arXiv subjects

Ingvar Lindgren

Publications and source records attributed to Ingvar Lindgren.

7 recordsLinked to original sources

arXiv2014

QED effects in scattering processes involving atomic bound states: Radiative recombination

The standard S-matrix formulation cannot generally be used in the treatment of atomic scattering processes, involving bound-state QED effects, due to the special type of singularity that can here appear. This type of singularity can be handled by means of methods designed for structure calculations. It is essentially a consequence of the optical theorem that similar techniques can be applied also in scattering processes. The optical theorem for free particles gives a relation between the effective Hamiltonian and the cross section, a relation that is valid also when bound states are present. We have found that the method with the Covariant-evolution-operator/Green's operator that we have developed primarily for structure problems can here be applied in a rather straightforward manner. The new procedure is demonstrated for the case of radiative recombination.

quant-ph↗

arXiv2012

Energy-dependent perturbation theory: Possibility for improved tests of quantum-electrodynamics

Measurements of energy separations in highly charged ions can in many cases nowadays be performed with very high accuracy, an accuracy that sometimes cannot be matched by the corresponding theoretical calcula- tions. Furthermore, it has recently been demonstrated that there is a systematic deviation between experimental and theoretical results for the K- alpha lines of medium-heavy heliumlike ions. We have during a number of years been developing a general procedure for energy-dependent perturbative calcu- lations, which opens up a unique possibility of incorporating the energy- dependent QED perturbations into the all-order many-body perturbation expansion in a rigorous way. Such an expansion will yield several important effects, never before accounted for in this type of analysis, which is expected to increase the theoretical accuracy considerably. Calculation of some of these effects have been performed at our laboratory in Gothenburg, and numerical results are given. Further work along this line is now in progress. To what extent the improved procedure might explain the discrepancy found by Chantler et al. remains to be seen.

physics.atom-ph↗

arXiv2011

Dimensional regularization of the free-electron self-energy and vertex correction in Coulomb gauge

There is presently a great interest in studying static and dynamic properties of highly charged ions that can be produced in large particle accelerators, like that at GSI in Darmstadt. To perform corresponding theoretical calculations with great accuracy requires a highly developed machinery of computational methods that have not until recently been available. In order to combine many-body perturbation theory with quantum electrodynamics, the calculations have generally to be performed in the Coulomb gauge, where applications have not been so developed as in, for instance, the Feynman gauge. Formulas for the free-electron self energy and vertex correction have been given without derivation by Adkins (Phys. Rev. D27, 1814 (1983); Phys. Rev. D34, 2489 (1986)). In the present paper the formulas of Adkins are verified with detailed derivations.

quant-ph↗

arXiv2008

The helium fine-structure controversy

There is presently disagreement between theory and experiment as well as between different theoretical calculations concerning the fine-structure splitting of the lowest P state of the neutral helium atom. We believe that we have found a minor error in the formulas used by Drake et al. (Can. J. Phys. 80, 1195 (2002)) in their calculations, and we may have an explanation how the error has occurred. To what extent this might resolve (part of) the discrepancy is not known at present.

quant-ph↗

arXiv2006

Many-body perturbation procedure for energy-dependent perturbation: Merging many-body perturbation theory with QED

A formalism for energy-dependent many-body perturbation theory (MBPT), previously indicated in our recent review articles (Lindgren et al., Phys.Rep. 389,161(2004), Can.J.Phys. 83,183(2005)), is developed in more detail. The formalism allows for a mixture of energy-dependent (retarded) and energy-independent (instantaneous) interactions and hence for a merger of QED and standard (relativistic) MBPT. This combination is particularly important for light elements, such as light heliumlike ions, where electron correlation is pronounced. It can also be quite significant in the medium-heavy mass range, as recently discussed by Fritzsche et al. (J.Phys. B38,S707(2005)), with the consequence that the effects might be significant also in analyzing the data of experiments with highly charged ions. A numerical procedure for treating the combined effect is described, and some preliminary numerical results are given for heliumlike ions. This represent the first numerical evaluation of effects beyond two-photon exchange involving a retarded interaction. It is found that for heliumlike neon the effect of one retarded photon (with Coulomb interactions of all orders) represents about 99% of the non-radiative effects beyond energy-independent MBPT.

quant-ph↗

arXiv2005

Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation

The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-body perturbation theory. At the same time this procedure is closely connected to the S-matrix and the Green's-function formalisms and can therefore serve as a bridge between various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. It has the same relation to the BS equation as has the standard Bloch equation to the ordinary Schroedinger equation and can be used to generate a perturbation expansion compatible with the BS equation also for a quasi-degenerate model space.

quant-ph↗

arXiv2004

The locality hypothesis in density-functional theory: An exact theorem

The locality hypothesis in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A \bf{58}, R12 (1998); \it{ibid.} A \bf{65}, 010502 (2001); Adv. Quant. Chem, \bf{43}, 1 (2003)] claimed that this hypothesis is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have in a Comment to the Physical Review [Phys. Rev. A \bf{67}, 056501 (2003)] commented upon these works and recently extended the arguments [Adv. Quant. Chem. \bf{43}, 95 (2003)]. We have shown that there is no such conflict and that the locality hypothesis is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the $1s2s ^3S$ state of helium that generates the many-body electron density and shown that the corresponding $2s$ Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. In addition to verifying the locality hypothesis, this confirms the theorem regarding the Kohn-Sham eigenvalue of the highest occupied orbital.

physics.atom-ph↗