A classical approximation to time dependent quantum mechanical scattering in the Møller formalism is presented. Numerically, our approach is similar to a standard Classical-Trajectory-Monte-Carlo calculation. Conceptually, however, our formulation allows one to release the restriction to stationary initial distributions. This is achieved by a classical forward-backward propagation technique. As a first application and for comparison with experiment we present fully differential cross sections for electron impact ionization of atomic hydrogen in the Erhardt geometry.
Collisional ionization between two Rydberg atoms in relative motion is examined. A classical trajectory Monte Carlo method is used to determine the cross sections associated with Penning ionization. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. For a given magnitude of angular momentum, there can exist a difference of a factor of up to $\sim2.5$ in the ionization cross section between the orientation with the highest and the lowest ion…
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.
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…
The calculated double differential cross sections for 60eV energy, where the cross sections are also maximum, agree with the measured results of Shyn (1992) in a much better way compaired to other theories for such energies.
To have a better understanding of a physical process, a comparison of ex-perimental data with theoretical values is mandatory. The comparison ismeaningful if the uncertainty in the experiment is accounted well. However,it is seldom seen, especially for a complex phenomenon. We take a test casethrough L subshell ionization of atoms by particle impact. Experimentally,x-ray production cross-sections are measured, but ionization cross-sectionsare calculated theoretically. Furthermore, the uncertainty of the x-ray pro-duction cross-section is mainly statistics and detector-efficiency driven. Bution…
We have investigated the universal scaling behavior of differential cross sections for the single K-shell ionization by electron or positron impact. The study is performed within the framework of non-relativistic perturbation theory, taking into account the one-photon exchange diagrams. In the case of low-energy positron scattering, the doubly differential cross section exhibits prominent interference oscillations. The results obtained are valid for arbitrary atomic targets with moderate values of nuclear charge number Z.
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.
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 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…
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…
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.
The electron impact ionization of atomic hydrogen is calculated for incident elrctron energy 76.46 eV. The Hartree-Fock approximation is used to calculate the initial state which includes both bound and continum wave functions. The final state continuum electron wave functions are obtained in the potential of hydrogen ion. The interaction between the two final state continuum electrons is approximated with the screening potential determined variationally.
This paper is focused on showing that the fully differential cross section of ionization during a collision of a proton and an antiproton with a hydrogen atom is directly expressed by the wave function in the coordinate representation. Wave function is converted from impact parameter representation to momentum transfer representation. In this case, the calculated wave function corresponds at a certain projectile angle of scattering. The square representation of this wave function module shows how the angular distribution of ionized electrons varies over time. The ionized electron's flow is dir…
Total ionization cross sections of H, He, Li, Be, B, C, N, O, F, Ne, P, S and Ar neutral atoms by impact of antiprotons, H^{+}, He^{2+}, Be^{4+}, % C^{6+} and O^{8+}. were calculated using the CDWEIS (continuum distorted wave -Eikonal Initial state) theoretical method. Cross section depending on of initial the quantum numbers n and l are reported in Tables for a range of impact energies covering from 100 keV/amu to 10 MeV/amu
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, where the theoretical ones are about 28-35% of the experimental results. Such difference is reduced to a good extent 51-56% if multiple ionization effects are taken into account. Remaining discrepancy may be attributed to the electron capture contribution.
