scholarly journals Calculations of QED Effects with the Dirac Green Function

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 800 ◽  
Author(s):  
Vladimir A. Yerokhin ◽  
Anna V. Maiorova
Keyword(s):  
Green Function ◽  
Quantum Electrodynamics ◽  
Nuclear Charge ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Strength Parameter ◽  
Theoretical Treatment ◽  
Binding Strength ◽  
Qed Effects ◽  
Nuclear Charge Number

Modern spectroscopic experiments in few-electron atoms reached the level of precision at which an accurate description of quantum electrodynamics (QED) effects is mandatory. In many cases, theoretical treatment of QED effects need to be performed without any expansion in the nuclear binding strength parameter Z α (where Z is the nuclear charge number and α is the fine-structure constant). Such calculations involve multiple summations over the whole spectrum of the Dirac equation in the presence of the binding nuclear field, which can be evaluated in terms of the Dirac Green function. In this paper we describe the technique of numerical calculations of QED corrections with the Dirac Green function, developed in numerous investigations during the last two decades.

scholarly journals Atomic Structure Calculations of Helium with Correlated Exponential Functions

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1246
Author(s):  
Vladimir A. Yerokhin ◽  
Vojtěch Patkóš ◽  
Krzysztof Pachucki
Keyword(s):  
Wave Function ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
Perturbation Expansion ◽  
Structure Constant ◽  
Basis Functions ◽  
Fine Structure Constant ◽  
Compact Representation ◽  
Electron Mass ◽  
Qed Effects

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1, r2 and r=|r→1−r→2|. The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order α5m (where m is the electron mass) are complemented with the systematic treatment of higher-order α6m and α7m QED effects.

Precision measurements of fine and hyperfine structure in lithium I and II

2005 ◽  
Vol 83 (4) ◽  
pp. 327-337 ◽  
Author(s):  
W A van Wijngaarden
Keyword(s):  
Fine Structure ◽  
Quantum Electrodynamics ◽  
Nuclear Charge ◽  
Structure Constant ◽  
Precision Measurements ◽  
Fine Structure Constant ◽  
Recent Measurement ◽  
Charge Radii ◽  
Fine And Hyperfine Structure

Recent advances in modeling Li I and II in conjunction with improved experimental techniques have enabled precise tests of quantum electrodynamics. For Li+, the hyperfine intervals of the 1s2s 3S1 and 1s2p 3P0,1,2 states are in excellent agreement with theory. A recent measurement of the 1s2p 3P1,2 fine-structure interval also agrees well with the calculated value and resolves a discrepancy found by two prior experiments. For neutral lithium, discrepancies exist among the results of various experiments for the 6,7Li D1 isotope shift and the 2P fine structure. However, all of the fine-structure measurements are several MHz larger than the theoretical value. Prospects for future experiments to improve the determination of the fine-structure constant and the relative 6,7Li nuclear charge radii are discussed. PACS Nos.: 32.10.Fn, 31.30.Gs, 42.62.Fi

scholarly journals Precision spectroscopy of atomic helium

2020 ◽  
Vol 7 (12) ◽  
pp. 1818-1827
Author(s):  
Yu R Sun ◽  
Shui-Ming Hu
Keyword(s):  
Fine Structure ◽  
Quantum Electrodynamics ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Nuclear Charge Radius ◽  
Precision Spectroscopy ◽  
Structure Splitting ◽  
Three Body ◽  
Atomic Helium

Abstract Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the ‘proton radius puzzle’. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.

scholarly journals Theory of the Anomalous Magnetic Moment of the Electron

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 28 ◽  
Author(s):  
Tatsumi Aoyama ◽  
Toichiro Kinoshita ◽  
Makiko Nio
Keyword(s):  
Fine Structure ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Penning Trap ◽  
Weak Interactions ◽  
Perturbation Expansion ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Best Value

The anomalous magnetic moment of the electron a e measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α , with an effective parameter α / π . Both numerical and analytic evaluations of a e up to ( α / π ) 4 are firmly established. The coefficient of ( α / π ) 5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to a e ( theory ) = 1 159 652 181.606 ( 11 ) ( 12 ) ( 229 ) × 10 − 12 , where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: α − 1 ( Cs ) = 137.035 999 046 ( 27 ) . The discrepancy between a e ( theory ) and a e ( ( experiment ) ) is 2.4 σ . Assuming that the standard model is valid so that a e (theory) = a e (experiment) holds, we obtain α − 1 ( a e ) = 137.035 999 1496 ( 13 ) ( 14 ) ( 330 ) , which is nearly as accurate as α − 1 ( Cs ) . The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of a e , in this order.

