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## Full-Text Articles in Physical Sciences and Mathematics

Long-Range Tails In Van Der Waals Interactions Of Excited-State And Ground-State Atoms, Ulrich D. Jentschura, V. Debierre

#### Long-Range Tails In Van Der Waals Interactions Of Excited-State And Ground-State Atoms, Ulrich D. Jentschura, V. Debierre

*Physics Faculty Research & Creative Works*

A quantum electrodynamic calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded 1/R^{7} Casimir-Polder form to a long-range tail - provided by the Wick-rotated term - proportional to cos[2(E_{m} - E_{n})R/(ħc)]/R^{2}, where E_{m} < E_{n} is the energy of a virtual ...

Virtual Resonant Emission And Oscillatory Long-Range Tails In Van Der Waals Interactions Of Excited States: Qedtreatment And Applications, Ulrich D. Jentschura, Chandra Mani Adhikari, Vincent Debierre

#### Virtual Resonant Emission And Oscillatory Long-Range Tails In Van Der Waals Interactions Of Excited States: Qedtreatment And Applications, Ulrich D. Jentschura, Chandra Mani Adhikari, Vincent Debierre

*Physics Faculty Research & Creative Works*

We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails that are due to virtual resonant emission and absorption into and from vacuum modes whose frequency equals the transition frequency to available lower-lying atomic states. For identical atoms, one of which is in an excited state, we also discuss the mixing term that depends on the symmetry of the two-atom wave function (these evolve into either the gerade or the ungerade state for close approach ...

Gravitational Correction To Vacuum Polarization, Ulrich D. Jentschura

#### Gravitational Correction To Vacuum Polarization, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

We consider the gravitational correction to (electronic) vacuum polarization in the presence of a gravitational background field. The Dirac propagators for the virtual fermions are modified to include the leading gravitational correction (potential term) which corresponds to a coordinate-dependent fermion mass. The mass term is assumed to be uniform over a length scale commensurate with the virtual electron-positron pair. The on-mass shell renormalization condition ensures that the gravitational correction vanishes on the mass shell of the photon, i.e., the speed of light is unaffected by the quantum field theoretical loop correction, in full agreement with the equivalence principle. Nontrivial ...

Long-Range Atom-Wall Interactions And Mixing Terms: Metastable Hydrogen, Ulrich D. Jentschura

#### Long-Range Atom-Wall Interactions And Mixing Terms: Metastable Hydrogen, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

We investigate the interaction of metastable 2S hydrogen atoms with a perfectly conducting wall, including parity-breaking S-P mixing terms (with full account of retardation). The neighboring 2P_{1/2} and 2P_{3/2} levels are found to have a profound effect on the transition from the short-range, nonrelativistic regime, to the retarded form of the Casimir-Polder interaction. The corresponding P state admixtures to the metastable 2S state are calculated. We find the long-range asymptotics of the retarded Casimir-Polder potentials and mixing amplitudes for general excited states, including a fully quantum electrodynamic treatment of the dipole-quadrupole mixing term. The decay width ...

One-Loop Dominance In The Imaginary Part Of The Polarizability: Application To Blackbody And Noncontact Van Der Waals Friction, Ulrich D. Jentschura, Grzegorz Lach, Maarten Dekieviet, Krzysztof Pachucki

#### One-Loop Dominance In The Imaginary Part Of The Polarizability: Application To Blackbody And Noncontact Van Der Waals Friction, Ulrich D. Jentschura, Grzegorz Lach, Maarten Dekieviet, Krzysztof Pachucki

*Physics Faculty Research & Creative Works*

Phenomenologically important quantum dissipative processes include blackbody friction (an atom absorbs counterpropagating blueshifted photons and spontaneously emits them in all directions, losing kinetic energy) and noncontact van der Waals friction (in the vicinity of a dielectric surface, the mirror charges of the constituent particles inside the surface experience drag, slowing the atom). The theoretical predictions for these processes are modified upon a rigorous quantum electrodynamic treatment, which shows that the one-loop "correction" yields the dominant contribution to the off-resonant, gauge-invariant, imaginary part of the atom's polarizability at room temperature, for typical atom-surface interactions. The tree-level contribution to the polarizability ...