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 non-resonant two-photon one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the K-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section, for the case of U, for example, they reduce the total cross section by a factor of two…
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…
We report measurements of electron impact ionization (EII) for Fe^13+, Fe^16+, and Fe^17+ over collision energies from below threshold to above 3000 eV. The ions were recirculated using an ion storage ring. Data were collected after a sufficiently long time that essentially all the ions had relaxed radiatively to their ground state before data were collected. For single ionization of $\fethirteen$ we find that previous single pass experiments are more than 40% larger than our results. Compared to our work, the theoretical cross section recommended by Arnaud & Raymond (1992) is more than 30% la…
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…
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…
In this work we present fully differential cross sections (FDCSs) calculations using post and prior version of CDW--EIS theory for helium single ionization by 100 MeV C$^{6+}$ amu$^{-1}$ and 3.6 MeV amu$^{-1}$ Au$^{24+}$ and Au$^{53+}$ ions. We performed our calculations for different momentum transfer and ejected electron energies. The influence of internuclear potential on the ejected electron spectra is taken into account in all cases. We compare our calculations with absolute experimental measurements. It is shown that prior version calculations give better agreement with experiments in al…
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…
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…
Electron-impact direct double ionization (DDI) process is studied as a sequence of two and three step processes. Contribution from ionization-ionization, ionization-excitation-ionization, and excitation-ionization-ionization processes is taken into account. The present results help to resolve the long-standing discrepancies; in particular, a good agreement with experimental measurements is obtained for double ionization cross-sections of $O^{1+}$, $O^{2+}$, $O^{3+}$, $C^{1+}$, and $Ar^{2+}$ ions. We show that distribution of the energy of scattered and ejected electrons, which participate in t…
The contribution to electron-impact ionization cross sections from excitations to high-nl shells and a consequent autoionization is investigated. We perform relativistic subconfiguration-average and detailed level-to-level calculations for this process. Ionization cross sections for the W27+ ion are presented to illustrate the large influence of the high shells (n >= 9) and orbitals (l >= 4) in the excitation-autoionization process. The obtained results show that the excitations to the high shells (n >= 9) increase cross sections of the indirect ionization process by a factor of 2 compared to …
Electron-impact ionization of lithium is studied using the convergent close-coupling (CCC) method at 25.4 and 54.4 eV. Particular attention is paid to the spin-dependence of the ionization cross sections. Convergence is found to be more rapid for the spin asymmetries, which are in good agreement with experiment, than for the underlying cross sections. Comparison with the recent measured and DS3C-calculated data of Streun et al (1999) is most intriguing. Excellent agreement is found with the measured and calculated spin asymmetries, yet the discrepancy between the CCC and DS3C cross sections is…
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…
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.
A fully classical explanation of the nonhydrogenic ionization threshold for low angular momentum Rydberg states of Alkali-metal atoms in a linearly polarized low frequency monochromatic microwave field is given: the classical equivalent to the quantum rate-limiting step, which is responsible for the n^(-5) scaling and which according to the literature initiates what then continues as essentially classical diffusion, is found.
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…
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.
Stimulated by a recent measurement of coherent control in photoionization of atomic barium, we have calculated one- and two-photon ionization cross sections of the aligned 6s6p^1P_1 state of barium in the energy range between the 5d_{3/2} and 5d_{5/2} states of Ba^+. We have also measured these photionization spectra in the same energy region, driving the one- or two-photon processes with the second or first harmonic of a tunable dye laser, respectively. Our calculations employ the eigenchannel R-matrix method and multichannel quantum defect theory to calculate the rich array of autoionizing r…
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…
The values of ion-atom ionization cross sections are frequently needed for many applications that utilize the propagation of fast ions through matter. When experimental data and theoretical calculations are not available, approximate formulas are frequently used. This paper briefly summarizes the most important theoretical results and approaches to cross section calculations in order to place the discussion in historical perspective and offer a concise introduction to the topic. Based on experimental data and theoretical predictions, a new fit for ionization cross sections is proposed. The ran…
A semiclassical impact parameter version of the continuum distorted wave-Eikonal initial state theory is developed to study the differential ionization of $Li$ atoms in collisions with $Li^{2+}$ ions. Both post and prior forms of the transition amplitude are considered. The fully differential cross sections are calculated for the lithium targets in their ground and their first excited states and for the projectile ions at 16~MeV impact energy. The role of the internuclear interaction as well as the significance of the post-prior discrepancy in the ejected electron spectra are investigated. The…
The $5p$ two-photon ionization cross section of xenon in the photon-energy range below the one-photon ionization threshold is calculated within the time-dependent configuration-interaction-singles (TDCIS) method. The TDCIS calculations are compared to random-phase-approximation (RPA) calculations [Wendin \textit{et al.}, J. Opt. Soc. Am. B \textbf{4}, 833 (1987)] and are found to reproduce the energy positions of the intermediate Rydberg states reasonably well. The effect of interchannel coupling is also investigated and found to change the cross section of the $5p$ shell only slightly compare…
An apparatus for production of various atomic and molecular ions inside a linear Paul trap has been set up. The system applies a custom-made, low energy, pulsed electron gun to produce ions in electron impact process. Such ionization method can find some interesting possible applications such as derivation of ions inaccessible other-ways, which can be used in molecular ion experiments. The technique allows also for determination of cross sections for various collisional processes. As a feasibility study, the apparatus was used for determination of ionization integral cross section of calcium i…
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…
Electron-impact ionization of an atom or ion in the presence of a neighboring atom is studied. The latter is first collisionally excited by the incident electron, whose energy is assumed to be high but nonrelativistic. Afterwards, the excitation energy is transferred radiationlessly via a two-center Auger process to the other atom or ion, leading to its ionization. We show that the participation of the neighboring atom manifests in a very pronounced resonance peak in the energy-differential cross section and can substantially enhance the total cross section of electron-impact ionization. We al…
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
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.
