Charge Cloud Movies

Charge Cloud Movies of Collisionally Excited States (1999–2001)

David Loveall, Melissa Hamley, Bruce Miller, and Klaus Bartschat

This page was created as part of a Research Experience for Undergraduates (REU) project. This project was undertaken in the Department of Physics and Astronomy at Drake University. It was funded by the National Science Foundation under grant PHY-9605124.

The goal of this project was the visualization of charge clouds representing collisionally excited atomic states. A small sample movie for a D-state is shown at the bottom of this page. The idea is based upon various reviews by Andersen and collaborators [1-4] who made a strong case for parameterizing such states in terms of observables that are directly related to the charge cloud representing the active electron(s), such as the length, width, and height, as well as the alignment angle. These parameters can be measured in electron–photon coincidence experiments, and they can be calculated from complex quantum mechanical scattering amplitudes or state multipoles.

We have been working on the fine-tuning of the graphs, the generalization to spin-dependent cases and the possibility of partly incoherent excitation (as in angle-integrated light polarization measurements), and situations where the coherence is partly destroyed by not performing a truly complete experiment. An example for the latter is S -> D excitation in which the D -> P photon is observed in coincidence with the scattered projectile, but the P -> S cascade photon is not detected [4]. This work was presented at the APS Centennial Conference in March of 1999. We also prepared a manuscript [5] in which the code was made available to the general public.

1. N. Andersen, J.W. Gallagher, and I.V. Hertel, Phys. Rep. 165, 1 (1988).
2. N. Andersen, J.T. Broad, E.E. Campbell, J.W. Gallagher, and I.V. Hertel, Phys. Rep. 278, 107 (1997).
3. N. Andersen, K. Bartschat, J.T. Broad and I.V. Hertel, Phys. Rep. 279, 251 (1997).
4. N. Andersen and K. Bartschat, J. Phys. B 30, 5071 (1997).
5. D. Loveall, M. Hamley, B. Miller, and K. Bartschat, Comp. Phys. Commun.  124, 90 (2000).

Note that the code submitted to CPC was tested under Mathematica 3. After testing with Mathematica 4, there are a few minor changes that need to be made to the code in order to work properly. At various points in the program, numbers of the form (a+bi) where b is extremely small were “chopped” to real numbers automatically by Mathematica 3. For running under version 4, one needs to add a “Chop” command to areas where this is not done (any problem areas).

You can read an article published on us (with a picture) by Update – Alumni News of Drake University here.

The first set of movies below are for electron impact excitation of Helium (1s2p) singlet state at an incident electron energy of 30 eV and (1s3d) and (1s4f) singlet states at an incident electron energy of 40 eV. The scattering angle (0-180 degrees) has been converted into a time step.

The second set of movies below are for electron impact excitation of Mercury (6s6p) triplet P (J=1) at an incident energy of 8 eV. There are cases for unpolarized electrons as well as in-plane transversally polarized electrons. In the latter case, the planar symmetry of the process is broken and, consequently, the charge cloud can not only rotate in the plane, but also twist and tilt out of the plane. To see the entire cloud below and above the scattering plane, select the “without Scattering Plane” movies.

The third set of movies below are for electron impact excitation-ionization to the final ionic state He^+(2p). The kinematics are:

incident energy of fast electron: 1585 eV
exit energy of fast electron: 1500 eV
scattering angle of fast electron: 4 degrees

exit energy of ejected electron: 20 eV
angles of ejected electron:
in plane:       0-360 degrees (counting to the right) in the plane
out of plane:   0-360 degrees (counting to the right) plus 45 degrees out of plane

Here are the links for some different graphs:

Excitation of He at 30 & 40 eV
P State
D State
D State (one-photon angular distribution)
F State

Excitation of Hg at 8 eV
P State Unpolarized Electrons
P State In-Plane Transversally Polarized Electrons

Excitation-Ionization of He at 1500 eV

In the Plane
Out of the Plane

Ion-Atom Collisions
Li-Na Density
Li-Na Current