Relativistic Reduced-Mass And Recoil Corrections To Vacuum Polarization In Muonic Hydrogen, Muonic Deuterium, And Muonic Helium Ions, Ulrich D. Jentschura

#### Relativistic Reduced-Mass And Recoil Corrections To Vacuum Polarization In Muonic Hydrogen, Muonic Deuterium, And Muonic Helium Ions, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Zα)^{4}μ^{3}/m^{2}_{N} is evaluated for muonic hydrogen and deuterium and muonic helium ions (μ is the reduced mass and m_{N} is the nuclear mass). Relativistic corrections to vacuum polarization of order α(Zα)^{4}μ are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to vacuum polarization of order α(Zα)^{5}-ln^{2}(Zα) μ^{2}/m_{N} is obtained in leading ...

Hydrogen-Deuterium Isotope Shift: From The 1s-2s-Transition Frequency To The Proton-Deuteron Charge-Radius Difference, Ulrich D. Jentschura, Arthur N. Matveev, Christian G. Parthey, Janis Alnis, Randolf Pohl, Th H. Udem, Nikolai N. Kolachevsky, Theodor Wolfgang Hansch

#### Hydrogen-Deuterium Isotope Shift: From The 1s-2s-Transition Frequency To The Proton-Deuteron Charge-Radius Difference, Ulrich D. Jentschura, Arthur N. Matveev, Christian G. Parthey, Janis Alnis, Randolf Pohl, Th H. Udem, Nikolai N. Kolachevsky, Theodor Wolfgang Hansch

*Physics Faculty Research & Creative Works*

We analyze and review the theory of the hydrogen-deuterium isotope shift for the 1S-2S transition, which is one of the most accurately measured isotope shifts in any atomic system, in view of a recently improved experiment. A tabulation of all physical effects that contribute to the isotope shift is given. These include the Dirac binding energy, quantum electrodynamic effects, including recoil corrections, and the nuclear-size effect, including the pertaining relativistic and radiative corrections. From a comparison of the theoretical result Δf_{th}=670999566.90(66)(60)kHz (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result Δf_{expt}=670994334605 ...

Self-Energy Correction To The Bound-Electron G Factor Of P States, Ulrich D. Jentschura

#### Self-Energy Correction To The Bound-Electron G Factor Of P States, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

The radiative self-energy correction to the bound-electron g factor of 2P_{1/2} and 2P_{3/2} states in one-electron ions is evaluated to order α(Zα)^{2}. The contribution of high-energy virtual photons is treated by means of an effective Dirac equation, and the result is verified by an approach based on long-wavelength quantum electrodynamics. The contribution of low-energy virtual photons is calculated both in the velocity and in the length gauge, and gauge invariance is verified explicitly. The results compare favorably to recently available numerical data for hydrogenlike systems with low nuclear charge numbers.

Relativistic (Zα)2 Corrections And Leading Quantum Electrodynamic Corrections To The Two-Photon Decay Rate Of Ionic States, Benedikt J. Wundt, Ulrich D. Jentschura

#### Relativistic (Zα)2 Corrections And Leading Quantum Electrodynamic Corrections To The Two-Photon Decay Rate Of Ionic States, Benedikt J. Wundt, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

We calculate the relativistic corrections of relative order (Zα) 2 to the two-photon decay rate of higher excited S and D states in ionic atomic systems, and we also evaluate the leading radiative corrections of relative order α (Zα) 2 ln [(Zα) -2]. We thus complete the theory of the two-photon decay rates up to relative order α3 ln (α). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Zα) 2 to the two-photon decay are given by the Zitterbewegung, by the spin-orbit coupling and by relativistic corrections to the electron mass ...

Feasibility Of Coherent Xuv Spectroscopy On The 1s-2s Transition In Singly Ionized Helium, Maximilian Herrmann, Martin K. Haas, Ulrich D. Jentschura, Franz Kottmann, Dietrich Leibfried, Guido Saathoff, Christoph Gohle, Akira Ozawa, V. Batteiger, S. Knunz, Nikolai N. Kolachevsky, H. A. Schussler, Theodor Wolfgang Hansch, Th H. Udem

#### Feasibility Of Coherent Xuv Spectroscopy On The 1s-2s Transition In Singly Ionized Helium, Maximilian Herrmann, Martin K. Haas, Ulrich D. Jentschura, Franz Kottmann, Dietrich Leibfried, Guido Saathoff, Christoph Gohle, Akira Ozawa, V. Batteiger, S. Knunz, Nikolai N. Kolachevsky, H. A. Schussler, Theodor Wolfgang Hansch, Th H. Udem

*Physics Faculty Research & Creative Works*

The 1S-2S two-photon transition in singly ionized helium is a highly interesting candidate for precision tests of bound-state quantum electrodynamics (QED). With the recent advent of extreme ultraviolet frequency combs, highly coherent quasi-continuous-wave light sources at 61 nm have become available, and precision spectroscopy of this transition now comes into reach for the first time. We discuss quantitatively the feasibility of such an experiment by analyzing excitation and ionization rates, propose an experimental scheme, and explore the potential for QED tests.

