Double Ionization Process Research Articles

Electron-impact double ionization cross sections and rate coefficients for Be-like ions: B+ to Ne6+

We report a detailed analysis of the electron-impact double ionization process for Be-like ions, spanning charge states from B+ to Ne6+. We considered both direct and indirect double ionization processes. For direct double ionization, we calculated the cross sections by considering three different processes: ionization-ionization (II), excitation-ionization-ionization (EII), and ionization-excitation-ionization (IEI). Our results show excellent agreement between the measured cross sections for Be-like-B and Be-like-O ions. The agreement is slightly weaker for Be-like-Ne ions when we take the potential of ionized ions in the distorted-wave method. For other ions for which experimental data are not available, our calculations should provide the missing data. We have summarized the trends of electron-impact double ionization cross sections with atomic number for isoelectronic sequences. Finally, we have provided the Maxwellian and non-Maxwellian rate coefficients for these Be-like ions. The data obtained should be useful for both equilibrium and non-equilibrium charge-state distributions in astrophysical research.

Correlated Coulomb-Volkov approach and its application to the angular distributions of two-photon double ionization of helium

We investigate the double-ionization process of helium in brief and intense laser fields of 10, 16, and 40 optical cycles, linearly polarized with an intensity of 5×1012Wcm−2. We calculate the total two-photon double-ionization cross section for photon energies ranging from 39.5 to 54 eV and the triple-differential cross sections at a photon energy of 42 eV, using the correlated Coulomb-Volkov approach, which takes into account the interaction of the laser field with each electron (Volkov phase) and interactions of Coulombian nature between electrons and between electrons and the nucleus. The proposed wave function has the advantage of being much less time consuming due to the fact that it does not require a numerical propagation of the wave packet. The results of our calculations obtained for the nonsequential double photoionization are compared with previously reported data and good agreement is found with approaches using projections onto uncorrelated continuum states. This indicates that the disagreements that remain between some theoretical models for the process studied cannot simply be attributed to the electronic correlation in the continuum states. Published by the American Physical Society 2024

Manipulating the electron dynamics in the non-sequential double ionization process of Ar atoms by an orthogonal two-color laser field

Electron dynamics during non-sequential double ionization (NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5π and 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization (RII) channel. This is attributed to the shorter delay time in the RII channel.

Precollision effect on the double ionization of an Ar atom driven by a two-color counter-rotating circularly polarized laser pulse

The double ionization process of an Ar atom driven by a two-color counter-rotating circularly polarized (TCCP) laser pulse is theoretically investigated. Classical trajectory analysis reveals that a significant portion of Nonsequential Double Ionization (NSDI) events occurs through precollision, rather than the well-known recollision mechanism. In the precollision-induced Nonsequential Double Ionization (PCDI) process, the two electrons exhibit a tendency for back-to-back emission, resulting in a lower electronic correlation effect, and the ion recoil momentum concentrated in the zero momentum region. On the other hand, in the recollision-induced Nonsequential Double Ionization (RCDI) process, the two electrons tend to emit in the same direction, leading to a higher electronic correlation effect, and the ion recoil momentum is situated far from the zero momentum region. Moreover, both PCDI and RCDI strongly depend on the parameters of the driving laser pulse. Therefore, the primary mechanism of double ionization can be experimentally probed by observing the corresponding ion recoil momentum.

Nonsequential double ionization channels control of CO2 molecules with counter-rotating two-color circularly polarized laser field by laser wavelength

Abstract Using the classical ensemble model, we investigate the effect of laser wavelength on the electron dynamics process of nonsequential double ionization (NSDI) for linear triatomic molecules driven by a counter-rotating two-color circularly polarized laser field. Based on the delay time between recollision and final double ionization, two particular ionization channels are separated: recollision-impact ionization (RII) and recollision-induced excitation with subsequent ionization (RESI). Numerical results show that with the increase of the laser wavelength, the triangle structure of the ion momentum distribution becomes more obvious, which indicates that the electron–electron correlation of NSDI is enhanced. In addition, we find that the ratio of the RESI channel gradually decreases with the increase of the laser wavelength, while the ratio of the RII channel is opposite. However, the dominant channel is still RESI. It means that the two ionization channels can be controlled effectively by changing the laser wavelength.

