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 the electric-dipole approximation. This includes a strong forward emission while, in dipole approxmation, the electron emission always occurs symmetric with respect to the plane which is perpendicular to the photon beam. Detailed computations for the dependence of the photoelectron angular distributions on the polarization of the incident light are carried out for the ionization of H, Xe$^{53+}$, and U$^{91+}$ (hydrogen-like) ions.
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…
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.
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…
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 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…
We study the ionization process involving antiproton and hydrogen in the energy range between 0.1 keV to 500 keV, using single center close coupling approximation. We construct the scattering wave function using B-spline bases. The results obtained for ionization of atomic hydrogen are compared with other existing theoretical calculations as well as with the available experimental data. The present results are found to be encouraging. We also employed this method to study the ionization of ionized helium in the energy range between 1 and 500 keV. On comparision, the present results are found t…
We extend the semiclassical two-step model for strong-field ionization that describes quantum interference and accounts for the Coulomb potential beyond the semiclassical perturbation theory to the hydrogen molecule. In the simplest case of the molecule oriented along the polarization direction of a linearly polarized laser field, we predict significant deviations of the two-dimensional photoelectron momentum distributions and the energy spectra from the case of atomic hydrogen. Specifically, for the hydrogen molecule the electron energy spectrum falls off slower with increasing energy, and th…
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…
We have implemented the paraxial approximation followed by the time-dependent Hartree-Fock method with frozen core for the single impact ionization of atoms and two-atomic molecules. It reduces the original scattering problem to the five-dimensional time-dependent Schrödinger equation solution. By using this method we calculated the multi-fold differential cross section of the impact single ionization of the helium atom, the hydrogen molecule and the nitrogen molecule by the intermediate energy electrons. Our results for the helium and the hydrogen are quite close to experimental data, but for…
The influence of nuclear polarization on the bound-electron $g$ factor in heavy hydrogenlike ions is investigated. Numerical calculations are performed for the K- and L-shell electrons taking into account the dominant virtual nuclear excitations. This determines the ultimate limit for tests of QED utilizing measurements of the bound-electron $g$ factor in highly charged ions.
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…
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.
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 …
Experiments have shown that the microwave ionization probability of a highly excited almost monodimensional hydrogen atom subjected to a microwave pulse sometimes grows in steps when the peak electric field of the pulse is increased. Classical pulsed simulations display the same steps, which have been traced to phase-space metamorphoses. Quantum numerical calculations again exhibit the same ionization steps. I show that the time-sequence of two level interactions, responsible for the observed steps in the quantum picture, is strictly related to the classical phase space structures generated by…
The multiply differential cross section of the ionization of hydrogen molecular ion by fast electron impact is calculated by a direct approach, which involves the reduction of the initial 6D Schrödinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics. This approach avoids the use of stationary Coulomb two-centre functions of the continuous spectrum of the ejected electron which demands cumbersome calculations. The results obtained, after verification of the procedure in the case atomic hydrogen, reveal interesting mechanisms in the case of small scatteri…
Relativistic strong-field ionization of hydrogen-like atoms or ions in a constant crossed electromagnetic field is studied. The transition amplitude is formulated within the strong-field approximation in Göppert-Mayer gauge, with initial and final electron states being described by the corresponding Dirac-Coulomb and Dirac-Volkov wave functions, respectively. Coulomb corrections to the electron motion during tunneling are taken into account by adjusting an established method to the present situation. Total and energy-differential ionization rates are calculated and compared with predictions fr…
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…
Theoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high-precision determination of the proton charge radius drastically reduced the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two- and three-loop QED effects, which calls for further advances in their calculations. We review the present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen-like ions …
It has been recently predicted theoretically that due to nuclear motion light and heavy hydrogen molecules exposed to strong electric field should exhibit substantially different tunneling ionization rates (O.I. Tolstikhin, H.J. Worner and T. Morishita, Phys. Rev. A 87, 041401(R) (2013) [1]). We studied that isotope effect experimentally by measuring relative ionization yields for each species in a mixed H2/D2 gas jet interacting with intense femtosecond laser pulses. In a reaction microscope apparatus we detected ionic fragments from all contributing channels (single ionization, dissociation,…
The static dipole polarizability for the hydrogen molecular ions H$_2^+$, HD$^+$, and D$_2^+$ are calculated. These new data for polarizability takes into account the leading order relativistic corrections to the wave function of the three-body system resulted from the Breit-Pauli Hamiltonian of $mα^4$ order. Our study covers a wide range of rotational ($L=0-5$) and vibrational ($v=0-10$) states, which are of practical interest for precision spectroscopy of the hydrogen molecular ions.
We investigate the strong-field ionization of atomic hydrogen in a few-cycle elliptically polarized infrared pulse by solving the time-dependent Schrödinger equation. The dependence of the photoelectron momentum distribution on the pulse intensity, ellipticity, length, envelope, and carrier envelope phase is analyzed. In particular, we explain the variation of the electron offset angle with asymptotic electron energy through the combined action of the field and the Coulomb potential, and demonstrate that low-ellipticity pulses make it possible to access the electron release time.
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 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 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…
In this work, analytical formulas for the static multipole polarizabilities of hydrogen-like ions are derived by using the analytical wave functions and the reduced Green function and by applying a numerical fitting procedure. Our results are then applied to the studies of blackbody radiation shifts to atomic energy levels at different temperatures. Our analytical results can be served as a benchmark for other theoretical methods.
