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 evaluated from the Lorentzian charge state distribution, where mean charge state is taken from the Fermi gas model [Phys. Rev. Lett. 30, 358 (1973)] and width from the Novikov and Teplova approach [Phys. Lett. A378, 1286-1289 (2014)]. The sum of the direct ionization cross-section and K-K + K-L capture cross-sections gives a good agreement with the measured cross-sections. Furthermore, we have validated this methodology with available data for Si-ion on Ti target. Such results may be useful in many solid target based applications.
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…
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…
Using the cold target recoil ion momentum spectroscopy (COLTRIMS) technique, we have measured the simultaneous projectile and target ionization in collisions of He$^+$ projectiles with a mixture of gaseous H$_2$ and D$_2$ for an incident projectile energy of 650 keV. Motivated by Cooper et al. [Phys. Rev. Lett. 100, 043204 (2008)], we look for differences in the ionization cross section of the two isotopes with the highest resolution and statistical significance. Contributions of the electron-electron and electron-nucleus interactions have been clearly separated kinematically by measuring 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.
Ionization collisions have important consequences in many physical phenomena, and the mechanism that leads to ionization is not universal. Double differential cross sections (DDCSs) are often used to identify ionization mechanisms because they exhibit features that distinguish close collisions from grazing collisions. In the angular DDCS, a sharp peak indicates ionization through a close binary collision, while a broad angular distribution points to a grazing collision. In the DDCS energy spectrum, electrons ejected through a binary encounter collision result in peak at an energy predicted fro…
The realization of electron vortex beams in the past decade has led to numerous proposed applications in fields from electron microscopy to control and manipulation of individual molecules. Yet despite the many unique characteristics and promising advantages of electron vortex beams, such as transverse momentum and quantized orbital angular momentum, there remains a limited understanding of their fundamental interactions with matter at the atomic scale. Collisions between electron vortex projectiles and atomic targets can provide some insight into these interactions and we present here fully d…
We report the energy and angular distribution of ejected electrons from CH$_4$ and H$_{2}$O molecules impacted by 1 MeV H$^+$, He$^+$ and 650 keV N$^+$ ions. Spectra were measured at different observation angles, from 2 eV to 2000 eV. The obtained absolute double-differential-electron-emission cross sections (DDCS) were compared with the results of CTMC and CDW-EIS calculations. For the bare H+ projectile both theories show remarkable agreement with the experiment at all observed angles and energies. The CTMC results are in similarly good agreement with the DDCS spectra obtained for impact by …
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…
Optical vortex beams have an extensive history in terms of both theory and experiment, but only recently have electron vortex beams been proposed and realized. The possible applications of these matter vortex waves are numerous, but a fundamental understanding of their interactions with atoms and molecules has not yet been developed. In this work, fully differential cross sections for fast (e,2e) collisions using electron vortex projectiles with small amounts of quantized orbital angular momentum are presented. A comparison is made with the fully differential cross sections using plane wave pr…
Positronium breakup versus hydrogen ionization in collisions with fast charged projectiles: a comparative study
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Heinrich-Heine-University of Düsseldorf（杜塞尔多夫大学）；University of Chinese Academy of Sciences（中国科学院大学）
A proposal is made by the University College of London Group [1] for measuring the target-ionization cross sections in Ps and atom scattering. We calculate the corresponding theoretical data for Ps-H and Ps-He systems including the effect of exchange on Coulomb-Born approximation for the projectile-elastic and projectile-inelastic processes and report the total target-ionization cross sections for the first time.
Fully differential cross sections are calculated for the ionization of H$_2$ by fast charged projectiles using a semiclassical model developed previously for the ionization of atoms. The method is tested in case of 4 keV electron and 6 MeV proton projectiles. The obtained results show good agreement with the available experimental data. Interference effects due to the two-center character of the target are also observed and analyzed.
We study relativistic collisions between helium-like uranium ions initially in the ground state and atoms in which, in a single collision event, one of the electrons of the ion is emitted and the other is transferred into an excited state of the residual hydrogen-like ion. We consider this two-electron process at not very high impact energies, where the action of the atom on the electrons of the ion can be well approximated as occurring solely due to the interaction with the nucleus of the atom and, hence, the process can be regarded as a four-body problem. Using the independent electron model…
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 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…
In this work our previous fully differential ionization cross section calculations using the semiclassical, impact parameter method are improved by a new method suitable to calculate impact parameter values corresponding to different momentum transfers. This goal is achieved by two successive steps. First, using the transverse momentum balance different projectile scattering angles are calculated for the binary and recoil peak regions as a function of the transferred momentum. Then, by treating the projectile scattering as a classical potential scattering problem, impact parameters are assigne…
Multiple ionization and charge equilibration in slow, multiply charged $\mathrm{Ar^{q+} + Ar}$ collision studied via L-MM Auger-Meitner electron spectroscopy
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Tata Institute of Fundamental Research（塔塔基础研究所）
We study the fragmentation of He$_2$ dimers into He$^+$ ions by relativistic highly-charged projectiles. It is demonstrated that the interaction between an ultrafast projectile with an extremely extended object -- the helium dimer -- possesses interesting features which are absent in collisions with "normal" molecules. It is also shown that such projectiles, due to their enormous interaction range, can accurately probe the ground state of the dimer and even be used for a precise determination of its binding energy.
