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 show that the relativistic mask method works very well and reproduces the electron energy and angular distributions calculated by the direct method in the energy range where both methods can be used. On the other hand, the relativistic mask method can be applied for longer laser pulses and/or higher photoelectron energies where the direct method may have difficulties.
Ionization of light atoms and ions during the nuclear $β^{-}$-decay is considered. To determine the final state probabilities of electron ionization we have developed a procedure based on the natural orbital expansions for the bound state wave functions of all atoms/ions involved in this process.
Ionization of highly charged relativistic ions by neutral atoms and ions is considered. Numerical results of recently developed computer codes based on the relativistic Born and the equivalent-photon approximations are presented. The ionization of the outer shells dominate. For the outer projectile electron shells, which give the main contribution to the process, the non-relativistic Schrödinger wave functions can be used. The formulae for the non-relativistic reduction of the Dirac matrix-elements are obtained for ionization of electrons with arbitrary quantum numbers $n$ and $\ell$.
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.
It is shown that recently measured cross sections for double ionization of negative ions ($H^-, O^-$, and $C^-$) possess a universal shape when plotted in suitable dimensionless units. The shape can be represented with a simple analytical function, following the same principles as it has been done in establishing a universal shape function for single ionization [Rost and Pattard 1997 Phys. Rev. A {\bf 55} R5]. Thereby, it is demonstrated that direct double ionization dominates the cross section for the targets considered.
The National Institute of Standards and Technology (NIST) database on ionization potentials for neutral atoms and ions is examined. For each isoelectronic sequence, we construct a regularized perturbative series that exactly matches the large-$Z$ and $Z\approx N-1$ regions. Comparison of the NIST data with this series allows the identification of problematic values in the reported data.
The non-resonant two-photon ionization of hydrogen-like ions is studied in second-order perturbation theory, based on the Dirac equation. To carry out the summation over the complete Coulomb spectrum, a Green function approach has been applied to the computation of the ionization cross sections. Exact second-order relativistic cross sections are compared with data as obtained from a relativistic long-wavelength approximation as well as from the scaling of non-relativistic results. For high-Z ions, the relativistic wavefunction contraction may lower the two-photon ionization cross sections by a…
We consider single ionization of lithium atom in collisions with $p$ and O$^{8+}$ projectiles. Doubly differential cross sections for ionization are calculated within a relativistic non-perturbative approach. Comparisons with the recent measurements and theoretical predictions are made.
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.
High-precision QED calculations of the ground-state ionization energies are performed for all boronlike ions with the nuclear charge numbers in the range $16 \leqslant Z\leqslant 96$. The rigorous QED calculations are performed within the extended Furry picture and include all many-electron QED effects up to the second order of the perturbation theory. The contributions of the third- and higher-order electron-correlation effects are accounted for within the Breit approximation. The nuclear recoil and nuclear polarization effects are taken into account as well. In comparison with the previous e…
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…
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…
The applicability of the Benford law for different data sets of atomic cross sections by ion impact is studied. We find that the data sets corresponding to theoretical ionization and capture cross sections of neutral targets by multicharged ions satisfy quite well the Benford law, not only for the first digits but also within a given order of magnitude. Experimental stopping power values from the International Atomic Energy Agency database were also scrutinized, but in this case the Benford conformity was not so satisfactory due to its small rank width. In all cases, errors, densities of prime…
