Quasiclassical treatment of the Auger effect in slow ion-atom collisions

A quasiclassical model based on the resolution of Hamilton equations of motion is used to get evidence for Auger electron emission following double-electron capture in 150-keV $\mathrm{N}{\mathrm{e}}^{10+}+\mathrm{He}$ collisions. Electron-electron interaction is taken into account during the collision by using pure Coulombic potential. To make sure that the helium target is stable before the collision, phenomenological potentials for the electron-nucleus interactions that simulate the Heisenberg principle are included in addition to the Coulombic potential. First, single- and double-electron captures are determined and compared with previous experiments and theories. Then, integration time evolution is calculated for autoionizing and nonautoionizing double capture. In contrast with single capture, the number of electrons originating from autoionization slowly increases with integration time. A fit of the calculated cross sections by means of an exponential function indicates that the average lifetime is $4.4\times {10}^{-3}\mathrm{a}.\mathrm{u}.$, in very good agreement with the average lifetime deduced from experiments and a classical model introduced to calculate individual angular momentum distributions. The present calculation demonstrates the ability of classical models to treat the Auger effect, which is a pure quantum effect.

Figure 1

Schematic expected behavior of ${\tilde{\sigma }}_{\mathrm{ADC}}$ (full curve), ${\tilde{\sigma }}_{\mathrm{NADC}}$ (dashed curve), and ${\tilde{\sigma }}_{\mathrm{SC}}+{\tilde{\sigma }}_{\mathrm{SI}}$ (dotted-dashed curve) as a function of integration time $t$. The short-dashed curve shows the time interval during which the quasimolecule is formed. In this interval, the electrons are shared between both nuclei.

Figure 2

Differential single capture cross sections as a function of the scattering angle of the projectile, in 150-keV $\mathrm{N}{\mathrm{e}}^{10+}+\mathrm{He}$ collisions. Present theoretical results, dotted-dashed curve and full line, using an independent and correlated CTMC model, respectively; experiment, full squares; quantum calculations, dashed curves.

Figure 3

Differential double capture cross sections as a function of the scattering angle of the projectile in 150-keV $\mathrm{N}{\mathrm{e}}^{10+}+\mathrm{He}$ collisions. Present theoretical results, dotted-dashed curve and full line, using independent and correlated CTMC model, respectively; experiment, full squares; quantum calculations, dashed curves.

Figure 4

Quantity ${\tilde{\sigma }}_{\mathrm{mol}}$ for producing a quasimolecule ${\left(\mathrm{Ne}-\mathrm{He}\right)}^{8+}$. Between $-t_o$ and $t_o$ both electrons are bound on Ne and He.

Figure 5

Results of the present calculations for time evolution of quantities ${\tilde{\sigma }}_{\mathrm{SI}}$ (a) and ${\tilde{\sigma }}_{\mathrm{SC}}$ (b), from $t=0-1600\mathrm{a}.\mathrm{u}.$, in 150-keV $\mathrm{N}{\mathrm{e}}^{10+}+\mathrm{He}$ collisions. Inset: Zoom of time evolution for integration times smaller than 160 a.u.

Figure 6

Time evolution of ${\tilde{\sigma }}_{\mathrm{ADC}}+{\tilde{\sigma }}_{\mathrm{TI}}$ (top of Fig. 6), ${\tilde{\sigma }}_{\mathrm{NADC}}$ (middle of Fig. 6), and the sum of these quantities (bottom of Fig. 6) using CE-CTMC model. For $\mathrm{ADC}+\mathrm{TI}$ and NADC, a fit using relation (2) has been performed (full line on top and dashed line for NADC) in order to determine an average autoionization width.

Figure 7

Comparison between ${\tilde{\sigma }}_{\mathrm{ADC}}$ (empty squares) and ${\tilde{\sigma }}_{\mathrm{TI}}$ (empty circles) as a function of time using an independent-electron classical model.

Figure 8

$L$ distributions of $3ln{l}^{\prime }$ ($n=4$, 6, and 9) configurations of $\mathrm{N}{\mathrm{e}}^{8+}$ (full squares), determined using a classical model developed for SC [48]. The sum of each $L$ distribution is normalized to experimental DC cross sections [26].