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.
For the first time, we report a theoretical methodology to predict charge state distribution of projectile ions inside a solid-target. The method utilizes either a simple Fermi gas model or an ab initio theoretical method and a certain parameterization of width for the Lorentzian charge state distributions. Results obtained from the two approaches are comparable, but the former has a certain edge over the latter. The projectile charge state distribution inside a solid-target plays a significant role in estimating electron capture cross-sections and then to describe the observed K-shell ionizat…
The Cold-target recoil-ion momentum spectroscopy (COLTRIMS) has been employed to study the single-electron capture processes in collisions of N3+ ions with He atoms at an impact energy of 30 keV. The relative differential cross sections for the capture to different orbitals of N3+ ions are obtained and are compared with other experiments at low energy. The predictions of the molecular Columbic barrier model have been made. From the longitudinal momentum spectrum of recoil ions, the different electronic configuration was identified and the metastable projectile ions were distinguished. The sing…
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 $\ell$.
In this chapter we analyze the multiple ionization by impact of |Z|=1 projectiles: electrons, positrons, protons and antiprotons. Differences and similarities among the cross sections by these four projectiles allows us to have an insight on the physics involved. Mass and charge effects, energy thresholds, and relative importance of collisional and post-collisional processes are discussed. For this purpose, we performed a detailed theoretical-experimental comparison for single up to quintuple ionization of Ne, Ar, Kr and Xe by particles and antiparticles. We include an extensive compilation of…
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 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…
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.
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-…
The two-center basis generator method is used to obtain cross sections for excitation, capture, and ionization in Li$^{3+}$, C$^{3+}$, and O$^{3+}$ collisions with ground-state hydrogen at projectile energies from 1 to 100 keV/u. The interaction of the C$^{3+}$ and O$^{3+}$ projectiles with the active electron is represented by a model potential. Comparisons of cross sections with previously reported data show overall good agreement while discrepancies in capture for C$^{3+}$ collisions at low energies are noted. The present results show that excitation and ionization are similar across the th…
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.
A description of the DEPOSIT computer code is presented. The code is intended to calculate total and m-fold electron-loss cross sections (m is the number of ionized electrons) and the energy T(b) deposited to the projectile (positive or negative ion) during a collision with a neutral atom at low and intermediate collision energies as a function of the impact parameter b. The deposited energy is calculated as a 3D-integral over the projectile coordinate space in the classical energy-deposition model. Examples of the calculated deposited energies, ionization probabilities and electron-loss cross…
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…
The multiple electron loss of heavy projectiles in fast ion-atom collisions has been studied in the framework of the sudden perturbation approximation. Especially, a model is developed to calculate the cross sections for the loss of any number of electrons from the projectile ion, including the ionization of a single electron and up to the complete stripping of the projectile. For a given collision system, that is specified by the (type and charge state of the) projectile and target as well as the collision energy, in fact, the experimental cross sections for just three final states of the pro…
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…
Angular distribution of Kα x rays following nonradiative double electron capture in relativistic collisions of Xe54+ ions with Kr and Xe atoms
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；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 Centre “Kurchatov Institute,”（俄罗斯国家研究中心“库尔恰托夫研究所”以B.P.康斯坦丁诺夫命名的圣彼得堡核物理研究所）；Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University（西北师范大学物理与电子工程学院甘肃省原子分子物理与功能材料重点实验室）；Department of Medical Imaging, Hangzhou Medical College（杭州医学院医学影像系）；School of Basic Medical Sciences, Shanxi Medical University（山西医科大学基础医学院）
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…
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 …
Two-electron one-photon transitions have been successfully observed for the Ne projectile and Al target at low energy regime. Experimental energy values of two-electron one-photon transitions are compared with previously reported theoretical and experimental values. Ionization cross-section of two-electron one-photon transition is reported.
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…
A new relativistic method based on the Dirac equation for calculating fully differential cross sections for ionization in ion-atom collisions is developed. The method is applied to ionization of the atomic hydrogen by antiproton impact, as a non-relativistic benchmark. The fully differential, as well as various doubly and singly differential cross sections for ionization are presented. The role of the interaction between the projectile and the target nucleus is discussed. Several discrepancies in available theoretical predictions are resolved. The relativistic effects are studied for ionizatio…
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…
At impact energies $ \stackrel{>}{\sim}1$ GeV/u the projectile-electron excitation and loss occurring in collisions between highly charged ions and neutral atoms is already strongly influenced by the presence of atomic electrons. In order to treat these processes in collisions with heavy atoms we generalize the symmetric eikonal model, used earlier for considerations of electron transitions in ion-atom collisions within the scope of a three-body Coulomb problem. We show that at asymptotically high collision energies this model leads to an exact transition amplitude and is very well suited to d…
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…
We present a fully {\it ab initio}, non-perturbative, time-dependent approach to describe single and double ionization of helium by proton and antiproton impact. A flexible and accurate finite-element discrete-variable-representation is applied to discretize the problem on the radial grid in spherical coordinates. Good agreement with the most recent experimental data for absolute angle-integrated cross sections is obtained over a wide range of incident projectile energies between 3 keV and 6 MeV. Furthermore, angle-differential cross sections for two-electron ejection are predicted for a proto…
