer.


Figure 1.3. A typical coincidence binding energy spectrum obtained for H2O. These data were measured in a coplanar geometry with outgoing electron energies of 20eV detected at theta1 = theta2 = 55°. The peaks in the spectrum correspond to the three highest orbitals, i.e. the 1b1, 3a1 and 1b2 orbitals as labelled. 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. Very little contamination is expected from neighbouring orbitals in the measured TDCS for the 3a1 state.


The experiments were carried out over a period of several months, using electron beam currents ~200nA for all data runs. 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. At commencement of experimentation, the filament current was 2100mA for a delivered beam current of 200nA, whereas after five months the operating current of the filament had reduced to 1020mA for the same beam current. These changes occurred sufficiently slowly to allow regular adjustment manually. 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.


Figure 1.4 shows the results of experiments using a symmetric geometry. The data is normalized to unity at thetaa = thetab = theta = 45°, since the results have not been placed on an absolute scale. Figure 1.4(a) shows the data at an excess energy 20eV above the ionization threshold. In this case, there is a clear forward scattering lobe which appears to be composed of a double structure, with peaks at theta ~ 32.5° and at theta ~ 45°. The minimum in the cross section occurs at theta ~ 80°, and a backscattering peak is seen which peaks at theta ~ 140°. The forward structure is larger than the backward peak by a ratio of ~1.3 : 1.



Figure 1.4. Experimental data using a coplanar symmetric geometry, at excess electron energies of 20eV, 40eV and 60eV above the 1b1 ionization threshold.


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. A two peak structure in the forward lobe is clearly seen for 60eV excess energy (Figure 1.4(c)), and is also visible at 40eV excess energy (Figure 1.4(b)), although the statistical variation in the data is significant at this energy. The variation in the forward lobe cross section compared to the peak in the backward direction is ~2.8 : 1 at 40eV excess energy and is ~3.2 : 1 at 60eV excess energy. The contrast between the maximum and minimum in the cross section increases as the energy increases. For 20eV excess energy, this ratio is ~4.1 : 1, whereas at 40eV and 60eV excess energies this rises to ~13 : 1 and ~32 : 1 respectively.


The measured coplanar asymmetric data is shown in figure 4, again normalized to unity at thetab = 45°. In this case the data is presented over the angular range from thetab = 30° to 290°, the region between thetab = 140° and thetab = 225° being inaccessible due to the position of the electron gun. Figure 1.5(a) shows the lowest energy results, with an incident energy 15eV above the ionization threshold. A single forward lobe is seen which peaks at thetab ~ 100°. A second peak occurs in the backscatter region, however the maximum of this peak appears to occur at thetab < 225°.



Figure 1.5. Experimental data using a coplanar asymmetric geometry, at excess electron energies of 15eV, 55eV and 95eV above the 1b1 ionization threshold.


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). The peaks occur at theta2 ~ 40° and 110°, whereas the minimum between these peaks is at thetab ~ 70°. The measured cross section in the backscatter region now peaks at thetab ~ 280°. 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 largest peak remains at thetab ~ 40°, the second peak is once more at thetab ~ 110° however the minimum moves to thetab ~ 85°. The results in the backward direction also have structure, with a minimum occurring when thetab ~ 250°.

 

1.3. Summary and Conclusions.

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.

The 3a1 state should provide a better target for theory (see below).

 

 

1.4 References.

 

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[4] J. Ullrich, R. Moshammer, A. Dorn, R. Dšrner, L.Ph. H. Schmidt and H. Schmidt-Bšcking, Rep. Prog. Phys. 66, 1463 (2003)

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[6] J. Gao, D.H. Madison and J.L. Peacher, Phys. Rev. A 72, 020701(R) (2005)

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[10] E. Weigold, S.T. Hood and P.J.O. Teubner, Phys. Rev. Lett. 30, 475 (1973)

[11] E. Weigold, S.T. Hood, I.E. McCarthy & P.J.O. Teubner, Phys. Lett.44A, 531 (1973)

[12] A.J. Murray, J. Phys. B 38, 1999 (2005)

[13] M. ChŽrid, A. Lahmam-Bennani, A. Duguet, R.W. Zurales, R.R. Lucchese, M.C. Dal Cappello and C. Dal Cappello, J. Phys. B 22, 3483 (1989)

[14] K. Jung, E. Schubert, D.A.L. Paul and H. Ehrhardt, J. Phys. B 8, 1330 (1975)

[15] M.J. Hussey and A.J. Murray, J. Phys. B 35, 3399 (2002)

[16] L. Avaldi, R. Camilloni, E. Fainelli and G. Stefani, J. Phys. B 25, 3551 (1992)

[17] J.P. Doering and J. Yang, Phys. Rev. A 54, 3977 (1996)

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[19] M.J. Hussey and A.J. Murray, J. Phys. B 38, 2965 (2005)

[20] D.S. Milne-Brownlie, S.J. Cavanagh, B. Lohmann, C. Champion, P.A. Hervieux & J. Hanssen , Phys. Rev. A 69, 032701 (2004)

