Multielectron Atoms Research Articles

Breit and Quantum Electrodynamics Energy Contributions in Multielectron Atoms from the Relativistic Screened Hydrogenic Model

The correction to the Coulomb repulsion between two electrons due to the exchange of a transverse photon, referred to as the Breit interaction, as well as the main quantum electrodynamics contributions to the atomic energies (self-energy and vacuum polarization), are calculated using the recently formulated relativistic screened hydrogenic model. Comparison with the results of multiconfiguration Dirac-Hartree-Fock calculations and experimental X-ray energies is made.

PENNING AND STOCHASTIC COLLISIONAL IONIZATION OF ATOMS IN AN EXTERNAL MAGNETIC FIELD: MODEL POTENTIAL SCHEME

The key physical aspects of the Penning and stochastic collisional ionization of atoms in an external magnetic field are considered and new model potential approach has been implemented in order to take into account an effect of magnetic field on multi-electron atom energy parameters and to compute the wave functions basis for next using in the collisional block. The corresponding Schrödinger equation for atom in a magnetic field and the Focker-Plank stochastic equation are solved within the standard differences-grid method.

Static field ionization rates for multi-electron atoms and small molecules

We present an application of the hybrid anti-symmetrized coupled channels approach to compute static field ionization rates for multi-electron atoms (He, Ne, Ar) and small molecules (H2, N2, CO). While inert gas atoms behave as effective single electron systems, molecules exhibit multi-electron effects in the form of core polarization. It is shown that at moderate field strengths, these effects can be modeled to about 10% accuracy using a few (5–6) channel ansatz. In the case of the CO molecule, description of core polarization is essential for the correct prediction of the maximum ionization direction and our converged results are in good agreement with the experimental measurements.

Circularly polarized high harmonics generated by a bicircular field from inert atomic gases in thepstate: A tool for exploring chirality-sensitive processes

$S$-matrix theory of high-order harmonic generation (HHG) is generalized to multielectron atoms. In the multielectron case the harmonic power is expressed via a coherent sum of the time-dependent dipoles, while for the one-electron models a corresponding incoherent sum appears. This difference is important for the inert atomic gases having a $p$ ground state as used in a recent HHG experiment with a bicircular field [Nat. Photonics 9, 99 (2015)]. We investigate HHG by such a bicircular field, which consists of two coplanar counter-rotating circularly polarized fields of frequency $r\ensuremath{\omega}$ and $s\ensuremath{\omega}$. Selection rules for HHG by a bicircular field are analyzed from the aspects of dynamical symmetry of the system, conservation of the projection of the angular momentum on a fixed quantization axis, and the quantum number of the initial and final atomic ground states. A distinction is made between the selection rules for atoms with closed [J. Phys. B 48, 171001 (2015)] and nonclosed shells. An asymmetry in emission of the left- and right-circularly polarized harmonics is found and explained by using a semiclassical model and the electron probability currents which are related to a nonzero magnetic quantum number. This asymmetry can be important for the application of such harmonics to the exploration of chirality-sensitive processes and for generation of elliptic or even circular attosecond pulse trains. Such attosecond pulse trains are analyzed for longer wavelengths than in Opt. Lett. 40, 2381 (2015), and for various field-component intensities.

SPECTROSCOPY OF ATOMS IN A STRONG LASER FIELD: NEW METHOD TO SENSING AC STARK EFFECT, MULTIPHOTON RESONANCES PARAMETERS AND IONIZATION CROSS-SECTIONS

The resonant multiphoton resonances shifts and widths and ionization cross-sections for multielectron atoms in a intense laser radiation field are studied. It is carried out a new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation. In relativistic theory, the Gell-Mann and Low adiabatic formula for energy shift is connected with electrodynamical scattering matrice, which includes interaction with as a laser field as a photon vacuum field (radiative decay). The optimized basis of the relativistic orbitals is generated with using a minimization procedure for the gauge-non-invariant contribution (the fourth-order of the QED perturbation theory) to the radiation width of atomic state. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction “atom- multimode laser pulse” is greater than the corresponding shift and width for a case of the “atom- single-mode pulse” (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.

