288 research outputs found
The two-loop self-energy for the ground state of medium-Z hydrogen-like ions
The two-loop self-energy correction to the ground state Lamb shift is
calculated for hydrogen-like ions with the nuclear charge Z=10-30 without any
expansion in the binding field of the nucleus. A calculational technique is
reported for treatment of Feynman diagrams in the mixed coordinate-momentum
representation, which yields significant improvement in numerical accuracy as
compared to previous results. An extrapolation of the all-order numerical data
towards Z=1 yields a result for the higher-order remainder function for
hydrogen. The previously reported disagreement between the all-order and the
perturbative approaches is reduced to the marginal agreement.Comment: 4 pages, 1 table, 3 figure
Relativistic configuration-interaction calculation of energy levels of core-excited states in lithium-like ions: argon through krypton
Large-scale relativistic configuration-interaction calculation of energy
levels of core-excited states of lithium-like ions is presented. Quantum
electrodynamic, nuclear recoil, and frequency-dependent Breit corrections are
included in the calculation. The approach is consistently applied for
calculating all core-excited states for all lithium-like ions starting
from argon () and ending with krypton (). The results obtained
are supplemented with systematical estimations of calculation errors and
omitted effects
Two-Loop Bethe Logarithms for non-S Levels
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 alpha^8 m_e c^2, where m_e 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 (alpha/pi)^2 (Z alpha)^6 ln[(Z
alpha)^(-2)] m_e c^2 for D states and all states with higher angular momenta.
For higher excited P and D states, a number of poles from lower-lying levels
have to subtracted in the numerical evaluation. We find that, surprisingly, the
corrections of the "squared decay-rate type" are the numerically dominant
contributions in the order (alpha/pi)^2 (Z alpha)^6 m_e c^2 for states with
large angular momenta, and provide an estimate of the entire B_60-coefficient
for Rydberg states with high angular momentum quantum numbers. Our results
reach the predictive limits of the quantum electrodynamic theory of the Lamb
shift.Comment: 14 pages, RevTe
Two-loop QED corrections with closed fermion loops for the bound-electron g factor
Two-loop QED corrections with closed fermion loops are calculated for the 1s
bound-electron g factor. Calculations are performed to all orders in the
nuclear binding strength parameter Z\alpha (where Z is the nuclear charge and
\alpha is the fine structure constant) except for the closed fermion loop,
which is treated within the free-loop (Uehling) approximation in some cases.
Comparison with previous Z\alpha-expansion calculations is made and the
higher-order remainder of order \alpha^2(Z\alpha)^5 and higher is separated out
from the numerical results
QED corrections of order alpha (Zalpha)^2 E_F to the hyperfine splitting of P_1/2 and P_3/2 states in hydrogenlike ions
The hyperfine structure (HFS) of a bound electron is modified by the
self-interaction of the electron with its own radiation field. This effect is
known as the self-energy correction. In this work, we discuss the evaluation of
higher-order self-energy corrections to the HFS of bound P states. These are
expressed in a semi-analytic expansion involving powers of Zalpha and
ln(Zalpha), where Z is the nuclear charge number and alpha is the
fine-structure constant. We find that the correction of relative order alpha
(Zalpha)^2 involves only a single logarithm ln(Zalpha) for P_1/2 states [but no
term of order alpha (Zalpha)^2 ln^2(Zalpha), whereas for P_3/2 states, even the
single logarithm vanishes. By a Foldy-Wouthuysen transformation, we identify a
nuclear-spin dependent correction to the electron's transition current, which
contributes to the HFS of P states. A comparison of the obtained analytic
results to a numerical approach is made.Comment: 12 oages; RevTe
Hyperfine structure of S states in Li and Be^+
A large-scale configuration-interaction (CI) calculation is reported for the
hyperfine splitting of the 2^2S and 3^2S states of ^7Li and ^9Be^+. The CI
calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with a
separate treatment of the QED, nuclear-size, nuclear-magnetization
distribution, and recoil corrections. The nonrelativistic limit of the CI
results is in excellent agreement with variational calculations. The
theoretical values obtained for the hyperfine splitting are complete to the
relative order of \alpha^2 and improve upon results of previous studies.Comment: 4 pages, 2 table
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