338 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
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
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 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
Two-loop self-energy contribution to the Lamb shift in H-like ions
The two-loop self-energy correction is evaluated to all orders in Z\alpha for
the ground-state Lamb shift of H-like ions with Z >= 10, where Z is the nuclear
charge number and \alpha is the fine structure constant. The results obtained
are compared with the analytical values for the Z\alpha-expansion coefficients.
An extrapolation of the all-order numerical results to Z=1 is presented and
implications of our calculation for the hydrogen Lamb shift are discussed
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