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 developed by Robicheaux and Gao. The seamless connection of that method with MQDT allows us to present high resolution spectra of the final state Rydberg resonances. Our analysis classifies the resonances above the $N=2$ threshold in terms of their group theory quantum numbers. Their dominant decay channels are found to obey the previously conjectured propensity rule far more weakly for these even parity states than was observed for the odd-parity states relevant to single photon ionization.
The multiconfigurational time-dependent Hartree-Fock method (MCTDHF) is applied for simulations of the two-photon ionization of Helium. We present results for the single- and double ionization from the groundstate for photon energies in the non-sequential regime, and compare them to direct solutions of the Schrödinger equation using the time-dependent (full) Configuration Interaction method (TDCI). We find that the single-ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI.
In a previous publication, procedures were proposed for unambiguously extracting amplitudes for single and double ionization from a time-dependent wavepacket by effectively propagating for an infinite time following a radiation pulse. Here we demonstrate the accuracy and utility of those methods for describing two-photon single and one-photon double ionization of helium. In particular it is shown how narrow features corresponding to autoionizing states are easily resolved with these methods.
Ground state ionization potential of the He^4 atom is evaluated to be 5 945 204 221 (42) MHz. Along with lower order contributions, this result includes all effects of the relative orders alpha^4, alpha^3*m_e/m_alpha and alpha^5*ln^2(alpha).
Ionization of helium-like ions with simultaneous excitation of the ns-states due to photon scattering is considered. The differential and total cross sections of the process are calculated to leading order of perturbation theory with respect to the interelectron interaction. The formulas obtained are applicable in the nonrelativistic energy range far beyond the ionization threshold.
In this paper, a quasistatic model is extended to describe the double ionization of Helium in intense linearly polarized field, yielding achieve an insight to the two-electron correlation effect in the ionization dynamics. Our numerical calculations reproduce the excessive double ionization and the photoelectron spectra observed experimentally both quantitatively and qualitatively. Moreover, it is shown that the classical collisional trajectories are the main source of the double ionization in the knee regime and responsible for the unusual angular distribution of the photoelectrons.
We investigate the laser-assisted single XUV photon double ionization of ground state helium. By solving full six-dimensional time-dependent schr{ö}dinger equation, we study the correlation and angular distribution. The discussion in joint energy and angular distributions reveals the competition in odd and even parity double ionization processes in the presence of weak laser field. The emission angle between two photoelectrons can be adjusted by the laser parameters. We depicts how the laser field enhance and/or enable the back-to-back and side-by-side emission of double ionization.
Attosecond pump-probe ionization process can be used to prepare atomic ions in the coherent superposition of states with opposite parity. The multiphoton shake-up ionization of Helium, in particular, generates ions with same principal quantum number and a net dipole moment that evolves on a time scale of few picoseconds, due to spin-orbit coupling. In this work we use an ab initio time-dependent close-coupling code to study how the coherence between levels of Helium ion can be controlled from the parameters of the ionizing-pulse sequence. The observed periodic revivals, on a picosecond time sc…
We explore the dependence of the double ionization of the He atom on the frequency of a strong laser field while keeping the ponderomotive energy constant. As we increase the frequency we find that the remarkable "finger-like" structure for high momenta recently found for $ω=0.055$ a.u. \cite{Staudte, Rudenko} persists for higher frequencies. At the same time, at $ω=0.187$ a.u. a new X-shape structure emerges for small momenta that prevails in the correlated momenta distribution. The role of this structure as a signature of the frequency dependence of non-sequential double ionization is discus…
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…
Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.
