Electron impact ionization of Rydberg atoms

The cross section for ionization of Rydberg atoms in collision with electrons at low and moderate energies is calculated using classical trajectories. The dependence of the total cross section on the initial angular momentum of the target is revealed. Low-discrepancy sequences of (quasirandom) numbers are compared with plain random numbers to confirm that they can lead to improved convergence of calculation in certain cases. A phenomenological parametrization using only two parameters is shown to describe well the classical cross section over a wide range of energies and angular momenta. Using the classical scaling law, the results are extended to any principal quantum number.

Figure 1

(Color online) A two-dimensional low-discrepancy sequence of numbers (left) and a two-dimensional sequence of conventional random numbers (right). 1000 points are used in both cases.

Figure 2

(Color online) Gray-scale (color-coded) maps showing the probabilities for (a) ionization, (b) excitation, and (c) quenching for given velocity $v$ and impact parameter $b$ of the projectile. The target Rydberg atom is in a low-angular-momentum state $(\ell ∕n=0.1)$.

Figure 3

(Color online) Gray-scale (color-coded) maps showing the probabilities for (a) ionization, (b) excitation, and (c) quenching for given velocity $v$ and impact parameter $b$ of the projectile. The target Rydberg atom is in a high-angular-momentum state $(\ell ∕n=1.0)$.

Figure 4

(Color online) Angle-integrated cross sections for electron impact ionization of Rydberg atom target in various initial angular momentum states.

Figure 5

(Color online) The ionization cross section obtained using the quasi-random and random distributions as a function of the number of points in the ensemble of initial conditions.

Figure 6

(Color online) Fit of the simulation data (symbols) with general expression (7) (solid lines). Also shown with dashed line is Vriens and Smeets’s binary encounter approximation [14].

Figure 7

(Color online) Angle-integrated cross sections for electron impact ionization: simulation results for low and high angular momentum (solid lines); experimental results of Shah et al. [22] for ionization of hydrogen ground state and of Dixon et al. [23] and Defrance et al. [24] for ionization of metastable hydrogen atoms (symbols). Time-dependent close-coupling calculation [25] of ionization of $\mathrm{H}\left(2s\right)$ and $\mathrm{H}\left(2p\right)$ states (stars).