Radiative corrections to the scattering of electrons and positrons by electrons

The e 6 corrections to the Moller formula for the scattering of electrons by electrons and the Bhabha formula for the scattering of positrons by electrons, arising from the interaction of the particles with virtual photons, are formulated using the Feynman-Dyson techniques. After removing ultra-violet divergences by mass and charge renormalization the cross-section still suffers from a logarithmic infra-red divergence. This is cancelled by adding on the cross-section for the production of a single real photon of low energy during the collision. The result is evaluated assuming that the maximum bremsstrahlung energy radiated is small compared with the rest energy of the electron, as viewed from the laboratory frame. Non-relativistic and extreme relativistic approximations to the formulae are presented, together with the results of exact calculations for a laboratory energy of 20 mc 2 .

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Elastic Scattering of Electrons and Positrons by Screened Nuclei

Zeitschrift für Naturforschung A ◽

10.1515/zna-1966-0901 ◽

1966 ◽

Vol 21 (9) ◽

pp. 1321-1327 ◽

Cited By ~ 13

Author(s):

Elmar Zeitler ◽

Haakon Olsen

Keyword(s):

Elastic Scattering ◽

Cross Section ◽

Cross Sections ◽

Relativistic Effects ◽

The Other ◽

Elastic Electron ◽

Positron Scattering ◽

Electrons And Positrons ◽

Two Factors ◽

The Cross

Results of calculations of cross sections for elastic electron and positron scattering are given in angular steps of 15 degrees for elements Z=6, 13, 29, 50, 82, and 92 and energies T=0.2, 0.4, 0.7, 1, 2, 4, and 10 MeV. The calculation is based on the separability of the cross section into two factors, one describing screening and the other, spin and relativistic effects. The first factor is obtained by the MOLIÈRE approximation 8. The second factor is taken from a paper by DOGGETT and SPENCER 5. Different screening potentials for Z=29 were applied.

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LABORATORY FRAME ANALYSIS OF e+e-→μ+μ- SCATTERING IN THE NONCOMMUTATIVE STANDARD MODEL AT LINEAR COLLIDER

International Journal of Modern Physics A ◽

10.1142/s0217751x12501412 ◽

2012 ◽

Vol 27 (24) ◽

pp. 1250141 ◽

Cited By ~ 3

Author(s):

PRASANTA KUMAR DAS ◽

ABHISHODH PRAKASH

Keyword(s):

Standard Model ◽

Cross Section ◽

Linear Collider ◽

Strong Dependence ◽

Laboratory Frame ◽

Angular Distributions ◽

Muon Pair ◽

The Standard Model ◽

The Cross ◽

Muon Pair Production

We study the muon pair production e+e-→μ+μ- in the framework of the nonminimal noncommutative standard model (NCSM) to the second-order of the noncommutative (NC) parameter Θμν at linear collider. The [Formula: see text] momentum-dependent NC interaction significantly modifies the cross-section and angular distributions which are different from the standard model. After including the effects of earth's rotation we analyze the time-averaged and time-dependent observables in detail. The time-averaged azimuthal distribution of the cross-section shows significant departure from the standard model which can be tested at the upcoming linear collider. We find strong dependence of total cross-section (time-averaged) and their distributions on the orientation and the magnitude of the NC electric vector (ΘE). Assuming that the future linear collider data will differ from the standard model result by 5%, we obtain Λ≥615 GeV and Λ≥946 GeV corresponding to the machine energy E com = 1000 GeV and 1500 GeV.

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PHOTONEUTRON REACTIONS IN G12 AND O16

Canadian Journal of Physics ◽

10.1139/p61-075 ◽

1961 ◽

Vol 39 (5) ◽

pp. 643-656 ◽

Cited By ~ 6

Author(s):

J. P. Roalsvig ◽

Ishwar C. Gupta ◽

R. N. H. Haslam

Keyword(s):

Cross Section ◽

Yield Curve ◽

Bremsstrahlung Energy ◽

The Cross ◽

Section Curve ◽

Maximum Bremsstrahlung Energy ◽

The University

Absolute yields of the reactions C12(γ,n)C11 and O16(γ,n)O15 have been determined at 22-Mev maximum bremsstrahlung energy using the University of Saskatchewan 24-Mev betatron. For the reaction C12(γ,n)C11 a yield curve from threshold to 24 Mev has been obtained and the cross-section curve for the reaction computed. A thorough comparison with other results has been made.