We consider single ionization of helium by fast highly charged ions. The ionization is treated as a three-body problem which involves the 'active' target electron, the target core (consisting of the target nucleus and the 'passive' target electron) and the projectile-ion. We show that, unless the transverse momentum transfer in the collision is large, the deviation of the interaction between the projectile and the target core from the purely coulomb law has a weak effect on the ionization. In particular, the account of this deviation does not enable one to get an agreement with experimental da…
Above 54.4 eV, two-photon double ionization of helium is dominated by a sequential absorption process, producing characteristic behavior in the single and triple differential cross sections. We show that the signature of this process is visible in the nuclear recoil cross section, integrated over all energy sharings of the ejected electrons, even below the threshold for the sequential process. Since nuclear recoil momentum imaging does not require coincident photoelectron measurement, the predicted images present a viable target for future experiments with new short-pulse VUV and soft X-ray so…
We present total cross sections for single and double ionization of helium by antiproton impact over a wide range of impact energies from 10 keV/amu to 1 MeV/amu. A non-perturbative time-dependent close-coupling method (TDCC) is applied to fully treat the correlated dynamics of the ionized electrons. Excellent agreement is obtained between our calculations and experimental measurements of total single and double ionization cross sections at high impact energies, whereas for lower impact energies, some discrepancies with experiment are found. At an impact energy of 1 MeV we also find that the d…
With the classical three-dimensional ensemble model, we have investigated the microscopic recollision dynamics in nonsequential double ionization of helium by 800 nm laser pulses at 2.0 PW/cm^2. We demonstrate that the asymmetric energy sharing between the two electrons at recollision plays a decisive role in forming the experimentally observed V-shaped structure in the correlated longitudinal electron momentum spectrum at the high laser intensity [Phys. Rev. Lett. 99, 263003 (2007)]. This asymmetric energy sharing recollision leaves footprints on the transverse electron momentum spectra, whic…
With a recently proposed quasiclassical ansatz [Geyer and Rost, J. Phys. B 35 (2002) 1479] it is possible to perform classical trajectory ionization calculations on many electron targets. The autoionization of the target is prevented by a Møller type backward--forward propagation scheme and allows to consider all interactions between all particles without additional stabilization. The application of the quasiclassical ansatz for helium targets is explained and total and partially differential cross sections for electron impact double ionization are calculated. In the high energy regime the cla…
In this paper, we have investigated the correlated electron emission of the nonsequence double ionization (NSDI) in an intense linearly polarized field. The theoretical model we employed is the semiclassical rescattering model, the model atom we used is the helium. We find a significant correlation between magnitude and direction of the momentum of two emission electrons, and give a good explanation for this striking phenomenon by observing the classical collisional trajectories. We argue that this correlation phenomenon is universal in NSDI process, as revealed by the recent experiment on the…
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 report on the observation of phase space modulations in the correlated electron emission after strong field double ionization of helium using laser pulses with a wavelength of 394~nm and an intensity of $3\cdot10^{14}$W/cm$^2$. Those modulations are identified as direct results of quantum mechanical selection rules predicted by many theoretical calculations. They only occur for an odd number of absorbed photons. By that we attribute this effect to the parity of the continuum wave function.
We investigate two-photon double ionization of helium by intense ($10^{15} W/cm^2$) ultrashort ($\approx 300$ as) soft X-ray pulses (E = 91.6 eV). The time-dependent two-electron Schrödinger equation is solved using a coupled channel method. We show that for ultrashort pulses the angular distribution of ejected electrons depends on the pulse duration and provides novel insights into the role of electron correlations in the two-electron photoemission process. The angular distribution at energies near the ``independent electron'' peaks is close to dipolar while it acquires in the ``valley'' of c…
We demonstrate the control of $^4$He(2$^3$S$_1$)-$^7$Li(2$^2$S$_{1/2}$) chemi-ionization reactions by all-optical electron-spin-state preparation of both atomic species prior to the collision process. Our results demonstrate that chemi-ionization is strongly suppressed (enhanced) for non-spin-conserving (spin-conserving) collisions at thermal energies. These findings are in good agreement with a model based on spin angular momentum coupling of the prepared atomic states to the quasi-molecular states. Small deviations from the model indicate the contribution of the $^4Σ^+$ channel to the reacti…
We present a unified treatment of the prevalence of different double ionization (DI) pathways as a function of the sum of the final electron energies in strongly driven Helium. We do so as a function of laser frequency and intensity. At small total energy a new DI pathway prevails where both electrons are ionized with a delay after re-collision. We find that three-body collisions between the two electrons and the nucleus underly this pathway--we refer to it as triple collision (TC) pathway. At high total energy the pathway that prevails is the one where one electron is ionized with a delay fol…
We show that time ordering underlying time-dependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of time-resolved two-photon double ionization (TPDI) of helium by an attosecond XUV pulse. The Eisenbud-Wigner-Smith time delay for the emission of a two-electron wavepacket and the time interval between subsequent emission events can be unambiguously determined by attosecond streaking. The delay between the two emission events sensitively depends on the energy, pulse duration, and angular dis…
We present the momentum distributions of the nucleus and of the electrons from double ionization of the helium atom by Compton scattering of photons with $hν=40$ keV. We find that the doubly charged ion momentum distribution is very close to the Compton profile of the nucleus in the ground state of the helium atom, and the momentum distribution of the singly charged ion to give a precise image of the electron Compton profile. To reproduce these results, non-relativistic calculations require the use of highly correlated initial- and final-state wavefunctions.
