Double Ionization Mechanism Research Articles

On the mechanisms for double ionization: a study of (e, 3 - 1e) experiments on argon

The recent double-ionization experiments (e, 3 - 1e) on argon by electron impact are, for the first time, investigated theoretically. Simple qualitative models and more elaborate theoretical calculations are proposed and discussed in order to understand the mechanism of double ionization at high electron impact.

Comparison of quasi-classical and quasi-static quantum approaches to the ionization of helium by a circularly polarized laser field

Employing the quasi-classical Fermi molecular dynamics (FMD) method, we find no evidence for the existence of a nonsequential double-ionization mechanism for helium interacting with a pulse of circularly polarized, high-intensity laser radiation. This contrasts with our earlier research, for linearly polarized laser light [ Phys. Rev. A49, R12 ( 1994)], in which effects of the nonsequential double ionization of helium were noted. We also compute emitted-electron kinetic energy spectra by FMD and compare these with spectra derived from a quasi-static tunneling model calculation. In this context we discuss the applicability of the FMD approach to simulations of the photoionization of multielectron systems by intense pulsed laser fields.

Single and double ionization of He by slow protons and antiprotons.

Double and single ionization of He by proton (p) and antiproton (p\ifmmode\bar\else\textasciimacron\fi{}) impact in the energy region below 50 keV is studied theoretically within a molecular picture. As the energy decreases, the ratio of the double- to single-ionization cross section is found to increase for p\ifmmode\bar\else\textasciimacron\fi{} impact and to decrease to p impact in agreement with recent measurements. For p impact, the dominant mechanism for double ionization at the lower energies seems to be sequential ladder climbing by the two electrons through various excited channels. For p\ifmmode\bar\else\textasciimacron\fi{} impact, in contrast, the approaching negative charge distorts the He electron cloud toward the other side of the nucleus and decreases the electron binding energies. These effects enhance the important role of electron-electron, interactions, increasing double ionization.

Double ionization of He(1s2) and He(1s2s 3S) by a single high-energy photon.

We have calculated the energy and angular distributions for double ionization of He(1[ital s][sup 2]) and He(1[ital s]2[ital s] [sup 3][ital S]) by one photon, over a range of photon energies up to a few keV. The calculations were based on using a fairly accurate initial-state wave function, determined so as to exactly satisfy the Kato cusp conditions, and a final-state wave function which is a product of three Coulomb wave functions modified by a short-range correction term. There are at least three different mechanisms for double ionization, and each one leaves a mark on the angular distribution. When the energies of the two electrons are equal, the contribution of each mechanism to the angular asymmetry parameter can be estimated on theoretical grounds; we compare these estimates with the calculated results to give a further indication of the roles of the various mechanisms. Concerning the shapes of the energy and angular distributions, we find significant differences between double ionization of singlet and triplet helium; in particular, the probability for one high-energy photon to eject two equal-energy electrons from triplet helium nearly vanishes owing to the Pauli exclusion principle and to interference effects resulting from antisymmetrization. In two appendixes we presentmore » some details of the integration involved in the calculations.« less

Double photoionization of helium using many-body perturbation theory.

Cross sections for double photoionization of He are calculated using the lowest-order many-body perturbation theory. There are three amplitudes contributing in the present calculation. They represent the three mechanisms for double ionization, namely, two-step-1, shake off, and ground-state correlation. It is explicitly shown that the cross section for each of these mechanisms depends strongly on the adopted form of the dipole interaction as indicated by Dalgarno and Sadeghpour [Phys. Rev. A 46, 3591 (1992)]. Our final results obtained by the sum of three amplitudes do not depend on the choice of the dipole formula at photon energies above 1 keV. The ratios of the cross sections for double ionization to single ionization are in excellent agreement with recent experimental results at energies 2--12 keV.

Electron-electron interaction in the electron loss of He + on H 2 and He

The simultaneous ionization of the projectile and the target is studied in He + +{H 2,He} collisions. The energy dependence of the cross section for this process is analyzed through experimental results obtained by coincidence measurements and theoretical calculations considering the antiscreening and two-center double-ionization mechanisms. The excellent agreement obtained between theory and experiment allows one to obtain a good understanding of the dynamics of this projectile loss mechanism.

Double ionization of helium by a single high-energy photon.

