scholarly journals Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

2005 ◽  
Vol 83 (4) ◽  
pp. 447-454 ◽  
Author(s):  
E -O Le Bigot ◽  
U D Jentschura ◽  
P Indelicato ◽  
P J Mohr
Keyword(s):  
High Precision ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
The Self ◽  
Level Shift ◽  
Atomic Systems ◽  
Self Energy ◽  
Rydberg Constant ◽  
Energy Level Shift ◽  
Nuclear Charge Number

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of quantum electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.PACS Nos.: 12.20.Ds, 31.30.Jv, 06.20.Jr, 31.15.–p

scholarly journals TECHNIQUES IN ANALYTIC LAMB SHIFT CALCULATIONS

2005 ◽  
Vol 20 (30) ◽  
pp. 2261-2276 ◽  
Author(s):  
ULRICH D. JENTSCHURA
Keyword(s):  
Quantum Electrodynamics ◽  
Numerical Algorithms ◽  
Bound State ◽  
Electron Mass ◽  
Atomic Systems ◽  
Self Energy ◽  
Theoretical Predictions ◽  
The One ◽  
Loop Bound ◽  
Nuclear Charge Number

Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum electrodynamics provides us with accurate theoretical predictions for the transition energies relevant to simple atomic systems, and steady theoretical progress relies on advances in calculational techniques, as well as numerical algorithms. In this brief review, we discuss one particular aspect connected with the recent progress: the evaluation of relativistic corrections to the one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge number, for excited non-S states, up to the order of α(Zα)6 in units of the electron mass. A few details of calculations formerly reported in the literature are discussed, and results for 6F, 7F, 6G and 7G states are given.

scholarly journals On the electrodynamic self-energy of the electron

1948 ◽  
Vol 195 (1041) ◽  
pp. 163-173
Keyword(s):  
Perturbation Theory ◽  
Wave Equation ◽  
Quantum Electrodynamics ◽  
Energy State ◽  
Energy Eigenvalue ◽  
Expansion Method ◽  
Negative Energy ◽  
The Self ◽  
Variation Principle ◽  
Self Energy

The stationary-state wave equation for an electron at rest in a negative-energy state in interaction with only its own electromagnetic field is considered. Quantum electrodynamics, single-electron theory and a ‘cut-off’ procedure in momentum-space are used. Expressions in the form of expansions in powers of e 2 /hc are derived for the wave function ψ and the energy-eigenvalue E by a method which (unlike perturbation theory) is not based on the assumption that the self-energy is small. The convergence of the expansion for E is not proved rigorously but the first few terms are shown to decrease rapidly. For low cut-off frequencies K 0 the expression for E behaves as the equivalent perturbation expression but for large K 0 it behaves as — J(e 2 /hc) hK0. The variation principle is applied to an approximation (obtained from the expansion method) for r/r, and it is proved rigorously that for large K 0 the self-energy is algebraically less than or equal to —J(e 2 /hc) hK 0 . Hence, if the electron wave-equation is considered as the limiting case of the ‘cut-off’ equation as K 0 ->ao, it is established that the divergences obtained are not merely due to improper use of perturbation theory and that the self-energy is indeed infinite.

ON THE POSSIBLE EXISTENCE OF A DERIVATIVE COUPLING IN QUANTUM ELECTRODYNAMICS

1959 ◽  
Vol 37 (12) ◽  
pp. 1339-1343
Author(s):  
F. A. Kaempffer
Keyword(s):  
Cross Section ◽  
Quantum Electrodynamics ◽  
Mass Difference ◽  
Large Mass ◽  
The Self ◽  
Nucleon Mass ◽  
Muon Scattering ◽  
Derivative Coupling ◽  
Self Energy ◽  
Classical Analogue

Within the framework of quantum electrodynamics there exists the possibility of a derivative coupling between source and photon field, referred to as eΛ-charge, which has no classical analogue. For calculations the usual graph technique can be used, provided the factor eγμ contributed by each vertex in a conventional graph is replaced by ieΛkμ, where Λ is a length characteristic of the new interaction. Using as cutoff the nucleon mass M one finds for a bare source of electronic mass m the self-energy in second order to be Λm/m ≈ 200, if Λ−1 ≈ 60 M. It is argued that the large mass difference between muon and electron may be due to this effect, assuming muon and electron to differ only in that the muon has eΛ-charge whereas the electron has not. An estimate is made of the muon–muon scattering cross section caused by the presence of eΛ-charge on the muon, and it is found that the existence of this derivative coupling may have escaped observation.

