Low-energy electron-impact ionization of argon: Three-dimensional cross section

Low-energy ($E_0$ $=$ 70.8 eV) electron-impact single ionization of a 3$p$ electron in argon has been studied experimentally and theoretically. Our measurements are performed using the so-called reaction microscope technique, which can cover nearly a full 4π solid angle for the emission of a secondary electron with energy below 15 eV and projectile scattering angles ranging from −8° to −30°. The measured cross sections are internormalized across all scattering angles and ejected energies. Several theoretical models were employed to predict the triple-differential cross sections (TDCSs). They include a standard distorted-wave Born approximation (DWBA), a modified version to account for the effects of postcollision interaction (DWBA-PCI), a hybrid second-order distorted-wave plus $R$-matrix (DWB2-RM) method, and the recently developed $B$-spline $R$-matrix with pseudostates (BSR) approach. The relative angular dependence of the BSR cross sections is generally found to be in reasonable agreement with experiment, and the importance of the PCI effect is clearly visible in this low-energy electron-impact ionization process. However, there remain significant differences in the magnitude of the calculated and the measured TDCSs.

Figure 1

Three-dimensional presentation of the TDCS for single ionization of Ar (3$p$) by 70.8 eV electron impact as a function of the low-energetic ($E_2$) electron emission angle for selected projectile scattering angles (θ${}_1$) and ejected electron energies ($E_2$). (a)−(d): θ${}_1$ $=$ −8° (±1.5°) and $E_2$ $=$ 3 eV (±1.0 eV); (a): experiment, (b) BSR theory, (c) DWB2−RM theory, (d) DWBA-PCI theory. (e)−(h): θ${}_1$ $=$ −15° (±2.5°) and $E_2$ $=$ 5 eV (±1.5 eV). (i)−(l): θ${}_1$ $=$ −20° (±3.0°) and $E_2$ $=$ 15 eV (±2.0 eV).

Figure 2

Three-dimensional presentation of the TDCS for single ionization of Ar (3$p$) by 70.8 eV electron impact as a function of the emission angle of an electron with kinetic energy $E_2$ $=$ 3 eV (±1.0 eV) and different projectile scattering angles (θ${}_1$). (a) and (b): θ${}_1$ $=$ −8°(±1.5°); (c) and (d): θ${}_1$ $=$ −10° (±2.0°); (e) and (f): θ${}_1$ $=$ −15° (±2.5°); (g) and (h): θ${}_1$ $=$ −20° (±3.0°); (i) and (j): θ${}_1$ $=$ −25° (±3.0°); (k) and (l) θ${}_1$ $=$ −30° (±3.5°). Left column: experiment. Right column: BSR theory.

Figure 3

Same as Fig. 2 but for $E_2$ $=$ 15 eV (±2.0 eV).

Figure 4

TDCS Ar (3$p$) as a function of the emission angle of an electron with kinetic energy $E_2$ $=$ 3 eV (±1.0 eV). The other electron's detection angle is: (a) and (b) θ${}_1$ $=$ −8°(±1.5°); (c) and (d) θ${}_1$ $=$ −10°(±2.0°); (e) and (f) θ${}_1$ $=$ −15°(±2.5°); (g) and (h) θ${}_1$ $=$ −20°(±3.0°); (i) and (j) θ${}_1$ $=$ −25°(±3.0°); (k) and (l) θ${}_1$ $=$ −30°(±3.5°). The experimental data are compared with theoretical predictions from the DWBA, DWBA-PCI, DWB2-RM, and BSR approaches. Left column: TDCS in the scattering plane. Right column: TDCS in the perpendicular plane.

Figure 5

Same as Fig. 4 but for $E_2$ $=$ 5 eV (±1.5 eV).

Figure 6

Same as Fig. 4 but for $E_2$ $=$ 15 eV (±2.0 eV).