Fast-electron scattering from Ne: A comparison of distorted-wave theory with experiment

We compare electron-scattering data from Ne with first-order Born and distorted-wave calculations in an energy range between 300 and 2500 eV and for scattering angles up to 135${}^{\circ }$ and for energy losses up to the ionization energy. At small angles the distorted-wave calculations and first-order Born calculations are in good agreement, but at large momentum transfer the intensity predicted by the first-order Born theory drops off much faster than the experiment and distorted-wave calculations. The present distorted-wave calculations reproduce most of the experimental observations quite well, except for monopole transitions and near the minima in dipole-allowed $s$-to-$p$ transitions. The first-order Born approximation fails completely at larger momentum transfer.

Figure 1

Generalized oscillator strength as calculated using the first-order Born approximation (dashed line) and RDW theory (solid line) for an energy of $E_0=2500$ eV. Examples of a dipole, quadrupole, and monopole transition are given. For the latter the outcome of the theory depends greatly on whether one uses the DCS1 scheme or DCS2 scheme, as explained in the main text.

Figure 2

Dots: Spectra taken at 45${}^{\circ }$ for the energies as indicated. Line: Corresponding calculated spectrum based on the theory described here, convoluted with a Gaussian representing the experimental resolution.

Figure 3

Same as Fig. 2, but now for a scattering angle of 90${}^{\circ }$.

Figure 4

Same as Fig. 2, but now for a scattering angle of 135${}^{\circ }$.

Figure 5

Spectra of Ref. [7] compared with the current theory based on the DCS1 scheme. The theory was convoluted with a Pearson-IV distribution describing the spectrometer energy resolution function. Experiment and theory are normalized using the first-loss feature.

Figure 6

Top panel: The DCS for the $3s{[3/2]}_1$ transition as measured by Cheng et al. compared with the present RDW theory. The theory agrees with experiment for small scattering angles, severely underestimates the experimental cross section around 7${}^{\circ }$, but appears to approach the experimental values again for the largest angle. Lower panel: The same tendency is seen for the 2250 eV measurement taken from [13] for the combined $3s{[3/2]}_1$ and $3s{[1/2]}_1$ transition based on measurements done at the ANU and McMaster University. Here the measured and calculated intensity is plotted as a fraction of the elastic peak strength.

Figure 7

The experimental GOS curve of the $3\overline{p}{[1/2]}_0$ transition as measured by Suzuki et al. at 300 eV (filled circles) and 500 eV (filled diamonds) [4], and those obtained by Cheng et al. at 2500 eV (filled squares) [7], with the calculated GOS curves obtained using the DCS1 (solid lines) and DCS2 (dashed lines) scheme. The theories at different energies are marked with the corresponding open symbols.