scholarly journals Leading Logarithmic Contribution to the Second-Order Lamb Shift Induced by the Loop-After-Loop Diagram

2001 ◽  
Vol 86 (10) ◽  
pp. 1990-1993 ◽  
Author(s):  
Vladimir A. Yerokhin
Keyword(s):  
Lamb Shift ◽  
Second Order ◽  
Loop Diagram ◽  
Logarithmic Contribution

Second-order self-energy–vacuum-polarization contributions to the Lamb shift in highly charged few-electron ions

1996 ◽  
Vol 54 (4) ◽  
pp. 2805-2813 ◽  
Author(s):  
Hans Persson ◽  
Ingvar Lindgren ◽  
Leonti N. Labzowsky ◽  
Günter Plunien ◽  
Thomas Beier ◽  
...  
Keyword(s):  
Lamb Shift ◽  
Vacuum Polarization ◽  
Second Order ◽  
Self Energy

scholarly journals SECOND-ORDER CORRECTIONS TO THE NONCOMMUTATIVE KLEIN–GORDON EQUATION WITH A COULOMB POTENTIAL

2011 ◽  
Vol 26 (23) ◽  
pp. 4133-4144 ◽  
Author(s):  
SLIMANE ZAIM ◽  
LAMINE KHODJA ◽  
YAZID DELENDA
Keyword(s):  
Hydrogen Atom ◽  
Coulomb Potential ◽  
Lamb Shift ◽  
Gordon Equation ◽  
Energy Levels ◽  
Space Time ◽  
Second Order ◽  
Noncommutative Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

We improve the previous study of the Klein–Gordon equation in a noncommutative space–time as applied to the hydrogen atom to extract the energy levels, by considering the second-order corrections in the noncommutativity parameter. Phenomenologically we show that noncommutativity is the source of Lamb shift corrections.

Relativistic many-body calculations of energies for doubly-excited 1s2l2l′ and 1s3l3l′ states in Li-like ions

2004 ◽  
Vol 82 (9) ◽  
pp. 743-764 ◽  
Author(s):  
U I Safronova ◽  
M S Safronova
Keyword(s):  
Experimental Data ◽  
Lamb Shift ◽  
Energy Levels ◽  
Second Order ◽  
Coulomb Interactions ◽  
Many Body ◽  
Comparison With Experiment ◽  
Order Energy ◽  
Doubly Excited ◽  
Many Body Perturbation Theory

Energies of 1s2l2l′ and 1s3l3l′ states for Li-like ions with Z = 6–100 are evaluated to second order in relativistic many-body perturbation theory. Second-order Coulomb and Breit–Coulomb interactions are included. The calculations start with a Dirac potential and include all possible 1s2l2l′ and 1s3l3l′ configurations. Correction for the frequency dependence of the Breit interaction is taken into account in lowest order. The Lamb-shift correction to the energies is also included in lowest order. A detailed discussion of the various contributions to the energy levels is given for Li-like iron (Z = 26). We found that the three-electron corrections to the energy contribute about 10–20% of the total second-order energy. Comparisons are made with available experimental data and excellent agreement for term splitting is obtained even for low-Z ions. These calculations are presented as a theoretical benchmark for comparison with experiment and theory.PACS Nos.: 32.30.Rj, 32.70.Cs, 31.25.Jf, 31.15.Md

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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