Coulomb-Field-Induced Conversion Of A High-Energy Photon Into A Pair Assisted By A Counterpropagating Laser Beam, Erik Lotstedt, Ulrich D. Jentschura, Christoph H. Keitel

#### Coulomb-Field-Induced Conversion Of A High-Energy Photon Into A Pair Assisted By A Counterpropagating Laser Beam, Erik Lotstedt, Ulrich D. Jentschura, Christoph H. Keitel

*Physics Faculty Research & Creative Works*

The laser-induced modification of a fundamental process of quantum electrodynamics, the conversion of a high-energy gamma photon in the Coulomb field of a nucleus into an electron-positron pair, is studied theoretically. Although the employed formalism allows for the general case where the gamma photon and laser photons cross at an arbitrary angle, we here focus on a theoretically interesting and numerically challenging setup, where the laser beam and gamma photon counterpropagate and impinge on a nucleus at rest. For a peak laser field smaller than the critical Schwinger field and gamma photon energy larger than the field-free threshold, the total ...

Relativistic Calculation Of The Two-Photon Decay Rate Of Highly Excited Ionic States, Ulrich D. Jentschura, Andrey S. Surzhykov

#### Relativistic Calculation Of The Two-Photon Decay Rate Of Highly Excited Ionic States, Ulrich D. Jentschura, Andrey S. Surzhykov

*Physics Faculty Research & Creative Works*

Based on quantum electrodynamics, we reexamine the two-photon decay of one-electron atoms. Special attention is paid to the calculation of the (two-photon) total decay rates which can be viewed as the imaginary part of the two-loop self-energy. We argue that our approach can be easily applied to the cases with a virtual state having an intermediate energy between the initial and the final state of the decay process leading, thus, to the resonance peaks in the two-photon energy distribution. In order to illustrate our approach, we obtain fully relativistic results, resolved into electric and magnetic multipole components, for the two-photon ...

Two-Loop Bethe Logarithms For Non- S Levels, Ulrich D. Jentschura

#### Two-Loop Bethe Logarithms For Non- S Levels, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in hydrogen at the order of α^{8} m_{e}c^{2}, where me is the electron mass and c is the speed of light, and scale as Z^{6}, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (απ)^{2} (Zα)^{6} ln [(Zα)^{-2}] m_{e}c ...

Quantum Electrodynamic Corrections To The Hyperfine Structure Of Excited S States, Ulrich D. Jentschura, Vladimir A. Yerokhin

#### Quantum Electrodynamic Corrections To The Hyperfine Structure Of Excited S States, Ulrich D. Jentschura, Vladimir A. Yerokhin

*Physics Faculty Research & Creative Works*

State-dependent quantum electrodynamic corrections are evaluated for the hyperfine splitting of nS states for arbitrary principal quantum number n. The calculations comprise both the self-energy and the vacuum-polarization correction of order α(Zα) 2 EF and the recoil correction of order (Zα)^{2} (m/M) E_{F}. Higher-order corrections are summarized and partly reevaluated as well. Accurate predictions for hydrogen hyperfine splitting intervals of nS states with n=2,...,8 are presented. The results obtained are important due to steady progress in hydrogen spectroscopy for transitions involving highly excited S states.

Benchmarking High-Field Few-Electron Correlation And Qed Contributions In Hg⁷⁵⁺ To Hg⁷⁸⁺ Ions. Ii. Theory, Zoltan Harman, I. I. Tupitsyn, Anton N. Artemyev, Ulrich D. Jentschura, Christoph H. Keitel, Jose R. Crespo Lopez-Urrutia, Antonio J. Gonzalez, Hiroyuki Tawara, Joachim Hermann Ullrich

#### Benchmarking High-Field Few-Electron Correlation And Qed Contributions In Hg⁷⁵⁺ To Hg⁷⁸⁺ Ions. Ii. Theory, Zoltan Harman, I. I. Tupitsyn, Anton N. Artemyev, Ulrich D. Jentschura, Christoph H. Keitel, Jose R. Crespo Lopez-Urrutia, Antonio J. Gonzalez, Hiroyuki Tawara, Joachim Hermann Ullrich

