High-energy electron-impact excitation process: The generalized oscillator strengths of helium

Abstract

The high-energy electron impact excitation cross sections are directly proportional to the generalized oscillator strengths ͑GOSs͒ of the target ͑an atom or molecule͒. In the present work, the GOSs of helium from the ground state to n 1 S, n 1 P, n 1 D ͑n → ϱ͒ and adjacent continuum excited states are calculated by a modified R-matrix code within the first Born approximation. In order to treat the bound-bound and bound-continuum transitions in a unified manner, the GOS density ͑GOSD͒ is defined based on the quantum defect theory. The GOSD surfaces of 1 S, 1 P, and 1 D channels are calculated and tested stringently by the recent experiments. With the recommended GOSD surfaces with sufficient accuracy, the GOSDs ͑i.e., GOSs͒ from the ground state into all n 1 S, n 1 P, and n 1 D excited states of helium can be obtained by interpolation. Thus, the high-energy electron impact excitation cross sections of all these excited states can be readily obtained. In addition to the high-energy electron impact excitation cross sections, a scheme to calculate the cross sections in the entire incident energy range is discussed.

Dynamic behavior of valence-shell excitations of atomic neon studied by high-resolution inelastic x-ray scattering

“…The intensity for the individual transition was determined by fitting the measured spectra. Then the previously calculated DCS of the 2 1 P of helium [8] was [9] at the incident electron energy of 2.5 keV; solid (navy blue) line: the RPAE calculations [17]. The (red) triangle, (green) down-triangle, and (violet) square are the results of Suzuki et al [33] measured at the incident electron energies of 300, 400, and 500 eV, respectively.…”

“…According to Bethe-Inokuti theory [1][2][3][4], the generalized oscillator strengths (GOSs), which are often measured by high-energy electron energy loss spectroscopy (EELS), are thought to be only determined by the target structure under the hypothesis that the first Born approximation (FBA) is satisfied [1][2][3][4]. For helium, Bethe-Inokuti theory is valid according to the experimental and theoretical investigations for more than 40 years [5][6][7][8]. However, for other atoms, the disagreements between the experimental results and theoretical calculations in the larger momentum transfer region were generally observed [9][10][11][12][13][14][15].…”

“…The variable collision length in the scattering angular range of 25 • -55 • of neon was simply calibrated by a factor of sin(2θ ) as described in our previous paper [5]. From the measured intensities of the excitations of neon and 2 1 P of helium at 20 • , the squared form factor ζ (q,ω n ) for the individual excitation of neon was normalized to the theoretical ζ (q,ω n ) of the 2 1 P of helium at 20 • calculated by Han and Li [8], which is similar to the normalization method used in our previous paper [6]. The experimental errors of ζ (q,ω n ) are attributed to the statistics of counts, the normalizing procedure, as well as the fitting procedure, which are shown in the corresponding figures.…”

Determination of the electronic structure of atoms and molecules in the ground state: Measurement of molecular hydrogen by high-resolution x-ray scattering

“…Because of the limited size of the gas cell, the collision length at 2θ ≤ 15 • deviated from the rule of 1/ sin(2θ ) and was corrected by measuring the elastic scattering of hydrogen and of the excitation of 2 1 P of helium since the ζ (q) of 2 1 P of helium is well known, and has been measured and calculated with a high accuracy and has proven to be reliable [8,[21][22][23]. In this way the variable collision lengths at 20 • -70 • of molecular hydrogen were simply calibrated by multiplying by a factor of sin(2θ ) while the ones at 10 • -15 • were calibrated by multiplying the intensity ratios of the elastic scattering of hydrogen to the 2 1 P of helium with the ζ (q) of the 2 1 P of helium [23]. Since the incident photon beam was linearly polarized and its direction was in the scattering plane, a factor of cos 2 2θ was corrected according Eq.…”

Inelastic x-ray scattering study of the state-resolved differential cross section of Compton excitations in helium atoms

“…The selection of helium is because it is the simplest multielectron system, for which a reliable theoretical calculation can be achieved. Therefore, the S( q,ω) measured with a high resolution would provide a benchmark to test the theoretical method stringently [13,14]. Historically, helium played an important role in the development of the Compton profile since a meaningful comparison between theory and experiment was feasible only on the helium atom at that time [15][16][17].…”