The angular distribution of the emitted electrons, following the two-photon ionization of the hydrogen-like ions, is studied within the framework of second order perturbation theory and the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron--photon interaction. For medium- and high-Z ions, in particular, the non-dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if compared with th…
The photon-ion merged-beams technique for the photoionization of mass/charge selected ionized atoms, molecules and clusters by x-rays from synchrotron radiation sources is introduced. Examples for photoionization of atomic ions are discussed by going from outer-shell ionization of simple few-electron systems to inner-shell ionization of complex many-electron ions. Fundamental ionization mechanisms are elucidated and the importance of the results for applications in astrophysics and plasma physics is pointed out. Finally, the unique capabilities of the photon-ion merged-beams technique for the …
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…
We report on the production of cold, state-selected H$_2^+$ molecular ions in a linear RF trap. The ions are produced by (3+1) resonance-enhanced multi-photon ionisation (REMPI) of H$_2$, and sympathetically cooled by laser-cooled Be$^+$ ions. After demonstrating and characterizing the REMPI process, we use photodissociation by a deep UV laser at 213~nm to verify the high vibrational purity of the produced H$_2^+$ ion samples. Moreover, the large difference between the photodissociation efficiencies of ions created in the $v=0$ and $v=1$ levels provides a way to detect a $v=0 \to 1$ transition…
The angular distribution of the emitted electrons, following the two--photon ionization of the hydrogen--like ions, is studied within the framework of second order perturbation theory \textit{and} the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron--photon interaction. For medium-- and high--Z ions, in particular, the non--dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if co…
The photon-ion merged-beams technique has been employed at the new Photon-Ion spectrometer at PETRA III (PIPE) for measuring multiple photoionization of Xe$^{q+}$ (q=1-5) ions. Total ionization cross sections have been obtained on an absolute scale for the dominant ionization reactions of the type hν+ Xe$^{q+}$ $\to$ Xe$^{r+}$ + (q-r) e$^-$ with product charge states q+2 $\le$ r $\le$ q+5. Prominent ionization features are observed in the photon-energy range 650-750 eV, which are associated with excitation or ionization of an inner-shell 3d electron. Single-configuration Dirac-Fock calculation…
We study static-field ionization of He-like ions with nuclear charge number in the range of $2\le Z \le 36$. Both the tunneling and over-the-barrier regimes are considered. We calculate the ionization rates by three approximate methods: a fitting formula based on the Perelemov-Popov-Terent'ev (PPT) formula, a perturbative expansion in powers of $1/Z$, and a single-active electron approximation, and compare them with reference ionization rates computed by the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach. The relative deviation of the rates computed by the PPT-based fitting f…
We study $N$-electron atoms with nuclear charge $Z$. It is well known that, in the cationic ($Z > N$) high-$Z$ region, the atom behaves as a weakly interacting system. The anionic ($Z < N$) regime, on the other hand, is characterized by an instability threshold at $Z_c \lesssim N-1$, below which the atom spontaneously emits an electron. We construct a regularized perturbative series (RPS) for the ionization potential of ions in an isoelectronic sequence that exactly reproduces both, the large $Z$ and the $Z$ near $Z_c$ limits. The large-$Z$ expansion coefficients are analytically computed from…
The L-subshell ionization mechanism is studied in an ultra-thin osmium target bombarded by 4-6 MeV/u fluorine ions. Multiple ionization effects in the collisions are considered through the change of fluorescence and Coster-Kronig yields while determining L-subshell ionization cross sections from L-line x-ray production cross sections. The L-subshell ionization, as well as L-shell x-ray production cross sections so obtained, are compared with various theoretical approximations. The Coulomb direct ionization contributions is studied by (i) the relativistic semi-classical approximations (RSCA), (…
A simple modification of the semiempirical model of Shevelko et al (J. Phys. B: At. Mol. Opt. Phys. 38, 525 (2005)) is proposed for the calculation of electron impact double ionization cross section of He^0, Li^(0,1+), B^(1+), C^(1+,3+), O^(0-3+), Ar^(0-7+), Fe^(1+,3+-6+), Kr^(0-4+), Xe^(0-8+), Pr^(1+-4+), Pb^(0-9+), Bi^(1+-3+,10+), and U^(0,10+,13+) atoms and positive ions. The contributions from the direct double ionization of outer shell and indirect processes of inner shells are also considered in the proposed modification. Ionic correction and relativistic factor are also incorporated. Th…