Critical points of metal vapors

A new method is proposed for calculating the parameters of critical points and binodals for the vapor–liquid (insulator–metal) phase transition in vapors of metals with multielectron valence shells. The method is based on a model developed earlier for the vapors of alkali metals, atomic hydrogen, and exciton gas, proceeding from the assumption that the cohesion determining the basic characteristics of metals under normal conditions is also responsible for their properties in the vicinity of the critical point. It is proposed to calculate the cohesion of multielectron atoms using well-known scaling relations for the binding energy, which are constructed for most metals in the periodic table by processing the results of many numerical calculations. The adopted model allows the parameters of critical points and binodals for the vapor–liquid phase transition in metal vapors to be calculated using published data on the properties of metals under normal conditions. The parameters of critical points have been calculated for a large number of metals and show satisfactory agreement with experimental data for alkali metals and with available estimates for all other metals. Binodals of metals have been calculated for the first time.

Photoexcitations of many-electron atoms and ions by twisted light

SynopsisThe photoexcitation of (multi-electron) atoms and ions by twisted light has been explored within the framework of the density matrix theory and Dirac's relativistic equation. It is shown that the population of the excited atoms and, hence, their fluorescence emission are sensitive with regard to the transverse linear momentum and the (projection of the) total angular momentum of the incident light.

Differential electron emission from multi-electronic targets under highly harged bare ion impact

SynopsisWe report a combined experimental and theoretical study of double differential electron emission in ionization of different multi-electronic atoms under fast highly charged bare ion impact. The main aim is to un-derstand the electron dynamics for these targets which is quite different from one or two electron systems.

On dissociation in weakly doped ice

Currently, there is some ambiguity in the problem of decay of a single donor into charged fragments. Thus, in the well-known Ostwald approximation used for semiconductors (ice being one of them) the donor dissociation degree of tends to its maximum value (i.e., unity) as the doping impurity concentration approaches zero. At the same time, the statistical theory of atom reveals within the Thomas–Fermi (or Debye–Hückel) approximation the existence of a thermodynamically equilibrium state of a single multi-electron atom (donor) where charged nucleus keeps the number of counterions just necessary for its neutralization. These scenarios do not show the atom dissociation at all. Discussed in the present paper is the alternative between the full dissociation of a single donor (i.e., dissociation degree equals unity) in a semiconducting media (ice, water, semiconductor) and zero dissociation degree.

Photoionization of few electron systems: a hybrid coupled channels approach

We present the hybrid anti-symmetrized coupled channels method for the calculation of fully differential photo-electron spectra of multi-electron atoms and small molecules interacting with strong laser fields. The method unites quantum chemical few-body electronic structure with strong-field dynamics by solving the time dependent Schrödinger equation in a fully anti-symmetrized basis composed of multi-electron states from quantum chemistry and a one-electron numerical basis. Photoelectron spectra are obtained via the time dependent surface flux (tSURFF) method. Performance and accuracy of the approach are demonstrated for spectra from the helium and beryllium atoms and the hydrogen molecule in linearly polarized laser fields at wavelengths from 21 to 400 nm. At long wavelengths, helium and the hydrogen molecule at equilibrium inter-nuclear distance can be approximated as single channel systems whereas beryllium needs a multi-channel description.

Green-function approach to the theory of tunneling ionization

We solve the problem of tunneling ionization of a multielectron atom in a static electric field by using the Green's function for the Stark-Coulomb problem. This allows us to incorporate the outgoing-wave boundary conditions at infinity. The interaction of the active electron with the atomic residue is described either by a model potential or by the $l$-dependent pseudopotential which prevents virtual transitions to orbitals occupied by inner electrons. The method works well in the broad range of electric fields including the region above the classical ionization threshold (the barrier-suppression region). Calculations of ionization of Ar demonstrate a noticeable difference between the model potential approach and the pseudopotential approach, but both sets of results agree with experimental data.

Polarization correction in the theory of energy losses by charged particles

A method for finding the polarization (Barkas) correction in the theory of energy losses by charged particles in collisions with multielectron atoms is proposed. The Barkas correction is presented in a simple analytical form. We make comparisons with experimental data and show that applying the Barkas correction improves the agreement between theory and experiment.

