Higher order vacuum polarization for finite radius nuclei

Gyulassy, Miklós

doi:10.1016/0375-9474(75)90554-0

Cited by 133 publications

(82 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(A3) and (A4), in order to prevent numerical overflow and underflow. Similar method of computation of the one-potential Green function was used long ago by M. Gyulassy in his evaluation of the vacuum-polarization [31].…”

Section: Appendix A: Dirac Green Function For a General Potentialmentioning

confidence: 96%

Nuclear-size correction to the Lamb shift of one-electron atoms

Yerokhin

2011

Phys. Rev. A

View full text Add to dashboard Cite

The nuclear size effect on the one-loop self energy and vacuum polarization is evaluated for the 1s, 2s, 3s, 2p 1/2 , and 2p 3/2 states of hydrogen-like ions. The calculation is performed to all orders in the binding nuclear strength parameter Zα. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter Zα. Extrapolation of the all-order numerical results obtained towards Z = 1 provides results for the radiative nuclear size effect on the hydrogen Lamb shift.PACS numbers: 31.30.jf, 12.20.Ds, 31.15.A- IntroductionThe distribution of charge of the nucleus influences the Dirac energies of atomic systems as well as the quantum electrodynamical corrections to the energy levels. This effect, termed as the nuclear size (NS) correction, is important for comparison of theoretical predictions with experimental data for the whole range of the nuclear charges Z, from hydrogen (Z = 1) up to uranium (Z = 92). The NS corrections to the one-loop self energy and vacuum polarization have been previously investigated both within the approach based on the expansion in the nuclear binding strength parameter Zα [1][2][3][4][5][6] (where α is the fine structure constant) and within the numerical approach that accounts the parameter Zα to all orders [7,8]. In the high-Z region, the numerical allorder approach provides accurate predictions for the NS effect on the radiative corrections. For lower Z, however, the NS effect diminishes and becomes increasingly more difficult to identify in a numerical calculation. On the contrary, the Zα-expansion approach provides accurate predictions for the low-Z ions and only the qualitative estimates in the high-Z region. A quantitative cross-check of the two complementary approaches is not simple and has not been accomplished up to now.The NS corrections became of particular interest recently, after the results of the muonic hydrogen Lambshift experiment were announced [9]. It turned out that the value for the proton charge radius r p deduced from the muonic hydrogen differs by five standard deviations from the spectroscopic value of r p derived from the hydrogen atom. This unexplained disagreement stimulates the scientific community to double-check all contributions originating from the nuclear charge distribution, both for the muonic and normal atoms.The aim of the present investigation is to perform an accurate numerical all-order calculation of the NS correction to the one-loop self energy and vacuum polarization and to make a detailed comparison with the Zα-expansion results available.The relativistic units (m = = c = 1) and the charge units α = e 2 /(4π) are used in this paper. I. NS CORRECTION TO DIRAC ENERGYThe leading-order NS correction to the energy levels of a hydrogen-like atom is defined as the difference of the corresponding eigenvalues of the Dirac equation with the point-Coulomb and the extended-nucleus potentials. The two most commonly used models of the nuclear charge distribution are the uniformly charged sphere ("sp...

show abstract

Section: Appendix A: Dirac Green Function For a General Potentialmentioning

confidence: 96%

Nuclear-size correction to the Lamb shift of one-electron atoms

Yerokhin

2011

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…[65,313,322,66]. On the other hand, some theoretical work has been done studying the possibility that pair production, due to bound states encountering the negative energy continuum, is prevented from occurring by higher order processes of quantum field theory, such as charge renormalization, electron self-energy and nonlinearities in electrodynamics and even Dirac field itself [222,323,324,325,326,327,328]. However, these studies show that various effects modify Z cr by a few percent, but have no way to prevent the binding energy from increasing to 2m e c 2 as Z increases, without simultaneously contradicting the existing precise experimental data on stable atoms [329].…”

Section: Positron Productionmentioning

confidence: 99%

Electron–positron pairs in physics and astrophysics: From heavy nuclei to black holes

Ruffini¹,

Vereshchagin²,

Xue³

2010

Physics Reports

496

305

View full text Add to dashboard Cite

Due to the interaction of physics and astrophysics we are witnessing in these years a splendid synthesis of theoretical, experimental and observational results originating from three fundamental physical processes. They were originally proposed by Dirac, by Breit and Wheeler and by Sauter, Heisenberg, Euler and Schwinger. For almost seventy years they have all three been followed by a continued effort of experimental verification on Earth-based experiments. The Dirac process, e + e − → 2γ, has been by far the most successful. It has obtained extremely accurate experimental verification and has led as well to an enormous number of new physics in possibly one of the most fruitful experimental avenues by introduction of storage rings in Frascati and followed by the largest accelerators worldwide: DESY, SLAC etc. The Breit-Wheeler process, 2γ → e + e − , although conceptually simple, being the inverse process of the Dirac one, has been by far one of the most difficult to be verified experimentally. Only recently, through the technology based on free electron X-ray laser and its numerous applications in Earth-based experiments, some first indications of its possible verification have been reached. The vacuum polarization process in strong electromagnetic field, pioneered by Sauter, Heisenberg, Euler and Schwinger, introduced the concept of critical electric field E c = m 2 e c 3 /(e ). It has been searched without success for more than forty years by heavy-ion collisions in many of the leading particle accelerators worldwide.The novel situation today is that these same processes can be studied on a much more grandiose scale during the gravitational collapse leading to the formation of a black hole being observed in Gamma Ray Bursts (GRBs). This report is dedicated to the scientific race. The theoretical and experimental work developed in Earth-based laboratories is confronted with the theoretical interpretation of space-based observations of phenomena originating on cosmological scales. What has become clear in the last ten years is that all the three above mentioned processes, duly extended in the general relativistic framework, are necessary for the understanding of the physics of the gravitational collapse to a black hole. Vice versa, the natural arena where these processes can be observed in mutual interaction and on an unprecedented scale, is indeed the realm of relativistic astrophysics.We systematically analyze the conceptual developments which have followed the basic work of Dirac and Breit-Wheeler. We also recall how the seminal work of Born and Infeld inspired the work by Sauter, Heisenberg and Euler on effective Lagrangian leading to the estimate of the rate for the process of electron-positron production in 1 a constant electric field. In addition of reviewing the intuitive semi-classical treatment of quantum mechanical tunneling for describing the process of electron-positron production, we recall the calculations in Quantum Electro-Dynamics of the Schwinger rate and effective Lagrangian for cons...

show abstract

“…These formulas usually contain infinite summations over intermediate electron states (summations over the bound states and integrations over the continuum). These sums are generally evaluated by using analytical expressions for the Dirac-Coulomb Green function [4,23,[87][88][89][90][91] or by using relativistic finite basis set methods [92][93][94][95][96][97]. In some cases the summation can be performed analytically by employing the generalized virial relations for the Dirac equation [98].…”

Section: A Methods Of Numerical Evaluations and Renormalization Procmentioning

confidence: 99%

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

2002

View full text Add to dashboard Cite

The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed. PACS number(s): 12.20.Ds, 31.30. Jv

show abstract

Higher order vacuum polarization for finite radius nuclei

Abstract: The calculation of the higher order, a(Za)n, n ~ 3,

Cited by 133 publications

References 22 publications

Nuclear-size correction to the Lamb shift of one-electron atoms

Nuclear-size correction to the Lamb shift of one-electron atoms

Electron–positron pairs in physics and astrophysics: From heavy nuclei to black holes

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

Contact Info

Product

Resources

About