Double Ionization Probability Research Articles

Electro-Nuclear Dynamics of Single and Double Ionization of H2 in Ultrafast Intense Laser Pulses.

We present an efficient method for modeling the single and double ionization dynamics of the H2 molecule in ultrashort, intense laser fields. This method is based on a semianalytical approach to calculate the time-dependent single and double molecular ionization rates and on a numerical approach to describe the vibrational motion that takes place in the intermediate molecular ion H2+. This model allows for the prediction of the single and double ionization probabilities of the H2 molecule to be made over a wide range of frequencies and laser intensities with limited computational time while providing a realistic estimate of the energy of the products of the dissociative ionization and of the Coulomb explosion of the H2 molecule. The effect of vibrational dynamics on ionization yields and proton kinetic energy release spectra is demonstrated and, in the case of the latter, is discussed in terms of basic strong-field molecular fragmentation mechanisms.

The optimized field amplitude ratio for nonsequential double ionization by counter-rotating two-color circularly polarized fields

With a classical trajectory Monte Carlo model, we systematically study the laser intensity and field amplitude ratio dependence of nonsequential double ionization by counter-rotating two-color circularly polarized fields (800 and 1600[Formula: see text]nm). The results show that the optimized field amplitude ratio changes with the laser intensity, which is attributed to the shift of the most probable amplitude ratio of electron returning with the laser intensity. Moreover, the laser intensity-dependent double ionization probability curve shows a remarkable dip in the transition region between the nonsequential and sequential channels. It can be well explained by the reduction of the probability of electron returning with the increase of the laser intensity.

Single and sequential double ionization of NO radical in intense laser fields.

We examine the dependences of the single and double ionization probabilities of NO radical on the angle between the NO axis and the laser polarization direction in an intense laser field (790nm, 100fs, 1-10 × 1014 W/cm2) and show that the double ionization is enhanced when the NO axis is parallel to the laser polarization direction. We reveal that the angular dependence of the sequential double ionization probability is determined by the shape of the 5σ orbital of NO+ from which the second photoelectron is emitted in the ionization from NO+ to NO2+. We also reveal that the fast oscillation in the probability of the tunnel ionization of NO originating from a coherent superposition of the two spin-orbit components in the electronic ground X2Π state is described well based on the molecular Ammosov-Delone-Krainov (MO-ADK) theory in which the time evolution of the electron density distribution of the 2π orbital is taken into account.

Dynamical effects of Pauli blocking on resonant multielectron ionization

We examine the dynamical role of the Pauli exclusion principle on resonant multielectron ionization. Using a simple essential-state model that permits us approximate but analytical solutions, we show that this principle can lead to several unexpected consequences. It has only a transient effect on the resonant multielectron dynamics and its dynamical impact decreases with increasing Rabi frequency. Due to mutually competing mechanisms, this principle can enhance the ionization probability, while at the same time it also decreases the probability for double ionization. Furthermore, it can also manifest itself in the energy distribution of the ionized electrons, but only if the energy accumulation range of the electronic detector is chosen to be sufficiently wide.

Comparative study of classical theoretical descriptions of the ionization of atoms induced by few-cycle laser pulses

We have investigated the performance of classical models in the description of the single and double ionization of argon induced by 4-fs, 750-nm linearly polarized laser pulses by comparing the calculated quantities with existing experimental data, primarily the results of the systematic measurements of K\"ubel at al. [Phys. Rev. A 93, 053422 (2016)], in the intensity range (1--10)$\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{14}\phantom{\rule{0.28em}{0ex}}{\mathrm{Wcm}}^{\ensuremath{-}2}$. The comparison involved different one- and two-electron models based on the classical ensemble approximation. The analysis covered single- and double-ionization probabilities and their ratios, longitudinal momentum distributions of the ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}^{2+}$ recoiled ions, and the carrier-envelope-phase-dependent asymmetry of the yield of the ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}^{2+}$ ions.