Disappearing resonance tunneling in photoelectron emission

We predict a phenomenon of disappearing resonance tunneling, found in the course of investigating photoionization microscopy of multielectronic atoms in the presence of a uniform external electric field. Li atoms are taken to illustrate that for multielectronic atoms, noticeable tunneling is slowly attenuated with increasing the lifetime of Stark resonance states and it finally becomes invisible. In order to decipher disappearing resonance tunneling, we propose a competition mechanism between transmission and transfer of electron waves. In this mechanism, it is crucial to relate the contribution of resonance tunneling to photoelectron emission of multielectronic atoms with the lifetime of Stark resonance states corresponding to the transmission broadening. The analysis shows that such a phenomenon should exist in any system of multielectronic atoms or molecules. The present findings should serve as a basis for explanation of disagreement between observations and theoretical calculations in Xe atoms. We expect that disappearing resonance tunneling predicted in this letter should be visible in experiment of photoionization microscopy for any multielectronic atom or molecule.

Study on equation of state based on Thomas-Fermi-Kirzhnits model

A wide-range semi-empirical equation of state is constructed for numerical simulation of high-energy density experiments, such as, wire-array Z-pinch etc. The equation of state consists of zero-temperature free energy term, and thermal contributions of electron and ion. Thomas-Fermi model, which was firstly put forward by Thomas and Fermi, is initially developed to study the electron distribution of multi-electron atoms. Since its advent, this model has been widely used in solid-state physics, atomic physics, astrophysics and equation of state computations. It is a particularly important model to describe the behavior of matter under extreme conditions of high temperature and high density. This model provides reasonably accurate results that are validated experimentally for some thermodynamic quantities, such as the pressure. However, the Thomas-Fermi model yields a pressure of a few GPa under normal density even at very low temperature, and the pressure is always positive, indicating an obvious limitation of this model. Kirzhnits has evaluated the influence of quantum effect and exchange effect on temperature-dependent Thomas-Fermi model and their contributions to the Thomas-Fermi equation of state. Basically, the Thomas-Fermi model with its quantum and exchange corrections which is called Thomas-Fermi-Kirzhnits model, can be applied to calculate the thermal contribution of electrons to the thermodynamic functions, which can lower the pressure given from the Thomas-Fermi model. The zero-temperature free energy term in the semi-empirical equation of state is described by a polynomial expression. The coefficients of the polynomial expression is calculated by using zero-temperature Thomas-Fermi-Kirzhnits model and the relation between thermodynamic quantities. A quasi-harmonic model is adopted to describe the behavior of ions. It is originally applied to calculate the contribution of ions in the condensed state. However, the quasi-harmonic model is close to an ideal equation of state in the high-temperature and low-density region. This model makes the description of the behavior of ions in the phase transition from the solid state to plasma state be approximated. Thomas-Fermi-Kirzhnits model is adopted to calculate the thermal contribution of electrons. The semi-empirical equation of state has the advantages of less calculation and clear physical concepts. Experimental data of isothermal compression at 300 K is fruitful and accurate. They can be used to verify the results of the semi-empirical equation of state. An isothermal compression curve is calculated by the present work and compared with experimental data. The pressures over a wide-range of temperature and density are derived and compared with corresponding data of SESAME database. The trajectory of the electrical explosion of aluminum is demonstrated from solid state to ideal plasma state.

A Review on Ab Initio Approaches for Multielectron Dynamics

In parallel with the evolution of femtosecond and attosecond laser as well as free-electron laser technology, a variety of theoretical methods have been developed to describe the behavior of atoms, molecules, clusters, and solids under the action of those laser pulses. Here, we review major ab initio wave-function-based numerical approaches to simulate multielectron dynamics in atoms and molecules driven by intense long-wavelength and/or ultrashort short-wavelength laser pulses. Direct solution of the time-dependent Schrodinger equation, though its applicability is limited to He, ${\rm H}_2$ , and Li, can provide an exact description and has been greatly contributing to the understanding of dynamical electron-electron correlation. Multiconfiguration self-consistent-field (MCSCF) approach offers a flexible framework from which a variety of methods can be derived to treat both atoms and molecules, with possibility to systematically control the accuracy. The equations of motion of configuration interaction coefficients and molecular orbitals for general MCSCF ansatz have recently been derived. Time-dependent extension of the $R$ -matrix theory, originally developed for electron-atom collision, can realistically and accurately describe laser-driven complex multielectron atoms.

