The cross section for single K-shell ionization by a high-energy photon is evaluated in the next-to-leading order of the nonrelativistic perturbation theory with respect to the electron-electron interaction. The screening corrections are of particular importance for light helium-like ions. Even in the case of neutral He atom, our analytical predictions turn out to be in good agreement with the numerical calculations performed with the use of the sophisticated wave functions. The universal high-energy behavior is studied for the ratio of double-to-single photoionization cross sections. We also discuss the fast convergence of the perturbation theory over the reversed nuclear charge number 1/Z.
We account for the different symmetries of the 2^{1,3}S helium excited states in a quasiclassical description of the knockout mechanism augmented by a quantum shakeoff contribution. We are thus able to formulate the separate contribution of the knockout and shakeoff mechanisms for double photoionization for any excess energy from the 2^{1,3}S states. Photoionization ratios and singly differential cross sections calculated for the 2^{1,3}S excited states of helium are found to be in very good agreement with recent theoretical results.
A fully relativistic calculation of the double photoionization of helium-like atoms is presented. The approach is based on the partial-wave representation of the Dirac continuum states and accounts for the retardation in the electron-electron interaction as well as the higher-order multipoles of the absorbed photon. The electron-electron interaction is taken into account to the leading order of perturbation theory. The relativistic effects are shown to become prominent already for the medium-Z ions, changing the shape and the asymptotic behaviour of the photon energy dependence of the ratio of…
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.
Hyperspherical partial wave approach has been applied here in the study of double photoionization of the helium atom for equal energy sharing geometry at 20 eV excess energy. Calculations have been done both in length and velocity gauges and are found to agree with each other, with the CCC results and with experiments and exhibit some advantages of the corresponding three particle wave function over other wave functions in use.
We investigate the angle-resolved photoelectron spectra from laser-assisted photoionization for helium and neon atoms using an \textit{ab initio} method based on time-dependent surface flux and configuration interaction singles. We find that the shape of the distributions can be interpreted using a propensity rule, an intrinsic difference in the absorption and emission processes, as well as interference effects between multiple paths to the final angular momentum state. In neon we find that the difference between absorption and emission is hidden in the first sideband due to the multiple compe…
In this work, we report an application of Hylleraas-$B$-spline basis set to the nonrelativistic Bethe logarithm calculation of helium. The Bethe logarithm for $n\ ^1S$, $n$ up to 10, states of helium are calculated with a precision of 7-9 significant digits in two gauges, which greatly improves the accuracy of the traditional $B$-spline basis set. In addition, to deal with the numerical linear correlation problem in Bethe logarithm calculation, we developed a multiple-precision generalized symmetric eigenvalue problem solver (MGSEPS). This program may be very useful to precision calculations.
Using the eigenchannel R-matrix method we calculate partial photoionization cross sections from the ground state of the helium atom for incident photon energies up to the N=9 manifold. The wide energy range covered by our calculations permits a thorough investigation of general patterns in the cross sections which were first discussed by Menzel and co-workers [Phys. Rev. A {\bf 54}, 2080 (1996)]. The existence of these patterns can easily be understood in terms of propensity rules for autoionization. As the photon energy is increased the regular patterns are locally interrupted by perturber st…
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.
