The calculation of partial two-photon ionization cross sections in the above-threshold energy region is discussed in the framework of exterior complex scaling. It is shown that with a minor modification of the usual procedure, which is based on the calculation of the outgoing partial waves of the second-order scattering wave function, reliable partial ionization amplitudes can be obtained. The modified procedure relies on a few-term least-squares fit of radial functions pertaining to different partial waves. To test the procedure, partial and total two-photon ionization cross sections of the helium atom have been calculated for a broad range of incident photon energies. The calculated cross sections may be seen to agree well with the results found in the literature. Furthermore, it is shown that, using a similar approach, partial photoionization cross sections of an atom in an autoionizing (resonance) state may be calculated in a relatively straightforward way. Such photoionization cross sections may find their use in enhanced few-parameter models describing the atom-light interaction in cases where a direct solution of the time-dependent Schroedinger equation becomes too resource-intensive.
The dynamics of the electron loss to the continuum (ELC) from the light neutral projectile positronium (Ps) atom in collision with the He atom is studied in the framework of the post collisional Coulomb Distorted Eikonal Approximation (CDEA). Both the fully differential (TDCS) and the double differential (DDCS) cross sections are investigated in the intermediate and high incident energies. Results are compared with the existing experiment and other theories, where possible.
We present results of high-resolution experiments on single ionization of He, Ne and Ar by ultra-short (25 fs, 6 fs) 795 nm laser pulses at intensities 0.15-2.0x10^15 W/cm^2. We show that the ATI-like pattern can survive deep in the tunneling regime and that the atomic structure plays an important role in the formation of the low-energy photoelectron spectra even at high intensities. The absence of ponderomotive shifts, the splitting of the peaks and their degeneration for few-cycle pulses indicate that the observed structures originate from a resonant process.
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 model describing the electronic transitions in an atom subject to a strong high frequency laser pulse is proposed in the velocity gauge. The model accounts for the initial state coupling with the the remaining discrete and continuum spectra. Continuum-continuum transitions are also taken into account following well known strong-field approximation. A single integro-differential equation for the initial state amplitude has been obtained. Exact numerical solutions of this equation are computed and compared with the full time dependent Schr{ö}dinger equation solution for Hydrogen atoms. The ini…
We present a numerical implementation of the infinite-range exterior complex scaling (irECS) [Phys. Rev. A 81, 053845 (2010)] as an efficient absorbing boundary to the time-dependent complete-active-space self-consistent field (TD-CASSCF) method [Phys. Rev. A 94, 023405 (2016)] for multielectron atoms subject to an intense laser pulse. We introduce Gauss-Laguerre-Radau quadrature points to construct discrete variable representation basis functions in the last radial finite element extending to infinity. This implementation is applied to strong-field ionization and high-harmonic generation in H…
A unitary model describing the electronic transitions in an atom subject to a strong high frequency laser pulse is proposed. The model fully accounts for the initial state coupling with the continuum spectrum. Continuum-continuum as well as discrete-discrete transitions are neglected. The model leads to a single integro-differential equation for the initial state amplitude. Exact numerical and approximate closed semi-analytical solutions of this equation are obtained. A comparison of present results with full time dependent Schrödinger equation solution for Hydrogen atoms subject to a laser pu…
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…
The terahertz (THz) generation in a dual-color field was investigated experimentally by precisely controlling the relative time delay $τ$ and polarization $θ$ of dual-color lasers, where the accompanying third-harmonic generation (THG) is employed to determine $τ$ up to the sub-wavelength accuracy. An anticorrelation of the yields between THz and THG with $τ$ was displayed. Compared with the theoretical simulations, the experimental results reveal that the continuum-continuum transitions of the released electron after single-atom ionization are the dominating mechanism for THz generation, whic…
