Physical Sciences and Mathematics Commons^™

Self-Inductance And Magnetic Flux, Diego Castano, Teresa M. Castano

Chemistry and Physics Faculty Articles

The canonical equation for self-inductance involving magnetic flux is examined, and a more general form is presented that can be applied to continuous current distributions. We attempt to clarify and extend the use of the standard equation by recasting it in its more versatile form.

Electromagnetic Radiation From A Spherical Static Current Source Coupled To Harmonic Axion Field, Railing Chang, Huai-Yi Xie, P. T. Leung

Physics Faculty Publications and Presentations

The electromagnetic fields generated from a static current source on a spherical surface are calculated in the framework of axion electrodynamics to first order in the coupling parameter. Comparisons of the results are made with reference to various results obtained in conventional Maxwell electrodynamics, as well as previous results obtained for point magnetic dipole source coupled to harmonic axion fields. Distinct features from the results so obtained are highlighted for possible experimental probing of the axions via electromagnetic interactions. In particular, electromagnetic radiation from sources with strong magnetic field is studied which may enable the detection of a cosmic …

What Is A Photon? Foundations Of Quantum Field Theory, Charles G. Torre

All Physics Faculty Publications

This is a brief, informal, and relatively low-level course on the foundations of quantum field theory. The prerequisites are undergraduate courses in quantum mechanics and electromagnetism.

Collected Papers (On Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics), Volume Xi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with 84 co-authors from 19 countries.

A First-Year Research Experience: The Freshman Project In Physics At Loyola University Chicago, Jonathan Bougie, Asim Gangopadhyaya, Sherita Moses, Robert Polak, Gordon Ramsey, Weronika Walkosz

Physics: Faculty Publications and Other Works

Undergraduate research has become an essential mode of engaging and retaining students in physics. At Loyola University Chicago, first-year physics students have been participating in the Freshman Projects program for over twenty years, which has coincided with a period of significant growth for our department. In this paper, we describe how the Freshman Projects program has played an important role in advancing undergraduate research at Loyola and the profound impact it has made on our program. We conclude with suggestions for adoption of similar programs at other institutions.

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/R⁷ Casimir-Polder form to a long-range tail - provided by the Wick-rotated term - proportional to cos[2(E_m - E_n)R/(ħc)]/R², where E_m < E_n is the energy of a virtual state, …

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), …

Radiation Reaction: Or How I Learned To Stop Worrying And Love E&M, Alexander R. Kaufman

Summer Research

Here we present some approaches to understanding the Abraham-Lotentz-Dirac equation and their features. And a behavior found in numerical solutions to the 1-dimensional ALD in a co-moving reference frame for a single charged particle in a Coulombic field.

No Contact Terms For The Magnetic Field In Lorentz- And Cpt-Violating Electrodynamics, Karl Schober, Brett David Altschul

Faculty Publications

In a Lorentz- and CPT-violating modification of electrodynamics, the fields of a moving charge are known to have unusual singularities. This raises the question of whether the singular behavior may include δ-function contact terms, similar to those that appear in the fields of idealized dipoles. However, by calculating the magnetic field of an infinite straight wire in this theory, we demonstrate that there are no such contact terms in the magnetic field of a moving point charge.

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 corrections …

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 dominates …

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 of the …

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)⁴μ³/m²_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)⁴μ 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-ln²(Zα) μ²/m_N is obtained in leading logarithmic approximation. …

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(15) Hz, we infer the …

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

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

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

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

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 …

A Dyad Theory Of Hydrodynamics And Electrodynamics, Preston Jones

Publications

The dyadic calculus is developed in a form suitable for the description of physical relations in curved space. The 4-space equations of hydrodynamics and electrodynamics are constructed using this dyadic calculus. As a demonstration of the relationship between gravity and electrodynamics a time varying metric is shown to generate electromagnetic radiation.

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 α⁸ m_ec², where me is the electron mass and c is the speed of light, and scale as Z⁶, 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] …

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. 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 Hg⁷⁵⁺ to Hg⁷⁸⁺ 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, …

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 …

Comparative Investigations Of Equatorial Electrodynamics And Low-To-Mid Latitude Coupling Of The Thermosphere-Ionosphere System, M J. Colerico, M Mendillo, C G. Fesen, J Meriwether

Dartmouth Scholarship

The thermospheric midnight temperature maxi-

mum (MTM) is a highly variable, but persistent, large scale

neutral temperature enhancement which occurs at low lati-

tudes. Its occurrence can impact many fundamental upper

atmospheric parameters such as pressure, density, neutral

winds, neutral density, and F-region plasma. Although the

MTM has been the focus of several investigations employ-

ing various instrumentation including photometers, satellites,

and Fabry-Perot interferometers, limited knowledge exists

regarding the latitude extent of its influence on the upper at-

mosphere. This is largely due to observational limitations

which confined the collective geographic range to latitudes

within ±23◦. This paper investigates the …

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 α²(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 α²(Zα)⁶ includes …

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 …

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.

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 α²(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=n³ΔE(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 of order …

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 Ar¹³⁺ 1s²2s²2p²P^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.