Reemission of ultrashort electromagnetic field pulses by multielectron atoms

We develop a method for calculating the spectra of reemission of ultrashort (attosecond and shorter) electromagnetic field pulses by neutral multielectron atoms with a nuclear charge from 1 to 92. The method makes it possible to exactly take into account the spatial nonuniformity of the field of an ultrashort pulse and photon momenta in reemission processes. The results are represented as analytical formulas with several coefficients and screening parameters tabulated for all atoms for which the electron densities can be described by the familiar Dirac-Hartree-Fock-Slater model. By way of example, the spectra of remission of ultrashort electromagnetic field pulses by carbon, silicon, germanium, tin, and lead atoms are calculated.

Bohr’s molecular model and the melding of classical and quantum mechanics

Svidzinsky, Scully, and Herschbach reply: We agree with M. Y. Amusia that a statement we made about the infinite dimension limit is “lacking in rigor.” It was intended simply to provide heuristic insight into why, for a wide variety of problems, the large-D limit has proven to be a useful starting approximation to obtain results for D = 3.Amusia’s other concerns are answered in a 1975 paper on a D-scaling treatment of helium by David Herrick and Frank Stillinger.11. D. R. Herrick, F. H. Stillinger, Phys. Rev. A 11, 42 (1975). https://doi.org/10.1103/PhysRevA.11.42 They gave a rigorous derivation of the D-dimensional hydrogen atom Hamiltonian, shown as equation 1 in Amusia’s letter. That solution applies for D ≥ 2, as implied in the figure included in box 1 of our article. Herrick and Stillinger also showed that for the correct D → 1 limit, the Z/r term becomes a δ-function. In D-scaling, contrary to Amusia’s assumption, the D = 3 form of Coulomb’s law can be used for dimensional continuation to the large-D limit. The D-dependent similarity transformation affects the Laplacian, not the potential energy. Both theory and application are amply presented in references given in our article (particularly references 8–11). D-scaling, using just elementary algebra, has attained correlation energies for multielectron atoms with accuracy comparable to or better than conventional electronic calculations.22. See, for example, S. Kais, R. Bleil, J. Chem. Phys. 102, 7472 (1995); https://doi.org/10.1063/1.469059D. K. Watson, D. Z. Goodson, Phys. Rev. A 51, R5 (1995), and references therein. https://doi.org/10.1103/PhysRevA.51.R5The papers of Leonard Mlodinow33. See D. R. Herschbach, J. Chem. Phys. 84, 838 (1986), for analysis of the papers cited in reference 1 of Mlodinow’s letter. https://doi.org/10.1063/1.450584 and several other authors, especially the earlier paper by Herrick and Stillinger,11. D. R. Herrick, F. H. Stillinger, Phys. Rev. A 11, 42 (1975). https://doi.org/10.1103/PhysRevA.11.42 fostered the development of D-scaling for electronic structure. Since the kinship of Bohr’s model to dimensional scaling was not recognized until 2005, we did not dwell on that history, other than citing the tutorial article by Edward Witten. The treatment of H2 that Mlodinow cites in the second part of his reference 3 is a deliberately drastic approximation and gives less than 40% of the bond dissociation energy.As emphasized by Petar Grujic, the bold, perplexing enterprise by Niels Bohr motivated much further work melding classical and quantum mechanics. We note that D-scaling has a distinctive character. It might aptly be termed “semiquantum” rather than semiclassical. Although in the large-D limit the equations become classical, quantum mechanics is hidden in the D-dependent units adopted for distance and energy. At that limit, electrons take fixed positions in the D-scaled space and the first-order correction in (1/D) has them execute harmonic vibrations about those positions. In the prequantum era, such behavior was postulated by Gilbert Lewis and Irving Langmuir,44. P. Coffey, Cathedrals of Science: The Personalities and Rivalries That Made Modern Chemistry, Oxford U. Press, New York (2008), chap. 5, esp. p. 139. motivated by chemical arguments but disdained by physicists and considered incompatible with the Bohr model.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. D. R. Herrick, F. H. Stillinger, Phys. Rev. A 11, 42 (1975). https://doi.org/10.1103/PhysRevA.11.42, Google ScholarCrossref, ISI2. See, for example, S. Kais, R. Bleil, J. Chem. Phys. 102, 7472 (1995); https://doi.org/10.1063/1.469059, Google ScholarCrossref, ISID. K. Watson, D. Z. Goodson, Phys. Rev. A 51, R5 (1995), and references therein. https://doi.org/10.1103/PhysRevA.51.R5, , Google ScholarCrossref, ISI3. See D. R. Herschbach, J. Chem. Phys. 84, 838 (1986), for analysis of the papers cited in reference 1 of Mlodinow’s letter. https://doi.org/10.1063/1.450584, Google ScholarCrossref, ISI4. P. Coffey, Cathedrals of Science: The Personalities and Rivalries That Made Modern Chemistry, Oxford U. Press, New York (2008), chap. 5, esp. p. 139. Google Scholar© 2014 American Institute of Physics.