We have calculated the energy and angular distributions for double ionization of He by one photon, over a range of photon energies up to 8 keV. We identify, from structures in the angular distributions, three different mechanisms for double ionization at high photon energies, and we compare the ratio of cross sections for double to single ionization with experimental data.

Double ionization mechanisms frome, (3?1)e and (e, 3e) experiments

Illustrative examples of energy and angular distributions from thee, (3–1)e and (e, 3e) double ionization processes in argon and krypton, at ∼ 5.5 keV impact energy are presented. The relevance of the resulting four-fold and five-fold differential cross sections to the identification of the double ionization mechanism is emphasized.

Interference effects in the double ionization of helium by charged particles

The interference between different double-ionization mechanisms by collisions of charged particles with helium is studied in the second order of perturbation theory series in terms of the interaction potential of the projectile with the helium electrons and the correlation potential of atomic electrons. It is shown that the contribution to the interference term in the integrated double-ionization cross section of helium comes only from the interference between the process of independent electron removal and the process in which an ejected electron, as a result of the interaction with the projectile electron, scatters on another helium electron, resulting in double ionization.

Energy dependence of the double ionization cross section of helium at high energies

The influence of the correlation interaction of atomic electrons upon the double ionization cross section of helium by charged particles and the helium double ionization mechanisms is studied. It is shown that the “shake-off” mechanism should not contribute to the double ionization amplitude when only the first correlation correction is made. The asymptotics of the double ionization cross section at high collision energies is obtained.

Electron-impact double ionization of argon studied by double and triple coincidence techniques: The first (e,3e) experiment.

Angular correlations between the three outgoing electrons in the double ionization of argon by electron impact have been measured for the first time. Double and triple coincidence techniques are used to determine simultaneously all final electron energies and angles, and provide fourfold and fivefold differential cross sections, respectively. The angular distributions are consistent with a two-step model for the double ionization mechanism. The present results clearly show the feasibility and potentiality of (e,3e) experiments.

Double ionization of helium by antiprotons

We have developed a calculational scheme, the forced impulse method, for going beyond the independent particle model in ion-atom collisions. Our first application has been to the double ionization of helium; this requires construction of double ionization pseudostates. Initial calculations yielded good agreement with experimental results on the double ionization by protons, antiprotons, and alpha particles in the MeV/amu collision energy regime, and in particular reproduced the observed difference in double ionization by protons and antiprotons. We report here the results of expanding the angular momenta included in our single-particle basis, double ionization cross sections for other two-electron targets, and impact parameter dependences. Emphasis is on what we learn from our calculations about the mechanism for double ionization, and the physical reason for the observed difference in double ionization by protons and antiprotons.

Differential charge state fractions of He following ionization by fast H − projectiles

The differential charge state fractions of He ions produced in ionization by fast H − projectiles have been measured at projectile scattering angles between 0.25 and 1.59 mrad and an impact energy of 1.0 MeV. These charge state fractions have been measured for each of the possible final charge states of the H − projectile (H −, H and p +). Combined with earlier measurements of simple ionization (no change in projectile charge state) by protons and of capture and ionization by protons, some systematics can be noted. The fraction of doubly charged He ions exhibits a distinct peak between 0.9 and 1.1 mrad for simple ionization. A similar peak is seen at ≈ 0.55 mrad for ionization accompanied by either capture by protons or by single stripping of H −. The data for proton impact suggest that all the peaks are related to double ionization of the target. The double-ionization mechanisms will be discussed in terms of their possible contribution to the observed structures.

Single and double ionization of helium by neutral-particle to fully stripped ion impact.

New measurements of direct single and double ionization of helium by hydrogen, helium, carbon, nitrogen, and oxygen ions are presented for projectile charge states ranging from 0 to 3+. These data are combined with previously published values to provide a detailed description of direct double ionization of helium for a wide range of experimental parameters, i.e., projectile ions include protons through oxygen, impact energies from 25 to 5000 keV/u, and projectile charge states ranging from neutral to fully stripped. The charge-state and impact-velocity dependencies of the measured cross sections are compared with the dependencies predicted by an independent electron multiple-ionization model. It is found that a multistep mechanism (i.e., the independent ionization of both target electrons) is the dominant direct double-ionization mechanism for charged-particle impact energies above 100 keV/u. This mechanism dominates until some maximum impact velocity, which depends on the projectile charge, is reached. For higher velocities a single-step ionization mechanism becomes important. The limited neutral-particle impact data indicate that the single-step mechanism becomes dominant at much lower impact velocities and there is no evidence of the multistep mechanism in the neutral-particle impact energy range investigated.

