Mapping equations of motion of the highly exited classical atom in a monochromatic field are generalized for the two-frequency microwave field. Analysis of the obtained equations indicates to the weak sensitivity of the position of the recently observed ionization peak near the main resonance to the frequency and amplitude of the additional microwave field. In the high frequency region, however, the sensitivity of the enhanced ionization peaks on the additional field frequency is predicted.
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…
Small Phase Space Structures and their Relevance to Pulsed Quantum Evolution: the Stepwise Ionization of the Excited Hydrogen Atom in a Microwave Pulse
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 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…
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.
Ionization of molecular hydrogen and deuterium by a frequency-doubled Ti:sapphire laser pulses
在$(2-13)\times10^{13} $ W cm $^{-2}$的强度范围内，对平行或垂直于线偏振激光脉冲（400 nm）的氢或氘分子的强场单电离进行了理论研究.该研究是基于非微扰处理，解决了完整的时间依赖的薛定谔方程的相关电子内固定的核和偶极子近似。各种核间分离的结果被用来获得分子氢和氘在其基态振动态的电离产额。一个原子模型是用来识别的影响，内在的双原子两中心字符的问题。
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 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.
Electron's anomalous magnetic moment effects on laser assisted ionization of atomic hydrogen by electronic impact
本文研究了在电子反常磁矩（AMM）作用下氢原子的电子碰撞电离。本文给出了Y. Attaourti和S. Taj [Phys.Rev.A69，063411（2004）]用于检查当异常$κ$取为零时我们的计算的一致性。我们表明，即使在第一玻恩近似中，包含AMM效应的项的贡献也具有重要的贡献，因此必须将其包括在任何可靠的分析中。给出了TDCS的全解析计算。
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 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 have designed a Euler approximation Monte-Carlo code for the calculation of the ionization of atomic hydrogen by protons with energies between 0.05 and 1.0 MeV. This code is used to calculate the total ionization cross sections s(E), the angular distribution double differential cross sections d2s/ (dW - dE) for electrons with energies of 150 eV ionized by 300 keV protons and the energy distribution d2s/ (dW - dE) for the ionized electrons emitted at 10o by protons of energy 300 keV. Our calculations are compared to experimental values of these quantities as well as independent calculations.…
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…
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…
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…
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…
The cosmic microwave background covers the entire universe, which suggests the absence of ay closed system, except the universe itself. In this paper, I consider the effect of the cosmic microwave background on the hydrogen atom, which must be very small, otherwise, changes in energy levels would have been measurable. But how small is small? This I compute by considering a system in an environment or bath. I derived the bath's, (in this case the CMB) effect on the hydrogen atom in the Feynman-Vernon approach to an open system. The effect is small and quantified in terms of a correction to the …
We analytically compute, in the first Born approximation for symmetric and asymmetric coplanar geometries, the triple differential cross sections for electron-impact ionization of hydrogen atom in the metastable 2S-state at both low and high energies. The process is investigated by using the relativistic Dirac-formalism and it is also shown that the nonrelativistic limit is accurately reproduced when using low incident kinetic energies. At high energies, relativistic and spin effects significantly affect the triple differential cross sections. Our analytical approach which seems exact is compa…
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 …