Direct double ionization for molecules of H2 and N2 induced by electron-impact

The direct double ionization of H2 and N2 molecules induced by electron-impact are investigated theoretically. Our theoretical calculation combines the binary-encounter-Bethe theory employed for molecular electron-impact single ionization and knock-out mechanism derived from the many-body perturbation theory. The process of electron-impact direct double ionization for molecules in our consideration is treated as the coupling of primary single ionization and knock-out process. The knock-out process is constituted by all the possible secondary single ionization processes. There is a good agreement between our theoretical results and available experimental measurements both for the molecules of H2 and N2. Our approach can obtain the cross section of each ionization channel, which is helpful to understanding for ionization competition mechanism of small homo-nuclear diatomic molecules.

Internal collision double ionization of molecules driven by co-rotating two-color circularly polarized laser pulses

The double ionization process of molecules driven by co-rotating two-color circularly polarized fields is investigated with a three-dimensional classical ensemble model. Numerical results indicate that a considerable part of the sequential double ionization (DI) events of molecules occur through internal collision double ionization (ICD), and the ICD recollision mechanism is significantly different from that in non-sequential double ionization (NSDI). By analyzing the results of internuclear distances R = 5 a.u. and 2 a.u., these two recollision mechanisms are studied in depth. It is found that the dynamic behaviors of the recollision mechanisms of NSDI and ICD are similar. For NSDI, the motion range of electrons after the ionization is relatively large, and the electrons will return to the core after a period of time. In the ICD process, electrons will rotate around the parent ion before ionization, and the distance of the electron motion is relatively small. After a period of time, the electrons will come back to the core and collide with another electron. Furthermore, the molecular internuclear distance has a significant effect on the electron dynamic behavior of the two ionization mechanisms. This study will help to understand the multi-electron ionization process of complex systems.

Generation of micro-Joule level coherent quasi-continuum extreme ultraviolet radiation using multi-cycle intense laser-atom interactions

In the present work we report on the current progress of the recently constructed GW attosecond extreme ultraviolet (XUV) source developed at the Institute of Electronic Structure and Laser of the Foundation for Research and Technology-Hellas (I.E.S.L-FO.R.T.H.). By the implementation of a compact-collinear polarization gating arrangement, the generation of a broadband, coherent XUV quasi-continuum produced by the interaction of a many-cycle infrared field with a gas phase medium is achieved. The spectral width of the XUV emission generated in Xenon, is spanning in the range of 17–32 eV and can support isolated pulses of duration in the range from 0.4 fs to 1.3 fs and pulse energy in the 1 μJ level. Theoretical calculations, taking into account the experimental conditions of this work, are supporting the observations, offering also an insight regarding the temporal profile of the emitted radiation. Finally, the high intensity of the produced XUV pulses has been confirmed by investigating the two-XUV-photon double ionization process of Argon atoms. The demonstrated results inaugurate the capability of the beamline of producing intense coherent quasi-continuum XUV radiation, supporting isolated as pulses, that can be exploited in studies of non-linear XUV processes, attosecond pulse metrology and XUV-pump–XUV-probe experiments.

Dynamics of Correlated Double-Ionization of Two-Electron Quantum Dots in Laser Fields.

Using an ab initio, time-dependent calculational method, we study the non-linear dynamics of a two-electron quantum dot in the presence of ultrashort Thz laser pulses. The analysis of the contribution of the various partial waves to two-electron joint radial and energy distribution patterns revealed strongly correlated electron ejection channels. In the double-ionization process, regardless of the photon energy, the two-electron wave packets are born and remain concentrated until the pulse's peak; at later times, and depending on the photon energy of the field, distinctly different patterns emerge. Our calculations also showed the gradual transition of the radial and energy patterns from a single-peak to a doubly peaked structure, associated with the direct and the sequential double-ionization mechanisms, respectively.

Single- and double-ionization processes of antiproton-helium and antiproton–molecular hydrogen collisions in the keV energy range

We report on an ab initio model to describe single- and double-ionization processes in antiproton collisions with atoms and molecules. Our model is based on a fully correlated close-coupling approach and a Dyson orbital analysis. Furthermore, we employ the concept of a correlation integral in order to quantify and gain insights into the effects of electronic correlation on the ionization processes. Our model is applied to the prototype antiproton-helium and antiproton--molecular hydrogen collision systems in the keV energy range.

