We present here triple differential cross sections for ionization of hydrogen atoms by electron impact at 1eV, 0.5eV and 0.3eV energy above threshold, calculated in the hyperspherical partial wave theory. The results are in very good agreement with the available semiclassical results of Deb and Crothers \cite{DC02} for these energies. With this, we are able to demonstrate that the hyperspherical partial wave theory yields good cross sections from 30 eV \cite{DPC03} down to near threshold for equal energy sharing kinematics.
The electron impact ionization of atomic hydrogen is calculated for incident elrctron energy 76.46 eV. The Hartree-Fock approximation is used to calculate the initial state which includes both bound and continum wave functions. The final state continuum electron wave functions are obtained in the potential of hydrogen ion. The interaction between the two final state continuum electrons is approximated with the screening potential determined variationally.
A new relativistic method based on the Dirac equation for calculating fully differential cross sections for ionization in ion-atom collisions is developed. The method is applied to ionization of the atomic hydrogen by antiproton impact, as a non-relativistic benchmark. The fully differential, as well as various doubly and singly differential cross sections for ionization are presented. The role of the interaction between the projectile and the target nucleus is discussed. Several discrepancies in available theoretical predictions are resolved. The relativistic effects are studied for ionizatio…
We study the ionization process involving antiproton and hydrogen in the energy range between 0.1 keV to 500 keV, using single center close coupling approximation. We construct the scattering wave function using B-spline bases. The results obtained for ionization of atomic hydrogen are compared with other existing theoretical calculations as well as with the available experimental data. The present results are found to be encouraging. We also employed this method to study the ionization of ionized helium in the energy range between 1 and 500 keV. On comparision, the present results are found t…
We extend the semiclassical two-step model for strong-field ionization that describes quantum interference and accounts for the Coulomb potential beyond the semiclassical perturbation theory to the hydrogen molecule. In the simplest case of the molecule oriented along the polarization direction of a linearly polarized laser field, we predict significant deviations of the two-dimensional photoelectron momentum distributions and the energy spectra from the case of atomic hydrogen. Specifically, for the hydrogen molecule the electron energy spectrum falls off slower with increasing energy, and th…
We have implemented the paraxial approximation followed by the time-dependent Hartree-Fock method with frozen core for the single impact ionization of atoms and two-atomic molecules. It reduces the original scattering problem to the five-dimensional time-dependent Schrödinger equation solution. By using this method we calculated the multi-fold differential cross section of the impact single ionization of the helium atom, the hydrogen molecule and the nitrogen molecule by the intermediate energy electrons. Our results for the helium and the hydrogen are quite close to experimental data, but for…
We studied nonrelativistic collision of antiproton with hydrogen atom by solving time-dependent Schrodinger equation numerically. Coulomb wave function discrete variable method (CWDVR) had been used to calculate electron wave function evolution, while projectile defined classically, moving along the straight line trajectories with constant velocity. The ionization amplitude calculated by projection of the wave function into continuum wave function of the hydrogen electron. The fully differential cross sections calculated depending on projectile impact energy, scattering angle and electron ejec…
The calculated double differential cross sections for 60eV energy, where the cross sections are also maximum, agree with the measured results of Shyn (1992) in a much better way compaired to other theories for such energies.