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Absorption cross-sections in the vacuum ultra-violet. - I. Continuous absorption of oxygen (1800 to 1300 Å)

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1953.0171 ◽

1953 ◽

Vol 220 (1140) ◽

pp. 61-70 ◽

Cited By ~ 35

Keyword(s):

Cross Section ◽

Cross Sections ◽

Ultra Violet ◽

Absorption Cross ◽

Absorption Spectrophotometry ◽

Maximum Value ◽

Continuous Absorption ◽

The Cross ◽

Quantitative Absorption ◽

Vacuum Ultra Violet

Absorption cross-sections for oxygen in the region 1670 to 1360 Å, corresponding to the process O 2 3 Ʃ g - + hv → O( 3 P ) + O( 1 D ), have been measured. The cross-section has a maximum value of 1⋅81 x 10 -17 cm 2 at 1450 Å and falls to half-value at 1567 and 1370 Å. The paper includes an account of technical methods of quantitative absorption spectrophotometry in this part of the vacuum ultra- violet.

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A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100073933 ◽

1973 ◽

Vol 31 ◽

pp. 698-699

Author(s):

V. Mizuhira ◽

Y. Futaesaku

Keyword(s):

Cross Section ◽

Tannic Acid ◽

Elastic Fiber ◽

The Other ◽

New Approach ◽

Tissue Block ◽

Active Reaction ◽

The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

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Energy Distribution in Electron Beams

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096096 ◽

1972 ◽

Vol 30 ◽

pp. 568-569

Author(s):

Tamotsu Ohno

Keyword(s):

Electron Beam ◽

Energy Distribution ◽

Cross Section ◽

Integral Curve ◽

Electron Beams ◽

Electron Gun ◽

Angular Divergence ◽

Apparent Increase ◽

Integral Width ◽

The Cross

The energy distribution in an electron; beam from an electron gun provided with a biased Wehnelt cylinder was measured by a retarding potential analyser. All the measurements were carried out with a beam of small angular divergence (<3xl0-4 rad) to eliminate the apparent increase of energy width as pointed out by Ichinokawa.The cross section of the beam from a gun with a tungsten hairpin cathode varies as shown in Fig.1a with the bias voltage Vg. The central part of the beam was analysed. An example of the integral curve as well as the energy spectrum is shown in Fig.2. The integral width of the spectrum ΔEi varies with Vg as shown in Fig.1b The width ΔEi is smaller than the Maxwellian width near the cut-off. As |Vg| is decreased, ΔEi increases beyond the Maxwellian width, reaches a maximum and then decreases. Note that the cross section of the beam enlarges with decreasing |Vg|.

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Research in the cross-section of community psychology and global climate change: A call for action

PsycEXTRA Dataset ◽

10.1037/e628592012-083 ◽

2009 ◽

Author(s):

Marci Culley ◽

Holly Angelique ◽

Courte Voorhees ◽

Brian John Bishop ◽

Peta Louise Dzidic ◽

...

Keyword(s):

Climate Change ◽

Cross Section ◽

Global Climate Change ◽

Community Psychology ◽

Global Climate ◽

The Cross

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Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

Promyshlennoe i Grazhdanskoe Stroitel stvo ◽

10.33622/0869-7019.2019.01.22-30 ◽

2019 ◽

pp. 22-30

Keyword(s):

Cross Section ◽

Cross Sections ◽

Applied Load ◽

Experimental Studies ◽

Strength Properties ◽

Research Topic ◽

Normative Values ◽

Laminated Glass ◽

The Cross ◽

Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

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