arXiv subjects

U. D. Jentschura

Publications and source records attributed to U. D. Jentschura.

At least 145 records · Page 8Linked to original sources

arXiv2005

Self-energy values for P states in hydrogen and low-Z hydrogenlike ions

We describe a nonperturbative (in Zalpha) numerical evaluation of the one-photon electron self energy for 3P_{1/2}, 3P_{3/2}, 4P_{1/2} and 4P_{3/2} states in hydrogenlike atomic systems with charge numbers Z=1 to 5. The numerical results are found to be in agreement with known terms in the expansion of the self energy in powers of Zalpha and lead to improved theoretical predictions for the self-energy shift of these states.

physics.atom-ph↗

arXiv2005

Laser-dressed vacuum polarization in a Coulomb field

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 the system. Consequently, the induced charge density is not spherically symmetric, and the energy correction therefore leads to a "polarized Lamb shift." In particular, the laser generates an additional potential with a quadrupole moment. The corresponding laser-dressed vacuum-polarization potential behaves like 1/r**3 at large distances, unlike the Uehling potential that vanishes exponentially for large r. Our investigation might be useful for other situations where quantum field theoretic phenomena are subjected to external fields of a rather involved structure.

physics.atom-ph↗

arXiv2005

Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]

Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for convergent series representations of both the real and the imaginary part of the QED effective action; these derivations were based on correct intermediate steps. In this comment, we argue that the physical significance of the "logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86, 1947 (2001)] in comparison to the usual expression for the QED effective action remains to be demonstrated. Further information on related subjects can be found in Appendix A of hep-ph/0308223 and in hep-th/0210240.

hep-th↗

arXiv2005

Some Recent Advances in Bound-State Quantum Electrodynamics

We discuss recent progress in various problems related to bound-state quantum electrodynamics: the bound-electron g factor, two-loop self-energy corrections and the laser-dressed Lamb shift. The progress relies on various advances in the bound-state formalism, including ideas inspired by effective field theories such as Nonrelativistic Quantum Electrodynamics. Radiative corrections in dynamical processes represent a promising field for further investigations.

hep-ph↗

arXiv2004

Nonrelativistic QED approach to the bound-electron g factor

Within a systematic approach based on nonrelativistic quantum electrodynamics (NRQED), we derive the one-loop self-energy correction of order alpha (Zalpha)^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 alpha^2 (Zalpha)^4 ln[(Zalpha)^-2] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g factor measurements.

hep-ph↗

arXiv2004

Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms

We investigate the gauge invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms. It is shown that an effective treatment of the correction using a Lamb-shift "potential" leads to equivalent results in both the length as well as the velocity gauges provided all relevant correction terms are taken into account. Specifically, the relevant radiative corrections are related to the energies that enter into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition that holds between the two photons; the form of all of these effects is different in the two gauges, but the final result is shown to be gauge invariant, as it should be. Although the actual calculation only involves integrations over nonrelativistic hydrogenic Green functions, the derivation of the leading logarithmic correction can be regarded as slightly more complex than that of other typical logarithmic terms. The dominant radiative correction to the 2S two-photon decay width is found to be -2.020536 (alpha/pi) (Zalpha)^2 ln[(Zalpha)^-2] in units of the leading nonrelativistic expression. This result is in agreement with a length-gauge calculation [S. G. Karshenboim and V. G. Ivanov, e-print physics/9702027], where the coefficient was given as -2.025(1).

physics.atom-ph↗

arXiv2004

New Limits to the Drift of Fundamental Constants from Laboratory Measurements

We have remeasured the absolute $1S$-$2S$ transition frequency $ν_{\rm {H}}$ in atomic hydrogen. A comparison with the result of the previous measurement performed in 1999 sets a limit of $(-29\pm 57)$ Hz for the drift of $ν_{\rm {H}}$ with respect to the ground state hyperfine splitting $ν_{\rm {Cs}}$ in $^{133}$Cs. Combining this result with the recently published optical transition frequency in $^{199}$Hg$^+$ against $ν_{\rm {Cs}}$ and a microwave $^{87}$Rb and $^{133}$Cs clock comparison, we deduce separate limits on $\dotα/α= (-0.9\pm 2.9)\times 10^{-15}$ yr$^{-1}$ and the fractional time variation of the ratio of Rb and Cs nuclear magnetic moments $μ_{\rm {Rb}}/μ_{\rm {Cs}}$ equal to $(-0.5 \pm 1.7)\times 10^{-15}$ yr$^{-1}$. The latter provides information on the temporal behavior of the constant of strong interaction.

