The relativistic interaction operator of two quasimolecular electrons within the third-order effect of quantum electrodynamics

2010 ◽  
Vol 27 (0) ◽  
pp. 88-96
Author(s):  
О. Ф. Павлик
Keyword(s):  
Quantum Electrodynamics ◽  
Order Effect ◽  
Third Order ◽  
Interaction Operator ◽  
The Third ◽  
Relativistic Interaction

scholarly journals The problem of two electrons within the third order of the quantum electrodynamics

2010 ◽  
Vol 14 (3) ◽  
Author(s):  
V. Yu. Lazur ◽  
O. F. Pavlyk ◽  
O. K. Reity
Keyword(s):  
Quantum Electrodynamics ◽  
Third Order ◽  
The Third

THE GENERALIZED BREIT OPERATOR OF A LONG-RANGE TYPE IN THE FRAMEWORK OF THE SECOND-ORDER EFFECTS OF QUANTUM ELECTRODYNAMICS

2010 ◽  
Vol 25 (25) ◽  
pp. 4775-4800
Author(s):  
V. YU. LAZUR ◽  
S. I. MYHALYNA ◽  
O. K. REITY
Keyword(s):  
Quantum Electrodynamics ◽  
Dipole Interaction ◽  
Order Effect ◽  
Second Order ◽  
Order Effects ◽  
Additional Contribution ◽  
Range Type ◽  
Modern Methods ◽  
Relativistic Interaction ◽  
Breit Operator

The problem of interaction of two quasimolecular electrons located at an arbitrary distance from each other and near different atoms (nuclei) is solved. The interaction is considered as a second-order effect of quantum electrodynamics in the coordinate representation. It is shown that a consistent account for the natural condition of the interaction symmetry with respect to both electrons leads to an additional contribution to the relativistic interaction of the two quasimolecular electrons compared with both the standard Breit operator and the generalized Breit operator known previously. The generalized Breit–Pauli operator and the operator of electric dipole–dipole interaction of two quasimolecular electrons located at an arbitrary distance from each other are obtained. Modern methods of accounting for the relativistic and correlative effects in the problem of ion–atom interactions are discussed.

scholarly journals Revisiting the third-order elastic constants of diamond: The higher-order effect

2021 ◽  
pp. 108490
Author(s):  
Mingqing Liao ◽  
Yong Liu ◽  
Yi Wang ◽  
Fei Zhou ◽  
Nan Qu ◽  
...  
Keyword(s):  
Elastic Constants ◽  
Order Effect ◽  
Higher Order ◽  
Third Order ◽  
The Third ◽  
Third Order Elastic Constants

scholarly journals On one-loop corrections to the CPT-even Lorentz-breaking extension of QED

2018 ◽  
Vol 33 (02) ◽  
pp. 1850018 ◽  
Author(s):  
T. Mariz ◽  
R. V. Maluf ◽  
J. R. Nascimento ◽  
A. Yu. Petrov
Keyword(s):  
Standard Model ◽  
Gauge Field ◽  
Quantum Electrodynamics ◽  
Renormalization Scheme ◽  
Standard Model Extension ◽  
Third Order ◽  
The Third ◽  
Model Extension ◽  
The Standard Model ◽  
Tensor Formula

In this paper, we describe the quantum electrodynamics added by Lorentz-violating CPT-even terms in the context of the standard model extension. We focus our attention on the fermion sector, represented by the CPT-even symmetric Lorentz-breaking tensor [Formula: see text]. We adopt a generic form that parametrizes the components of [Formula: see text] in terms of one four-vector, namely, [Formula: see text]. We then generate perturbatively, up to the third order in this tensor, the aether-like term for the gauge field. Finally, we discuss the renormalization scheme for the gauge propagator, by taking into account [Formula: see text] traceless [Formula: see text] and, trivially, [Formula: see text] [Formula: see text].

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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