We describe a nonperturbative (in Zalpha) numerical evaluation of the one-photon electron self energy for 3P_{1/2}, 3P_{3/2}, 4P_{1/2} and 4P_{3/2} states in hydrogenlike atomic systems with charge numbers Z=1 to 5. The numerical results are found to be in agreement with known terms in the expansion of the self energy in powers of Zalpha and lead to improved theoretical predictions for the self-energy shift of these states.
In this paper a 4-component Dirac theory of ionization of hydrogen molecular ion in a super-intense laser field is developed. Simple analytic expressions for the spin specific as well as the total ionization currents emitted from the ground state of the ion are derived. The results are given for all polarization and finite propagation vectors of the field. They apply for inner-shell ionization of analogous heavier molecular ions as well. The presence of molecular two-slit interference effect, first found in the non-relativistic case, and the spin-flip ionization current, and an asymmetry of th…
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…
Polarization properties of the photons emitted in the two-photon decay of hydrogen-like ions are studied within the framework of the density matrix and second-order perturbation theory. In particular, we derive the polarization correlation function that gives the probability of the (two-photon) coincidence measurement performed by polarization-sensitive detectors. Detailed calculations of this function are performed for the $2s_{1/2} \to 1s_{1/2}$ transition in neutral hydrogen as well as Xe$^{53+}$ and U$^{91+}$ ions. The obtained results allow us to understand the influence of relativistic a…
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 present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultra violet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time dependent Dirac equation and compare its predictions with those of the corresponding non-relativistic Schr{ö}dinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduces a finite yet small decrease i…
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…
One- and two-photon transitions in the hydrogen atom are analytically evaluated in the absence and in the presence of an external electric field. The emission probabilities are different for the hydrogen and anti-hydrogen atoms due to the existence of contributions, linear in electric field. The magnitude of these contributions is evaluated within the nonrelativistic limit. The Coulomb Green function method is applied. Different nonrelativistic "forms" for the decay probabilities in combination with different gauge choices are considered. The three-photon E1E1E1 2p-1s transition probability 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…
We present a semi-relativistic model for the description of the ionization process of atomic hydrogen by electron impact in the first Born approximation by using the Darwin wave function to describe the bound state of atomic hydrogen and the Sommerfeld-Maue wave function to describe the ejected electron. This model, accurate to first order in $Z/c$ in the relativistic correction, shows that, even at low kinetic energies of the incident electron, spin effects are small but not negligible. These effects become noticeable with increasing incident electron energies. All analytical calculations are…
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 …
We develop {\it ab initio} relativistic QED theory for elastic electron scattering on hydrogen-like highly charged ions for impact energies where, in addition to direct (Coulomb) scattering, the process can also proceed via formation and consequent Auger decay of autoionizing states of the corresponding helium-like ions. Even so the primary goal of the theory is to treat electron scattering on highly charged ions, a comparison with experiment shows that it can also be applied for relatively light ions covering thus a very broad range of the scattering systems. Using the theory we performed cal…
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 …
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 …
Comparison of precision frequency measurements to quantum electrodynamics (QED) predictions for Rydberg states of hydrogen-like ions can yield information on values of fundamental constants and test theory. With the results of a calculation of a key QED contribution reported here, the uncertainty in the theory of the energy levels is reduced to a level where such a comparison can yield an improved value of the Rydberg constant.
Quasi-static models of barrier suppression have played a major role in our understanding of the ionization of atoms and molecules in strong laser fields. Despite their success, in the case of diatomic molecules these studies have so far been restricted to fields aligned with the molecular axis. In this paper we investigate the locations and heights of the potential barriers in the hydrogen molecular ion in an electric field of arbitrary orientation. We find that the barriers undergo bifurcations as the external field strength and direction are varied. This phenomenon represents an unexpected l…
Electron-impact ionization of atomic hydrogen with the electron's anomalous mag- netic moment (AMM) effects are examined. The formulas for the laser-assisted relativis- tic triple differential cross section (TDCS) in the coplanar binary geometry developed earlier by Y. Attaourti and S. Taj [Phys. Rev. A 69, 063411 (2004)] are used to check the consistency of our computations when the anomaly $κ$ is taken to be zero. We show that the contribution of the terms containing the AMM effects even in the first Born approximation has an important contribution, so it must be included in any reliable ana…
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…
Two--photon decay of hydrogen--like ions is studied within the framework of second--order perturbation theory, based on relativistic Dirac's equation. Special attention is paid to the effects arising from the summation over the negative--energy (intermediate virtual) states that occurs in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the $2s_{1/2} - 1s_{1/2}$ and $2p_{1/2} - 1s_{1/2}$ transitions in neutral hydrogen H as well as for hydrogen--like xenon Xe$^{53+}$ and uranium U$^{91+}$ ions. We found that for a correct evalu…
The dynamics of the electron impact multiphoton ionization of a hydrogen atom in the presence of an intense laser field has been studied theoretically, with a view to comparing (qualitatively) the results with the recent kinematically complete experiments of Horr et al [ Phys. Rev. Lett., vol. 94, 153201, (2005) ] for the He target. Significant laser modifications are noted in the present doubly (DDCS) and the fully differential cross sections (TDCS). For most of the explored kinematics (chosen in accordance with the experiment), the present binary peak intensity of the laser-assisted TDCS is …
Within the framework of the coplanar binary geometry where it is justified to use plane wave solutions for the study of the $(e,2e)$ reaction and in the presence of a circularly polarized laser field, we introduce as a first step the DVRPWBA1 (Dirac-Volkov Plane Wave Born Approximation1) where we take into account only the relativistic dressing of the incident and scattered electrons. Then, we introduce the DVRPWBA2 (Dirac-Volkov Plane Wave Born Approximation2) where we take totally into account the relativistic dressing of the incident, scattered and ejected electrons. We then compare the cor…