In a recent paper, El-Maaref et al. [J. Quant. Spectrosc. Radiat. Transfer 2019, 224:147] have reported atomic data for Zn-like W~XLV. Their results are mainly for energy levels, radiative rates, collision strengths ($Ω$) for electron impact excitation, and cross sections for ionization, but for only for a few levels/transitions, and in a very limited range of energy. For the calculations of $Ω$ they have adopted the DARC code. In this comment, through our independent calculations, we demonstrate that their results for $Ω$ are highly underestimated by over two orders of magnitude, and hence ar…
Accurate cross section data for electron impact ionization (EII) are needed in order to interpret the spectra of collisionally ionized plasmas both in astrophysics and in the laboratory. Models and spectroscopic diagnostics of such plasmas rely on accurate ionization balance calculations, which depend, in turn, on the underlying rates for EII and electron-ion recombination. EII measurements have been carried out using the TSR storage ring located at the Max-Planck-Institut fuer Kernphysik in Heidelberg, Germany. Storage ring measurements are largely free of metastable contamination, resulting …
Observation of molecular dynamics with quantum state resolution is one of the major challenges in chemical physics. Complete characterization of collision dynamics leads to the microscopic understanding and unraveling of different quantum phenomena such as scattering resonances. We present a new experimental approach for observing molecular dynamics involving neutral particles and ions that is capable in providing state-to-state mapping of the dynamics. We use Penning ionization reaction between argon and metastable helium to generate argon ion and ground state helium atom pairs at separation …
The K x-ray spectra of different targets (Cu, Zn, and Ge) induced by 3 to 5 MeV/u Si projectile ions have been measured to determine the K-shell ionization cross-section. A significant difference is observed between the measurements and theoretical estimates, with the latter being about 50% below the experimental results. This underestimation} is attributed to the charge-exchange from target K-shell to projectile K- and L-shells. Such observation can only be possible if the projectile ions attain up to H- and He-like charge states. Corresponding projectile charge state fractions have been eval…
Calculations on the dynamics of ions and electrons in near-infrared laser fields at intensities up to $3 \times 10^{23}$ W/cm$^2$ are presented. We explore the acceleration of ions in a laser focus by conservation of canonical momentum during ionization events and by the ponderomotive force in the f/1 focal geometry required to reach such intensity. At intensity exceeding 10$^{23}$ W/cm$^2$, highly charged ions are expelled from the laser focus before they can interact with the laser pulse at peak intensity, decreasing the predicted ionization yields of deeply-bound states. We consider the int…
We study the single ionization of hydrogen and helium by the impact of a highly-charged Coulomb projectile. To interpretate the cross section we introduce a diagonal Padé approximant. We find that the use of Padé% [4,4] describes very well the Continnum Distorted Wave Eikonal Initial State theory within its range of validity. The nodes of the denominator of the Pad% é approximant give rise to four poles in the velocity complex plane: two in the upper plane and their conjugate in the lower plane. The dependence of these poles with the projectile charge can be reasonably fitted to give a closed-…
Aims. In the context of accretion disks around black holes, we estimate plasma-environment effects on the atomic parameters associated with the decay of K-vacancy states in highly charged iron ions, namely Fe xvii - Fe xxv. Methods. Within the relativistic multiconfiguration Dirac-Fock (MCDF) framework, the electron-nucleus and electron-electron plasma screenings are approximated with a time-averaged Debye-Huckel potential. Results. Modified ionization potentials, K thresholds, wavelengths, radiative emission rates and Auger widths are reported for astrophysical plasmas characterized by electr…
Presented here is a description of the ionization of hydrogen and hydrogenic ions by antiproton-impact, based on very large scale numerical solutions of the time-dependent Schrödinger equation in three spatial dimensions and on analysis of the topology of the electronic eigenenergy surfaces in the plane of complex internuclear distance. Comparison is made with other theories and very recent measurements.