Without a formal derivation, we propose a formula for the total and single-differential cross in the problem of one-photon double ionization of an atom. The formula is benchmarked against accurate experimental data for the total cross section of helium. Furthermore, a direct comparison with ab initio calculations for the double ionization of Li+ suggests that the framework is valid for the entire helium isoelectronic sequence. To this end, we introduce a formula for the double ionization of lithium, as well as for the triple ionization of lithium and beryllium.
We study resonant two-photon ionization of helium atoms via the $1s3p$, $1s4p$ and $1s5p^1$P$_1$ states using the 15$^\mathrm{th}$ harmonic of a titanium-sapphire laser for the excitation and a weak fraction of the laser field for the ionization. The phase of the photoelectron wavepackets is measured by an attosecond interferometric technique, using the 17$^\mathrm{th}$ harmonic. We perform experiments with angular resolution using a velocity map imaging spectrometer and with high energy resolution using a magnetic bottle electron spectrometer. Our results are compared to calculations using th…
In this article we present triple differential cross sections for equal energy sharing kinematics for double photoionization of the helium atom at 20 and 40eV above threshold in the framework of the hyperspherical partial wave theory. This supplements our earlier work \cite{DCP03} in which we were successful in showing fully, gauge independence of the results in our formalism. Also in this work we treat cases in which the Stokes parameter S$_1 < 1$ so that partial polarization of the photon source is also taken into account. Agreement in shape with the Convergent Close Coupling \cite{BK03,HB98…
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 …
Testing Exotic Electron-Electron Interactions with the Helium Ionization-Energy Anomaly
Helmholtz Institute Mainz（亥姆霍兹马因茨研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Johannes Gutenberg University（约翰内斯·古腾堡大学）；Faculty of Mathematics, University of Vienna（维也纳大学数学学院）；Gravitational Physics Group, University of Vienna（维也纳大学引力物理组）；Department of Physics, University of California at Berkeley（加州大学伯克利分校物理系）
Compton scattering is one of the fundamental interaction processes of light with matter. Already upon its discovery [1] it was described as a billiard-type collision of a photon kicking a quasi-free electron. With decreasing photon energy, the maximum possible momentum transfer becomes so small that the corresponding energy falls below the binding energy of the electron. Then ionization by Compton scattering becomes an intriguing quantum phenomenon. Here we report a kinematically complete experiment on Compton scattering at helium atoms below that threshold. We determine the momentum correlati…
Recent angle-resolved RABBITT experiments have shown that the photoionization time delay depends on the emission angle of the photoelectron. In this work we demonstrate that for photoemission from helium accompanied by shake-up (correlation satellites), the angular variation of the time delay is dramatically enhanced by the dipolar coupling between the photoelectron and the highly polarizable bound electron in the IR field. We show that the additivity rule for the time delays due to the atomic potential, the continuum-continuum (cc) coupling by the IR field, and due to this two-electron proces…
We theoretically investigate the single and double ionization of the He atom by antiproton impact for projectile energies ranging from $3$~keV up to $1000$~keV. We obtain accurate total cross sections by directly solving the fully correlated two-electron time-dependent Schrödinger equation and by performing classical trajectory Monte-Carlo calculations. The obtained quantum-mechanical results are in excellent agreement with the available experimental data. Along with the total cross sections, we also present the first fully \textit{ab initio} doubly differential data for single ionization at 1…
The helium ground state nonrelativistic energy with 24 significant digits is presented. The calculations are based on variational expansion with randomly chosen exponents. This data can be used as a benchmark for other approaches for many electron and/or three-body systems.
It is shown that it is feasible to use ultrashort time delay between two XUV femtosecond pulses in order to control two photon resonant ionization. The proposal is demonstrated on the spectrum of Helium, in terms of nonperturbative solutions of the time dependent Schroedinger equation. Comparison with results from second order time dependent perturbation theory provides additional insight.
