Super-elastic Electron Scattering Studies using a

Magnetic Angle Changing (MAC) Device

Page constructed by Andrew Murray

This page describes the super-elastic scattering studies that are being conducted in Manchester.

Useful papers in this area from members of the group:


The purpose of this page is to detail for the interested reader the Super-elastic electron scattering experiments which have been conducted in the

  1. Atomic, Molecular & Laser Manipulation Group, School of Physics & Astronomy, Schuster Laboratory, Manchester University, Manchester, M13 9PL, United Kingdom.

Although there is an implicit assumption that the reader has a familiarity with these experiments, it is not completely necessary to enjoy this page and the associated pages that accompany this home page.

For those who are interested, numerous papers are available on this subject, including those in which we have been associated. The papers from members of the group are shown above.

The references found in these papers give a good appreciation of the work that has been done in this area from different groups around the world.

Overview of Inelastic Scattering Experiments

Most detail about inelastic collision process is obtained from COINCIDENCE measurements.

Experiments catch SINGLE electron which excites SINGLE atom, then look for time-correlated PHOTON emitted from this atom.

Measure this many times to build up a picture of the excited atom

COINCIDENCE Measurements - Inelastically scattered electron measured as function of scattering angle

FIG 1. The coincidence experiment showing the scattering geometry and position of detectors.

Information on state of atom obtained from Fluorescence Polarization

Complete Description of excitation obtained by measuring polarization of photon in coincidence with scattered electron.

This allows us to Fully Characterise Atomic state (ie measure it's 'shape')

Note Coincidence technique slow as have to wait for photon correlated to detected electron (ie if photon is emitted in direction where detector is not positioned, there is no correlated photon for detected electron).

- Alternative Method - 

What if we Run experiment backwards in time?  (?emit ni sdrawkcab tnemirepxe nuR)


Superelastic Scattering using Laser Prepared Atoms

FIG 2. The superelastic experiment showing the scattering geometry and position of lasers and detectors.

Atomic Collision Parameters


Lperp = angular momentum orthogonal to scattering plane.


Plin, gamma = alignment of P-state in scattering plane.


 Ptot = degree of polarization.

Note laser photon is ALWAYS in same direction!!

Only have to wait for a super-elastically scattered electron 

Don’t have to wait for both electrons & photons!

Get same information as with coincidence technique by varying laser polarization in 3 steps, not 4. Hence the xxperiment produces data 102 - 106 times faster than the Coincidence Method!

We can therefore measure very small signals at high scattering angles.

Obviously this is a very attractive method for producing data! So what are the disadvantages?

    1. Need very well controlled laser system.

We use a Coherent MBR-110 Ti:Sapphire laser, MBD-200 external Doubler and a 10W Verdi Pump laser to produce radiation with a bandwidth of 1 part in 1010!

Laser output:

1.5W (Ti:Sapphire)   ~150mW (MBD-200)

TEM00 mode  (Ti:Sapphire)   ~ (MBD-200)

Linewidth: 100kHz (Ti:Sapphire)

    2. Need an atom that can be excited by the Laser Beam!

In present studies we choose Calcium as it can be excited by our laser system at a wavelength of ~423nm.


Calcium is Good for our teeth & bones!


Calcium also looks a bit like Helium – It has 2 electrons in outer shell, so models which assume a 'frozen' core may be applicable.

FIG 3. Simple representation of Helium and Calcium showing the similarity between the systems ((assuming frozen core approximation).

This means that models that work for the simpler atom (Helium) might also be applicable for Calcium, which actually has 20 electrons!

Also, the Energy Level structure of Calcium is simple (which makes it easy to theoretically model the laser-atom interaction)

FIG 4. Excitation of Calcium at ~423nm, showing the electron energy levels and the states excited by different laser polarizations.

Note that the structure is very simple for this excitation (no hyperfine structure).

So why do scattering experiments in a Magnetic field?

Conventional apparatus limited in angular range by physical size of electron gun and analyser

FIG 5. Conventional electron spectrometer from above, showing restricted angular range.

Application of Magnetic Field allows measurements to be conducted over the complete scattering plane, since incident and scattered electron trajectories can be ‘steered’ by the B-Field.

FIG 6. Trajectories of electrons in MAC field, with a B-field of 20 Gauss for an Electron Energy of 45eV

By using the Magnetic Angle Changer (MAC device) in an electron spectrometer, a FULL comparison with theoretical models can therefore be made for first time over the complete scattering plane!

FIG 7. Excitation of Calcium in a B-field, showing the Zeeman split energy levels and the states excited by different laser polarizations.

Application of Magnetic field complicates Laser Interaction due to Zeeman Splitting of energy levels

However, new model of the interaction has been developed to allow for this effect.

The New Magnetic Angle Changing (MAC) Spectrometer developed at Manchester.

FIG 8. Figure of the new spectrometer at Manchester.

FIG 9. Photograph of the new spectrometer which has been developed at Manchester.

FIG 10. Photograph of Excitation of Calcium Atoms between MAC coils using radiation at 423nm

Experiments have now been carried out from 55eV down to 17eV equivalent Incident Energy.

FIG 11. Example of results for equivalent coincidence Incident Energy of 45eV, showing the regions of inaccessibility (the MAC was not used for these experiments).


FIG 12. Movie of the shape of the charge cloud as calculated from theory (quicktime movie).

The MAC device is now being used to measure the shape of the atoms created by electron excitation over the full scattering geometry.

Experimental results will be shown soon!