Experiments have shown that the microwave ionization probability of a highly excited almost monodimensional hydrogen atom subjected to a microwave pulse sometimes grows in steps when the peak electric field of the pulse is increased. Classical pulsed simulations display the same steps, which have been traced to phase-space metamorphoses. Quantum numerical calculations again exhibit the same ionization steps. I show that the time-sequence of two level interactions, responsible for the observed steps in the quantum picture, is strictly related to the classical phase space structures generated by…
The multiply differential cross section of the ionization of hydrogen molecular ion by fast electron impact is calculated by a direct approach, which involves the reduction of the initial 6D Schrödinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics. This approach avoids the use of stationary Coulomb two-centre functions of the continuous spectrum of the ejected electron which demands cumbersome calculations. The results obtained, after verification of the procedure in the case atomic hydrogen, reveal interesting mechanisms in the case of small scatteri…
Relativistic strong-field ionization of hydrogen-like atoms or ions in a constant crossed electromagnetic field is studied. The transition amplitude is formulated within the strong-field approximation in Göppert-Mayer gauge, with initial and final electron states being described by the corresponding Dirac-Coulomb and Dirac-Volkov wave functions, respectively. Coulomb corrections to the electron motion during tunneling are taken into account by adjusting an established method to the present situation. Total and energy-differential ionization rates are calculated and compared with predictions fr…
It has been recently predicted theoretically that due to nuclear motion light and heavy hydrogen molecules exposed to strong electric field should exhibit substantially different tunneling ionization rates (O.I. Tolstikhin, H.J. Worner and T. Morishita, Phys. Rev. A 87, 041401(R) (2013) [1]). We studied that isotope effect experimentally by measuring relative ionization yields for each species in a mixed H2/D2 gas jet interacting with intense femtosecond laser pulses. In a reaction microscope apparatus we detected ionic fragments from all contributing channels (single ionization, dissociation,…
We investigate the strong-field ionization of atomic hydrogen in a few-cycle elliptically polarized infrared pulse by solving the time-dependent Schrödinger equation. The dependence of the photoelectron momentum distribution on the pulse intensity, ellipticity, length, envelope, and carrier envelope phase is analyzed. In particular, we explain the variation of the electron offset angle with asymptotic electron energy through the combined action of the field and the Coulomb potential, and demonstrate that low-ellipticity pulses make it possible to access the electron release time.
The non-resonant two-photon ionization of hydrogen-like ions is studied in second-order perturbation theory, based on the Dirac equation. To carry out the summation over the complete Coulomb spectrum, a Green function approach has been applied to the computation of the ionization cross sections. Exact second-order relativistic cross sections are compared with data as obtained from a relativistic long-wavelength approximation as well as from the scaling of non-relativistic results. For high-Z ions, the relativistic wavefunction contraction may lower the two-photon ionization cross sections by a…
In this paper a 4-component Dirac theory of ionization of hydrogen molecular ion in a super-intense laser field is developed. Simple analytic expressions for the spin specific as well as the total ionization currents emitted from the ground state of the ion are derived. The results are given for all polarization and finite propagation vectors of the field. They apply for inner-shell ionization of analogous heavier molecular ions as well. The presence of molecular two-slit interference effect, first found in the non-relativistic case, and the spin-flip ionization current, and an asymmetry of th…
We present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultra violet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time dependent Dirac equation and compare its predictions with those of the corresponding non-relativistic Schr{ö}dinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduces a finite yet small decrease i…
We present a semi-relativistic model for the description of the ionization process of atomic hydrogen by electron impact in the first Born approximation by using the Darwin wave function to describe the bound state of atomic hydrogen and the Sommerfeld-Maue wave function to describe the ejected electron. This model, accurate to first order in $Z/c$ in the relativistic correction, shows that, even at low kinetic energies of the incident electron, spin effects are small but not negligible. These effects become noticeable with increasing incident electron energies. All analytical calculations are…
We calculate ionization energies and fundamental vibrational transitions for H$_2^+$, D$_2^+$, and HD$^+$ molecular ions. The NRQED expansion for the energy in terms of the fine structure constant $α$ is used. Previous calculations of orders $mα^6$ and $mα^7$ are improved by including second-order contributions due to the vibrational motion of nuclei. Furthermore, we evaluate the largest corrections at the order $mα^8$. That allows to reduce the fractional uncertainty to the level of $7\cdot10^{-12}$ for fundamental transitions and to $4\cdot10^{-12}$ for the ionization energies.