Accurate local Kohn-Sham potentials have been constructed for the ground $1s^2 ^1S$ state and, in particular, for the lowest triplet $1s2s ^{3}S$ state of the helium atom, using electron densities from many-body calculations and the procedure of van Leeuwen and Baerends (Phys. Rev. A{\bf49}, 2138 (1994)). The resulting Kohn-Sham orbitals reproduce the many-body densities very accurately, and furthermore we have demonstrated that the negative of the energy eigenvalue of the outermost electron orbital agrees with the corresponding ionization energy with extreme accuracy. The procedure is also ap…
The momentum distribution of the electron in the reaction p+He $\rightarrow$ H + He$^{2+}$ + $e$ is measured for projectile energies $E_p$=300 and 630 keV/u at very small scattering angles of hydrogen. We mainly present two dimensional distributions parallel $(k_{||})$ and perpendicular $(k_{\perp})$ to the projectile beam. Theoretical calculations were carried out within the Plane Wave First Born Approximation (PWFBA), which includes both electron emission mechanisms, shake-off and sequential capture and ionization. It is shown that electron correlations in the target wave function play the m…
Even though ion/atom-collision is a mature field of atomic physics great discrepancies between experiment and theoretical calculations are still common. Here we present experimental results with highest momentum resolution on single ionization of helium induced by 1\,MeV protons and compare these to different theoretical calculations. The overall agreement is strikingly good and already the first Born approximation yields good agreement between theory and experiment. This has been expected since several decades, but so far has not been accomplished. The influence of projectile coherence effect…
We explore excitation and ionization by neutron impact as a novel tool for the investigation of electron-electron correlations in helium. We present single and double ionization spectra calculated in accurate numerical ab-initio simulations for incoming neutrons with kinetic energies of up to 150 keV. The resulting electron spectra are found to be fundamentally different from photoioniza- tion or charged particle impact due to the intrinsic many-body character of the interaction. In particular, doubly excited resonances that are strongly suppressed in electron or photon impact become prominent…
Triple differential cross sections (TDCSs) for electron vortex projectile ionization of helium into the azimuthal plane are calculated using the distorted wave Born approximation. In this collision geometry, the TDCSs at low and intermediate energies exhibit unique qualitative features that can be used to identify single and double scattering mechanisms. In general, our results predict that the ionization dynamics for vortex projectiles are similar to those of their non-vortex counterparts. However, some key differences are observed. For non-vortex projectiles, a double scattering mechanism is…
The collision-ionization mechanism of nonsequential double ionization (NSDI) process in IR+XUV two-color laser fields [\PRA \textbf{93}, 043417 (2016)] has been investigated by us recently. Here we extend this work to study the collision-excitation-ionization (CEI) mechanism of NSDI processes in the two-color laser fields with different laser conditions. It is found that the CEI mechanism makes a dominant contribution to the NSDI as the XUV photon energy is smaller than the ionization threshold of the He$^+$ ion, and the momentum spectrum shows complex interference patterns and symmetrical str…
By using the B-spline numerical method, we investigate a two-photon double-ionization (TPDI) process of helium in a high-frequency laser field with its frequency ranging from 1.6~a.u. to 3.0~a.u. and the pulse duration ranging from 75 to 160~attoseconds. We found that there exists a characteristic time $t_{c}$ for a TPDI process, such that the pattern of energy distribution of two ionized electrons presents a peak or two, depending respectively on whether the pulse duration is shorter or longer than $t_{c}$. Especially, as the pulse duration is larger than $t_c$, the TPDI spectrum shows a doub…
We study resonant two-color two-photon ionization of Helium via the 1s3p 1P1 state. The first color is the 15th harmonic of a tunable titanium sapphire laser, while the second color is the fundamental laser radiation. Our method uses phase-locked high-order harmonics to determine the {\it phase} of the two-photon process by interferometry. The measurement of the two-photon ionization phase variation as a function of detuning from the resonance and intensity of the dressing field allows us to determine the intensity dependence of the transition energy.
Recent experimental developments of high-intensity, short-pulse XUV light sources are enhancing our ability to study electron-electron correlations. We perform time-dependent calculations to investigate the so-called "sequential" regime (photon energy above 54.4 eV) in the two-photon double ionization of helium. We show that attosecond pulses allow to induce and probe angular and energy correlations of the emitted electrons. The final momentum distribution reveals regions dominated by the Wannier ridge break-up scenario and by post-collision interaction.