[21] A.J. Murray, B.C.H Turton, F.H. Read, Rev. Sci. Instrum. 63, 3346 (1992)

[22] A.J. Murray and F.H. Read, Phys. Rev. A 47, 3724 (1993)

[23] A.J. Murray and D. Cvejanovic, J. Phys. B 36, 4875 (2003)

[24] A.J. Murray, Phys. Rev. A 72, 062711 (2005)

[25] Newport 325 temperature controller, Newport Corp. 1791 Deere Avenue, Irvine CA 92606, USA

[26] J. Gao, D.H. Madison and J.L. Peacher, J. Chem. Phys. 123, 204314 (2005)

[27] J. Gao, D. H. Madison, and J. L. Peacher, J. Phys B 39, 1275 (2006)

[28] M.W. Schmidt, K.K. Baldridge, J.A. Boats, S.T. Elbert, M.S.

Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen,S.J. Su, T.L.

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1347 (1993)

[29] J.B. Furness and I.E.McCarthy, J.Phys. B, 6, 2280 (1973)

[30] J.P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)

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[32] A. Danjo and H. Nishimura, J. Phys. Soc. Japan, 54, 1224 (1985)

 


2. Low energy symmetric-coplanar and symmetric-non coplanar (e,2e) studies from the 3a1 state of water

 

 

2.0 Abstract

 

Experimental results are presented for electron impact ionization of water in the energy regime from near threshold to intermediate energies. Results were taken in symmetric coplanar and non-coplanar geometries, with both equal and non-equal outgoing electron 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. Phys. B: At. Mol. Opt. Phys. 43 (2010) 035201 for details of these calculations) .

 

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.

 

2.1. Introduction

 

Water is one of the most abundant molecules on earth. 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.

 

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 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.

 

These low energy electrons have an effect over a much wider volume than the targeted cancer site. Knowledge of the collision dynamics of low energy electrons with biological systems is hence needed, so as to develop robust models of these processes.

 

  1. (e,2e) studies fully characterize the collision dynamics of electron impact ionization. In such experiments the energy and momenta of the outgoing electrons are measured, giving a five fold differential cross section.

 

  1. 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. 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.

 

  1. 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.

 

Molecular targets provide a significant challenge due to their distributed nuclei. This contrasts to atoms which have a single nuclear scattering centre, and which can hence be described using a spherical basis. Molecular wave-functions are generally not spherical, the nuclei within the molecule providing multiple scattering centres.

 

A key challenge is hence in developing an accurate multi-centered wave-function. 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. This becomes a computationally intensive problem, and so approximations are usually made to allow these calculations to become tractable.

 

Recent experiments studying simple diatomic targets including H2 and N2 have provided benchmark data. 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 apparatus at Manchester can also access non-coplanar geometries, and so has provided additional data to further test these models.

 

2.1.1 Water.

 

  1. H2O has five molecular orbitals; the 1a1, 2a1, 1b2, 3a1 and 1b1 (HOMO). 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.

 

In a previous study the groups at Manchester and Missouri investigated the 1b1 (HOMO) state of H2O in coplanar kinematics. 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.

 

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 molecular orbital used in the model therefore should not suffer from the same cancellation problem during the orientational averaging procedure.

 

2.2. Experimental Apparatus

 

The experimental triple differential cross sections (TDCS) presented here were measured in the (e,2e) apparatus at the University of Manchester. This apparatus is fully computer controlled and computer optimized, allowing it to operate continuously without user intervention. Full details of this spectrometer are found on other web pages on this fileserver.

 

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 = 0°, figure 2.1). The electron gun can also rotate out of the detection plane, (0°< psi <90°) to access non-coplanar geometries, with psi = 90° being termed the perpendicular geometry.

 


Figure 2.1: Schematic of the scattering geometry, depicting the various angles employed. A coplanar geometry (psi = 0¡) is defined when all three electrons are in the detection plane. The analyzer angles xi1. xi2 are measured with respect to the projection of the incident electron beam k0 onto this plane as shown. For non-coplanar geometries the electron gun is lifted out of the plane, and is defined by the angle psi. Psi = 90° is called the perpendicular geometry.

 

The two outgoing electron analyzers rotate independently in the detection plane as shown. The analyzer angles xi1 & xi2 are referenced to the incident electron beam direction. In this study the analyzers were always kept in a symmetric configuration with xi1 = xi2 = xi.

 

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. The coincidence energy resolution was typically ~1.3eV, sufficient to resolve the H2O 3a1 orbital from those at higher and lower binding energies, as shown in figure 1.3 above.

 

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 angular resolution of the apparatus is estimated as ±3°, based on geometric considerations of the electrostatic lenses at those energies.

 

2.2.1 Preparation of the water sample.

 

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 vessel was connected to the scattering chamber via 6.35mm copper tubing. A needle valve at the entrance to the scattering chamber controlled the flow of target H2O vapour into the interaction region.

 

The sample vessel and gas handling line were held at a constant temperature of 50¡C throughout data collection, so as to create sufficient driving pressure for the target beam. 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.