Exterior complex scaling method in TDDFT: HHG of Ar atoms in intense laser fields

The exterior complex scaling (ECS) method is applied in the framework of time-dependent density-functional theory (TDDFT) to study high-order harmonic generation (HHG) of multielectron atoms in intense laser fields. With the help of ECS, correct outgoing-wave boundary conditions can be imposed on the wave functions at large distances. In our implementation, ECS is combined with the time-dependent generalized pseudospectral method for accurate and efficient solution of the time-dependent Kohn-Sham equations. We make use of LB94 exchange-correlation potential which appears quite accurate in calculations of unperturbed electronic structure of Ar. Calculations of HHG are performed for the laser fields with the wavelength of 800 nm and several peak intensities. The HHG spectrum exhibits an intensity-independent minimum corresponding to the photon energy of about 51 eV which is closely related to the Cooper minimum in the photoionization cross section of Ar. We found that HHG spectra calculated with the frozen-core potential (not including dynamic response of the electron density) differ significantly from those obtained by TDDFT.

Exterior complex scaling method in TDDFT: HHG of Ar atoms in intense laser fields

Exterior complex scaling (ECS) method is applied in the framework of the time-dependent density functional theory to study high-order harmonic generation (HHG) of multielectron atoms in intense laser fields. ECS allows to impose correct (outgoing-wave) boundary conditions on the wave functions at large distances. In the present work, ECS is combined with the time-dependent generalized pseudospectral method for accurate and efficient solution of the time-dependent Kohn-Sham equations. Results for HHG of Ar atoms are presented.

A thin diffuse component of the Galactic ridge X-ray emission and heating of the interstellar medium contributed by the radiation of Galactic X-ray binaries

We predict a thin (scale height $\sim$ 80 pc) diffuse component of the Galactic Ridge X-ray emission (GRXE) arising from the scattering of the radiation of bright X-ray binaries (XBs) by the interstellar medium (ISM). The morphology of this scattered component is expected to trace the clumpy molecular and HI clouds. We calculate this contribution to the GRXE from known Galactic XBs assuming that they are all persistent. The known XBs sample is incomplete, however, because it is flux limited and spans the lifetime of X-ray astronomy ($\sim 50$ years). We therefore also use a simulated sample of sources, to estimate the diffuse emission we should expect in an optimistic case assuming that the X-ray luminosity of our Galaxy is on average similar to that of other galaxies. In the calculations we also take into account the enhancement of the total scattering cross-section due to coherence effects in the elastic scattering from multi-electron atoms and molecules. This scattered emission can be distinguished from the contribution of low X-ray luminosity stars by the presence of narrow fluorescent K-$\alpha$ lines of Fe, Si, and other abundant elements present in the ISM and by directly resolving the contribution of low X-ray luminosity stars. We find that within $1^\circ$ latitude of the Galactic plane the scattered emission contributes on average $10-30\%$ of the GRXE flux in the case of known sources and over $50\%$ in the case of simulated sources. In the latter case, the scattered component is found to even dominate the stellar emission in certain parts of the Galactic plane. X-rays with energies $\gtrsim 1$ keV from XBs should also penetrate deep inside the HI and molecular clouds, where they are absorbed and heat the ISM. We find that this heating rate dominates the heating by cosmic rays (assuming a solar neighborhood energy density) in a considerable part of the Galaxy. [abridged]