Strong field non-Franck–Condon ionization of H$$_2$$: a semi-classical analysis

Single ionization of H $$_2$$ molecules exposed to strong and short laser pulses is investigated by a semi-classical method. Three laser characteristics are considered: (i) The carrier-wave frequency corresponds to wavelengths covering and bridging the two ionization regimes: From tunnel ionization (TI) at 800 nm to multiphoton ionization (MPI) at 266 nm. (ii) Values of the peak intensity are chosen within a window to eliminate competing double ionization processes. (iii) Particular attention is paid to the polarization of the laser field, which can be linearly or circularly polarized. The results and their interpretation concern two observables, namely the end-of-pulse total ionization probability and vibrational distribution generated in the cation H $$_2^+$$ . The most prominent findings are an increased ionization efficiency in circular polarization and a vibrational distribution of the cation that favors lower-lying levels than those that would be populated in a vertical (Franck–Condon) ionization, leading to non-Franck–Condon distributions, both in linear and circular polarizations.

Nonsequential double ionization of Ne with elliptically polarized laser pulses

We show through simulation that the improved quantitative rescattering model (QRS) can successfully predict the nonsequential double ionization (NSDI) process by intense elliptically polarized laser pulses. Using the QRS model, we calculate the correlated two-electron and ion momentum distributions of NSDI in Ne exposed to intense elliptically polarized laser pulses with a wavelength of 788 nm at a peak intensity of $5.0\ifmmode\times\else\texttimes\fi{}{10}^{14}$ W/${\mathrm{cm}}^{2}$. We analyze the asymmetry in the doubly charged ion momentum spectra observed by Kang et al. [Phys. Rev. Lett. 120, 223204 (2018)] in going from linearly to elliptically polarized laser pulses. Our model reproduces the experimental data well. Furthermore, we find that the ellipticity-dependent asymmetry arises from the drift velocity along the minor axis of the elliptic polarization. We explain how the correlated electron momentum distributions along the minor axis provide access to the subcycle dynamics of recollision. From these findings, we expect that we can extend the QRS model for NSDI toward more complicated laser fields in the future.

Classical multielectron model atoms with optimized ionization energies.

We propose a method to build stable classical multielectron model atoms with the ionization energies optimized to experimental values. Based on the work of Kirschbaum and Wilets [Phys. Rev. A21, 834 (1980)10.1103/PhysRevA.21.834], which introduces auxiliary potentials to simulate quantum mechanical effects, we implement a genetic algorithm to optimize the related parameters such that the model atoms yield correct (first few) ionization energies. Ionization-energy optimized model atoms automatically show separated electron shells, consistent to normal expectations. Numerical examples are given to demonstrate the importance of correct ionization energies, as well as new perspectives to double ionization processes.

The nonsequential double ionization of Ar atoms with different initial angular momenta irradiated by a circularly polarized laser pulse

The non-sequential double ionization process of Ar atoms with different initial angular momenta in the 500 nm circularly polarized field is investigated with a classical ensemble model. The numerical results show that, under the circularly polarized laser pulse, the double ionization yield as a function of the laser intensity for Ar atoms with different initial angular momenta exhibit an obvious Knee structure. The ionization yield in the counter-rotating case where the electronic initial rotation direction is opposite to the vector potential of the laser field, significantly higher than that in the co-rotating case where the electronic initial rotation direction is consistent with the vector potential of the laser field. Based on the classical trajectory analysis, it is found that this ionization difference comes from the angle between the direction of the electronic momentum and the force of the laser field at the single ionization instant. The angle in the counter-rotating case is greater than that in the co-rotating case, and the counter-rotating electrons are more likely to return to the parent ion for recollision. Besides, the recollision intants of Ar atoms with the different initial angular momenta are mapped to the electron momentum spectrum. This may provide a method to obtain the electron’s recollision instant of Ar atoms with different initial angular momenta.

Recollision of excited electron in below-threshold nonsequential double ionization

Recollision is the most important post-tunneling process in strong-field physics, but so far has been restricted to interaction between the first ionized electron and the residual ion in nonsequential double ionization. Here we identify the role of recollision of the second ionized electron in the below-threshold nonsequential double ionization process by introducing a Coulomb-corrected quantum-trajectories method. We will reproduce the experimentally observed cross-shaped and anti-correlated patterns in correlated two-electron momentum distributions, and the transition between them. Both the cross-shaped and anti-correlated patterns are attributed to recolliding trajectories of the second electron. The effect of recollision of the second electron is significantly enhanced by the stronger Coulomb potential of the higher valence residual ion, and is further strengthened by the recapture process of the second electron. Our work paves a potential way to image ultrafast dynamics of atoms and molecules in intense laser field.