Quasi-static models of barrier suppression have played a major role in our understanding of the ionization of atoms and molecules in strong laser fields. Despite their success, in the case of diatomic molecules these studies have so far been restricted to fields aligned with the molecular axis. In this paper we investigate the locations and heights of the potential barriers in the hydrogen molecular ion in an electric field of arbitrary orientation. We find that the barriers undergo bifurcations as the external field strength and direction are varied. This phenomenon represents an unexpected l…
Electron-impact ionization of atomic hydrogen with the electron's anomalous mag- netic moment (AMM) effects are examined. The formulas for the laser-assisted relativis- tic triple differential cross section (TDCS) in the coplanar binary geometry developed earlier by Y. Attaourti and S. Taj [Phys. Rev. A 69, 063411 (2004)] are used to check the consistency of our computations when the anomaly $κ$ is taken to be zero. We show that the contribution of the terms containing the AMM effects even in the first Born approximation has an important contribution, so it must be included in any reliable ana…
Approximate scaling laws with respect to the nuclear charge are introduced for the time-dependent Dirac equation describing hydrogen-like ions subject to laser fields within the dipole approximation. In particular, scaling relations with respect to the laser wavelengths and peak intensities are discussed. The validity of the scaling relations is investigated for two-, three-, four-, and five-photon ionization of hydrogen-like ions with the nuclear charges ranging from $Z=1$ to $92$ by solving the corresponding time-dependent Dirac equations adopting the properly scaled laser parameters. Good a…
The dynamics of the electron impact multiphoton ionization of a hydrogen atom in the presence of an intense laser field has been studied theoretically, with a view to comparing (qualitatively) the results with the recent kinematically complete experiments of Horr et al [ Phys. Rev. Lett., vol. 94, 153201, (2005) ] for the He target. Significant laser modifications are noted in the present doubly (DDCS) and the fully differential cross sections (TDCS). For most of the explored kinematics (chosen in accordance with the experiment), the present binary peak intensity of the laser-assisted TDCS is …
Within the framework of the coplanar binary geometry where it is justified to use plane wave solutions for the study of the $(e,2e)$ reaction and in the presence of a circularly polarized laser field, we introduce as a first step the DVRPWBA1 (Dirac-Volkov Plane Wave Born Approximation1) where we take into account only the relativistic dressing of the incident and scattered electrons. Then, we introduce the DVRPWBA2 (Dirac-Volkov Plane Wave Born Approximation2) where we take totally into account the relativistic dressing of the incident, scattered and ejected electrons. We then compare the cor…
The tunneling ionization of a hydrogen atom excited in the presence of a static electric field is investigated for the case where, before being extracted, the electron has an orbital angular momentum L perpendicular to the field E. The escaping electron has a nonzero mean transverse velocity <vT> in the direction of E cross <L>. This asymmetry is similar to the Collins effect in the fragmentation into hadrons of a transversely polarized quark. In addition, the linear Stark effect make <L> and <vT> oscillate in time. The degree of asymmetry is calculated at leading order in E for an initial sta…
The alignment- and internuclear-distance dependent ionization of H$_2$ exposed to intense, ultrashort laser fields is studied by solving the time-dependent two-electron Schrödinger equation. In the regime of perturbative few-photon ionization, a strong dependence of the ionization yield on the internuclear distance is found. While this finding confirms a previously reported breakdown of the fixed-nuclei approximation for parallel alignment, a simpler explanation is provided and it is demonstrated that this breakdown is not due to vibrational dynamics during the laser pulse. The persistence of …
We present experimental data on the non-adiabatic strong field ionization of atomic hydrogen using elliptically polarized femtosecond laser pulses at a central wavelength of 390 nm. Our measured results are in very good agreement with a numerical solution of the time-dependent Schrödinger equation (TDSE). Experiment and TDSE show four above-threshold ionization (ATI) peaks in the electron's energy spectrum. The most probable emission angle (also known as 'attoclock-offset angle' or 'streaking angle') is found to increase with energy, a trend that is opposite to standard predictions based on Co…
Presented here is a description of the ionization of hydrogen and hydrogenic ions by antiproton-impact, based on very large scale numerical solutions of the time-dependent Schrödinger equation in three spatial dimensions and on analysis of the topology of the electronic eigenenergy surfaces in the plane of complex internuclear distance. Comparison is made with other theories and very recent measurements.