REVERSAL OF DOPING INDUCED ENERGY LEVEL SHIFT IN ORGANIC SEMICONDUCTORS

2007 ◽  
Vol 06 (02) ◽  
pp. 125-129 ◽  
Author(s):  
HUANJUN DING ◽  
YONGLI GAO
Keyword(s):  
Electronic Structure ◽  
Energy Level ◽  
Organic Semiconductors ◽  
Energy Levels ◽  
Photoemission Spectroscopy ◽  
Level Shift ◽  
Highest Occupied Molecular Orbital ◽  
Energy Level Shift ◽  
Fine Tune ◽  
Gap State

We have investigated the electronic structure of the interface formed by depositing Au on Cs -doped and Na -doped tris(8-hydroxyquinoline) aluminum (Alq) film using ultraviolet and X-ray photoemission spectroscopy (UPS and XPS). The initial Au deposition quenches the Al q gap state caused by the alkali metal doping. Further Au depositions shift gradually the energy levels opposite to that induced by Cs doping, especially the highest occupied molecular orbital (HOMO) that shows approximately full recovery to the pristine Al q position. However, the recovery is only partial for other levels, most noticeably the C 1s core level. The results indicate that the gap state and energy level positions can be decoupled in the organic semiconductors, and that it is possible to fine tune the electronic structure by selective doping in the interface region.

Optical contrast of a photonic crystal and the self energy shift of the energy levels of atoms

2012 ◽  
Vol 76 (12) ◽  
pp. 1301-1305 ◽  
Author(s):  
R. Kh. Gainutdinov ◽  
M. Kh. Salakhov ◽  
M. A. Khamadeev
Keyword(s):  
Photonic Crystal ◽  
Energy Levels ◽  
Energy Shift ◽  
The Self ◽  
Optical Contrast ◽  
Self Energy

scholarly journals From first principles of QED to an application: hyperfine structure of P states of muonic hydrogenThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

2011 ◽  
Vol 89 (1) ◽  
pp. 109-115 ◽  
Author(s):  
Ulrich D. Jentschura
Keyword(s):  
Hyperfine Structure ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
Muonic Hydrogen ◽  
Intense Laser ◽  
Theoretical Treatment ◽  
Intense Laser Fields ◽  
Atomic Systems ◽  
Atomic Energy Levels ◽  
Interesting Area

The purpose of this article is twofold. First, we attempt to give a brief overview of the different application areas of quantum electrodynamics (QED). These include fundamental physics (prediction of atomic energy levels), where the atom may be exposed to additional external fields (hyperfine splitting and g factor). We also mention QED processes in highly intense laser fields and more applied areas like Casimir and Casimir–Polder interactions. Both the unifying aspects as well as the differences in the the theoretical treatment required by these application areas (such as the treatment of infinities) are highlighted. Second, we discuss an application of the formalism in the fundamentally interesting area of the prediction of energy levels, namely, the hyperfine structure of P states of muonic hydrogen.

Antihydrogen Physics at ALPHA/CERNThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

2009 ◽  
Vol 87 (7) ◽  
pp. 791-797 ◽  
Author(s):  
C. L. Cesar ◽  
G. B. Andresen ◽  
W. Bertsche ◽  
P. D. Bowe ◽  
C. C. Bray ◽  
...  
Keyword(s):  
High Precision ◽  
Quantum Electrodynamics ◽  
Fundamental Constants ◽  
Cpt Violation ◽  
Cpt Symmetry ◽  
Trapped Atoms ◽  
Fundamental Physics ◽  
Atomic Systems ◽  
Unique System ◽  
Recent Developments

