QED corrections in heavy atoms

Mohr, Peter J.; Plunien, G.; Soff, G.

doi:10.1016/s0370-1573(97)00046-x

Cited by 402 publications

(392 citation statements)

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“…(19) and (20). Comparison of the numerical results obtained in this work for the Wichmann-Kroll correction with those reported in previous calculations [15,25] is presented in Table V.…”

Section: Ns Correction To Vacuum Polarizationsupporting

confidence: 52%

“…(19) and (20). Comparison of the numerical results obtained in this work for the Wichmann-Kroll correction with those reported in previous calculations [15,25] is presented in Table V.The nuclear-size vacuum-polarization (NVP) correction is defined as the difference between the oneloop vacuum-polarization corrections evaluated with the point-Coulomb potential and the potential of the extended-charge nucleus. The NVP correction can be parameterized in the same way as the one-loop radiative corrections,…”

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confidence: 71%

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

Yerokhin

2011

Phys. Rev. A

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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...

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“…(19) and (20). Comparison of the numerical results obtained in this work for the Wichmann-Kroll correction with those reported in previous calculations [15,25] is presented in Table V.…”

Section: Ns Correction To Vacuum Polarizationsupporting

confidence: 52%

mentioning

confidence: 71%

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

Yerokhin

2011

Phys. Rev. A

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“…They were first calculated for the (2P − 2S) Lamb shift in muonic hydrogen in [40,41]. An estimate of their contribution to the Lamb shift is included in Tables I-III. Finally, there exists another one-loop vacuum polarization correction of order α(Zα) 4 in the Lamb shift known as the Wichmann-Kroll correction [42,43]. Its calculation was discussed repeatedly in [15,31], so we restrict ourselves here by including numerical results in the final Tables as well as the whole light-by-light contribution (see detailed calculation in [44]).…”

Section: Effects Of Vacuum Polarization In the One-photon Interacmentioning

confidence: 99%

Lamb shift in muonic ions of lithium, beryllium, and boron

Krutov

Martynenko

et al. 2016

Phys. Rev. A

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We present a precise calculation of the Lamb shift (2P 1/2 − 2S 1/2 ) in muonic ions (µ 6 3 Li) 2+ , (µ 7 3 Li) 2+ , (µ 9 4 Be) 3+ , (µ 10 4 Be) 3+ , (µ 10 5 B) 4+ , (µ 11 5 B) 4+ . The contributions of orders α 3 ÷α 6 to the vacuum polarization, nuclear structure and recoil, relativistic effects are taken into account. Our numerical results are consistent with previous calculations and improve them due to account of new corrections. The obtained results can be used for the comparison with future experimental data, and extraction more accurate values of nuclear charge radii.

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“…the successive filling of shells as established for instance by the periodic table of elements, the (analytical) solutions of the 'hydrogen atom' help understand many atomic processes in Nature, at least qualitatively. During the last decades, moreover, Dirac's theory of the hydrogen-like ions has been applied successfully for describing energetic collisions of high-Z ions with atomic targets [3] or for testing quantum-electrodynamical (QED) effects [4], if Furry's picture and field-theoretical concepts are taken into account.…”

Section: Long Write-up 1 Introductionmentioning

confidence: 99%

Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

Surzhykov

Koval

Fritzsche

2005

Computer Physics Communications

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Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the Dirac program which has been developed originally for studying the properties and dynamical behaviour of the (hydrogen-like) ions. In the present version, a set of Maple procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the Dirac program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. * To whom correspondence should be addressed (surz@physik.uni-kassel. Keywords: Analytical solution, Coulomb-Green's function, Coulomb problem, Dirac equation, energy level, expectation value, hydrogen-like ion, hydrogenic wavefunction, matrix element, radial integral, special functions. Nature of the physical problem:Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure of the hydrogen-like ions, however, the underlying 'mathematics' is not always that easy to deal with. Apart from the well-known level structure of these ions as obtained from either the Schrödinger or Dirac equation, namely, a great deal of other properties are often needed. These properties are related to the interaction of bound electron(s) with external particles and fields and, hence, require to evaluate transition amplitudes, including wavefunctions and (transition) operators of quite different complexity. Although various special functions, such as the Laguerre polynomials, spherical harmonics, Whittaker functions, or the hypergeometric functions of various kinds can be used in most cases in order to express these amplitudes in a concise form, their derivation is time consuming and prone for making errors. In addition to their complexity, moreover, there exist a large number of mathematical relations among these functions which are difficult to remember in detail and which have often hampered quantitative studies in the past. Method of solution:A set of Maple procedures is developed which provides both the nonrelativistic and relativistic (analytical) solutions of the 'hydrogen atom model' and which facilitates the symbolic evaluation of various transition amplitudes. 2 Restrictions onto the complexity of the problem:Over the past decades, a large number of representati...

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QED corrections in heavy atoms

Cited by 402 publications

References 225 publications

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

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

Lamb shift in muonic ions of lithium, beryllium, and boron

Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

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