In a joint experimental and theoretical endeavour, photoionization of metastable C4+(1s 2s 3S1) ions via intermediate levels with hollow, double-K-vacancy configurations 2s2p, 2s3p, 2p3s, 2p3d, 2s4p, 2p4s and 2p4d has been investigated. High-resolution photon-ion merged-beams measurements were carried out with the resolving power reaching up to 25,000 which is sufficient to separate the leading fine-structure components of the 2s2p 3P term. Many-body perturbation theory was employed to determine level-to-level cross sections for K-shell excitation with subsequent autoionization. The resonance …
We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wavepacket resulting from the integration of the time-dependent Schroedinger equation in a finite-element discrete variable representation basis. These techniques are: projection on products of hydrogenic bound and continuum states, projection onto multi-channel scattering states computed in a B-spline clos…
Using extreme-ultraviolet attosecond-pulse-trains, we investigate the photoionization dynamics of a Helium atom in the presence of moderately-strong (~10^12 W/cm^2) femtosecond laser pulses. The electronic structure of a laser-dressed atom is traced in real-time through precision measurements of ion-yields and photo-electron angular distributions. Quantum interferences between photo-excitation paths are interpreted using the Floquet formalism. As the laser pulse intensity ramps on femtosecond timescales, we observe transitions between ionization channels mediated by different atomic resonances…
We discuss the results of the calculation of the photoionization with de-excitation of excited He and helium-like ions Li$^{+}$ and B$^{3+}$ at high but non-relativistic photon energies $ω$. Several lower $^{1}S$ and $^{3}S$ states are considered. We present and analyze the ratios $R_{d}^{+\ast}$ of the cross sections of photoionization with de-excitation, $σ_{(d)}^{+\ast}(ω)$, and of the photo-ionization with excitation, $σ^{+\ast}(ω)$. The dependence of $R_{d}^{+\ast}$ on the excitation of the target object and the charge of its nucleus is presented. Apart to theoretical interest, results ob…
The dynamics of vibrational wave packets in triplet states of rubidium dimers (Rb2) formed on helium nanodroplets are studied using femtosecond pump-probe photoionization spectroscopy. Due to fast desorption of the excited Rb2 molecules off the droplets and due to their low internal temperature, wave packet oscillations can be followed up to very long pump-probe delay times >1.5ns. In the first excited triplet state (1)^3Σ_g^+, full and fractional revivals are observed with high contrast. Fourier analysis provides high-resolution vibrational spectra which are in excellent agreement with ab ini…
We consider a general procedure to evaluate the Bethe logarithm for a general few-body atomic or molecular system. As benchmarks we use calculation for the ground states of a helium atom and H_2^+ molecular ion. The obtained values are: β_He=4.37016022306(2) for the helium atom and β_{H_2^+} = 3.012230335(1) for the H_2^+. Both results substantially improve the best known values for these quantities.
We calculate the double differential distributions and distributions in recoil momenta for the high energy non-relativistic double photoionization of helium. We show that the results of recent experiments is the pioneering experimental manifestation of the quasifree mechanism for the double photoionization, predicted long ago in our papers. This mechanism provides a surplus in distribution over the recoil momenta at small values of the latter, corresponding to nearly "back-to-back" emission of the electrons. Also in agreement with previous analysis the surplus is due to the quadrupole terms of…
We consider photoionization of a system bound by the central potential $V(r)$. We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann--Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the an…
Nonrelativistically forbidden, single-photon transition rates between low lying states of the helium atom are rigorously derived within quantum electrodynamics theory. Equivalence of velocity and length gauges, including relativistic corrections is explicitly demonstrated. Numerical calculations of matrix elements are performed with the use of high precision variational wave functions and compared to former results.
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine-structure constant $α$. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, $r_1$, $r_2$ and $r = |\vec{r}_1-\vec{r}_2|$. The choice of the exponential basis functions of the form $\exp(-αr_1 -βr_2 -γr)$ allows us to construct an accurate and c…
We calculated ab initio the three-fold differential cross section of a double single-photon Helium photoionization at equal energy sharing, and obtained from one the Gaussian width parameter, describing the angular interelectron correlations, for the total electrons energies range E from 0.1 eV to 100 eV. The results are in excellent agreement with experimental data but indicate that the Wannier threshold law for angular distribition is not correct at energies attainable in modern experiments. It is shown that the Gaussian width parameter dependence on energy is much better described by the mo…
The photoionization of the four-electron beryllium-like isoelectronic series from the neutral to Fe^{+22} has been studied for ground ^1S and metastable ^3P initial states. The wave functions of the final-state (target) ions were built using the CIV3 code. Both nonrelativistic LS-coupling R-matrix and relativistic Breit-Pauli (BP) R-matrix methods were used to calculate the cross sections in the photon-energy range between the first ionization threshold and the 1s^2 4f_{7/2} threshold for each ion. Our total cross sections compare well with experiment which is available for Be, B^+, C^{+2}, N^…
We outline a non-perturbative procedure for calculating the total photoionization cross-section of two-electron atomic systems. The procedure is based on the Floquet-Fourie representation of the solution of the time-dependent Schrodinger equation. The Floquet-Fourie ansatz produces a set of equations which is recast into a generalized eigenvalue problem by means of the complex rotation procedure. With the use of the Hylleraas-type basis functions, the total photoionization cross-sections are obtained within the accuracy of a fraction of a percent. The total photoionization cross-sections for n…
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.