physics.optics↗

arXiv2004

Relativistic and Radiative Energy Shifts for Rydberg States

We investigate relativistic and quantum electrodynamic effects for highly-excited bound states in hydrogenlike systems (Rydberg states). In particular, hydrogenic one-loop Bethe logarithms are calculated for all circular states (l = n-1) in the range 20 <= n <= 60 and successfully compared to an existing asymptotic expansion for large principal quantum number n. We provide accurate expansions of the Bethe logarithm for large values of n, for S, P and circular Rydberg states. These three expansions are expected to give any Bethe logarithms for principal quantum number n > 20 to an accuracy of five to seven decimal digits, within the specified manifolds of atomic states. Within the numerical accuracy, the results constitute unified, general formulas for quantum electrodynamic corrections whose validity is not restricted to a single atomic state. The results are relevant for accurate predictions of radiative shifts of Rydberg states and for the description of the recently investigated laser-dressed Lamb shift, which is observable in a strong coherent-wave light field.

physics.atom-ph↗

arXiv2004

Physics of Skiing: The Ideal-Carving Equation and Its Applications

Ideal carving occurs when a snowboarder or skier, equipped with a snowboard or carving skis, describes a perfect carved turn in which the edges of the ski alone, not the ski surface, describe the trajectory followed by the skier, without any slipping or skidding. In this article, we derive the "ideal-carving" equation which describes the physics of a carved turn under ideal conditions. The laws of Newtonian classical mechanics are applied. The parameters of the ideal-carving equation are the inclination of the ski slope, the acceleration of gravity, and the sidecut radius of the ski. The variables of the ideal-carving equation are the velocity of the skier, the angle between the trajectory of the skier and the horizontal, and the instantaneous curvature radius of the skier's trajectory. Relations between the slope inclination and the velocity range suited for nearly ideal carving are discussed, as well as implications for the design of carving skis and snowboards.

physics.class-ph↗

arXiv2003

Convergence Acceleration Techniques

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the acceleration of slowly convergent and the summation of divergent series that are ubiquitous in relevant applications. The computing time is reduced in many cases by orders of magnitude.

math.NA↗

arXiv2003

The 2S-2P Lamb Shift in He+

The current theoretical status of the Lamb shift in He+ is discussed. Recent calculations of two-loop binding corrections to the Lamb shift significantly shift the theoretical value of the "classic" Lamb shift in He+, i.e. of the 2S_1/2-2P_1/2-interval. In this brief research note, we present a new (theoretical) value for this interval which reads 14041.474(42) Mhz. The theoretical uncertainty is reduced as well as the discrepancy between theory and experiment. Planned measurements should be of help in further elucidating the situation.

physics.atom-ph↗

arXiv2003

Renormalization-Group Analysis of the Generalized sine-Gordon Model and of the Coulomb Gas for d >= 3 Dimensions

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d >= 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.

hep-th↗

arXiv2003

The Study of the Heisenberg-Euler Lagrangian and Some of its Applications

The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of this Lagrangian and a few of its applications in this study. [In an appendix, we discuss issues related to the renormalization - and the renormalization-group invariance - of the Heisenberg-Euler Lagrangian and its two-loop generalization.]

hep-ph↗

arXiv2003

Lamb Shift of Laser-Dressed Atomic States

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.

quant-ph↗

arXiv2002

Implementation of the Combined--Nonlinear Condensation Transformation

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of importance in linguistics, statistical-mechanics theory, and biophysics (statistical analysis of DNA sequences). We also discuss applications of the transformation in experimental mathematics, and we briefly expand on further applications in theoretical physics. Finally, we discuss a related Mathematica program for the computation of Lerch's transcendent.

math.NA↗

arXiv2002

Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift

Self-energy corrections involving logarithms of the parameter Zalpha can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by alpha the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy ``potentials'' that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient B_62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B_62 based on nonrelativistic quantum electrodynamics (NRQED). In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach.

hep-ph↗

arXiv2002

A Problematic Set of Two-Loop Self-Energy Corrections

We investigate a specific set of two-loop self-energy corrections involving squared decay rates and point out that their interpretation is highly problematic. The corrections cannot be interpreted as radiative energy shifts in the usual sense. Some of the problematic corrections find a natural interpretation as radiative nonresonant corrections to the natural line shape. They cannot uniquely be associated with one and only one atomic level. While the problematic corrections are rather tiny when expressed in units of frequency (a few Hertz for hydrogenic P levels) and do not affect the reliability of quantum electrodynamics at the current level of experimental accuracy, they may be of importance for future experiments. The problems are connected with the limitations of the so-called asymptotic-state approximation which means that atomic in- and out-states in the S-matrix are assumed to have an infinite lifetime.

hep-ph↗

arXiv2002

Breit Hamiltonian and QED Effects for Spinless Particles

We describe a simplified derivation for the relativistic corrections of order $α^4$ for a bound system consisting of two spinless particles. We devote special attention to pionium, the bound system of two oppositely charged pions. The leading quantum electrodynamic (QED) correction to the energy levels is of the order of $α^3$ and due to electronic vacuum polarization. We analyze further corrections due to the self-energy of the pions, and due to recoil effects, and we give a complete result for the scalar-QED leading logarithmic corrections which are due to virtual loops involving only the scalar constituent particles (the pions); these corrections are of order $α^5 \ln α$ for S states.

hep-ph↗