The angular distribution of the emitted electrons, following the two-photon ionization of the hydrogen-like ions, is studied within the framework of second order perturbation theory and the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron--photon interaction. For medium- and high-Z ions, in particular, the non-dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if compared with th…
We have implemented three variants of the exterior complex scaling procedure in prolate spheroidal coordinates (PS-ECS) to study the dissociative electron impact ionization-excitation of hydrogen molecule, where the emerging electrons and one of the protons are detected in coincidence for the first time in a recent experiment. In the first variant, designated PSECS-1B, the two target electrons are treated ab initio while the interaction of the incident-scattered electron is taken into account using the first term of the Born series. In the second, PSECS-2BCD, the second Born term is introduced…
A time-dependent coupled-channel approach was used to calculate ionization, excitation, and energy-loss cross sections as well as energy spectra for antiproton and proton collisions with molecular hydrogen for impact energies 8 keV < E < 4000 keV.
Hyperspherical partial wave theory has been applied here in a new way in the calculation of the triple differential cross sections for the ionization of hydrogen atoms by electron impact at low energies for various equal-energy-sharing kinematic conditions. The agreement of the cross section results with the recent absolute measurements of Röder \textit {et al} [51] and with the latest theoretical results of the ECS and CCC calculations [29] for different kinematic conditions at 17.6 eV is very encouraging. The other calculated results, for relatively higher energies, are also generally satisf…
In the recent work of Herath et al. [Phys. Rev. Lett. 109, 043004 (2012)] the first experimental observation of a dependence of strong-field ionization rate on the sign of the magnetic quantum number m (of the initial bound state (n,l.m)) was reported. The experiment with nearly circularly polarized light could not distinguish which sign of m favors faster ionization. We perform ab initio calculations for the hydrogen atom initially in one of the four bound sub states with the principal quantum number n=2 and irradiated by a short circularly polarized laser pulse of 800nm. In the intensity ran…
The angular distribution of the emitted electrons, following the two--photon ionization of the hydrogen--like ions, is studied within the framework of second order perturbation theory \textit{and} the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron--photon interaction. For medium-- and high--Z ions, in particular, the non--dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if co…
We study the field-ionization threshold behavior when a Rydberg atom is ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are considered. The required threshold field amplitude is found to scale \emph{inversely} with the binding energy when the pulse duration becomes shorter than the classical Rydberg period, and, thus, more weakly bound electrons require larger fields for ionization. This threshold scaling behavior is confirmed by both 3D classical trajectory Monte Carlo simulations and numerically solving the time-dependent Schrödinger equation. More surprisingly, t…
We present a theoretical model for atomic hydrogen ionization by electron impact in the instantaneous approximation and the more accurate non-instantaneous approach using the methods of Quantum Electrodynamics, for the binary coplanar and the coplanar asymmetric geometries. All electrons are described by plane wave functions in the coplanar binary geometry but in the asymmetric geometry the ejected electron is described by a Sommerfeld-Maue wave function. It is shown that the two models give the same results in the non relativistic limit for the binary coplanar geometry where the interactions …
Optical vortex beams have an extensive history in terms of both theory and experiment, but only recently have electron vortex beams been proposed and realized. The possible applications of these matter vortex waves are numerous, but a fundamental understanding of their interactions with atoms and molecules has not yet been developed. In this work, fully differential cross sections for fast (e,2e) collisions using electron vortex projectiles with small amounts of quantized orbital angular momentum are presented. A comparison is made with the fully differential cross sections using plane wave pr…
We investigate the multi-photon process of above-threshold ionization for the light elements hydrogen, carbon, nitrogen and oxygen in the hard x-ray regime. Numerical challenges are discussed and by comparing Hartree-Fock-Slater calculations to configuration-interaction-singles results we justify the mean-field potential approach in this regime. We present a theoretical prediction of two-photon above-threshold-ionization cross sections for the mentioned elements. Moreover, we study how the importance of above-threshold ionization varies with intensity. We find that for carbon, at x-ray intensi…
The convergent close-coupling method is applied to the calculation of fully differential cross sections for ionization of atomic hydrogen by 15.6 eV electrons. We find that even at this low energy the method is able to yield predictive results with small uncertainty. As a consequence we suspect that the experimental normalization at this energy is approximately a factor of two too high.
