58 research outputs found

### Extrapolation of the Zalpha-Expansion and Two--Loop Bound--State Energy Shifts

Quantum electrodynamic (QED) effects that shift the binding energies of
hydrogenic energy levels have been expressed in terms of a semi-analytic
expansion in powers of Zalpha and ln[(Zalpha)^{-2}], where Z is the nuclear
charge number and alpha is the fine-structure constant. For many QED effects,
numerical data are available in the domain of high Z where the Zalpha expansion
fails. In this Letter, we demonstrate that it is possible, within certain
limits of accuracy, to extrapolate the Zalpha-expansion from the low-Z to the
high-Z domain. We also review two-loop self-energy effects and provide an
estimate for the problematic nonlogarithmic coefficient B_60.Comment: 10 pages, LaTeX, Phys. Lett. B, in pres

### 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.Comment: 14 pages, 1 figure; references added and typographical errors
corrected; to appear in Phys. Rev.

### Extension of the sum rule for the transition rates between multiplets to the multiphoton case

The sum rule for the transition rates between the components of two
multiplets, known for the one-photon transitions, is extended to the
multiphoton transitions in hydrogen and hydrogen-like ions. As an example the
transitions 3p-2p, 4p-3p and 4d-3d are considered. The numerical results are
compared with previous calculations.Comment: 10 pages, 4 table

### Two-Loop Effects and Current Status of the 4He+ Lamb Shift

We report on recent progress in the treatment of two-loop binding corrections
to the Lamb shift, with a special emphasis on S and P states. We use these and
other results in order to infer an updated theoretical value of the Lamb shift
in 4He+.Comment: 11 pages, nrc1 style; paper presented at PSAS (2006), Venic

### Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil

The current discrepancy of theory and experiment observed recently in muonic
hydrogen necessitates a reinvestigation of all corrections to contribute to the
Lamb shift in muonic hydrogen muH, muonic deuterium muD, the muonic 3He ion, as
well as in the muonic 4He ion. Here, we choose a semi-analytic approach and
evaluate a number of higher-order corrections to vacuum polarization (VP)
semi-analytically, while remaining integrals over the spectral density of VP
are performed numerically. We obtain semi-analytic results for the second-order
correction, and for the relativistic correction to VP. The self-energy
correction to VP is calculated, including the perturbations of the Bethe
logarithms by vacuum polarization. Subleading logarithmic terms in the
radiative-recoil correction to the 2S-2P Lamb shift of order alpha (Zalpha)^5
mu^3 ln(Zalpha)/(m_mu m_N) are also obtained. All calculations are
nonperturbative in the mass ratio of orbiting particle and nucleus.Comment: 10 pages; svjour style; to appear in the European Physical Journal

### Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

The method and status of a study to provide numerical, high-precision values
of the self-energy level shift in hydrogen and hydrogen-like ions is described.
Graphs of the self energy in hydrogen-like ions with nuclear charge number
between 20 and 110 are given for a large number of states. The self-energy is
the largest contribution of Quantum Electrodynamics (QED) to the energy levels
of these atomic systems. These results greatly expand the number of levels for
which the self energy is known with a controlled and high precision.
Applications include the adjustment of the Rydberg constant and atomic
calculations that take into account QED effects.Comment: Minor changes since previous versio

### 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.Comment: 12 pages, nrc1 LaTeX styl

### Generalized Nonanalytic Expansions, PT-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators

The concept of a generalized nonanalytic expansion which involves nonanalytic combinations of exponentials, logarithms and powers of a coupling is introduced and its use illustrated in various areas of physics. Dispersion relations for the resonance energies of odd anharmonic oscillators are discussed, and higher-order formulas are presented for cubic and quartic potentials

### Spectrum of One-Dimensional Anharmonic Oscillators

We use a power-series expansion to calculate the eigenvalues of anharmonic
oscillators bounded by two infinite walls. We show that for large finite values
of the separation of the walls, the calculated eigenvalues are of the same high
accuracy as the values recently obtained for the unbounded case by the
inner-product quantization method. We also apply our method to the Morse
potential. The eigenvalues obtained in this case are in excellent agreement
with the exact values for the unbounded Morse potential.Comment: 11 pages, 5 figures, 4 tables; there are changes to match the version
published in Can. J. Phy

### Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy
displacement of a hydrogenic bound state in an electric field (known as the
Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal
power series in the electric field strength. The perturbation series exhibits a
rich singularity structure in the Borel plane. Resummation methods are
presented which appear to lead to consistent results even in problematic cases
where isolated singularities or branch cuts are present on the positive and
negative real axis in the Borel plane. Two resummation prescriptions are
compared: (i) a variant of the Borel-Pade resummation method, with an
additional improvement due to utilization of the leading renormalon poles (for
a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317,
p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with
an analytic continuation by conformal mapping, and Pade approximations in the
conformal variable. The singularity structure in the case of the LoSurdo-Stark
effect in the complex Borel plane is shown to be similar to (divergent)
perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results
enhanced; one section and one appendix added and some minor changes and
additions; to appear in phys. rev.

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