scholarly journals QED Response of the Vacuum

Physics ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 14-21 ◽  
Author(s):  
Gerd Leuchs ◽  
Margaret Hawton ◽  
Luis L. Sánchez-Soto
Keyword(s):  
Electromagnetic Field ◽  
Quantum Electrodynamics ◽  
Displacement Vector ◽  
Electric Displacement ◽  
Structure Constant ◽  
Universal Constant ◽  
Field Vector ◽  
Fine Structure Constant ◽  
Source Current ◽  
New Perspective

We present a new perspective on the link between quantum electrodynamics (QED) and Maxwell’s equations. We demonstrate that the interpretation of the electric displacement vector D = ε 0 E , where E is the electric field vector and ε 0 is the permittivity of the vacuum, as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter runs, as it should.

scholarly journals The annihilation of fast positrons by electrons in the K-shell

1934 ◽  
Vol 146 (859) ◽  
pp. 723-736 ◽  
Keyword(s):  
Kinetic Energy ◽  
Cosmic Radiation ◽  
Nuclear Charge ◽  
Structure Constant ◽  
Photoelectric Effect ◽  
High Energy ◽  
Negative Energy ◽  
Fine Structure Constant ◽  
Quantum Process ◽  
High Energies

The probability of the simultaneous of a positron and an electron, with the emission of two quanta of radiation, has been calculated by Dirac and several other authors. From considerations of energy and momentum it follows that an electron and positron can only annihilate one another with the emission of one quantum of radiation in the presence of a third body. An electron bound in an atom could, therefore, annihilate a positron, represented by a hole on the Dirac theory, by jumping into a state of negative energy which happens to be free, the nucleus taking up the extra momentum. The process is now mathematically analogous to the photoelectric transitions to states of negative energy in the sense that the matrix elements concerned are the same, and we might expect that the effect would be most important for the electrons in the K-shell. Fermi and Uhlenbeck have calculated the process approximately, for the condition where the kinetic energy of the positron is of the order of magnitude of the ionization energy of the K-shell. The result they obtained was very small compared with the two quantum process, which is to be explained by the fact that for these small energies, the positron does not get near the nucleus. In view of the fact that positrons of energies of the order 100 mc 2 occur in considerable quantities in the showers produced by cosmic radiation, and that the primary cosmic radiation itself may consist, in part, of positrons, it becomes of interest to calculate the cross-section for the annihilation of positrons of high energy by electrons in the K-shell, and their absorption in matter, and also to compare this process with the two quantum process for high energies. In the photoelectric effect for hard γ -rays, the electron the electron leaves the atom in states of different angular momentum (described by the azimuthal quantum number l ), and the terms which give the largest contribution are roughly those for which l is of the order of the energy of the γ -ray in terms of mc 2 . For high energies, therefore, a calculation by the method of Hulme, in which the last step is carried out numerically, is out of the question, and we must find some approximate method of effecting a summation. We shall use an adaptation of Sauter's method, in which we shall treat as small the product of the fine structure constant and the nuclear charge. This method may be expected to give a good approximation for small nuclear charge. Our method has the further restriction that it is valid only when the kinetic energy of the positron is not small compared with mc 2 .

Introductory remarks

1982 ◽  
Vol 304 (1482) ◽  
pp. 3-4
Keyword(s):  
World War Ii ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Power Series Expansion ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Abelian Gauge

The title of this meeting, which refers to gauge theories, could equivalently have specified renormalizable quantum field theories. The first quantum field theory arose from the quantization by Dirac, Heisenberg and Pauli of Maxwell’s classical theory of electromagnetism. This immediately revealed the basic problem that although the smallness of the fine-structure constant appeared to give an excellent basis for a power-series expansion, corrections to lowest order calculations gave meaningless infinite results. Quantum electrodynamics (QED ) is, of course, an Abelian gauge theory, and the first major triumph o f fundamental physics after World War II was the removal of the infinities from the theory by the technique of renormalization developed by Schwinger, Feynman and Dyson, stimulated by the measurement of the Lamb shift and the anomalous magnetic moment of the electron. In the intervening years, especially through the beautiful experiments at Cern on the anomalous magnetic moment of the muon, the agreement between this theory and experiment has been pushed to the extreme technical limits of both measurement and calculation.

scholarly journals State of the art in the determination of the fine structure constant: test of Quantum Electrodynamics and determination of h/mu

2013 ◽  
Vol 525 (7) ◽  
pp. 484-492 ◽  
Author(s):  
Rym Bouchendira ◽  
Pierre Cladé ◽  
Saida Guellati-Khélifa ◽  
Francois Nez ◽  
Francois Biraben
Keyword(s):  
Fine Structure ◽  
Quantum Electrodynamics ◽  
State Of The Art ◽  
Structure Constant ◽  
Fine Structure Constant
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