Coulomb Green Function Research Articles

Analysis of correlation effects in autoionizing doubly excited states of barium using Coulomb Green's function

Though one would expect that large-angular momentum doubly excited states exhibit weak electronic correlations, it is shown in this paper that a first-order perturbation theory ignoring such correlations may completely fail in predicting correct autoionization probabilities: quadrupolar transitions are poorly described by lowest-order perturbation theory, except for very large angular momenta. Inclusion of second-order dipole-dipole term considerably improves the accuracy of the method. This effect is computed using Coulomb Green’s function in its analytical form, probably applied here for the first time to autoionization processes. Examples are given in barium for 5dj 5g [k] states (j = 3/2, 5/2) and for 5d5/2nl [k] states with l > 4.

Radiative double-electron capture in collisions of fast heavy ions with solid carbon targets

Two-electron capture with an emission of a single photon (TESP) in collisions of highly charged ions with light atoms is considered. Such a process is actually a time-reversed double photoionization but occurring at specific kinematics. In the lowest order in the interelectron interaction, the TESP probability is determined by two diagrams which are evaluated analytically by means of the Coulomb Green's function. The calculated ratio of the radiative double-electron capture and single recombination cross sections is in fair agreement with the data obtained in the recent experimental study of this phenomenon.

The Dirac - Coulomb Sturmians and the series expansion of the Dirac - Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom

Two relativistic Sturmian basis sets are constructed by solving first-order Sturm - Liouville problems for the Dirac - Coulomb equation. The Sturmian expansions of the Dirac - Coulomb Green function and the reduced Dirac - Coulomb Green function are derived. Their utility is illustrated by calculating static electric dipole polarizabilities for hydrogen-like atoms with .

One-electron charge exchange between and positive multiply charged ions. 1. Collisions

The cross section for one-electron transfer is calculated in this paper. The collisional system is treated as a three-electron one and matrix elements for the formation of excited helium in both singlet and triplet states (1S, , P and , P, D) are obtained. Close-coupling calculations were done for the 27 (1S, , P and , P, D) final states covering the range 1 - of the relative collision velocity. An approximation is used for the effective potential of and Coulomb Green's functions are used to describe the weakly bound electron of . A satisfactory agreement is obtained with the experimental cross section.

Single- and double-electron detachment in slow collisions of H− ions with highly-charged ions

At the previous conference, HCI94, we reported the solution of the problem on double-electron detachment in collisions of H− ions with highly charged ions (HCI) at medium and large collision energies using the approach based on the non-stationary continuum-distorted-wavefunction method. At small velocities, the close-coupling based on the two-center expansion is appropriate. In the case of the "outer" electron removal, the two-center problem has the exact analytic solution in terms of the Coulomb Green's function. The "inner" electron removal is reduced to the problem of atomic hydrogen collision with the HCI. The leading process is the double-electron capture into excited ionic states followed by radiative and autoionizing decay. The cross sections of single- and double-electron detachment are calculated at collision energies from 0.5-500eV. The results are found in reasonable agreement with the experimental data available. The scaling laws are discussed.

Solution of the Dirac-Coulomb problem by the second-order Dirac equation approach

A complete solution of the relativistic Coulomb problem is presented on the basis of the second-order Dirac equation. A set of fundamental solutions of the linear and squared relativistic equation is investigated. The different forms of both the ordinary and the reduced relativistic Coulomb Green functions and the wavefunctions are discussed.

The correlation and relativistic corrections in transition probabilities in the He-like ions

The results of analytical calculations for transition probability in the He-like ions in the first order of perturbation theory of electron interaction are presented. Both nonrelativistic and relativistic expression are obtained on the base of the Coulomb Green function method. The approximation finite series are found to present wide information for electric dipole transitions for 1snl → 1sn'l' states at n ⩽ 5, l = s, p, d, n' = 2, l' = s, p.

Radiative double electron capture in fast heavy ion-atom collisions

Two-electron capture with emission of a single photon (TESP) in collisions of highly charged ions with light atoms is considered. Such a process is actually a time-reversed double photoionization but occurring at specific kinematics. In the lowest order in the inter-electron interaction, the TESP probability is determined by two diagrams which are evaluated analytically by means of the Coulomb Green function. The calculated ratio of the TESP and single recombination cross sections is in fair agreement with the data obtained in the recent experimental study of this phenomena.