We present a generalization of the pioneering results obtained for single K-shell photoionization of H-like ions by M. Stobbe [Ann. Phys. 7 (1930) 661] to the case of the helium isoelectronic sequence. The total cross section of the process is calculated, taking into account the correlation corrections to first order of the perturbation theory with respect to the electron-electron interaction. Predictions are made for the entire non-relativistic energy domain. The phenomenon of dynamical suppression of correlation effects in the ionization cross section is discussed.
We present the hybrid anti-symmetrized coupled channels method for the calculation of fully differential photo-electron spectra of multi-electron atoms and small molecules interacting with strong laser fields. The method unites quantum chemical few-body electronic structure with strong-field dynamics by solving the time dependent Schrödinger equation in a fully anti-symmetrized basis composed of multi-electron states from quantum chemistry and a one-electron numerical basis. Photoelectron spectra are obtained via the time dependent surface flux (tSURFF) method. Performance and accuracy of the …
Time delays of electrons emitted from an isotropic initial state and leaving behind an isotropic ion are assumed to be angle-independent. Using an interferometric method involving XUV attosecond pulse trains and an IR probe field in combination with a detection scheme, which allows for full 3D momentum resolution, we show that measured time delays between electrons liberated from the $1s^2$ spherically symmetric ground state of helium depend on the emission direction of the electrons relative to the linear polarization axis of the ionizing XUV light. Such time-delay anisotropy, for which we me…
The total cross section for double ionization of lithiumlike ions by a high-energy photon is calculated in leading order of the nonrelativistic perturbation theory. The partial contributions due to simultaneous and sequential emissions of two electrons are taken into account. The cross section under consideration is shown to be related to those for double photoeffect on the ground and excited 2^{1,3}S states of heliumlike ions. The double-to-single ionization ratio is equal to R = 0.288/Z^2 for lithiumlike ions with moderate nuclear charge numbers Z. However, even for the lightest three-electr…
Theory for the Rydberg states of helium: quantum defect extensions and comparison with experiment up to $n = 102$ for the singlet and triplet $P$-states
University of Windsor（温莎大学）；Drake University（德雷克大学）
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…
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 introduce the time-dependent restricted active space Configuration Interaction method to solve the time-dependent Schrödinger equation for many-electron atoms, and particularly apply it to the treatment of photoionization processes in atoms. The method is presented in a very general formulation and incorporates a wide range of commonly used approximation schemes, like the single-active electron approximation, time-dependent Configuration Interaction with single-excitations, or the time-dependent R-matrix method. We proof the applicability of the method by calculating the photoionization cro…
Autoionization, which results from the interference between direct photoionization and photoexcitation to a discrete state decaying to the continuum by configuration interaction, is a well known example of the important role of electron correlation in light-matter interaction. Information on this process can be obtained by studying the spectral, or equivalently, temporal complex amplitude of the ionized electron wavepacket. Using an energy-resolved interferometric technique, we measure the spectral amplitude and phase of autoionized wavepackets emitted via the sp2+ and sp3+ resonances in heliu…
We continue our studies of the high energy nonrelativistic asymptotics for the photoionization cross section of the systems bound by a central field $V(r)$. We consider the bound states with the orbital momentum $\ell=1$. We show, that as well as for the $s$ states the asymptotics can be obtained without solving of the wave equations for the bound and outgoing electrons. The asymptotics of the cross sections is expressed in terms of the asymptotics of the Fourier transform $V(p)$ of the field and its derivative $V'(p)$ by employing the Lippmann--Schwinger equation. The shape of the energy depe…