The three-body dynamics of the ionization of the atomic hydrogen by 30 keV antiproton impact has been investigated by calculation of fully differential cross sections (FDCS) using the classical trajectory Monte Carlo (CTMC) method. The results of the calculations are compared with the predictions of quantum mechanical descriptions: The semi-classical time-dependent close-coupling theory, the fully quantal, time-independent close-coupling theory, and the continuum-distorted-wave-eikonal-initial-state model. In the analysis particular emphasis was put on the role of the nucleus-nucleus (NN) inte…
We apply time-dependent R-matrix theory to investigate harmonic generation from ground state Ar+ with M=0 at a wavelength of 390 nm. Contributions associated with the different 3s(2)3p(4) ionization thresholds are assessed, including the interference between these. The dominant contribution originates from the second ionization threshold, 3s(2)3p(4) (1)D. Changes to the harmonic yields arising from the higher 3s3p(5) thresholds are also assessed. We further confirm that Ar+ has a higher harmonic yield than He for the same laser pulse, despite having a higher ionization threshold.
Stochastic ionization of highly excited relativistic hydrogenlike atom in the monochromatic field is considered. A theoretical analisis of chaotic dynamics of the electron based on Chirikov's criterion is given. Critical value of the external field is evaluated analytically.
Application of the convergent close-coupling (CCC) method to electron-impact ionization of the ground state of atomic hydrogen is considered at incident energies of 15.6, 17.6, 20, 25, 27.2, 30, 54.4, 150 and 250 eV. Total through to fully differential cross sections are presented. Following the analysis of Stelbovics [submitted to Phys. Rev. Lett. (physics/9905020)] the equal-energy sharing cross sections are calculated using a solely coherent combination of total-spin-dependent ionization amplitudes, which are found to be simply a factor of two greater than the incoherent combination suggest…
Stochastic ionization of highly excited relativistic hydrogenlike atom in the monochromatic field is investigated. A theoretical analisis of chaotic dynamics of the relativistic electron based on Chirikov criterion is given for the cases of one- and three-dimensional atoms. Critical value of the external field is evaluated analitically. The diffusion coefficient and ionization time are calculated.
Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We …
We present the first experimental data on strong-field ionization of atomic hydrogen by few-cycle laser pulses. We obtain quantitative agreement at the 10% level between the data and an {\it ab initio} simulation over a wide range of laser intensities and electron energies.