 

The purity of the target beam was verified with a Spectra VacScan mass spectrometer fitted to the scattering chamber. Typical operational ratios of H2O to N2 were > 25:1, and it was observed that the partial pressure of N2 did not change appreciably from the background value when the needle valve was opened. This indicates that an H2O target molecular beam of high purity was created, as confirmed from binding energy spectral studies. The purity of this beam was monitored regularly using the mass spectrometer throughout this study.

 

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. Over time the emission current from the filament dramatically increased, when a constant current was delivered to the filament. This increase in emission current was often more than a factor of 2 within a 24 hour period. To ensure constant incident electron beam current throughout the measurements as required, the filament current was hence also placed under computer control.

 

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. To illustrate the scale of these changes, over the duration of this study (~5 months) the filament current required to produce a beam current of 300nA reduced from 2.1A at commencement of these studies to less than 1.0A.

 

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 reason for the steadily decreasing filament current is hence unknown at this time.

 

All data were taken using a constant chamber pressure and constant beam current. 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 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.

 

2.3. Theoretical Framework

 

Details of the molecular 3-body distorted wave (M3DW) approximation can be found in J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 035201, as noted above.

 

2.4. Results and Discussion

 

2.4.1 Symmetric Coplanar Kinematics

 

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.

 


Figure 2.2: Triple differential cross sections for ionisation of the 3a1 state of H2O using coplanar symmetric kinematics. The energies of the outgoing electrons are shown on the respective plots. 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). The experimental and theoretical data has been independently normalised to unity at each energy.

 

The experimental data show the typical characteristics from measurements such as these.

 

  1. There is a strong binary peak at forward scattering angles (xi < 90°) and a recoil peak at backwards scattering angles (xi > 90°). 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.

 

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. This repulsion is called the post-collision-interaction (PCI).

 

  1. PCI would cause the binary peak to shift towards xi = 90° as seen. PCI would also be expected to shift the recoil peak towards xi = 90°, although this cannot be confirmed in the data. This trend is much clearer in the present data compared to that from the 1b1 state measured at higher energies.

 

  1. 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. This agreement diminishes as the energy increases, which is unexpected since the MDW model is usually more accurate at higher energies.

 

2.4.2 Symmetric Non-Coplanar Kinematics

 

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 = 90°) 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 value of the TDCS at xi = 90° is then used to re-normalize the remaining data. For the theoretical model, the coplanar TDCS has also been normalized to unity for both MDW and M3DW models. This scaling factor is then applied to all subsequent data sets at the various gun angles.

 

  1. 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 TDCS measured in the perpendicular plane is almost constant over all analyzer angles, which is very different to what is observed for atomic targets.

 


Figure 2.3. Triple differential cross sections for the ionisation of the 3a1 state of H2O. These measurements were taken in a series of symmetric non-coplanar geometries with outgoing electron energies of 10eV. The angle of the electron gun (psi) is shown on the respective plots. The data and theory are normalised to unity at the peak in the coplanar geometry. The data within the remaining plots are normalised at the 90° point.

 

  1. 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 progression in both models shows a decrease in cross section from psi = 0° to 45°, after which the intensity once again increases. The M3DW model follows a trend that is closer to the experimental data, although neither model accurately predicts the results that have been obtained.

 

2.4.3 Unequal Energy Sharing, Coplanar and Perpendicular Geometries

 

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. Figure 2.4a and 2.4b reproduce the data in figure 2.3 at these angles when E1=10eV and E2=10eV, figures 2.4c and 2.4d show data for E1=5eV and E2=15eV, while figures 2.4e and 2.4f show results for E1=2eV and E2=18eV. 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.

 


Figure 2.4. Triple differential cross sections for ionisation of the 3a1 state of H2O. Symmetric geometries were adopted for these data with unequal energy sharing kinematics. Both coplanar and perpendicular geometries were utilised. In all plots the excess energy is 20eV, with the outgoing electron energies as shown. The electron gun angle psi is also shown on the respective plots.

 

  1. 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. There also appears to be a narrowing in the main binary peak as the asymmetry increases, with a new shoulder appearing around xi = 60°. The minimum around 90° in this geometry does not change substantially as the energy sharing changes.

 

      In the perpendicular plane the experimental cross section becomes almost completely featureless at the highest asymmetry, although none of the data show any significant structure. This contrasts markedly with the calculations, which predict triple peaks in the perpendicular plane that change magnitude only marginally with the asymmetry.

 

2.5 Conclusions

 

       Experimental (e,2e) data for the ionization of water at low energies in both coplanar and non-coplanar geometries have been presented together with the results of theory.

 

  1. Agreement is mixed, and rather surprisingly gives best results at low energies, where it might be expected that the approximations are least accurate.

 

  1. For non-coplanar measurements the comparison becomes poorer as the gun angle increases. This discrepancy is seen both for equal energy and for non-equal energy data, which have been taken in coplanar and perpendicular geometries.

 

  1. 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.

 

Acknowledgements

This work was supported by the University of Manchester and the US National Science Foundation under Grant. No. PHY-0757749. Dr Kate Nixon thanks the British Council for funding under the research exchange programme, and the Royal Society for a Newton International Fellowship.

 

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