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A Toroidal Spectrometer for Photoionization StudiesJ Wightman1, S Collins1, G Bagley1, G Richmond1, C Dawson1, S Cvejanovic1, D Seccombe2, and T Reddish2

1 Physics Department, University of Newcastle, Newcastle upon Tyne, U.K., NE1 7RU2 Physics Department, University of Windsor, 401 Sunset Ave, Windsor, Ontario, Canada, N9B 3P4.

†Email: reddish@uwindsor.ca Web-Site: http://zeus.uwindsor.ca/courses/physics/reddish/TJRWelcome.htm

IntroductionToroidal Photoelectron Spectrometer

We have developed a photoelectron-photoelectron multi-coincidence spectrometer in which the two electrons, of specified energies, are detected over a wide range of emission angles. The spectrometer based on a toroidal geometry, which has properties ideally suited for measuring electron angle distributions. Toroidal analysers have the capability to energy select the photoelectrons while preserving the initial angle of emission. As a direct consequence of their focusing properties, the angular distribution of the electrons is mapped directly on to the detector. A schematic diagram of the apparatus is shown, indicating the relative orientation of the two partial toroidal analysers and their respective detectors. The electrostatic analysers are independent, i.e. they are able to detect dissimilar electron energies, with different resolutions. Electrons emerge from central interaction region defined by the intersection of the photon and gas beams. Photoelectrons emitted in the plane orthogonal to the photon beam that enter the analysers are focused at the toroidal entrance slit. Electrons of a specific energy traverse the gap between two toroidal surfaces to the exit slits of each analyser. The exit lenses accelerate and re-focus the energy-resolved electrons to their respective two-dimensional position-sensitive detectors. The final images are circular arcs in shape (with circle centres on the photon axis), in which the position around the perimeter is directly related to the initial azimuthal photoelectron emission angle. This emission angle is of course relative to the light polarisation direction.

The multi-coincidence capability can be realised as electrons arriving anywhere on one detector can be correlated with electrons detected simultaneously anywhere on the other detector. This enables independent angular distributions to be measured concurrently. This capability is one of the novel features of the apparatus and is a great asset in compensating for the small photodouble ionization, (,2e), cross sections.

Gasinlet

Photonbeam

Photodiode100 (60 ) analysero o

180 (140 ) analysero o

Electron Lenses(Left) A scale diagram showing the entrance lenses and target region in the spectrometer in the radial - or energy-dispersive - plane. In the diagram, the photon beam enters the interaction region from above and the flux is monitored with an aluminium photodiode. The entrance lenses are the slits formed by a series of coaxial cylindrical surfaces of increasing radii. The acceptance angle in the radial plane is 8 and the slit width variation among the lens elements is also shown.

(Right) A scale diagram of the exit lens which transports the angle-dispersed, energy-resolved electrons from the exit of the toroidal analyser to the two-dimensional position-sensitive detector. The elements are formed from slits in the curved surfaces on a series of co-axial cones and the electron beam impinges on the first of two microchannel plates at an angle of 52 to the normal.

T h e o r y3D GeometryCharacterisedby:

Cylindricalradius a,Sphericalradius b, and Deflection Angle .

In principle, toroidal analysers can be

made to focus simultaneously in

both in energy and angle.

Toroids are the ‘topological link’ between hemispherical(c = 0) and 127 cylindrical (c = ) analysers

Toffoletto et al, Nuc Inst & Meth B12 (1985) 282-297.

Cylindrical Radius a

(Electron Lenses not shown)

Energy-Dispersive Preserves Angular Information

Design Notes:

      Entrance / Exit Lenses – Cylindrical / Conical Symmetry

      Require ‘small’ interaction region –relative to ‘cylindrical radius’

      Electric field termination – lenses and toroids

      Needs rigorous 3-D mechanical alignment!

       Rejection of metal-scattered electrons

       Requires calibration (angular scale and efficiency)

Interaction Region

Spherical Radius b

b

a

c = a / b

0.01 0.1 1 10 10080

100

120

140

160

180

200

Toroidal Focusing

ConditionsDeflectionAngle () "Point-to-Point"

(Energy-Dispersive)

"Parallel-to-Point"(Angle-Dispersive)

C Ratio

Figure 1 A schematic diagram showing the configuration of the two (partial) toroidal analysers along with lines indicating central trajectories of electrons with a selection of emission angles. (The electron lenses are not shown for reasons of clarity).