Positronium breakup versus hydrogen ionization in collisions with fast charged projectiles: a comparative study
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Heinrich-Heine-University of Düsseldorf（杜塞尔多夫大学）；University of Chinese Academy of Sciences（中国科学院大学）
Time-dependent close-coupling calculations of the ionization and excitation cross section for antiproton collisions with molecular hydrogen ions are performed in an impact-energy range from 0.5 keV to 10 MeV. The Born-Oppenheimer and Franck-Condon approximations as well as the impact parameter method are applied in order to describe the target molecule and the collision process. It is shown that three perpendicular orientations of the molecular axis with respect to the trajectory are sufficient to accurately reproduce the ionization cross section calculated by [Sakimoto, Phys. Rev. A 71, 06270…
We perform ab initio calculations for the hydrogen atom initially in one of the six circular bound states with the principal quantum numbers n = 2, 3 and 4, irradiated by a short circularly polarized laser pulse of 400 nm. The field propagates in the direction parallel to the z-component of the angular momentum of the atom. We investigate probabilities for the atom to ionize or to get on some bound (excited) state or to remain in the initial state after the end of the laser pulse. In most cases, we find pronounced differences in ionization probabilities for atoms in states having different sig…
We show through simulation that quantum interference in non-sequential double ionization can be used to control the recollision with subsequent ionization (RESI) mechanism. This includes the shape, localization and symmetry of RESI electron-momentum distributions, which may be shifted from a correlated to an anti-correlated distribution or vice versa, far below the direct ionization threshold intensity. As a testing ground, we reproduce recent experimental results by employing specific coherent superpositions of excitation channels. We examine two types of interference, from electron indisting…
A theoretical study of the intense-field single ionization of molecular hydrogen or deuterium oriented either parallel or perpendicular to a linear polarized laser pulse (400 nm) is performed for different internuclear separations and pulse lengths in an intensity range of $(2-13)\times10^{13} $W cm$^{-2}$. The investigation is based on a non-perturbative treatment that solves the full time-dependent Schrödinger equation of both correlated electrons within the fixed-nuclei and the dipole approximation. The results for various internuclear separations are used to obtain the ionization yields of…
Multiphoton ionization provides a clear window into the nature of electron correlations in the helium atom. In the present study, the final state energy range extends up to the region near the $N=2$ and $N=3$ ionization thresholds, where two-photon ionization proceeds via continuum intermediate states above the lowest threshold. Our calculations are performed using multichannel quantum defect theory (MQDT) and the streamlined R-matrix method. The sum and integration over all intermediate states in the two-photon ionization amplitude is evaluated using the inhomogeneous R-matrix method develope…
It is shown that the geometry of multi-electron threshold ionization in atoms depends on the initial configuration of bound electrons. The reason for this behavior is found in the stability properties of the classical fixed point of the equations of motion for multiple threshold fragmentation. Specifically for three-electron break-up, apart from the symmetric triangular configuration also a break-up of lower symmetry in the form of a T-shape can occur, as we demonstrate by calculating triple photoionization for the lithium ground and first excited states. We predict the electron break-up geome…
In this paper we present Classical Trajectory Monte Carlo (CTMC) calculations for single and multiple electron ionization of Argon atoms and ions in the threshold region. We are able to recover the Wannier exponents a for the power-law behavior of the cross section s versus excess energy: the exact value of the exponent as well as the existence of its saturation for multiple ionization appear to be related to how the total binding energy is shared between target electrons.
I show that the theory developed for quantum delocalization of an excited Hydrogen atom in a two-frequency linearly polarized microwave field can be used with a few adaptions to explain the quantum delocalization of Alkali atoms in a linearly polarized monochromatic field in the regime where it deviates from Hydrogenic behaviour. Comparison with numerical and laboratory experiments is satisfactory: apart from a constant factor, independent from the microwave frequency, the same dependence from the initial quantum number is observed.
When molecules interact with intense light sources of femtosecond or shorter duration the rotational degrees of freedom are frozen during the response to the strong nonperturbative interaction. We show how the frozen degrees of freedom affect the measurable signals in high-harmonic generation and above threshold ionization. High-harmonic generation exhibits optical coherence in the signal from different orientations of the molecule. For ionization, the contributions from different orientations are added incoherently. The effects are demonstrated for realistic alignment and orientation schemes.
Accurate molecular imaging via high-order harmonic generation relies on comparing the harmonic emission from a molecule and an adequate reference system. However, an ideal reference atom with the same ionization properties as the molecule does not always exist. We show that for suitably designed, very short laser pulses, a one-to-one mapping between high-order harmonic frequencies and electron momenta in above-threshold ionization exists. Comparing molecular and atomic momentum distributions then provides the electron return amplitude in the molecule for every harmonic frequency. We show that …
