Electron scattering from argon: Data evaluation and consistency

The demand for coherent scattering data for modeling electron transport in matter has increased in recent years. While much effort has been devoted to the improvement of models describing electron transport and scattering, the updating of fundamental data sets on the basis of recent experimental results has often been neglected. The use of a well-validated set of electron cross sections ensures accurate calculations of transport parameters and ionization yields, with typical applications in material analysis, detector response studies, plasma diagnostics, physics of the atmosphere, and radiotherapy. Data consistency can be verified on the basis of various theoretical requirements, and systematic errors can be minimized by cross-checking results obtained from independent experiments. For example, the oscillator strength distribution of an atom can be obtained both from photoabsorption experiments and from zero-angle electron-atom collisions at high energy, on the basis of the Bethe theory. A considerable number of all electron-scattering experiments are concerned with light noble gases, in particular with argon. This gas is a dominant constituent of noble-gas discharge plasmas and plays an important role in rare-gas halide lasers and proportional scintillator counters. This work reviews electron-scattering cross sections and optical data for the argon atom, discusses the progress made in the field of electron scattering and photoabsorption, and focuses on the most appropriate criteria for verifying data consistency.

Figure 1

Example of experimental setup for a crossed-beam experiment. The molecular (or atomic) beam is directed perpendicularly to the page. In this setup, the energy analyzer and a beam-stability monitor rotate about the collision center and the Faraday cup is used to measure the beam attenuation (see text for more details). Adapted from 56.

Figure 2

Energy-loss spectrum measured in an electron collision experiment for argon as a function of the electron energy $E$. In this example, $T=500\mathrm{eV}$. The Auger electrons emitted after ionization of the $L$ shell can also be observed. Figure courtesy of W. Y. Baek (PTB).

Figure 3

Different ways of populating atomic levels after electron-impact excitation. Solid arrows show how electron impact directly excites the atom from the ground state and, consequently, populates levels $k_1$, $k_2$, and $i$. Level $i$, which decays to the lower levels $j_1$ and $j_2$ emitting light (dotted arrows), can also be populated by cascades from higher levels $k_1$ and $k_2$ (dashed arrows). Adapted from the website of the University of Wisconsin Atomic Collision Group (see Sec. 5C).

Figure 4

Example of experimental setup for the measurement of excitation functions by means of optical methods. Adapted from the website of the University of Wisconsin Atomic Collision Group (see Sec. 5C).

Figure 5

Example of an experimental setup for measurements with a double ionization chamber. From 115.

Figure 6

Schematic diagram of discrete optical oscillator strengths $f_n$ (ordinate axis) for transitions from the ground state of the argon atom (indicated on the abscissa in Paschen notation).

Figure 7

Optical oscillator strength distributions in the energy range (a) $10–1000\mathrm{eV}$ and (b) $10\mathrm{eV}–1\mathrm{MeV}$. Solid line, 88; dashed line, NIST XCOM database (9); experimental data: ★, 146; ◆, 115; ○, 123; ▵, 128; ◻, 24. The data recommended by 62 and 10 are not shown for clarity.

Figure 8

Differential elastic cross sections for an electron-impact energy $T=10\mathrm{eV}$. Experimental data: *, 125; ◻, 102; ●, 95; ▿, 53. Phase-shift analysis: solid line, 53. Theoretical models as follows. Dashed line, 8. This calculation is based on an $R$-matrix theory and does not take into account spin-orbit coupling. Short dashed line, 94. This relativistic treatment takes into account polarization and dynamic distortion effects. dotted line, 97. This nonrelativistic treatment takes into account the target polarization, but does not consider spin-orbit effects.

Figure 9

Differential elastic cross sections for an electron-impact energy $T=100\mathrm{eV}$. Experimental data: ◻, 102; ◇, 125; ○, 71; ▿, 38; ▵, 34. Calculations: dashed line, NIST database (69); solid line, 113.

Figure 10

Differential elastic cross sections for an electron-impact energy $T=1\mathrm{eV}$. Experimental data: ◻, 142; *, 53; dashed line, 59. Calculations: solid line, 94.

Figure 11

Integrated elastic cross sections for Ar. Experimental results: *, 53; ▵, 102; ○, 65; ◻, 125; ◆, 38; ▴, 49; solid line: 142; dashed line: 59. The data adopted by 60 are also shown for comparison (dotted line).