A rapid and relatively simple scheme of calculation is elaborated and applied to cosmological recombination of helium. Employing the nonrelativistic Coulomb Green's function, a wavefunction of a colliding electron is represented in an integral form applicable for calculations. Bound electrons of helium are described by the Hartree-Fock wavefunctions. The free-bound transition probabilities into excited states of helium, and the probabilities of bound-bound transitions in helium are calculated in different modes. It is revealed that free-bound transition probabilities weakly depend on to what e…
Collinear configurations of the helium-like atomic systems, relevant, e.g., for the quasifree mechanism of the double photoionization of helium, are studied, parameterized by the single scalar parameter $-1\leq λ\leq1$ ("collinear parameter") where $λ=0$ corresponds to the electron-nucleus ($\textbf{e-n}$) coalescence and $λ=1$ corresponds to the electron-electron ($\textbf{e-e}$) coalescence. In general, $λ>0$ corresponds to the \textbf{n-e-e} configuration, and $λ<0$ to the \textbf{e-n-e} configuration. Simple mathematical representations of the expectation values of the Dirac delta function…
A review of some recently developed methods of calculating multiple differential cross-sections of photoionization and electron impactionization of atoms and molecules having two active electrons is presented. The methods imply original approaches to calculating three-particle Coulomb wave functions. The external complex scaling method and the formalism of the Schroedinger equation with a source in the right-hand side are considered. Efficiency of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. An orig…
We study the photoionization and autoionization of Helium atom subject to ultrashort laser pulses by using a Feshbach formalism in the time domain. We solve the time-dependent Schrödinger equation in terms of a configuration interaction (CI) spectral method, in which the total wavefunction is expanded with configurations defined within bound-like ($\mathcal{Q}$) and scattering-like ($\mathcal{P}$) halfspaces. The method allowsone to provide accurate descriptions of both the atomic structure (energy positions and widths) and the photodynamics. We illustrate our approach by i) calculating the ti…
Attosecond photoionisation time delays reveal information about the potential energy landscape an outgoing electron wavepacket probes upon ionisation. In this study we experimentally quantify, for the first time, the dependence of the time delay on the angular momentum of the liberated photoelectrons. For this purpose, electron quantum-path interference spectra have been resolved in energy and angle using a two-color attosecond pump-probe photoionisation experiment in helium. A fitting procedure of the angle-dependent interference pattern allows us to disentangle the relative phase of all four…
We calculate the distributions in recoil momenta and their energy distributions for the high energy non-relativistic double photoionization of helium caused by the quasifree mechanism of the process. The distributions obtain local maxima at small values of the recoil momenta. This is in agreement with the earlier predictions and with recently obtained experimental data. We obtained also the angular correlations, which reach the largest value in the "back-to-back" configuration of the photoelectrons. Our analysis is valid in all high energy nonrelativistic region. Particular equations are true …
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 h…
We investigate the electronic structure of the helium atom in a magnetic field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic system with two interactin g electrons and a fixed nucleus. Scaling laws are provided connecting the fixed-nucleus Hamiltonia n to the one for the case of finite nuclear mass. Respecting the symmetries of the electronic Ham iltonian in the presence of a magnetic field, we represent this Hamiltonian as a matrix with res pect to a two-particle basis composed of one-particle states of a Gaussian basis set. The corresponding generalized eigenvalue probl…
Recent developments toward the production and laboratory use of pulses of high intensity, and/or of very high frequency, and/or of ultrashort duration, make possible experiments which can produce time-resolved data on ultrafast transformations involving motions of electrons. The formulation, quantitative understanding and prediction of related new phenomena entail the possibility of computing and applying solutions of the many-electron time-dependent Schroedinger equation, for arbitrary electronic structures, including the dominant effects of Rydberg series, of multiply excited states and of t…