We study the process of single ionization of Li in collisions with H$^+$ and O$^{8+}$ projectile ions at 6 MeV and 1.5-MeV/amu impact energies, respectively. Using the frameworks of the independent-electron model and the impact parameter picture, fully (FDCS) and doubly (DDCS) differential cross sections are evaluated in the continuum distorted-wave with eikonal initial-state approximation. Comparisons are made with the recent measurements of LaForge \textit{et al} [J. Phys. B \textbf{46} 031001 (2013)] for the DDCS and Hubele \textit{et al} [Phys. Rev. Lett. \textbf{110} 133201 (2013)] for th…
We demonstrate the efficient generation of Be$^+$ ions with a 60 ns and 150 nJ laser pulse near 235 nm for two-step photo-ionization, proven by subsequent counting the number of ions loaded into a linear Paul trap. The bandwidth and power of the laser pulse are chosen in such a way that a first, resonant step fully saturates the entire velocity distribution of beryllium atoms effusing from a thermal oven. The second excitation step is driven by the same light field causing efficient non-resonant ionization. Our ion-loading scheme is more than 15 times more efficient as compared to former pathw…
Time-dependent close-coupling calculations of the ionization and excitation cross section for antiproton collisions with molecular hydrogen ions are performed in an impact-energy range from 0.5 keV to 10 MeV. The Born-Oppenheimer and Franck-Condon approximations as well as the impact parameter method are applied in order to describe the target molecule and the collision process. It is shown that three perpendicular orientations of the molecular axis with respect to the trajectory are sufficient to accurately reproduce the ionization cross section calculated by [Sakimoto, Phys. Rev. A 71, 06270…
The time-dependent Dirac equation can be solved exactly for ionization induced by ultrarelativistic heavy ion collisions. Ionization calculations are carried out in such a framework for a number of representative ion-ion pairs. For each ion-ion pair, the computed cross section consists of two terms, a constant energy independent term and a term whose coefficient is ln(gamma). Scaled values of both terms are found to decrease with increasing Z of the nucleus that is ionized.
Rate coefficients for photorecombination (PR) and cross sections for electron-impact ionization (EII) of Fe$^{14+}$ forming Fe$^{13+}$ and Fe$^{15+}$, respectively, have been measured by employing the electron-ion merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR and EII of Fe$^{14+}$ ions in a plasma are derived from the experimental measurements. Simple parametrizations of the experimentally derived plasma rate coefficients are provided for use in the modeling of photoionized and collisionally ionized plasmas. In the temperature ranges where Fe$^{14+}$ is expected …
The formation of $^{40}$Ca$_2^+$ molecular ions is observed in a hybrid $^{40}$Ca magneto-optical and ion trap system. The molecular ion formation process is determined to be two-photon photo-associative ionization of ultracold $^{40}$Ca atoms. A lower bound for the two-body, two-photon rate constant is found to be $\barβ \geq 2 \pm 1 \times 10^{-15}$ cm$^{3}$ Hz. $\textit{Ab initio}$ molecular potential curves are calculated for the neutral Ca$_2$ and ionic Ca$_2^+$ molecules and used in a model that identifies the photo-associative ionization pathway. As this technique does not require a sep…
We develop a relativistic Coulomb-corrected strong field approximation (SFA) for the investigation of spin effects at above-threshold ionization in relativistically strong laser fields with highly charged hydrogen-like ions. The Coulomb-corrected SFA is based on the relativistic eikonal-Volkov wave function describing the ionized electron laser-driven continuum dynamics disturbed by the Coulomb field of the ionic core. The SFA in different partitions of the total Hamiltonian is considered. The formalism is applied for direct ionization of a hydrogen-like system in a strong linearly polarized l…
Experimental and theoretical total cross sections for single and double ionization of the open-$4d$-shell ions Xe$^{12+}$, Xe$^{13+}$, and Xe$^{14+}$ by electron impact
The analytical R-matrix (ARM) theory has been known for an efficient description of the Coulomb effects of the atomic core in strong-field ionization in the nonrelativistic regime. We generalize the ARM theory into the relativistic domain aiming at the application to strong-field ionization of highly-charged ions in ultrastrong laser fields. Comparison with the relativistic Coulomb-corrected strong field approximations (SFA) is provided, highlighting the advantages and disadvantages. The weakly relativistic asymptotics and its accordance with the nondipole Coulomb-corrected SFA are examined. A…
Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2GeV I$^{-}$ and Cs$^{+}$ ions. A large difference in cross section, up to a factor of six, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stripping cross sections at high energies for electron orbitals with low ionization potential.