Figure 2: The mechanical acceptance angles within the perpendicular plane are 100 and 180, but these are reduced to 60 and 140 respectively, due to electric field termination effects within the electron optics. The acceptance angle out of the perpendicular plane is ~8.

Reddish et al Rev. Sci. Instrum. 68 (1997) 2685 Multilayered Conical Gas Jet

Photons

Interaction Region

HypodermicNeedle

Gas Flow

(a) PerpendicularGeometry

InteractionRegion Gas Flow

(b) 'Coaxial' Geometry

Conical Gas Inlet

Photons

Gas Flow

Problem: Hypodermic needle not perpendicular to the detection plane.

 

Solution: Gas jet coaxial with photon beam. However, larger surface area of metal- hence the potential for more background

noise.

Central hole =4mm3 Layers - 90 grooves

Each 0.25mm wide and ~25 mm long, with tilt angles of: 55, 45

and 35 for layers 1-3.

Gas focuses at 2-3mm away

from exit face.

Seccombe et al (2001) Rev Sci Instrum 72 2550

Photoelectron Angular Distributions The differential cross section in perpendicular plane with S2 = 0 is:

a) determine the degree of polarisation of the light source,

b) determine the angular extent of the imagec) derive a normalisation curve, for each

photoelectron energy, to correct the beer

Red Analyser Angle

Blue Analyser Angle

•Energies of detected electrons set by

spectrometer (calibrated by other methods).

•Angles given by position around the

perimeter of circular arc-shaped images.

•Grid size determined after the experiment –

subject to available statistics.

•Angular scale and efficiencies are

determined

and applied to the data.

Angular map of Raw Coincidence Data

E1, x1, y1, E2, x2, y2, and t recorded

at each photon energy.

True coincidence count rate: 

He ~ 1s-1 , D2 ~ 1min-1

(integrated over all angles) 

0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

cos2 3S+14

)(+1

4

(E)

d

d1

E = +2 = 0 = -1      

S1 = +1

where (E) = Asymmetry parameter (-1 +2), andS1 is a Stoke’s parameter giving the degree of linear polarization. He+ n = 1 state has a of 2 for all photoelectron Energies (i.e: cos2 distribution). He+ n = 2 state has variable , and acts as important consistency check.

Measurements are made regularly throughout the data collection process and are used to:

Data from: Wehlitz et al J. Phys. B., 26 (1993) L783

measured spectra for the differences in detection efficiency as a function of emission angle.

Electron-Electron Coincidences

Detector Images and Coincidence Peak

Image fromthe small

(60 - red) analyser

Image from the large (180 - blue)

analyser

24.9 25.0 25.1 25.2 25.380

90

100

110

120

130

140

150

160

170

180

190

Ang

le (

degr

ees)

Photon Energy (eV)24.9 25.0 25.1 25.2 25.3

80

90

100

110

120

130

140

150

160

170

180

190

Ang

le (

degr

ees)

Photon energy (eV)

24.9 25.0 25.1 25.2 25.3

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Bet

a P

aram

eter

Photon Energy (eV)

24.9 25.0 25.1 25.2 25.3

0.5

1.0

1.5

2.0

Bet

a P

aram

eter

Photon Energy (eV)

Photoelectron angular distributions from single ionisation processes can be imaged directly on a position-sensitive detector.

     Toroidal analyser gives‘simultaneous’ view of physicallyuseful angular range.     Record angular image whilescanning photoelectron energy.

Angular distribution surface plots. The strong variations in the distributions are due to resonance interference, which are also shown in the more usual parameter form.

Wightman et al J. Elec. Spec. 95 (1998) 203

Angle-Dispersed Photoelectron Spectroscopy

Kr+ 2P3/2Kr+ 2P1/2

He D2

Photodouble Ionization of Heliumand D2 with E1 = E2 = 10eV, S1 = 0.67

Characteristic two lobes with node at 12 = .

1 = 132°

1 = 98°

The results obtained have extended our theoretical understanding of fundamental processes in atomic and molecular physics and are providing stringent tests for emerging theories

Reddish et al Phys Rev Letts (1997) 79 2438,

Wightman et al J Phys B (1998) 31 1753

Seccombe et al J Phys B 35 (2002) 3767

Funding Agencies:

Graduate Students Working on Project