Methods of the approximate treatment of the two-photon bremsstrahlung in point Coulomb field

We introduce simple methods for the approximate calculation of the compound two-photon dipole free-free matrix element in a Coulomb field which characterizes the amplitude of the two-photon bremsstrahlung process. Methods are based on the accurate treatment of the diagonal singularity in the one-photon dipole matrix elements, which appear in the compound-matrix element. We demonstrate that the exact results presented by Florescu and Djamo, Veniard and co-workers and Dondera and Florescu, where the two-photon free-free matrix element in the Coulomb field was obtained using the explicit form of the Coulomb Green function, can be reproduced quite accurately (error <3%) with the use of the formulae given in this paper.

Green's functions for separable potentials

The convergence properties of approximate one-particle Green's functions derived from separable potential expansions are examined. A convergence criterion for the basis set to be used in a Lowdin-type inner projection is established and illustrated by calculations of matrix elements of the Coulomb Green's function based on separable potentials of finite rank. It is then suggested that a separable potential ansatz for a many-electron wave function may be introduced into Frenkel's time-dependent variation principle in order to obtain approximate response functions with the continuum of one-particle states explicitly included. A preliminary outline of the formalism at the time-dependent Hartree-Fock level is presented.

Operator representation of the Dirac Coulomb Green function and relativistic polarizability of hydrogen-like atoms

The Dirac Coulomb Green function in the representation of the annihilation and creation operators is established and on the basis of the application of this new operator representation an algebraic method of calculation of atomic characteristics is briefly discussed. The relativistic polarizability of hydrogen-like atoms is calculated and its simple analytical formula is obtained.

Influence of intermediate-state Coulomb scattering on the behaviour of the two-particle scattering amplitude at small momentum transfer

The leading singularity as the momentum transfer tends towards zero of the elastic, off-shell, two-particle, Coulomb scattering amplitude is investigated and shown to coincide with that of second Born approximation, independently of whether the intermediate-state Coulomb scattering is represented by the exact or only by the asymptotic Coulomb Green function. This indicates that for investigations of this type Coulomb rescattering in the intermediate state can be neglected. Proofs of this result are developed in both momentum as well as coordinate space.

The algebraic method for two-dimensional quantum atomic systems

The authors propose an easy and effective variant of the realization of the dynamical symmetry of hydrogen-like atoms in two-dimensional space, based on the relationship between the Schrodinger equation for the isotropic harmonic oscillator in one-dimensional complex space and the Schrodinger equation for the one-electron atom in two-dimensional space, that permits them to use the operator method to solve the Schrodinger equation for the two-dimensional atomic system. For illustration of the algebraic method, they consider the problem of the two-dimensional hydrogenic donor in a magnetic field. By the use of the path integral they also establish the relationship between the two-dimensional Coulomb Green function and the Green function for the isotropic harmonic oscillator in one-dimensional complex space.

Simplified derivation of a one‐range addition theorem of the Yukawa potential

AbstractThe one‐range addition theorem [J. Fernández Rico, R. López, and G. Ramírez, Int. J. Quantum Chem. 34, 121 (1988)] for the Yukawa potential is rederived in a very simple manner using weakly convergent expansions [E. J. Weniger, J. Math. Phys. 26, 276 (1985)] of plane waves in the Fourier representation. It is discussed in which sense the addition theorem converges. The relation to Sturmian expansions of Coulomb Green functions is pointed out. © 1992 John Wiley &amp; Sons, Inc.

Time-independent mean field theory of collisions: the case of long range forces

Instead of diagonalizing the many-body Hamiltonian H, the authors invert E-H, where E is a complex energy, which is eventually made real. All the traditional approximations to diagonalization may be adopted for the evaluation of (E-H)-1. Mean field methods are specially investigated. Previous papers reported several numerically soluble cases where a time-independent mean field approximation (TIMF) was tested with success for the calculation of collision amplitudes with short range forces. They test the validity of TIMF for a long range interaction: the Coulomb Green function for two particles is found to be successfully approximated by TIMF.

On the hydrogen-like atom in five-dimensional space

The authors propose an easy and effective variant of the realization of the dynamical symmetry of hydrogen-like atoms in five-dimensional space, based on the relationship between the Schrodinger equation for the isotropic harmonic oscillator in four-dimensional complex space and the Schrodinger equation for the one-electron atom in five-dimensional space. By the use of the path integral they also establish the relationship between the Coulomb Green function and the Green function for the isotropic harmonic oscillator in four-dimensional complex space.