Many applications are in need of accurate photoionization cross-sections, especially in the case of complex atoms. Configuration-interaction relativistic many-body perturbation theory (CI-RMBPT) that has been successful in predicting atomic energies, matrix elements between discrete states, and other properties is quite promising, but it has not been applied to photo-ionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photo-ionization cross sections with minimal…
We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of convergence of the approach, and to demonstrate the relative superiority of complex over real Gaussian expansions. We then consider the photoionization of atomic hydrogen, and ionization by electron impact in the first Born approximation, for which the closed form cross sections serve as a solid benchmark. Using the proposed complex Gaussian representation of th…
We demonstrate that by changing the direction of the chirp in VUV pulses one can switch between excitation and ionization with very high contrast, if the carrier frequency of the light is resonant with two bound states. This is a surprising consequence if rapid adiabatic passage is extended to include transitions to the continuum. The chirp phase locks the linear combination of two resonantly coupled bound states whose ionization amplitudes interfere constructively or destructively depending on the chirp direction under suitable conditions. We derive the phenomenon in a minimal model and verif…
Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically within the framework of second-order perturbation theory. The non-relativistic results are compared with the relativistic calculations in the dipole and no-pair approximations as well as with the complete relativistic approach. The calculations are performed in both velocity and length gauges. Our results show a significant decrease of the total cross section for heavy atoms as compared to the non-relativistic treatment, which is mainly due to the relativistic wavefunction contract…
During multi-photon ionization of an atom it is well understood how the involved photons transfer their energy to the ion and the photoelectron. However, the transfer of the photon linear momentum is still not fully understood. Here, we present a time-resolved measurement of linear momentum transfer along the laser pulse propagation direction. Beyond the limit of the electric dipole approximation we observe a time-dependent momentum transfer. We can show that the time-averaged photon radiation pressure picture is not generally applicable and the linear momentum transfer to the photoelectron de…
The efficient photoionization of a Bose-Einstein condensate requires the creation of ions with the smallest possible transfer of atoms from the condensate into the thermal phase. The spontaneous decay from excited states into atomic states with momentum different from the initial one should be reduced. We investigate theoretically the two-photon ionization of a rubidium condensate using near resonant excitation to the 6P state and second photon at 421 nm or 1002 nm into the continuum. Different ionization schemes with coherent control of the first excitation and reduction of the spontaneous de…
We consider an analytic approach to the elucidation of the role played by Coulomb interaction in the formation of the spectrum and angular distributions of the electrons produced by above threshold ionization of the atoms. Our approach is based on allowance for the multiple scattering of a photoelectron by the Coulomb potential of the residual ion, with pickup of a field photon in each scattering act. The amplitude of a process with direct ionization of the atom and subsequent scattering of the photoelectron in the continuum by the Coulomb potential of the residual ion are found.
An exterior complex scaling technique is applied to compute Stark resonance parameters for two molecular orbitals ($1b_{1}$ and $1b_{2}$) represented in the field-free limit in a single-center expansion. For electric DC field configurations that guarantee azimuthal symmetry of the solution the calculation is carried out by solving a two-dimensional partial differential equation in spherical polar coordinates using a finite-element method. The resonance positions and widths as a function of electric field strengths are shown for field strengths starting in the tunnelling ionization regime, and …
Phase retrieval from angular streaking of XUV atomic ionization
Research School of Physics, The Australian National University（澳大利亚国立大学物理研究生院）；General, Theoretical and Computer Physics, Saratov State University（萨马拉国立大学一般、理论与计算物理）；Center for Relativistic Laser Science, Institute for Basic Science (IBS)（基础科学研究院相对论激光科学中心）；Stanford PULSE Institute, SLAC National Accelerator Laboratory（斯坦福PULSE研究所，SLAC国家加速器实验室）