Frustrated double ionization of atoms in circularly polarized laser fields

We theoretically study frustrated double ionization (FDI) of atoms subjected to intense circularly polarized laser pulses using a three-dimensional classical model. We find a ‘knee’ structure of FDI probability as a function of intensity, which is similar to the intensity dependence of nonsequential double ionization probability. The observation of FDI is more favourable when using targets with low ionization potentials and short driving laser wavelengths. This is attributed to the crucial role of recollision therein, which can be experimentally inferred from the photoelectron momentum distribution generated by FDI. This work provides novel physical insights into FDI dynamics with circular polarization.

Studies of H2 photoionization by a strong ultrashort x-ray pulse on base of a trajectory method

Photoionization of the hydrogen molecule was studied using our previously developed semiclassical trajectory method. The focus was on the parameters of the field for which there are no other results, namely a short photo-pulse with photon energies from soft to hard x-rays and with intensities including superatomic values. We calculated photoionization probabilities for the single and double ionization of H2. In the superatomic field we observed the transient from single-photon to multiphoton double photoionization, the inversion of single and double ionization probabilities, and distinct stabilization effect for the single photoionization. We also observed a specific behavior in the single photoionization probability dynamics with a dip in the middle of the pulse, which becomes extremely deep for a field approaching relativistic intensity. The agreement of our previous results with independent data on the helium atom in superatomic field is an important argument in favor of the efficiency of the used method. This allows us to hope that the probabilities of photoionization of a hydrogen molecule in an atomic and superatomic x-ray field obtained in this work are not only the first, but also quite reasonable results on the indicated process.

Double-ionization mechanisms of magnesium driven by electron impact

We study double ionization of Mg by electron impact through the vantage point of classical mechanics. We consider all electron-electron correlations in a Coulomb four-body problem, where three electrons belong to the atom and the fourth electron causes the impact ionization. From our model we compute the double-ionization probability of Mg for impact energies from 15, to 125 eV. Double ionization occurs through eight double-ionization mechanisms, which we classify into four categories: inner shell capture, direct, delay and ionized inner shell mechanisms. We show that delay and ionized inner shell mechanisms require electron-electron correlations among the four electrons, and are responsible for the second increase in the double-ionization probability. Furthermore, we show that our theoretical prediction about the relative prominence of certain double ionization mechanisms is in agreement with experimental results on the relative prominence of non-first- over first-order mechanisms.

Dynamics of strong-field double ionization of H2 in co-rotating two-color circularly polarized laser fields

Double ionization of H2 in a co-rotating two-color circularly polarized (TCCP) laser field is theoretically investigated. By changing the ratio of electric field peak amplitudes of the TCCP laser pulses, the double ionization probability as a function of the laser intensity shows a clear knee structure, which is suppressed significantly in the case of the atom. Due to the large spatial range of the electronic initial distribution, with the analysis of classical trajectories of ionized electrons, it is found that the ionization of the electron in the farther distance increases the probability of recollision. Furthermore, the yield of nonsequential double ionization created by the recollision can be enhanced by controlling the amplitude ratio of the TCCP laser field.

Enhanced double ionization rate from O2 molecules driven by counter-rotating circularly polarized two-color laser fields.

We report that the nonsequential double ionization (NSDI) probability of an O 2 target can be enhanced greatly in a counter-rotating circularly polarized two-color driving field. The field is composed of a fundamental frequency and its third harmonic, and the combined electric field traces out a four-leaf-clover pattern. The electron ionized by such a field has more chances to collide with the valence electrons in the O 2 molecule, which significantly enhances the NSDI probability. This effect is more evident in low-intensity fields. We also find that the enhancement appears in a broad range of the field ratio of two colors and that both the NSDI yield and the underlying electronic behavior varies notably with the field ratio.