Dynamic toroid polarizability of atomic hydrogen

The concept of toroid polarizability introduced in previous work is examined within the familiar context of nonrelativistic quantum Coulomb systems, in a way unbiased by approximations. The dynamic (i.e., frequency (ω) dependent) toroid dipole polarizability γ(ω) of a (nonrelativistic, spinless, ground-state) hydrogenlike atom is calculated analytically in terms of (essentially) one Gauss hypergeometric function. The static result takes on the simple form γ(ω = 0) = 23 60 α 2Z −4a 0 5 (α = fine structure constant, Z = nucleus charge number, a 0 = Bohr radius). γ(ω) characterizes the linear response of the system to a conduction and/or displacement (time dependent) external current. The method of calculation (based on the use of the integral representation for the nonrelativistic Coulomb Green's function) is presented in detail. The imaginary part of γ(ω) above ionization threshold is also computed in a simple closed form. Comparing γ(ω = 0) with the already known (exact) results for the electric multipole polarizabilities (for which, as a byproduct, we present in an Appendix a considerably simplified expression, to our knowledge the simplest reported as yet), one sees that although for H-like atoms the toroid effects appear as very small indeed, they are however increasing with Z. A comparison with analogous (but, this time, only order of magnitude) evaluations for (charged) pions, indicates that the role of the induced toroid moments (as against that of the usual electric ones) increases drastically when passing from atomic to hadron physics; it is argued that this trend might continue further, at the sub-hadronic level.

Perturbative calculation of the ac Stark effect by the complex rotation method.

We have calculated the high-order ac Stark effect for the ground state of atomic hydrogen by applying Rayleigh-Schr\"odinger perturbation theory to a complex-rotated Hamiltonian. We present results for the level-shift and multiphoton-ionization rate, which include effects of above-threshold ionization. Our results indicate that the field intensities at which high-order contributions become dominant can be as low as ${10}^{11}$ W/${\mathrm{cm}}^{2}$, much lower than is commonly expected. A systematic treatment of the frequency dependence of the perturbation coefficients in the vicinity of multiphoton resonances and ionization thresholds is provided by reference to the analytical properties of the Coulomb Green's function.

Dynamic toroid polarizability of atomic hydrogen: A. Costescu. Department of Physics, University of Bucharest, P.O. Box Mg-11, Bucharest, Romania; and E. E. Radescu. International Center for Theoretical Physics, Trieste, Italy, and Institute of Atomic Physics, P.O. Box Mg-6, Bucharest, Romania

Abstract The concept of toroid polarizability introduced in previous work is examined within the familiar context of nonrelativistic quantum Coulomb systems, in a way unbiased by approximations. The dynamic (i.e., frequency (ω) dependent) toroid dipole polarizability γ(ω) of a (nonrelativistic, spinless, ground-state) hydrogenlike atom is calculated analytically in terms of (essentially) one Gauss hypergeometric function. The static result takes on the simple form γ(ω = 0) = 23 60 α 2 Z −4 a 0 5 (α = fine structure constant, Z = nucleus charge number, a0 = Bohr radius). γ(ω) characterizes the linear response of the system to a conduction and/or displacement (time dependent) external current. The method of calculation (based on the use of the integral representation for the nonrelativistic Coulomb Green's function) is presented in detail. The imaginary part of γ(ω) above ionization threshold is also computed in a simple closed form. Comparing γ(ω = 0) with the already known (exact) results for the electric multipole polarizabilities (for which, as a byproduct, we present in an Appendix a considerably simplified expression, to our knowledge the simplest reported as yet), one sees that although for H-like atoms the toroid effects appear as very small indeed, they are however increasing with Z. A comparison with analogous (but, this time, only order of magnitude) evaluations for (charged) pions, indicates that the role of the induced toroid moments (as against that of the usual electric ones) increases drastically when passing from atomic to hadron physics; it is argued that this trend might continue further, at the sub-hadronic level.

Transformed Coulomb Green function Sturmian expansion

Two Coulomb Green function Sturmian expansions are presented. Both of them are used to derive the transformed Coulomb Green function Sturmian expansion. The new Coulomb Green function representation is tested for calculating two-photon above-threshold ionization cross sections for atomic hydrogen. The new representation may be useful also in the case of more excess photons as well as for calculating free-free transitions.