Non-dipole effects on angular distribution of photoelectrons in sequential two-photon double ionization of Ar atom and K<sup>+</sup> ion

Owing to the development of XUV and X ray of the free-electron lasers, the photoelectron angular distribution in the sequential two-photon double ionization has received increasing attention of theorists and experimentalists, because it provides the valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanisms and pathways of the two-photon double ionization. In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the non-dipole effects, is obtained based on the multi-configuration Dirac-Fock method and the density matrix theory, and the corresponding calculation code is also developed. Based on the code, the sequential two-photon double ionization process of the 3p and 2p shells of Ar atom and K<sup>+</sup> ion are studied, in which, the dipole and the non-dipole parameters of photoelectron angular distribution are investigated systematically. It is found that the angular distributions of the first- and second-step electrons in sequential two-photon double ionization are similar and the two photoionization processes affect each other. Near the ionization threshold, the photoionization cross-sections and anisotropy parameters for the 3p shell and the 2p shell show a large difference. While away from the threshold, the cross-section and angular anisotropy parameters of the 3p and 2p shells show similar behaviors. At the position of Cooper minimum of the photoionization cross section, the contribution of the electric dipole is suppressed, and the non-dipole effect is obvious. The non-dipole effect leads to a forward-backward asymmetric distribution of photoelectrons relative to the direction of incident light. The results of this paper will be helpful in studying the nonlinear processes of photon and matter interaction in the XUV range.

Study of Alpha Particle Impact Double Ionization Cross Sections of Cu Atom

Semi-classical binary encounter approximation has been used for the study of ionization cross sections of Cu atom at ground state. Projectile, alpha particle, with energy varying from threshold to 360 keV/amu are considered for direct double ionizations cross section. Out of the two path ways of ionization we have ruled out the indirect process (like excitation-auto ionization, Auger effect) of double ionization. We considered direct - ionization of outer shells of Cu atom. Vriens accurate expression of cross section for energy transfer ΔE(σΔE ) and Hertree-Fock velosity distribution function for the target electrons are used. The theoretical value of double ionization cross sections at impact energy 300 keV/amu is 0.98 x 10-16 cm2 which is same as experimental values at that impact energy. Above energy of 300 keV/amu, the calculated results underestimates the experimental data and at 360 keV/amu their magnitude are 0.77 x 10-16 and 1.0 x 10-16 respectively. Above impact energy of 75keV/amu, all the theoretical results have ratio factor within 2. Out of the total number of theoretical data 75% are under valid range of ratio factor 2 and among the valid range 41% have ratio factor below 1.325 and hence calculated results of double ionization cross section lie in the acceptable range. The linear correlation coefficient (R square) and standard deviation (SD) of linear fit are 0.6984 and 0.7883 respectively. In low energy range the theoretical results are more apart from corresponding experimental values and possess relatively more error compared to intermediate and higher energy region. Calculated results are in satisfactory agreement with experiment in intermediate and high energy range.

Intensity dependence of ionic-state-resolved electron-electron correlation in strong-field double ionization

In this paper, we theoretically investigate the nonsequential double ionization (NSDI) process of Ne induced by linearly polarized laser field using strong field approximation theory. It is found that, with increasing laser intensity, the correlated electron momentum distributions (CEMDs) corresponding to multiple-return-collision process, which is believed to predominate in NSDI process at high intensity, exhibit a dependence on the wave function of the intermediate ionic state. This observation indicates that the information of the intermediate ionic state in NSDI process can be extracted from CEMD at specific laser intensity.

Ionic-state-resolved electron–electron correlation in strong-field double ionization

In this paper, we theoretically investigate the nonsequential double ionization (NSDI) process of Ne induced by 400 nm linearly polarized laser field with a intensity above the recollision threshold using the S-matrix theory. It is unexpected to find that, significantly different from the results for wavelength longer than 800 nm, both the electron momentum correlated distribution and the longitudinal momentum distribution of Ne2+ exhibit a strong dependence on the wave function of the intermediate ionic state from which the second electron is ionized. This observation provides a potential way to extract the information about the ionic-state wave function based on NSDI process.

Influence of Coulomb force between two electrons on double ionization of He-like atoms

In strong-field double ionization, two electrons are ionized by intense laser field. These two electrons move in the laser field and the state is described by a Coulomb–Volkov state, where the repulsive Coulomb state describes the relative motion of the two electrons and the Volkov state describes the center-of-mass motion of the two electrons in the laser field. In the frame of scattering theory, we derive a simple analytical formula of the double ionization of He-like atoms. The effect of the Coulomb force between two electrons on the double ionization process is discussed. Numerical studies disclose that the Coulomb force enhances the ionization rate of high-energy electrons but suppresses the ionization rate of the lowest-energy electrons.