Phase-shift differences and amplitude ratios of the outgoing $s$ and $d$ continuum wave packets generated by two-photon ionization of helium atoms are determined from the photoelectron angular distributions obtained using velocity map imaging. Helium atoms are ionized with ultrashort extreme-ultraviolet free-electron laser pulses with a photon energy of 20.3, 21.3, 23.0, and 24.3 eV, produced by the SPring-8 Compact SASE Source test accelerator. The measured values of the phase-shift differences are distinct from scattering phase-shift differences when the photon energy is tuned to an excited …
The dissociative ionization of H2+ interacting with intense, femtosecond extreme-ultraviolet laser pulses is investigated theoretically. This is done by numerical propagation of the time-dependent Schrödinger equation for a colinear one-dimensional model of H2+, with electronic and nuclear motion treated exactly within the limitations of the model. The joint-energy spectra (JES) are extracted for the fragmented electron and nuclei by means of the t-SURFF method. The dynamic interference effect, which was first observed in one-electron atomic systems, is in the present work observed for H2+, em…
We have investigated the energy correlation of the two electrons from nonsequential double ionization of helium atom in 800 nm laser fields at intensities below the recollision threshold by quantum calculations. The circular arcs structure of the correlated electron momentum spectra reveals a resonant double ionization process in which the two electrons transit from doubly excited states into continuum states by simultaneously absorbing and sharing excess energy in integer units of the photon energy. Coulomb repulsion between the two electrons in continuum states is responsible for the dominan…
We provide theoretical investigations of the response of the Ar and H atoms to an intense elliptically polarized few-cycle laser pulse, as a function of light ellipticity. The time-dependent Schr{ö}dinger equation describing the least-bound electron is solved numerically, and differential quantities such as the momentum distribution, the electron density in the continuum, and the above-threshold ionization spectra are computed. These quantities provide insight into the ionization dynamics and the electron rescattering process as a function of light ellipticity, and reveal great similarities be…
In this work we study the single ionization of hydrogen and helium by the impact of a punctual Coulomb projectile. To interpretate the cross section we introduce a series of Padé approximant. The nodes of the denominator of the Padé approximant give rise to poles in the charge complex plane. These poles move with the projectile velocity following a certain pattern. We find the positions of the poles of the Continuum Distorted Wave theory and an ensamble of experimental results. It was found that the ionization cross section may have oscillations in terms of the incident charge for a given impa…
We present rigorous results for quantum systems with both bound and continuum states subjected to an arbitrary strength time-periodic field. We prove that the wave function takes the form of a sum of time-periodic resonant states with complex quasi-energies and dispersive part of the the solution given by a power series in t^{-1/2}. Generally, the imaginary part of each resonance is negative, leading to ionization of the atom, but we also give examples where the ionization rate is zero implying the existence of a time-periodic Floquet bound state. The complex quasi-energy has a convergent pert…
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…
Total ionization cross sections of H, He, Li, Be, B, C, N, O, F, Ne, P, S and Ar neutral atoms by impact of antiprotons, H^{+}, He^{2+}, Be^{4+}, % C^{6+} and O^{8+}. were calculated using the CDWEIS (continuum distorted wave -Eikonal Initial state) theoretical method. Cross section depending on of initial the quantum numbers n and l are reported in Tables for a range of impact energies covering from 100 keV/amu to 10 MeV/amu
Multiple electron processes occur widely in atoms, molecules, clusters, and condensed matters when they are interacting with energetic particles or intense laser fields. In this work, a unified and accurate theoretical formalism is proposed on the direct multielectron processes of atoms including the multiple Auger decay and multiple ionization by an impact of an energetic electron or a photon based on the atomic collision theory described by a correlated many-body Green's function. Such a practical treatment is made possible due to different coherence features of the particles (matter waves) …
We report on a kinematically complete measurement of double ionization of helium by a single 1100 eV circularly polarized photon. By exploiting dipole selection rules in the two-electron continuum state, we observed the angular emission pattern of electrons originating from a pure quadrupole transition. Our fully differential experimental data and companion ab initio nonperturbative theory show the separation of dipole and quadrupole contributions to photo-double-ionization and provide new insight into the nature of the quasifree mechanism.