Nonsequential double ionization (NSDI) of helium in an intense few-cycle laser pulse is investigated by applying the three-dimensional semi-classical re-scattering method. It is found that the momentum distribution of He$^{2+}$ shows a single-double-single peak structure as the pulse intensity increases. According to the different mechanisms dominating the NSDI process, the laser intensity can be classified into three regimes where the momentum distribution of He$^{2+}$ exhibits different characteristics. In the relatively high intensity regime, an NSDI mechanism named the "laser-assisted coll…
The nonrelativistic ionization energy levels of a helium atom are calculated for $S$, $P$, $D$ and $F$ states. The calculations are based on the variational method of "exponential" expansion. The convergence of the calculated energy levels is studied as a function of the number of basis functions $N$. This allows us to claim that the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate up to 28-35 significant digits. Calculations of the nonrelativistic ionization energy of the negative hydrogen ion H$^-$ are also presented.
Quantum electrodynamical (QED) calculations of ionization energies of the $1snd\,D$ states are performed for the helium atom. We reproduce the previously known relativistic and QED effects up to order $mα^5$ and extend the theory by calculating the complete $mα^6$ correction. The total contribution of the $mα^6$ effects is shown to be much smaller than previously estimated, due to a large cancelation between the radiative and non-radiative parts of this correction. As a result of our calculations, we confirm the previously reported deviations between measured transition energies and theoretica…
We analyze a transfer ionization (TI) reaction in the fast proton-helium collision $\rm H^+ + He \to H^0 + He^{2+} + e^-$ by solving a time-dependent Schrödinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. In addition, we construct various time independent analogues of our model using lowest order perturbation theory in the form of the Born series. By comparing various aspects of the TDSE and the Born series calculations, we conclude that the recent discrepancies of experimental and theoretical data may be attributed to deficiency of the B…
We analyze how bound-state excitation, electron exchange and the residual binding potential influence above-threshold ionization (ATI) in Helium prepared in an excited $p$ state, oriented parallel and perpendicular to a linearly polarized mid-IR field. Using ab initio B-spline Algebraic Diagrammatic Construction (ADC), and several one-electron methods with effective potentials, including the Schrödinger solver Qprop, modified versions of the Strong-Field Approximation and the Coulomb-Quantum Orbit Strong-Field Approximation (CQSFA), we find that these specific physical mechanisms leave signifi…
We report on a kinematically complete experiment on strong field double ionization of helium using laser pulses with a wavelength of 394\,nm and intensities of $3.5-5.7\times10^{14}\,W/cm^2$. Our experiment reaches the most complete level of detail which previously has only been reached for single photon double ionization. We give an overview over the observables on many levels of integration, starting from the ratio of double to single ionization, the individual electron and ion momentum distributions over joint momentum and energy distributions to fully differential cross sections showing th…
We revisit recent developments in the theoretical foundations of time-dependent density functional theory (TDDFT). TDDFT is then applied to the calculation of total cross sections for ionization processes in the antiproton-Helium collision system. The Kohn-Sham potential is approximated as the sum of the Hartree-exchange potential and a correlation potential that was proposed in the context of laser-induced ionization. Furthermore, some approaches to the problem of calculating the ionization probabilities from the density are discussed. Small projectile energies below 5keV are considered as we…
We illustrate how attosecond light pulses can be used to directly mapping out the time-dependence of the correlated motion of two excited atomic electrons, discuss how the two-electron correlations manifest themselves in realistic attosecond measurements, and propose the following for experimental exploration: (a) The single ionization signals which directly reveal bending-vibrational motion of the correlated electron pair, (b) and also its rotational motion. (c) The double ionization signals which directly reveal the two-electron density in momentum space. To facilitate the description of the…
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 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 present a theoretical method for calculating multiphoton ionization amplitudes and cross sections of few-electron atoms. The present approach is based on an extraction of partial wave amplitudes from a scattering wave function, which is calculated by solving a system of driven Schroedinger equations. The extraction relies on a description of partial waves in terms of a small number of Coulomb waves with fixed wave numbers. The method can be used for photon energies below and above the ionization threshold and to treat resonance-enhanced multiphoton ionization. We use it to calculate two-, t…
We perform quantum electrodynamic calculations of the ionization energy of the $1s3d$ states of the $^4$He atom, including a complete evaluation of the $mα^6$ correction. We find a large contribution from the nonradiative part of this correction, which has not been accounted for in previous investigations. The additional contribution shifts theoretical predictions for ionization energies by about 10$\,σ$. Despite this shift, we confirm the previously reported systematic deviations between measured experimental results and theoretical predictions for transitions involving $3D$ states. The reaso…