We introduce a time-dependent R-matrix theory generalised to describe double ionization processes. The method is used to investigate two-photon double ionization of He by intense XUV laser radiation. We combine a detailed B-spline-based wavefunction description in a extended inner region with a single-electron outer region containing channels representing both single ionization and double ionization. A comparison of wavefunction densities for different box sizes demonstrates that the flow between the two regions is described with excellent accuracy. The obtained two-photon double ionization cr…
We report ionization cross section measurements for electron impact single ionization (EISI) of Fe^11+$ forming Fe^12+ and electron impact double ionization (EIDI) of Fe^11+ forming Fe^13+. The measurements cover the center-of-mass energy range from approximately 230 eV to 2300 eV. The experiment was performed using the heavy ion storage ring TSR located at the Max-Planck-Institut fur Kernphysik in Heidelberg, Germany. The storage ring approach allows nearly all metastable levels to relax to the ground state before data collection begins. We find that the cross section for single ionization is…
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…
Recent Letter of T.Pattard and J.M.Rost (Phys.Rev.Lett 80, 5081 (1998)) suggests that there exist logarithmic corrections to the near threshold cross section for the processes of break up of a particle into several charged fragments. This comment shows that it is incorrect, the logarithmic terms never exist. The cross section for all processes behaves as some power of the above-threshold energy, similarly to the known Wannier problem.
We present here triple differential cross sections for ionization of hydrogen atoms by electron impact at 1eV, 0.5eV and 0.3eV energy above threshold, calculated in the hyperspherical partial wave theory. The results are in very good agreement with the available semiclassical results of Deb and Crothers \cite{DC02} for these energies. With this, we are able to demonstrate that the hyperspherical partial wave theory yields good cross sections from 30 eV \cite{DPC03} down to near threshold for equal energy sharing kinematics.
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-…
Theoretical expressions for ionization cross sections by electron impact based on the binary encounter Bethe (BEB) model, valid from ionization threshold up to relativistic energies, are proposed. The new modified BEB (MBEB) and its relativistic counterpart (MRBEB) expressions are simpler than the BEB (nonrelativistic and relativistic) expressions because they require only one atomic parameter, namely the binding energy of the electrons to be ionized, and use only one scaling term for the ionization of all sub-shells. The new models are used to calculate the K-, L- and M-shell ionization cross…
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), (…
We have compiled a set of electron-impact multiple ionization (EIMI) cross sections for astrophysically relevant ions. EIMI can have a significant effect on the ionization balance of non-equilibrium plasmas. For example, it can be important if there is a rapid change in the electron temperature or if there is a non-thermal electron energy distribution, such as a kappa distribution. Cross sections for EIMI are needed in order to account for these processes in plasma modeling and for spectroscopic interpretation. Here, we describe our comparison of proposed semiempirical formulae to the availabl…
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…