E–e recollision dynamics of nonsequential double ionization with mid-infrared laser field

We have investigated the recollision dynamics of correlated electron from nonsequential double ionization (NSDI) with 3200 nm laser fields at a wide range of intensities using a full-dimensional classical ensemble method. The numerical results show that for the mid-infrared laser fields, the double ionization probability versus laser peak intensity still displays a much clear “traditional” knee structure representing NSDI. At low intensity, the electron momentum correlated spectrum along the laser polarization direction shows a V-shaped structure; whereas at high intensity, the spectrum exhibits a clearly cross-shaped structure. We demonstrate that both the V-shaped structure and the cross-shaped structure are the results of extremely asymmetric energy sharing of the two electrons at recollision. Moreover, the most prominent contribution to NSDI is from the second-returning trajectory and the first-returning trajectory is significantly suppressed. What’s more, the mechanism of NSDI is from recollision impact ionization (RII) channel as well as recollision-excitation-with-subsequent-ionization (RESI) channel. We find that at low intensity, only the RII channel contributes to V-shaped structure; whereas at high intensity, both the RII and RESI channels have comparable contribution to the cross-shaped structure. Further, we diagnose the recolliding electron and the bound electron separately by tracing the classical trajectories.

The probe of electron correlation along the He isoelectronic sequence by intense and short laser pulses

The two-photon double ionization process along the He isoelectronic sequence (He − Ne8+) is investigated by solving the full-dimensional time-dependent Schrödinger equation in an intense laser field. The ionization is triggered from the ground state of each system with photons of energy higher than its second ionization potential, in which case the sequential two-electron ejection is allowed. The results of the total two-photon double ionization probability and the energy distribution of ejected electrons demonstrate the important effect of the nuclear charge Z on the dynamics of the interaction between the two ejected electrons.

Multiphoton double ionization of H2 using circularly polarized laser pulses

A time-dependent close-coupling method is used to calculate the multiphoton double ionization of H2 using circularly polarized laser pulses. Total double ionization probabilities are calculated for 2, 3, and 4 photon absorption in the energy range from 10 to 50 eV. Single and triple differential probabilities are calculated at photon energies where the total ionization probability is near a maximum. For one electron emitted along the internuclear axis, the angular distribution for the other electron is similar for 2, 3, and 4 photon absorption. As one electron is emitted further away from the internuclear axis, the angular distribution for the other electron is similar for 2 and 4 photon absorption, but quite different for 3 photon absorption.

Knee structure in double ionization of noble atoms in circularly polarized laser fields

Nonsequential double ionization is characterized by a knee structure in the plot of double-ionization probability versus laser intensity. In circularly polarized (CP) laser fields, this structure has only been observed for Mg atoms. By choosing laser fields according to a scaling law, we exhibit the knee structure in CP laser fields for Ar and He atoms. The collision of the ionized electron with the core enhances the ionization of the second electron and forms the knee structure. The electron recollision is universal in CP laser fields, but the ionization probability in the knee region decreases as the wavelength of the driven field increases. For experimental observations, it is beneficial to use target atoms with small ionization potentials and laser fields with short wavelengths.

Theoretical study on non-sequential double ionization of carbon disulfide with different bond lengths in linearly polarizedlaser fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574117 and 11604131).

By using a two-dimensional Monte-Carlo classical ensemble method, we investigate the double ionization (DI) process of the CS2 molecule with different bond lengths in an 800-nm intense laser field. The double ionization probability presents a “knee” structure with equilibrium internuclear distance R = 2.9245 a.u. (a.u. is short for atomic unit). As the bond length of CS increases, the DI probability is enhanced and the “knee” structure becomes less obvious. In addition, the momentum distribution of double ionized electrons is also investigated, which shows the momentum mostly distributed in the first and third quadrants with equilibrium internuclear distance R = 2.9245 a.u. As the bond length of CS increases, the electron momentum becomes evenly distributed in the four quadrants. Furthermore, the energy distributions and the corresponding trajectories of the double-ionized electrons versus time are also demonstrated, which show that the bond length of CS in the CS2 molecule plays a key role in the DI process.