Cold antihydrogen has been produced at CERN (Amoretti et al. (Nature, 419, 456 (2002)), Gabrielse et al. (Phys. Rev. Lett. 89, 213401 (2002))), with the aim of performing a high-precision spectroscopic comparison with hydrogen as a test of the CPT symmetry. Hydrogen, a unique system used for the development of quantum mechanics and quantum electrodynamics, has been continuously used to produce high-precision tests of theories and measurements of fundamental constants and can lead to a very sensitive search for CPT violation. After the initial production of cold antihydrogen atoms by the ATHENA group, the ALPHA Collaboration ( http://alpha.web.cern.ch/ ) has set forth on an experiment to trap and perform high-resolution laser spectroscopy on the 1S-2S transition of both atoms. In this contribution, we will review the motivations, goals, techniques, and recent developments towards this fundamental physics test. We present new discussion on predicted lineshapes for the 1S-2S spectroscopy of trapped atoms in a regime not discussed before.

scholarly journals AN ANALYSIS OF THE SELF-ENERGY PROBLEM FOR THE ELECTRON IN QUANTUM ELECTRODYNAMICS

1952 ◽  
Vol 30 (1) ◽  
pp. 70-78
Author(s):  
P. N. Daykin
Keyword(s):  
Quantum Electrodynamics ◽  
The Self ◽  
Positive Energy ◽  
Energy Problem ◽  
Electron Theory ◽  
Hole Theory ◽  
Self Energy ◽  
Virtual Photons ◽  
S Matrix ◽  
The One

Feynman's S-matrix for the self-energy of the free resting electron is evaluated without the restriction that the virtual photons in the intermediate state have only positive energy. Both the one-electron theory and the hole theory of the positron are treated. It is shown that in the one-electron theory the normally quadratically divergent transverse part of the self-energy vanishes if the photon field is assumed to be symmetric in positive and negative energies. A similar theorem does not hold in the hole theory. A particular type of interaction leads to a vanishing self-energy in one-electron theory. However, this does not solve the self-energy problem, as in this case radiation corrections to scattering would vanish as well. The S-matrix for the self-energy of a bound electron is evaluated in a similar manner. The decay probability for an excited state is calculated as the imaginary part of the self-energy. The correct value is obtained only in hole theory and in interaction with positive energy photons. In the special case in which the external field is a uniform magnetic field, again only hole theory with this same interaction gives the correct value for the anomalous magnetic moment.

High-precision spectroscopy as a test of quantum electrodynamics in light atomic systems

2008 ◽  
Vol 86 (1) ◽  
pp. 45-54 ◽  
Author(s):  
G WF Drake ◽  
Z -C Yan
Keyword(s):  
Excited States ◽  
High Precision ◽  
Quantum Electrodynamics ◽  
Structure Constant ◽  
Rydberg States ◽  
Fine Structure Constant ◽  
Precision Spectroscopy ◽  
Significant Discrepancy ◽  
Atomic Systems ◽  
Good Agreement

This paper presents a review of recent progress in high-precision calculations for the ground state and low-lying excited states of helium, including the nonrelativistic energy, relativistic corrections of α2 Ry, and quantum electrodynamic (QED) corrections of lowest order α3 Ry and next-to-leading-order α4 Ry, where α is the fine-structure constant. The calculations include the terms of order α4 Ry recently obtained by Pachucki (Phys. Rev. A, 74, 062510 (2006)). Estimates of the terms of order α5 Ry, including two-loop binding corrections, are included. Comparisons with experimental ionization energies indicate reasonably good agreement for the 1s2 1S0, 1s2s 1S0, 1s2s 3S1, and 1s2p 3Pcm states, but there is a significant discrepancy for the 1s2p 1P1 state of 5.6± 3.2 MHz. An asymptotic formula for the calculation of the Bethe logarithm for Rydberg states with large angular momentum L is presented in an Appendix. PACS Nos.: 31.30.Gs, 31.30.Jv

The electron-phonon interaction, according to the adiabatic approximation

1956 ◽  
Vol 52 (4) ◽  
pp. 693-697 ◽  
Author(s):  
J. C. Taylor
Keyword(s):  
Adiabatic Approximation ◽  
Energy Levels ◽  
The Self ◽  
Electron Configuration ◽  
Phonon Interaction ◽  
Conduction Electrons ◽  
Electron Phonon Interaction ◽  
Self Energy

ABSTRACTThe interaction of conduction electrons with a vibrating metallic lattice has been considered by Ziman in terms of non-adiabatic perturbations to the adiabatic approximation of the Born-Oppenheimer theory. This programme is continued to calculate the self-energy of the electrons. When account is taken of the dependence of the energy levels of the adiabatic Hamiltonian itself upon the electron configuration, the final result is the same as the standard one.

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