ELECTRON SCATTERING FROM ATOMIC TARGETS

Principal Investigator: Dr. M.A. Khakoo
Cal State Fullerton

[1] Electron Scattering from Helium

[a] Electron-Photon Coincidence Measurements in Helium

Undergrads involved: David Roundy, Felix Rugamas, Gary Yeakley, Elizabeth Bubion

We have measured ratios of Differential Cross-Sections (DCSs) ratios for the electron-impact excitation of the 11S » 21P / 11S » 31P and 11S » 21P / 11S » 41P transitions. We employ a cascade-resolved method using UV emitted-photon detection in coincidence with the energy-loss identified scattered electron. There ratios were converted into qualitative DCSs for the 11S » 31P and 41P transitions using available quantitative DCSs for the excitation of the 11S » 21P by electron impact.

Papers:
M. A. Khakoo, D. Roundy and F. Rugamas Phys. Rev. Letts. 75, 41 (1995) [PDF]
-ibid. Phys. Rev. A 54, 4004 (1996) [PDF]

Electron-photon coincidence spectra from the excitation, from the ground state, of the n=3 and n=4 manifold of levels of He, by electron impact. Convoluted integral fits to the data (green lines) are used to extricate the various decaying photo- emission routes from the excited-states to the ground state.

Red - Present Data
Green Lines - Convoluted integral fits to data

DCS ratios  and DCS Ratios for the electron excitation of the 11S » 21P / 11S » 31P and 11S » 21P/ 11S » 41P  transitions in He. The DCSs are obtained through normalization of the ratios to well-established experimental 11S » 21P DCSs. The incident  electron energy =40eV.

Red - Present Data
Solid Line - Convergent Close-Coupling
Small Dashes - First-Order Many-Body Theory
Long Dashes - Distorted- Wave Born Approximation

The R-Matrix is not shown here, but it does not give good agreement with experiment, even at low energies.

[b] Electron Impact Ionization of He- Doubly differential cross-sections

We have used our moveable target source method to measure doubly differential electron scattering cross-sections for impact energies from near threshold to about 15eV above threshold. Our results have been recently accepted for publication in Phys. Rev. A.

A typical result at 28.25eV and 30eV shows that the present data are an improvement over earlier results (Roder et al. and Pichou et al.), but only in good agreement with the CCC of Igor Bray and Dmitry Fursa. Our error bars are a bit large in the 20-25% range. We intend to reduce these to 15-20% in future experiments. However, the measurements involved heavy data analysis of a large number of continuum-discrete spectra.

What has interested theorists are our Single-Differential Cross-sections which do not indicate the smile at the edges of the energy distribution that is obtained by the CCC theory.

Electron Impact Ionization of He – Doubly Differential Cross-sections, E. Schow, K. Hazlett, C. Medina, G. Vitug, J. G.Childers, I. Bray, D. V. Fursa and M. A. Khakoo

 

[2] Electron Scattering from Atomic Hydrogen

Undergrads involved: Bryan Paolini, Mike Larsen.

[a] Initial Investigations

We have made measurements of the DCSs for excitation of the H (12S » 22S+22P) transition over a range of incident energies from 30eV to 100eV) and for scattering angles from 10° to 127°. These DCSs showed excellent agreement with the Convergent Close-Coupling theory of Bray and Stelbovics, 1994. The method of mixtures with He was used to obtain accurate H DCSs, and we used the  n=1 » n=2 DCSs in He as a calibration standard.

Electron Energy Loss Spectrum of a H and He mixture.  The H (n=2) feature’s line intensity was normalized to that of the He (21S+23P+21P) line intensity, to obtain relative DCS for H (n=2) feature. The absolute DCSs for H (n=2) were determined by measuring the H/He mixture composition using theory at 200eV and 25 ° scattering angle.

DCSs for H (n=2) electron excitation of the levels at 100eV impact energy.  Experimental results are drawn with error bars. Theoretical and previous experimental data are shown.


Papers: M.A. Khakoo et al, Phys. Rev. Letts. 82,20 (1999) [PDF]

[b]  Electron Impact Ionization and Excitation of H

Electron impact ionization of H was carried out at low energies (1eV above threshold) to measure quantitative doubly differential cross-sections using a novel moveable target beam method. The results (obtained in a direct determination of a pure e+H spectrum) showed very good agreement with the Exterior Complex-Scaling and Convergent Close-Coupling models. This is very nice, because for ionization at low energies for this basic target, theory and two models show excellent agreement in many cases.

Electron Impact Ionization of Atomic Hydrogen, J. Childers, K. James, M. Hughes, I. Bray, M. Baertschy and M. A. Khakoo, Phys. Rev. A: Rapid Communications, A 68, 030702R (2003)

Low Energy Electron Scattering from Atomic Hydrogen I: Ionization, J. Childers, K. James, M. Hughes, I. Bray, M. Baertschy I. Kanik and M. A. Khakoo, Phys. Rev. A 69, 022709 (2004)

Low Energy Electron Scattering from Atomic Hydrogen II: Elastic and Inelastic Scattering, K.E. James, J. Childers, M. Hughes, I. Bray, M. Baertschy and M. A. Khakoo, Phys. Rev. A 69, 022710 (2004)

First published Eenergy loss spectrum of pure H at 17.6eV incident energy and at 30o scattering angle


Energy Loss spectrum of H at 40eV incident energy at 30 degree scattering angle


ECS (Baertschy et al., (Tom Rescigno, Bill McCurdy, the Bay Area wizards)

CCC (Igor Bray, Andris Stelbovics and Dmitry Fursa, the theory Aussies)

 

Additionally, our elastic and excitation n=3,4 DCSs clearly resolve important discrepancies existing in the literature regarding these DCSs in the past.