Multiphoton double ionization of helium using femtosecond laser pulses

A time-dependent close-coupling method is used to calculate the multiphoton double ionization of He using femtosecond laser pulses. Total double ionization probabilities are calculated for 2, 3, 4, and 5 photon absorption in the photon energy range from 10 to 60 eV. Single and triple differential probabilities are calculated for 2, 3, 4, and 5 photon absorption at energies where the total ionization probability is near a maximum. For circular polarization the total and differential probabilities are consistently smaller compared to linear polarization as the number of photons absorbed is increased while keeping the radiation field intensity constant. For linear polarization, the total and differential probabilities vary substantially as a function of photons absorbed due to the presence of more absorption pathways.

Nonsequential Double Ionization by Counterrotating Circularly Polarized Two-Color Laser Fields.

We report on nonsequential double ionization of Ar by a laser pulse consisting of two counterrotating circularly polarized fields (390 and 780nm). The double-ionization probability depends strongly on the relative intensity of the two fields and shows a kneelike structure as a function of intensity. We conclude that double ionization is driven by a beam of nearly monoenergetic recolliding electrons, which can be controlled in intensity and energy by the field parameters. The electron momentum distributions show the recolliding electron as well as a second electron which escapes from an intermediate excited state of Ar^{+}.

Two-photon double ionization of helium by chirped few-cycle attosecond pulses: From nonsequential to sequential regime**Project supported by the National Natural Science Foundation of China (Grant Nos. 11322437 and 11574010) and the National Basic Research Project of China (Grant No. 2013CB922402).

The two-photon double ionization (TPDI) dynamics of helium by chirped attosecond pulses are theoretically studied by solving the two-electron time-dependent Schrödinger equation in its full dimensions. We show that both the differential and the total double ionization probability can be significantly controlled by adjusting the chirp. The dependence of the TPDI on the chirp can be quite different for different photon energies, relying on the central photon energy being in the sequential region, nonsequential region, or translation region. The physics which lead to the chirp dependence for different photon energies are addressed. Present findings are well reproduced by a model based on the second-order time-dependent perturbation theory.

Carrier-envelope-phase effects and V-like structure in nonsequential double ionization by elliptical polarization

The nonsequential double ionization (NSDI) of atom is revisited by elliptically polarized few-cycle laser pulse with the classical ensemble method. We focus on the events that both electrons emit into the same direction along the long and short axis of the laser polarization plane, and how do the correlated electron momentum spectra of these two events depends on the carrier-envelope-phase (CEP). We first exhibit that the double-ionization probability has a negligible dependence on CEP. Back analysis shows that the ionization dynamics of the second electron are strongly depend on the CEP, which is significantly responsible for the CEP-dependent correlated electron momentum spectra. Besides, the correlated electron momentum spectrum along the long axis of the laser polarization plane reproduces the so-called V-like structure (also called the figurelike structure) observed in experiments [A. Staudte, et al., Phys. Rev. Lett. 99, 263002 (2007); A. Rudenko, et al., Phys. Rev. Lett. 99, 263003 (2007)]. We sort the V-like shape into two regions and find that the different regions exhibit significantly different dynamics behaviors. Simultaneously, we demonstrate that the electron pairs emitted into the same direction along the short axis of the laser polarization plane is a result of the nuclear–electron attraction, and both the nuclear–electron attraction and e–e repulsion significantly contribute to the V-like structure.

Five-photon double ionization of helium

A time-dependent close-coupling method is used to calculate the five-photon double ionization of He. It is found that the generalized cross section used in the past for two-photon double ionization of He cannot be extended to five-photon double ionization of He. Therefore only five-photon double ionization probabilities that depend on specific radiation field pulses can be calculated.