Large-angle scattering of energetic electrons from Xe: A combined theoretical and experimental approach

We study the inelastic excitations of Xe for electrons with relatively high energies (500 or 750 eV) scattered over large angles, both experimentally and theoretically. In particular, we focus on the shape and intensity of the spectra of inelastically scattered electrons at the sharp dip in the elastic cross section near 135${}^{\circ }$ at 750 eV. Under these conditions, the first Born approximation predicts virtually zero intensity. However, in reality, measurable intensity is observed. Calculations carried out using the relativistic distorted-wave method describe the measurements reasonably well. A comparison is made between the calculations and previously published high-resolution studies. Overall agreement is quite good, especially for the lowest-energy excitations, but substantial differences are found for certain higher levels. The theory reproduces quite well the variations in intensity of the inelastic excitations for measurements near the dip in the elastic-scattering cross section, somewhat surprisingly, as the theories for elastic scattering and inelastic scattering are developed along completely different lines.

Figure 1

Schematic working of the deflectors. Without the deflectors the electron trajectory follows the solid line, with deflector voltages applied it follows the dotted line. A1 and A2 denote apertures 1 and 2; D1 and D2 denote deflectors 1 and 2; F.C. denotes Faraday cup; A denotes analyzer.

Figure 2

Comparison of the 500-eV spectra, taken for a scattering angle of 5.1${}^{\circ }$ as measured by Suzuki et al. [13] with the RDW present theory.

Figure 3

The intensity of the 6$s$, 7$s$, and 5$d$ levels as a fraction of the elastic peak intensity for 500 eV electrons scattered from Xe. The experimental data are from Suzuki et al. [7, 8], and the theoretical values are from the theory described here. Note that the $J=1$ transitions are sharply forward peaked, in contrast to the $J=3$ transitions.

Figure 4

Comparison of the 500-eV spectra, taken for a scattering angle of 90${}^{\circ }$ as measured by Urpelainen et al. with the present theory. Vertical scale of the experiment is arbitrary. The vertical scale of the theory is chosen in such a way that for nonoverlapping peaks the spectrum height corresponds to the differential cross sections in atomic units (a.u.).

Figure 5

Comparison of the 500 eV spectra, taken for a scattering angle of 90${}^{\circ }$ with a spectrum generated from the output of the ROP code (elastic peak) and RDW code (inelastic excitations). The experiment and theory are normalized on equal peak height for the elastic peak.

Figure 6

Comparison with theory of the 750 eV spectra, taken for scattering angles of 45${}^{\circ }$ and 90${}^{\circ }$. The vertical scale is normalized to the elastic peak.

Figure 7

A comparison of the elastic peaks (in arbitrary units) of a Xe-H${}_2$ gas mixture as a function of the scattering angle (left panels). The peak near 0 eV energy loss is associated with electrons scattered from Xe, the peak near 1.5 eV is due to electrons scattered from H. The right panels show the inelastic signal for pure Xe under these conditions and this is compared with calculations. Theory (in a.u.) and experiment are normalized using the calculated and measured elastic peak strength. See the main text for discussion of the offset in theoretical angle.

Figure 8

A comparison of the elastic differential cross section of 750-eV electrons as calculated using the ROP [10] and elsepa [17] programs (both with absorption) in the angular range corresponding to a pronounced dip in the elastic cross section. The experimentally obtained ratio of H and Xe elastic peak strength is shown as well (dots).

Figure 9

The calculated DCS for elastic scattering and several inelastic channels for 750-eV electrons in the angular region of the pronounced dip in the elastic DCS.