DCSs for excitation of H(n=3,4). The triangles are Shyn’s group in Ann Arbor (2001). The dots are our results. To see our resolution of disagreements for inelastic scattering, see Childers et al (2004) paper II.


[3] Electron Scattering from the Rare Gases

Measurements of the electron energy loss spectra of the excitation of the lowest …np5 (n+1)s  configuration of Ne to Xe have been made in collaboration with JPL (Drs. Isik Kanik and Sandor Trajmar). However, at CSUF we have focused on the use of DCS ratios to provide a stringent test of theoretical models (both in the solution of the scattering Hamiltonian as well as in the target wavefunctions used). Our simple test was probably one of the first to alert our confident theorists that some of their target structure codes need medication. We thank many theorists for addressing this problem: Klaus Bartschat (Drake, IA) Chris Fontes (LANL) and Don Madison and Alan Stauffer/ Rajesh Srivastava (York, Canada and Roorkee, India).

DCS ratios for excitation of the first four levels e.g. of Kr are defined as follows:

The 4p55s levels in Kr can be expressed in the simplified intermediate-coupling scheme  (Cowan, 1981) within the single configuration restriction as:

|5s[3/2]2> = |5 3P2>
|5s[3/2]1> = β |5 1P 1> - α |5 3P1>,
|5s’[1/2]0> = |5 3P0>  and
|5s’[1/2]1> = α |5 1P1> + β |5 3P1>.

Here a and b are the intermediate-coupling (unitary) mixing coefficients.

A listing of these α and β, intermediate-coupling (unitary) mixing coefficients, can be found in the following publication.

Papers: Khakoo, Beckmann, Trajmar and Csanak, J. Phys. B, 27, 3159 (1994) [PDF].

The DCS ratio r considers excitation to optically-forbidden levels excitable only via spin-exchange, in the above coupling scheme. In the limiting case of degenerate fine-structure levels (Khakoo, 1992) and where spin-orbit interactions are absent, r should attain its LS coupling limit of 5, i.e., the statistical weight ratio of the respective levels, with J = 2 and J = 0. Complementarily, r’ considers excitations to the optically-allowed J=1 levels. However, these allowed levels have mixed triplet-singlet character. In the optical limit (high incident electron energy and small scattering angle), application of dipole selection rules easily reveal, within this single-configuration coupling scheme, a limit for r’:

Lim r’ = β2/ α2

Deviation from the optical limit could indicate the importance of the triplet part of the J = 1 components or additional singlet levels which are needed to describe these mixed levels.

We started out with Xe, hoping to test theory, and then to Kr hoping to get better agreement with theory. In both cases, we find unsatisfactory agreement with theory.

The results of the Kr and Xe work may be found in:
Xe: Khakoo, Trajmar, LeClair, Kanik, Csanak and Fontes, J. Phys. B, 29, 3455 (1996) [PDF]
Kr: Guo, Khakoo, Mathews, Mikaelian, Crowe, Kanik, Trajmar, Zeman, Bartschat and Fontes, J. Phys. B, 32, L155 (1999) [PDF]
Kr letter: -ibid J. Phys. B, 33, 1895 (2000) [PDF]

Recently, we have investigated Ne in a similar way, but the results are over a very large energy range. For Kr and Ne all experimental work was done at CSUF. Agreement with the UFOMBT and the Rmatrix (semi-relativistic) found to be greatly improved, over Kr, Xe, but still unsatisfactory.

Ne:electron Impact Excitation of the 2p53s configuration of Neon, M. A. Khakoo, J. Wrkich, M. Larsen, G. Kleiban, I. Kanik, S. Trajmar, M. J. Brunger, P.J.O. Teubner, A. Crowe, C.J. Fontes, R. E. H. Clark,V. Zeman, K. Bartschat, D.H. Madison, R. Srivastava and A. D. Stauffer, Phys. Rev. A 65, 062711 (2002).

Below are some examples of our measurements at 30eV.

DCSs for excitation of the summed 2p53s config. levels of Ne.Expts:
Open circles are present data;
Crosses are Register et al. (1984) at JPL; 
Triangles are the DCSs of Brunger (& Teubner) (Brunger’s thesis) at Flinders. 

Agreement with ours and Brunger’s DCSs is found to be excellent across the entire set of data taken.

Theories:
Solid red line is RM of Bartschat (unpublished)
Dashed mauve line is the UFOMBT Theory of Fontes and Csanak (Los Alamos).
Dashed green line is the Unitarized Distorted-Wave Theory of Fontes and Csanak (Los Alamos)

DCS r’ ratios for Ne.Expts:
Open red circles are present data;
Crosses are Register et al. (1984) at JPL.
Not shown are earlier CSUF/JPL data  (1994) which are in excellent agreement  with experiments.


Thus we see that Ne shows more agreement with theory than Xe or Kr (agreement with theory is reasonable for the UFOMBT at small scattering angles) but overall improvements are yet needed.


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