Structure in the differential charge-state fractions of He following ionization by fast protons.

The differential cross sections for double and single ionization and the corresponding charge-state fractions of He resulting from impact of fast protons have been measured as functions of both the scattering angle (0.25-4.1 mrad) and the impact energy (300-1000 keV) of the proton. The differential cross sections smoothly decrease with the scattering angle, but the fraction of doubly charged ions, ${F}_{2}$, exhibits a distinct peak at \ensuremath{\cong}0.9 mrad. This peak is not easily explained in terms of the single- and double-ionization mechanisms thought to operate at these energies.

Many-body approach to two- and three-photon double ionization and excitation of xenon.

We investigate different processes which may be responsible for ejection of two electrons from the external shell of xenon through the absorption of two and three photons, namely two-photon direct double ionization and three-photon sequential double ionization via the ion in an excited state or in the ground state. We calculate the cross sections of the ionization processes involved, using many-body perturbation theory. These cross sections are then used within a rate equation model for comparing the relative efficiencies of the different double-ionization mechanisms.

Interference between direct and rearrangement mechanisms for double ionization.

In double ionization at very high collision velocities Becker has pointed out that so-called direct mechanism obeys the dipole selection rule while the rearrangement mechanism is a monopole transition, and since s and p waves cannot interfere in total cross sections, interference between these mechanisms is forbidden. It is shown here that interference is possible due to dipole-forbidden contributions to the direct mechanism or rearrangement process.

Collisional mechanisms for single and double ionization of He by protons and antiprotons.

Classical trajectory Monte Carlo calculations have been used to elucidate the collision mechanisms responsible for the differences in the single- and double-ionization cross sections of He atoms by protons and antiprotons in the energy range from 250 to 1000 keV. The calculations employed the Bohr helium-atom model which includes the $\frac{1}{{r}_{12}}$ electron-electron interaction. The unexpected large observed difference [Andersen et al., Phys. Rev. Lett. 57, 2149 (1986)] in the ratio $R$ of double to single ionization for proton and antiproton collisions is reproduced by the calculations. The calculations indicate that the antiproton double-ionization cross section is larger than that for protons because of two effects. The first effect is that the antiproton can push one electron into the other from larger impact parameters than for protons which must be between the nucleus and the first electron in order to pull it into a trajectory which collides with the second electron. The most important effect, however, is that at small impact parameters the antiproton screens the helium nucleus causing a Coulomb explosion while the proton increases the binding of the two electrons. The calculations also show a component of the difference in the ratio $R$ at low energies ($E<~500$ keV) is due to the single-ionization cross sections with protons predicted to have a larger cross section than antiprotons (36% difference at 250 keV).

Ionization of helium by highly charged ions at 1.4 MeV/amu.

Experimental cross sections for ionization of helium by projectile ions with charge Z up to Z=44 are presented at a fixed velocity v=7.48 a.u. corresponding to 1.4 MeV/amu. Total cross sections, summed over projectile charge states, for single ionization, ${\ensuremath{\sigma}}^{+}$, are compared to Born and Glauber calculations for point projectiles of charge Z. The Glauber calculations give a better fit to the Z dependence of the single-ionization cross sections than do the Born calculations. For double ionization, the ratio of ${\ensuremath{\sigma}}^{2+}$/${\ensuremath{\sigma}}^{+}$ increases as ${Z}^{2}$ for the smaller Z and less rapidly than ${Z}^{2}$ for larger Z projectiles, suggesting that the so called ``direct'' mechanism for double ionization is dominant, but that the first Born approximation is breaking down for the larger Z.

Single-photon double ionization of mercury clusters using synchrotron radiation

Single-photon doublet-ionization experiments have been carried out on mercury resulting in the formation of doubly charged clusters. The efficiency is very high and similar to that obtained by electron impact. The mechanism of double ionization is discussed and our results favor a two-step process both in photon and electron impact ionization.