8,583 research outputs found
Two-Loop Bethe Logarithms
We calculate the two-loop Bethe logarithm correction to atomic energy levels
in hydrogen-like systems. The two-loop Bethe logarithm is a low-energy quantum
electrodynamic (QED) effect involving multiple summations over virtual excited
atomic states. Although much smaller in absolute magnitude than the well-known
one-loop Bethe logarithm, the two-loop analog is quite significant when
compared to the current experimental accuracy of the 1S-2S transition: it
contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The
two-loop Bethe logarithm has been the largest unknown correction to the
hydrogen Lamb shift to date. Together with the ongoing measurement of the
proton charge radius at the Paul Scherrer Institute its calculation will bring
theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to
the level of 10^(-7).Comment: 4 pages, RevTe
Lamb Shift of 3P and 4P states and the determination of
The fine structure interval of P states in hydrogenlike systems can be
determined theoretically with high precision, because the energy levels of P
states are only slightly influenced by the structure of the nucleus. Therefore
a measurement of the fine structure may serve as an excellent test of QED in
bound systems or alternatively as a means of determining the fine structure
constant with very high precision. In this paper an improved analytic
calculation of higher-order binding corrections to the one-loop self energy of
3P and 4P states in hydrogen-like systems with low nuclear charge number is
presented. A comparison of the analytic results to the extrapolated numerical
data for high ions serves as an independent test of the analytic
evaluation. New theoretical values for the Lamb shift of the P states and for
the fine structure splittings are given.Comment: 33 pages, LaTeX, 4 tables, 4 figure
Coordinate-space approach to the bound-electron self-energy: Self-Energy screening calculation
The self-energy screening correction is evaluated in a model in which the
effect of the screening electron is represented as a first-order perturbation
of the self energy by an effective potential. The effective potential is the
Coulomb potential of the spherically averaged charge density of the screening
electron. We evaluate the energy shift due to a , ,
, or electron screening a , ,
, or electron, for nuclear charge Z in the range . A detailed comparison with other calculations is made.Comment: 54 pages, 10 figures, 4 table
QED self-energy contribution to highly-excited atomic states
We present numerical values for the self-energy shifts predicted by QED
(Quantum Electrodynamics) for hydrogenlike ions (nuclear charge ) with an electron in an , 4 or 5 level with high angular momentum
(). Applications include predictions of precision transition
energies and studies of the outer-shell structure of atoms and ions.Comment: 20 pages, 5 figure
Higher-order binding corrections to the Lamb shift of 2P states
We present an improved calculation of higher-order corrections to the
one-loop self energy of 2P states in hydrogen-like systems with small nuclear
charge Z. The method is based on a division of the integration with respect to
the photon energy into a high- and a low-energy part. The high-energy part is
calculated by an expansion of the electron propagator in powers of the Coulomb
field. The low-energy part is simplified by the application of a
Foldy-Wouthuysen transformation. This transformation leads to a clear
separation of the leading contribution from the relativistic corrections and
removes higher order terms. The method is applied to the 2P_{1/2} and 2P_{3/2}
states in atomic hydrogen. The results lead to new theoretical values for the
Lamb shifts and the fine structure splitting.Comment: 18 pages, LaTeX. In comparison to the journal version, it contains an
added note (2000) which reflects the current status of Lamb shift
calculation
Calculation of the Electron Self Energy for Low Nuclear Charge
We present a nonperturbative numerical evaluation of the one-photon electron
self energy for hydrogenlike ions with low nuclear charge numbers Z=1 to 5. Our
calculation for the 1S state has a numerical uncertainty of 0.8 Hz for hydrogen
and 13 Hz for singly-ionized helium. Resummation and convergence acceleration
techniques that reduce the computer time by about three orders of magnitude
were employed in the calculation. The numerical results are compared to results
based on known terms in the expansion of the self energy in powers of (Z
alpha).Comment: 10 pages, RevTeX, 2 figure
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
X-Ray Microanalysis of Hollow Heart Potatoes
Electron microprobe and X-ray fluorescence techniques were used to study elemental gradients associated with the physiological disorder hollow heart i n potato tubers. Gradients were found along the length and across the width of mature tubers. These were not rela ted to the disorder, however . Tubers with advanced symptoms of the disorder had elemental levels and gradients similar to those in healthy, control tubers. The results suggest that if the disorder is initially caused by an elemental deficiency, as has sometimes been proposed , the deficiency is temporary and no longer exists in mature tubers with advanced hollow heart. Radial gradients were associated rnd inly with two contrasting tissues . the centra 1 pith and the surrounding perimedullary zone. Tissue differences are critical in microprobe studies involving small samples Microprobe studies of developing tubers containing incipient stages of hollow heart. employing strip samples restricted to the central pith where the disorder originates and taken so as to traverse the small lesions, showed a dramatic increase in Mg in lesion areas. It is suggested that a nutrient imbalance may trigger the onset of the cell necrosis that characterizes the initiation of hollow heart in potato . A localized Mg toxicity or Ca deficiency due to high Mg:Ca ratio is implicated
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