Self-energy corrections to the ionization energies in sodium-like ions: comparison of the \textit{ab initio} QED and model-QED-operator approaches
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新学院）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, St. Petersburg State University（圣彼得堡国立大学物理系）；Petersburg Nuclear Physics Institute named by B.P. Konstantinov of National Research Center “Kurchatov Institute”（库尔恰托夫国家研究中心B.P.康斯坦丁诺夫彼得堡核物理研究所）；School of Physics and Engineering, ITMO University（ITMO大学物理与工程学院）
The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target (atoms) with regard to the beam …
A simple model for sequential multiphoton ionization by ultra-intense x-rays is presented. The derived scaling of the ion yield with pulse energy quantitatively reproduces the experimental data, which shows that the ion yield increases according to the "power law" behavior typical of multiphoton ionization, followed by saturation at high pulse energies. The calculated average time interval between ionizations for producing ions at a certain charge state is found to be proportional to the pulse duration and independent of all other x-ray pulse parameters. This agrees with previous studies where…
We have performed classical trajectory Monte Carlo (CTMC) studies of electron capture and ionization in multiply charged (Q=8) ion-Rydberg atom collisions at intermediate impact velocities. Impact parallel to the minor and to the major axis, respectively, of the initial Kepler electron ellipse has been investigated. The important role of the initial electron momentum distribution found for singly charged ion impact is strongly disminished for higher projectile charge, while the initial spatial distribution remains important for all values of Q studied.
Spin effects in the tunneling regime of strong field ionization of hydrogenlike highly charged ions in linearly as well as circularly polarized laser fields are investigated. The impact of the polarization of a laser field on the spin effects are analyzed. Spin-resolved differential ionization rates are calculated employing the relativistic Coulomb-corrected strong-field approximation (SFA) developed in the previous paper of the series. Analytical expressions for spin asymmetries and spin flip probability, depending on the laser's polarization, are obtained for the photoelectron momentum corre…
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…
A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones in length gauge only if the negative-energy states are included in the time propagation. On the other hand, for the considered laser parameters, no significant difference is found in length gauge if the negative-energy states are included or not. Within the adopted dipole approximation the main relativistic effect is the shift of the ionization potential. A…
A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse.
We show that zero ejection energy of the photoelectrons is classically impossible for hydrogen-like ions, even when field ionization occurs adiabatically. To prove this we transform the basic equations to those describing two 2D anharmonic oscillators. The same method yields an alternative way to derive the anomalous critical field of hydrogen-like ions. The analytical results are confirmed and illustrated by numerical simulations. PACS Number: 32.80.Rm
We study the electron-impact induced ionization of O$_{2}$ from threshold to 120 eV using the electron spectroscopy method. Our approach is simple in concept and embodies the ion source with a collision chamber and a mass spectrometer with a quadruple filter as a selector for the product ions. The combination of these two devices makes it possible to unequivocally collect all energetic fragment ions formed in ionization and dissociative processes and to detect them with known efficiency. The ion source allows to vary and tune the electron-impact ionization energy and the target-gas pressure. W…
Aiming at the investigation of above-threshold ionization in super-strong laser fields with highly charged ions, we develop a Coulomb-corrected strong field approximation (SFA). The influence of the Coulomb potential of the atomic core on the ionized electron dynamics in the continuum is taken into account via the eikonal approximation, treating the Coulomb potential perturbatively in the phase of the quasi-classical wave function of the continuum electron. In this paper the formalism of the Coulomb-corrected SFA for the nonrelativistic regime is discussed employing velocity and length gauge. …
Past and ongoing research activities at the Heidelberg heavy-ion storage-ring TSR are reviewed which aim at providing accurate absolute rate coefficients and cross sections of atomic collision processes for applications in astrophysics and magnetically confined fusion. In particular, dielectronic recombination and electron impact ionization of iron ions are discussed as well as dielectronic recombination of tungsten ions.