Tables of ab-initio total cross sections, probabilities at zero impact parameter, and impact parameter moments are presented concerning the ionization of Ne, Ar, Kr, and Xe by proton impact in the energy range (0.1-10) MeV. Calculations correspond to the continuum distorted wave eikonal initial state approximation (CDW-EIS) for energies up to 1MeV, and to the first Born approximation for larger energies. Results displayed in the tables are disaggregated for the different initial bound states, considering all shells for Ne and Ar, L-M-N shells of Kr and M-N-O shells of Xe. Our inner-shell ioniz…
We describe in detail how attosecond delays in laser-assisted photoionization can be computed using perturbation theory based on two-photon matrix elements. Special emphasis is laid on above-threshold ionization, where the electron interacts with an infrared field after photoionization by an extreme ultraviolet field. Correlation effects are introduced using diagrammatic many-body theory to the level of the random-phase approximation with exchange (RPAE). Our aim is to provide an ab initio route to correlated multi-photon processes that are required for an accurate description of experiments o…
We study excitation and ionization in the 1.5 MeV/amu O$^{8+}$-Li collision system, which was the subject of a recent reaction-microscope-type experiment [Fischer \textit{et al.}, Phys. Rev. Lett. \textbf{109}, 113202 (2012)]. Starting from an independent-electron model based on determinantal wave functions and using single-electron basis generator method and continuum distorted-wave with eikonal initial-state calculations we show that pure single ionization of a lithium $K$-shell electron is too weak a process to explain the measured single differential cross section. Rather, our analysis sug…
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…
Ionization, excitation, and de-excitation to the ground state is studied theoretically for the first excited singlet state B $^1Σ_u^+$ of H$_2$ exposed to intense laser fields with photon energies in between about 3 eV and 13 eV. A parallel orientation of a linear polarized laser and the molecular axis is considered. Within the dipole and the fixed-nuclei approximations the time-dependent Schrödinger equation describing the electronic motion is solved in full dimensionality and compared to simpler models. A dramatic break-down of the single-active-electron approximation is found and explained …
We formulate a computationally efficient time-independent method based on the multi-electron molecular R-matrix formalism. This method is used to calculate transition matrix elements for the multi-photon ionization of atoms and molecules under the influence of a perturbative field. The method relies on the partitioning of space which allows us to calculate the infinite-range free-free dipole integrals analytically in the outer region, beyond the range of the initial bound wave function. This approach is valid for an arbitrary order, that is, any number of photons absorbed both in the bound and…
The presence of vortices in the ionisation of hydrogen atoms by positrons at intermediate impact energies is investigated. The present findings show that a previously reported minima in the fully-differential cross section is the signature of a vortex in the continuum positron-electron-proton system. The behaviour of the real and imaginary parts of the complex-valued transition matrix is studied in order to determine and characterize the vortex in momentum space. The obtained information is translated to fully-differential ionisation cross sections, feasible of being measured with currently av…
Wave-particle duality is an inherent peculiarity of the quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. In this letter, we report on the observation of two-center interference in the molecular frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which were measured in coincidence with e…
We present a comprehensive study of electron collisions with calcium atoms by using the convergent \emph{B}-spline \emph{R}-matrix method. Elastic, excitation, and ionization cross sections were obtained for all transitions between the lowest 39 physical states of calcium (except for $3p^6 4s5g\ ^{3,1}G$) up to the $3p^6 4s8s\ ^1S$ state, for incident electron energies ranging from threshold to 100~eV. A multi\-configuration Hartree-Fock method with non\-orthogonal term-dependent orbitals was employed to generate accurate wave functions for the target states. Close-coupling expansions includin…
