34 research outputs found
The second-order electron self-energy in hydrogen-like ions
A calculation of the simplest part of the second-order electron self-energy
(loop after loop irreducible contribution) for hydrogen-like ions with nuclear
charge numbers is presented. This serves as a test for the
more complicated second-order self-energy parts (loop inside loop and crossed
loop contributions) for heavy one-electron ions. Our results are in strong
disagreement with recent calculations of Mallampalli and Sapirstein for low
values but are compatible with the two known terms of the analytical
-expansion.Comment: 13 LaTex pages, 2 figure
Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields
The equivalence of the covariant renormalization and the partial-wave
renormaliz ation (PWR) approach is proven explicitly for the one-loop
self-energy correction (SE) of a bound electron state in the presence of
external perturbation potentials. No spurious correctio n terms to the
noncovariant PWR scheme are generated for Coulomb-type screening potentia ls
and for external magnetic fields. It is shown that in numerical calculations of
the SE with Coulombic perturbation potential spurious terms result from an
improper treatment of the unphysical high-energy contribution. A method for
performing the PWR utilizing the relativistic B-spline approach for the
construction of the Dirac spectrum in external magnetic fields is proposed.
This method is applied for calculating QED corrections to the bound-electron
-factor in H-like ions. Within the level of accuracy of about 0.1% no
spurious terms are generated in numerical calculations of the SE in magnetic
fields.Comment: 22 pages, LaTeX, 1 figur
Two-Loop Self-Energy Corrections to the Fine-Structure
We investigate two-loop higher-order binding corrections to the fine
structure, which contribute to the spin-dependent part of the Lamb shift. Our
calculation focuses on the so-called ``two-loop self-energy'' involving two
virtual closed photon loops. For bound states, this correction has proven to be
notoriously difficult to evaluate. The calculation of the binding corrections
to the bound-state two-loop self-energy is simplified by a separate treatment
of hard and soft virtual photons. The two photon-energy scales are matched at
the end of the calculation. We explain the significance of the mathematical
methods employed in the calculation in a more general context, and present
results for the fine-structure difference of the two-loop self-energy through
the order of .Comment: 19 pages, LaTeX, 2 figures; J. Phys. A (in press); added analytic
results for two-loop form-factor slopes (by P. Mastrolia and E. Remiddi
Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms
We present a numerical evaluation of the loop-after-loop contribution to the
second-order self-energy for the ground state of hydrogenlike atoms with low
nuclear charge numbers Z. The calculation is carried out in the Fried-Yennie
gauge and without an expansion in Z \alpha. Our calculation confirms the
results of Mallampalli and Sapirstein and disagrees with the calculation by
Goidenko and coworkers. A discrepancy between different calculations is
investigated. An accurate fitting of the numerical results provides a detailed
comparison with analytic calculations based on an expansion in the parameter Z
\alpha. We confirm the analytic results of order \alpha^2 (Z\alpha)^5 but
disagree with Karshenboim's calculation of the \alpha^2 (Z \alpha)^6 \ln^3(Z
\alpha)^{-2} contribution.Comment: RevTex, 19 pages, 4 figure
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.
Logarithmic two-loop corrections to the Lamb shift in hydrogen
Higher order logarithmic corrections to the
hydrogen Lamb shift are calculated. The results obtained show the two-loop
contribution has a very peculiar behavior, and significantly alter the
theoretical predictions for low lying S-states.Comment: 14 pages, including 2 figures, submitted to Phys. Rev. A, updated
with minor change
Logarithms of alpha in QED bound states from the renormalization group
The velocity renormalization group is used to determine ln(alpha)
contributions to QED bound state energies. The leading order anomalous
dimension for the potential gives the alpha^5 ln(alpha) Bethe logarithm in the
Lamb shift. The next-to-leading order anomalous dimension determines the
alpha^6 ln(alpha), alpha^7 ln^2(alpha), and alpha^8 ln^3 (alpha) corrections to
the energy. These are used to obtain the alpha^8 ln^3(alpha) Lamb shift and
alpha^7 ln^2(alpha) hyperfine splitting for Hydrogen, muonium and positronium,
as well as the alpha^2 ln(alpha) and alpha^3 ln^2(alpha) corrections to the
ortho- and para-positronium lifetimes.Comment: 4 page
Electron Self Energy for the K and L Shell at Low Nuclear Charge
A nonperturbative numerical evaluation of the one-photon electron self energy
for the K- and L-shell states of hydrogenlike ions with nuclear charge numbers
Z=1 to 5 is described. Our calculation for the 1S state has a numerical
uncertainty of 0.8 Hz in atomic hydrogen, and for the L-shell states (2S and
2P) the numerical uncertainty is 1.0 Hz. The method of evaluation for the
ground state and for the excited states is described in detail. The numerical
results are compared to results based on known terms in the expansion of the
self energy in powers of (Z alpha).Comment: 21 pages, RevTeX, 5 Tables, 6 figure
Theory of Light Hydrogenlike Atoms
The present status and recent developments in the theory of light hydrogenic
atoms, electronic and muonic, are extensively reviewed. The discussion is based
on the quantum field theoretical approach to loosely bound composite systems.
The basics of the quantum field theoretical approach, which provide the
framework needed for a systematic derivation of all higher order corrections to
the energy levels, are briefly discussed. The main physical ideas behind the
derivation of all binding, recoil, radiative, radiative-recoil, and
nonelectromagnetic spin-dependent and spin-independent corrections to energy
levels of hydrogenic atoms are discussed and, wherever possible, the
fundamental elements of the derivations of these corrections are provided. The
emphasis is on new theoretical results which were not available in earlier
reviews. An up-to-date set of all theoretical contributions to the energy
levels is contained in the paper. The status of modern theory is tested by
comparing the theoretical results for the energy levels with the most precise
experimental results for the Lamb shifts and gross structure intervals in
hydrogen, deuterium, and helium ion , and with the experimental data on
the hyperfine splitting in muonium, hydrogen and deuterium.Comment: 230 pages, 106 figures, 24 tables. Discussion of muonic hydrogen is
added, list of references expanded, some minor corrections and amendment