*Physics Faculty Research & Creative Works*

Theoretical resonance energies for KLL dielectronic recombination into He-, Li-, Be-, and B-like Hg ions are calculated by various means and discussed in detail. We apply the multiconfiguration Dirac-Fock and the configuration interaction Dirac-Fock-Sturmian methods, and quantum electrodynamic many-body theory. The different contributions such as relativistic electron interaction, quantum electrodynamic contributions, and finite nuclear size and mass corrections are calculated and their respective theoretical uncertainties are estimated. Our final results are compared to experimental data from the preceding paper. The comparison of theoretical values with the experimental energies shows a good overall agreement for most transitions and illustrates the significance ...

Benchmarking High-Field Few-Electron Correlation And Qed Contributions In Hg⁷⁵⁺ To Hg⁷⁸⁺ Ions. I. Experiment, Antonio J. Gonzalez, Jose R. Crespo Lopez-Urrutia, Jean Pierre Braun, Gunter Brenner, Hjalmar Bruhns, Alain Lapierre, Vladimir Sergeyevich Mironov, R. Soria Orts, Hiroyuki Tawara, Michael Trinczek, Joachim Hermann Ullrich, Anton N. Artemyev, Zoltan Harman, Ulrich D. Jentschura, Christoph H. Keitel, James H. Scofield, I. I. Tupitsyn

#### Benchmarking High-Field Few-Electron Correlation And Qed Contributions In Hg⁷⁵⁺ To Hg⁷⁸⁺ Ions. I. Experiment, Antonio J. Gonzalez, Jose R. Crespo Lopez-Urrutia, Jean Pierre Braun, Gunter Brenner, Hjalmar Bruhns, Alain Lapierre, Vladimir Sergeyevich Mironov, R. Soria Orts, Hiroyuki Tawara, Michael Trinczek, Joachim Hermann Ullrich, Anton N. Artemyev, Zoltan Harman, Ulrich D. Jentschura, Christoph H. Keitel, James H. Scofield, I. I. Tupitsyn

*Physics Faculty Research & Creative Works*

The photorecombination of highly charged few-electron mercury ions Hg^{75+} to Hg^{78+} has been explored with the Heidelberg electron beam ion trap. By monitoring the emitted x rays (65-76 keV) and scanning the electron beam energy (45-54 keV) over the KLL dielectronic recombination (DR) region, the energies of state-selected DR resonances were determined to within ±4 eV (relative) and ±14 eV (absolute). At this level of experimental accuracy, it becomes possible to make a detailed comparison to various theoretical approaches and methods, all of which include quantum electrodynamic (QED) effects and finite nuclear size contributions (for a 1s electron ...

Nonrelativistic Qed Approach To The Lamb Shift, Ulrich D. Jentschura, Andrzej Czarnecki, Krzysztof Pachucki

#### Nonrelativistic Qed Approach To The Lamb Shift, Ulrich D. Jentschura, Andrzej Czarnecki, Krzysztof Pachucki

*Physics Faculty Research & Creative Works*

We calculate the one- and two-loop corrections of order α(Zα)^{6} and α^{2}(Zα)^{6}, respectively, to the Lamb shift in hydrogenlike systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results valid for all hydrogenic states with nonvanishing orbital angular momentum and for the normalized difference of S states. These results involve the expectation value of local effective operators and relativistic corrections to Bethe logarithms. The one-loop correction is in agreement with previous calculations for the particular cases of S, P, and D states. The two-loop correction in the order α^{2}(Zα)^{6} includes ...

Laser-Dressed Vacuum Polarization In A Coulomb Field, A. I. Milstein, Ivan S. Terekhov, Ulrich D. Jentschura, Christoph H. Keitel

#### Laser-Dressed Vacuum Polarization In A Coulomb Field, A. I. Milstein, Ivan S. Terekhov, Ulrich D. Jentschura, Christoph H. Keitel

*Physics Faculty Research & Creative Works*

We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbation theory, leads to a correction to atomic energy levels. The external laser field breaks the rotational symmetry of ...

