CSUF Physics - Dr Murtadha Khakoo

ELECTRON SCATTERING FROM MOLECULAR TARGETS

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

[1] Electron Scattering from H₂

Using our high resolution spectrometer, we have made new measurement of the electron impact excitation of the states in the energy loss region from 11 to 14eV. The states are the B, C, a, c and E/F states. We have made good progress in this area as compared to our earlier measurements of 1986 (Khakoo and Trajmar, 1986). We have generated our own Franck-Condon factors from numerical solution of the H₂ potential obtained by Kolos and Wolneiwicz and coworkers.

However, we have a more sophisticated fitting routine to unfold the H₂ spectrum.

Using these tools, we have preliminary DCSs as are shown here.

This plot depicts Electron Energy Loss spectra of Molecular Hydrogen taken at 30eV Incident Electron Energy and several scattering angles.

Note the clearly observable change in the spectra due to increasing presence of the a and c dipole- forbidden features.

Below we see the DCSs for electron impact excitation of the B¹Σ_g⁺, C¹Π_u, c³Π_u, E,F¹Σ_g⁺, a³Σ_g⁺, and e³Σ_u⁺ states of H₂ taken at E₀=30eV and compared with other experimental and theoretical work.

Experiments
Red Circles - present work with error bars
Grey Circles - Khakoo and Trajmar (1986b)
Green Triangles - Srivastava and Jensen (1977)

Theories
Purple Line - Fliflet and McKoy (1980)
Blue Line - Lima et al (1988)
Black Line - Parker et al (1991)

Papers:
J. Wrkich, D. Mathews, I. Kanik, S. Trajmar and M.A. Khakoo, J. Phys. B, 35, 4695 (2002) [PDF]

[2] Electron Scattering from N₂

[a] Initial Investigations

Similar to H₂, we have finished some low energy work with N₂ in collaboration with the Jet Propulsion Laboratory.

Preliminary DCSs were measured for the four most intense electronic states (viz. the A³Σ_u⁺, B³Π_g, W³Δ_u and a¹Π_g states) of N₂ at 10, 12.5 and 15eV incident electron energies using energy loss spectra taken in the region of 6.7eV to 9.85eV energy loss.

Results for 12.5eV are shown below along with the previous results of Zetner and Cartwright/Trajmar. As can be seen, the Khakoo and Zetner results are in excellent agreement.

This figure shows an unfolding of the electron energy loss spectrum of N₂. The unfolded states are stacked up above in order of increasing energy loss.

The bottom graph (red) shows the composite results of our experimental data and the overall fit to this data.

[b] Further Investigations

We have recently re-measured these cross-sections with improved energy resolution for a wide range of energies from 10eV to 100eV and scattering angle up to 130 degrees, in 5 degree intervals.

Two spectra are shown below. These were unfolded using Franck-Condon factors (as before) except that the results were check carefully against available time-of-flight absolute DCSs and also used the moveable source.

The data are published in the following article.
Differential cross sections for the electron impact excitation of the A ³ Sigma ⁺_u , B ³ Pi _g , W ³ Delta _u , B^' ³ Sigma ^-_u , a^' ¹ Sigma ^-_u , a ¹ Pi _g , w ¹ Delta _u , and C ³ Pi _u states of N₂ (2005), M. A. Khakoo, P. V. Johnson, I. Ozkay, P Yan, S Trajmar, and I Kanik, Phys. Rev. A 71, 062703, (2005)

Sample electron energy loss spectra of N2 taken at 15eV for two scattering angles.

In the left spectrum, the energies and relative vibrational intensities of the electronic-vibrational manifolds are shown.

The a ¹ Pi _g state which gives rise to the Lyman-Birge-Hopfield bands dominates the low angle spectra, but is overcome by the other forbidden transitions from the ground state. All transitions here are non-dipole.

Some of the DCSs obtained from our data (this is about 3% of our data). Agreement with the previous tabulated data of Zetner and Trajmar remains good (their data were taken at 15eV).

We are now investigating the excitation of higher-lying Rydberg-Valence levels of N2 (e.g. for the b,c,o 1Pu levels, which are strongly dipole-coupled to the ground state, and produce prominent VUV lines observed in space. The degeneracy between these levels cause perturbative interactions to mix these states, with the result that the excitation of these states has coherently mixed scattering amplitudes which interfere. Thus Franck-Condon factor unfolding is not applicable here. The apparent Franck-Condon factors (to loosely term them) fluctuate wildly in some cases. So e.g. for the b(6) excitation we see the following.

Intensity of the b(0) excitation as a fraction of the summed b(v) spectrum, for 30eV electrons.