Figure 12

Viscosity cross sections for Ar. Results from beam experiments: ○, 102; results from a MERT analysis of phase shifts: ◻, 149 with phase shifts from 93; ▴, 149 with phase shifts from 143.

Figure 13

Momentum transfer cross sections for Ar. Results from beam experiments: ●, [53]; ▴, 102; ○, 125. Results from swarm experiments: long dashed line, 118; solid line, 48; ◻, 99; ◇, 129. Theoretical results: short dashed line, 94; dotted line, 97.

Figure 14

Sum cross section for levels $1s_2$ and $1s_4$. Experimental data: ◻, 1; ○, 75; ◼, 83; ▴, 133; ▵, 43; *, 30. Compilations: solid line, this work; (–×–), 40.

Figure 15

Differential cross sections for the level $1s_2$ at $T=20\mathrm{eV}$. *, 75; ◼, 43; ▵, 30.

Figure 16

Fano plot for the levels (a) $1s_2$ and (b) $1s_4$. ▵, 1; ●, 133; *, new compilation. Solid line, linear fit to the new compiled data.

Figure 17

Excitation cross sections for the states $2s_2$ (▵), $2s_4$ (●), and $3d_5$ (◻). The lines represent the respective interpolation functions obtained using Eq. (47).

Figure 18

Sum cross sections for levels $1s_3$ and $1s_5$. Experimental data: ●, 75; ▴, 44; ○, 30; ◻, 117. Compilations: solid line, this work; dashed line, 40.

Figure 19

Sum cross sections for $4p$ levels. Experimental results: ●, 27; ◻, 30. Compilations: solid line, this work; dashed line, 40; dotted line, IAEA database; *, 60.

Figure 20

Sum cross sections for levels $2s_3$ and $2s_5$. The experimental data (●) of 28 are fitted (solid line) with Eq. (47).

Figure 21

Comparison between the total excitation cross sections obtained in this work (▵) and other compilations: *, 40; ◻, 35; ●, 148.

Figure 22

Cross sections for single, double, and triple ionization. ▿, 110; ◇, 141; ▵, 85; ⋆, 127; ●, 90; ◻, 81.

Figure 23

Total ionization cross section. The solid line represents the interpolation function of the adopted set, according to Eq. (49), with $b=(3.66\pm 0.11)\times {10}^{-3}$, $c=(1.43\pm 4.88)\times {10}^{-4}$, $d=(6.76\pm 0.74)\times {10}^{-3}$. For clarity, only the experimental data of 127 (◼), 123 (○), 141 (▵), and 109 (◇) are shown.

Figure 24

Fano plot of the total ionization cross-section data for argon. ▿, 109; ◇, 85; ▵, 90; ●, 127; ○, 110; *, 123. Solid line: linear fit of the adopted data set.

Figure 25

Available DDCS data for electron ionization in argon. $T=500\mathrm{eV}$: ◼, 116 $(\theta =0°)$; ◇, 101 $(\theta =90°)$; ★, 39 $(\theta =90°)$. $T=1\mathrm{keV}$: ●, 89 $(\theta =90°)$; ▿, 135 $(\theta =90°)$; *, 116 $(\theta =0°)$.

Figure 26

Available SDCS data for electron ionization in argon. $T=500\mathrm{eV}$: ○, 101; ●, 39; $T=1\mathrm{keV}$: ▿, 135. Solid and dashed lines: BEB approximations, with $df∕dw=A∕{(1+w)}^2$, $A=0.411\pm 0.028$.

Figure 27

Platzman plot of SDCS cross sections of Ar shown in Fig. 26 for (a) electron ionization and (b) photoionization. $Y\left(E\right)$ is the scaled SDCS, according to Eq. (50). $T=500\mathrm{eV}$: ○, 101; ●, 39; $T=1\mathrm{keV}$: ▵, 135. $E$ is (a) the electron energy or (b) the photon impact energy.

Figure 28

$K$-shell ionization cross section for argon in the energy range (a) $1\mathrm{keV}–100\mathrm{MeV}$ and (b) $5–25\mathrm{keV}$. ●, compilation provided by 84. Calculations: solid line, BEB approximation (80); dotted line, 13; (+), 122. Semiempirical evaluation: dashed line, 22.

Figure 29

Comparison between the argon total cross section as a function of the electron energy, obtained by adding the inelastic and elastic cross sections adopted in this work (●), and independent measurements of the total scattering cross section: *, 137; ▿, 2; ◇, 131; ○, 17. The set recommended by 148 is also shown for comparison (◻).