Calculation Of The One- And Two-Loop Lamb Shift For Arbitrary Excited Hydrogenic States, Andrzej Czarnecki, Ulrich D. Jentschura, Krzysztof Pachucki

#### Calculation Of The One- And Two-Loop Lamb Shift For Arbitrary Excited Hydrogenic States, Andrzej Czarnecki, Ulrich D. Jentschura, Krzysztof Pachucki

*Physics Faculty Research & Creative Works*

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order α(Zα)^{6}] and for the two-loop Lamb shift [of order α^{2}(Zα)^{6}] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of S states, defined as Δ_{n}=n^{3}ΔE(nS)-ΔE(1S). We present numerical results for one-loop and two-loop corrections for excited S, P, and D states. In particular, the normalized Lamb shift difference of S states is calculated with an uncertainty ...

Precise Calculation Of Transition Frequencies Of Hydrogen And Deuterium Based On A Least-Squares Analysis, Ulrich D. Jentschura, Svetlana A. Kotochigova, Eric Olivier Le Bigot, Peter J. Mohr, Barry N. Taylor

#### Precise Calculation Of Transition Frequencies Of Hydrogen And Deuterium Based On A Least-Squares Analysis, Ulrich D. Jentschura, Svetlana A. Kotochigova, Eric Olivier Le Bigot, Peter J. Mohr, Barry N. Taylor

*Physics Faculty Research & Creative Works*

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g factor of the electron, which was previously the most accurate prediction of QED.

Relativistic Electron Correlation, Quantum Electrodynamics, And The Lifetime Of The 1s²2s²2p²P^{O}_{3/2} Level In Boronlike Argon, Alain Lapierre, Ulrich D. Jentschura, Jose R. Crespo Lopez-Urrutia, Jean Pierre Braun, Gunter Brenner, Hjalmar Bruhns, Daniel A. Fischer, Antonio J. Gonzalez, Zoltan Harman, Walter Johnson, Christoph H. Keitel, Vladimir Sergeyevich Mironov, C. J. Osborne, Guenther Sikler, R. Soria Orts, Vladimir M. Shabaev, Hiroyuki Tawara, I. I. Tupitsyn, Joachim Hermann Ullrich, Andrey V. Volotka

#### Relativistic Electron Correlation, Quantum Electrodynamics, And The Lifetime Of The 1s²2s²2p²PO3/2 Level In Boronlike Argon, Alain Lapierre, Ulrich D. Jentschura, Jose R. Crespo Lopez-Urrutia, Jean Pierre Braun, Gunter Brenner, Hjalmar Bruhns, Daniel A. Fischer, Antonio J. Gonzalez, Zoltan Harman, Walter Johnson, Christoph H. Keitel, Vladimir Sergeyevich Mironov, C. J. Osborne, Guenther Sikler, R. Soria Orts, Vladimir M. Shabaev, Hiroyuki Tawara, I. I. Tupitsyn, Joachim Hermann Ullrich, Andrey V. Volotka

*Physics Faculty Research & Creative Works*

The lifetime of the Ar^{13+} 1s^{2}2s^{2}2p^{2}P^{o}_{3/2} metastable level was determined at the Heidelberg Electron Beam Ion Trap to be 9.573(4)(5)ms(stat)(syst). The accuracy level of one per thousand makes this measurement sensitive to quantum electrodynamic effects like the electron anomalous magnetic moment (EAMM) and to relativistic electron-electron correlation effects like the frequency-dependent Breit interaction. Theoretical predictions, adjusted for the EAMM, cluster about a lifetime that is approximately 3σ shorter than our experimental result.

Complete Two-Loop Correction To The Bound-Electron Factor, Krzysztof Pachucki, Andrzej Czarnecki, Ulrich D. Jentschura, Vladimir A. Yerokhin

#### Complete Two-Loop Correction To The Bound-Electron Factor, Krzysztof Pachucki, Andrzej Czarnecki, Ulrich D. Jentschura, Vladimir A. Yerokhin

*Physics Faculty Research & Creative Works*

Within a systematic approach based on dimensionally regularized nonrelativistic quantum electrodynamics, we derive a complete result for the two-loop correction to order ( α/ π )^{2} ( Zα )^{4} for the g factor of an electron bound in an nS state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from g-factor measurements. D

Positronium Formation In Positron-Li And Positron-Na Collisions At Low Energies, Anh-Thu Le, M. W. J. Bromley, C. D. Lin

#### Positronium Formation In Positron-Li And Positron-Na Collisions At Low Energies, Anh-Thu Le, M. W. J. Bromley, C. D. Lin

*Physics Faculty Research & Creative Works*

We present the positronium formation cross sections for a positron colliding with lithium and sodium for the collision energies from 0.01 eV up to 20 eV by the hyperspherical close-coupling method. For Li, our results agree with the experimental data and with other calculations. Our results for Na remain in agreement with previous close-coupling calculations, but do not support the latest experimental data for Na below 1 eV. To validate our model potentials and method in the low-energy regime, the binding energies of positronic lithium and positronic sodium as well as the s-wave scattering lengths for positronium scattering from ...