The absolute generalized cross sections and angular distribution parameters of photoelectrons for the two-photon above threshold $3p$-ionization of Ar were calculated in the exciting photon energy range from 15.76 to 36 eV. The correlation function technique developed earlier was extended for the case when an intermediate-state function is of a continuum-type. We show that two-photon ionization of Ar near the $3p^{4}$ threshold to a large extent is determined by the $(3p\dashrightarrow\varepsilon d)^{2}$ two-photon absorption via the giant resonance. This many-electron correlation causes (i) a…
We report on the fragmentation of the water molecule by $1$ MeV H$^{+}$, He$^{+}$ and 650 keV N$^{+}$ ion impact. The fragment-ion energy spectra were measured by an electrostatic spectrometer at different observation angles. The obtained double-differential fragmentation cross sections for N$^{+}$ is found to be more than an order of magnitude higher, than that for H$^{+}$. The relative ratios of the fragmentation channels are also different for the three projectiles. Additional fragmentation channels were observed in the spectra for He$^{+}$ and for N$^{+}$ impact, which are missing in the c…
We present a multichannel photoelectron interferometry technique based on trichromatic pulse shaping for unambiguous determination of quantum phases in multiphoton ionization (MPI) of potassium atoms. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the $3d$-state resulting in a (2+1) resonance-enhanced MPI (REMPI), a (1+2) REMPI occurs via the non-resonant intermediate $4p$-state with an initial green or blue pulse. We show that ionization via a non-resonant intermed…
Energy and Angular-Momentum Redistribution in Hydrogen Migdal Ionization
School of Physics, Yantai University（烟台大学物理学院）；Department of Physics and Institute of Theoretical Physics, Nanjing Normal University（南京师范大学物理科学与技术学院/理论物理研究所）；College of Science, China University of Petroleum (East China)（中国石油大学（华东）理学院）
We present accurate time-dependent ab initio calculations on fully differential and total integrated (generalized) cross sections for the nonsequential two-photon double ionization of helium at photon energies from 40 to 54 eV. Our computational method is based on the solution of the time-dependent Schroedinger equation and subsequent projection of the wave function onto Coulomb waves. We compare our results with other recent calculations and discuss the emerging similarities and differences. We investigate the role of electronic correlation in the representation of the two-electron continuum …
We study laser-assisted photoionization by attosecond pulses using a time-independent formalism based on diagrammatic many-body perturbation theory. Our aim is to provide an ab inito route to the "delays" for this above-threshold ionization process, which is essential for a quantitative understanding of attosecond metrology. We present correction curves for characterization schemes of attosecond pulses, such as "streaking", that account for the delayed atomic response in ionization from neon and argon. We also verify that photoelectron delays from many-electron atoms can be measured using simi…
The process of nonsequential two-photon double ionization of helium is studied by two complementary numerical approaches. First, the time-dependent Schr{ö}dinger equation is solved and the final wave function is analyzed in terms of projection onto eigenstates of the uncorrelated Hamiltonian, i.e., with no electron-electron interaction included in the final states. Then, the double ionization probability is found by means of a recently developed approach in which the concept of absorbing boundaries has been generalized to apply to systems consisting of more than one particle. This generalizati…
The B-spline R-matrix and the convergent close-coupling methods are used to study electron collisions with neutral beryllium over an energy range from threshold to 100 eV. Coupling to the target continuum significantly affects the results for transitions from the ground state, but to a lesser extent the strong transitions between excited states. Cross sections are presented for selected transitions between low-lying physical bound states of beryllium, as well as for elastic scattering, momentum transfer, and ionization. The present cross sections for transitions from the ground state from the …
Absorbing boundaries are frequently employed in real-time propagation of the Schrödinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an implicit description of observables involving infinitely extended continuum states. In the literature, several boundary absorbers have been proposed. They mostly fall into three main families: mask function absorbers, complex absorbing potentials, and exterior complex-scaled potentials. To date none of the proposed absorbers is perfect, and all present a certain…