Two-Loop Bethe Logarithms For Higher Excited S Levels, Ulrich D. Jentschura

#### Two-Loop Bethe Logarithms For Higher Excited S Levels, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

Processes mediated by two virtual low-energy photons contribute quite significantly to the energy of hydrogenic S states. The corresponding level shift is of the order of ( α / π )^{2} ( Z α )^{6} m_{e}c^{2} and may be ascribed to a two-loop generalization of the Bethe logarithm. For 1 S and 2 S states, the correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev. Lett. 91, 113005 (2003)]. Here, we generalize the approach to higher excited S states, which in contrast to the 1 S and 2 S states can decay to P states via the electric-dipole ...

Nonrelativistic Qed Approach To The Bound-Electron G Factor, Krzysztof Pachucki, Ulrich D. Jentschura, Vladimir A. Yerokhin

#### Nonrelativistic Qed Approach To The Bound-Electron G Factor, Krzysztof Pachucki, Ulrich D. Jentschura, Vladimir A. Yerokhin

*Physics Faculty Research & Creative Works*

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order α ( Z α )^{4} to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order α^{2} ( Z α )^{4} ln [ ( Z α )^{- 2} ] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1 S bound-electron g factor and influence the ...

Electron Self-Energy For Higher Excited S Levels, Ulrich D. Jentschura, Peter J. Mohr

#### Electron Self-Energy For Higher Excited S Levels, Ulrich D. Jentschura, Peter J. Mohr

*Physics Faculty Research & Creative Works*

A nonperturbative numerical evaluation of the one-photon electron self-energy for the 3S and 4S states with charge numbers Z=1 to 5 is described. The numerical results are in agreement with known terms in the expansion of the self-energy in powers of Zα.

Self-Energy Correction To The Two-Photon Decay Width In Hydrogenlike Atoms, Ulrich D. Jentschura

#### Self-Energy Correction To The Two-Photon Decay Width In Hydrogenlike Atoms, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

We investigate the guage invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms, was investigated. The effective treatment of the correction using a Lamb-shift led to the equivalent results in both the length and velocity gages. The relevant radiative corrections were found to be related to the energies that entered into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition, that holds between two photons. The results show that the dominant radiative correction to the 2S two-photon decay width is about -2.020 536(α/π)(Zα ...

Lamb Shift Of Laser-Dressed Atomic States, Ulrich D. Jentschura, Jorg Evers, Martin K. Haas, Christoph H. Keitel

#### Lamb Shift Of Laser-Dressed Atomic States, Ulrich D. Jentschura, Jorg Evers, Martin K. Haas, Christoph H. Keitel

*Physics Faculty Research & Creative Works*

We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.

Two-Loop Bethe-Logarithm Correction In Hydrogenlike Atoms, Krzysztof Pachucki, Ulrich D. Jentschura

#### Two-Loop Bethe-Logarithm Correction In Hydrogenlike Atoms, Krzysztof Pachucki, Ulrich D. Jentschura

*Physics Faculty Research & Creative Works*

We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogenlike systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1 S – 2 S transition: It contributes - 8.19 and - 0.84 k H z for the 1 S and the 2 S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift ...

Asymptotic Properties Of Self-Energy Coefficients, Ulrich D. Jentschura, Eric Olivier Le Bigot, Peter J. Mohr, Paul Indelicato, Gerhard Soff

#### Asymptotic Properties Of Self-Energy Coefficients, Ulrich D. Jentschura, Eric Olivier Le Bigot, Peter J. Mohr, Paul Indelicato, Gerhard Soff

*Physics Faculty Research & Creative Works*

We investigate the asymptotic properties of higher-order binding corrections to the one-loop self-energy of excited states in atomic hydrogen. We evaluate the historically problematic A_{60} coefficient for all P states with principal quantum numbers n ≤ 7 and D states with n ≤ 8 and find that a satisfactory representation of the n dependence of the coefficients requires a three-parameter fit. For the high-energy contribution to A_{60}, we find exact formulas. The results obtained are relevant for the interpretation of high-precision laser spectroscopic measurements.