Paarerzeugung durch langsame geladene Teilchen im Coulombschen Feld

1961 ◽  
Vol 16 (2) ◽  
pp. 155-161
Author(s):  
E. Hara
Keyword(s):  
Total Cross Section ◽  
Cross Section ◽  
Correction Factor ◽  
Born Approximation ◽  
Plane Waves ◽  
Coulomb Field ◽  
Pair Creation ◽  
Wave Functions ◽  
Heavy Particles ◽  
Order Of Magnitude

The pair creation cross section for heavy particles in the COULOMB field is calculated using SCBRÖDINGER-COULOMB wave functions for the heavy incident particles and plane waves for the created pair. It is shown that the order of magnitude of the cross section thus obtained is given by the product of the value deduced by HEITLER and NORDHEIM 1 with BORN approximation, and the SOMMERFELD correction factor, which is known for the emission of Bremsstrahlung. The total cross section is computed for proton energies of 8 m c2, 12 m c2 and 16 m c2. It turns out to be smaller than the result of HEITLER and NORDHEIM by several orders of magnitude.

The energy loss by radiation of fast electrons in a Coulomb field

1943 ◽  
Vol 39 (2) ◽  
pp. 127-130
Author(s):  
J. C. Jaeger
Keyword(s):  
Exact Solution ◽  
Energy Loss ◽  
Cross Sections ◽  
Born Approximation ◽  
Coulomb Field ◽  
Wave Functions ◽  
Fast Electrons ◽  
Low Energies ◽  
Relativistic Coulomb ◽  
Relativistic Equations

The problem of the energy loss by radiation of an electron in a Coulomb field has been solved, using relativistic equations and the Born approximation, by Bethe and Heitler, and, using exact non-relativistic equations, by Sommerfeld; the first of these solutions is valid only for relatively high and the second for relatively low energies. In this paper an exact solution of the problem is given using the relativistic Coulomb wave functions, but depending on a final stage of numerical computation. The method is an extension of that used to determine cross-sections for pair production.

The application of variational methods to atomic scattering problems II. Impact excitation of the 2s level of atomic hydrogen-distorted wave treatment

1952 ◽  
Vol 212 (1111) ◽  
pp. 521-530 ◽  
Keyword(s):  
Cross Section ◽  
Atomic Hydrogen ◽  
Plane Waves ◽  
Wave Functions ◽  
Impact Excitation ◽  
Wave Method ◽  
Distorted Wave ◽  
Scattering Problems ◽  
The Cross ◽  
Distorted Wave Method

The cross-section for excitation of the 2 S level of atomic hydrogen by electrons is calculated using the distorted wave method with full allowance for exchange. The distorted wave functions used in the calculations are determined by Hulthèn’s variational method. The initial wave functions, representing the motion of an electron in the field of a normal atom with allowance for exchange, are taken to be those calculated by Massey & Moiseiwitsch (1950). The final wave functions, representing the motion of an electron in the field of a hydrogen atom in the 2 S state, have been obtained by a modification of the same method. Exchange effects are found to be less important in determining the forms of these wave functions. The cross-sections obtained are considerably smaller than those calculated by the Born-Oppenheimer method, in which the electron wave functions are undistorted plane waves. This is largely because the symmetrical cross-section, which has the greater weight in determining the mean cross-section, is much greater than the antisymmetrical according to the Born-Oppenheimer method, but the reverse is true if distortion is allowed for. In no case does the distorted wave method give results exceeding the theoretical upper limit, whereas with plane waves this limit is exceeded at certain electron energies by the symmetrical cross-section.

The theory of the T + D reaction

1951 ◽  
Vol 204 (1079) ◽  
pp. 503-513 ◽  
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Logarithmic Derivative ◽  
Coulomb Field ◽  
Absolute Magnitude ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Complex Reaction ◽  
Strong Spin

The energy dependence and absolute magnitude of the cross-section for the T + D reaction are described in terms of the exact wave-functions of the Coulomb field and a complex reaction length defined by the logarithmic derivative of the wave-function on the reaction surface. Previous difficulties in the interpretation of the experiments are largely attributed to the failure of the Wentzel-Kramers-Brillouin approximation. It is sufficient, but not necessary, to assume that the whole cross-section is due to s -waves; but in either case the presence of strong spin-orbit coupling is indicated.

HOW MUCH CAN BE LEARNT ABOUT PION WAVE FUNCTION FROM THE DRELL–YAN PROCESS?

1993 ◽  
Vol 08 (15) ◽  
pp. 2605-2621 ◽  
Author(s):  
SHAHIN S. AGAEV
Keyword(s):  
Wave Function ◽  
Transverse Momentum ◽  
Cross Section ◽  
Production Cross ◽  
Wave Functions ◽  
Feynman Diagrams ◽  
High Twist ◽  
Dilepton Production ◽  
Pion Wave Function ◽  
Order Of Magnitude

Contribution of the high twist Feynman diagrams to the dilepton production cross section in pion–hadron collisions is investigated. In calculations the asymptotic, Chernyak–Zhitnitsky and two other pion model wave functions P2, P3 are used. It is shown that this contribution depends on the choice of wave functions and for large dilepton transverse momentum pT and invariant mass Q in the limit [Formula: see text] exceeds the leading one by an order of magnitude. Perspectives of the Drell–Yan process in the context of the pion wave function investigation are discussed.

Electron Excitation of 21S, 23S, 21P, and 23P States of Helium

1975 ◽  
Vol 53 (20) ◽  
pp. 2289-2295 ◽  
Author(s):  
H. G. P. Lins de Barros ◽  
H. S. Brandi
Keyword(s):  
Total Cross Section ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Theoretical Calculations ◽  
Electron Excitation ◽  
Wave Functions ◽  
Excitation Cross Sections ◽  
Characteristic Values ◽  
The One

Calculations for the total excitation cross sections of the 21S, 23S, 21P, and 23P states of He by electron impact have been carried out assuming the Born–Ochkur approximation for the scattering amplitude and a parametrization previously proposed by the authors for the total cross section. For the atomic wave functions we used LS coupling and obtained the one electron orbitals using the Xα method for three characteristic values of the parameter α. The results are compared with other experimental and theoretical calculations.

K+ PRODUCTION FROM pn, pp AND pd INTERACTIONS AT ANKE/COSY

2007 ◽  
Vol 22 (02n03) ◽  
pp. 514-517
Author(s):  
◽  
YURY VALDAU
Keyword(s):  
Experimental Data ◽  
Phase Space ◽  
Total Cross Section ◽  
Cross Section ◽  
Final State ◽  
Constant Matrix ◽  
Order Of Magnitude ◽  
Simple Phase ◽  
Three Body ◽  
Exclusive Measurement

In order to understand experimental data for K+ production in proton-deuteron interactions and draw conclusions about the ratio between K+ production in pn and pp, one needs to develop an approach for the description of all relevant pp results. We perform an analysis of the pp data available in COSY energy range for three reaction channels. It can be concluded that Λ and Σ0 production channels can be well described by the three-body phase space incorporating the hyperon-nucleon final-state interactions under the assumption of a constant matrix element. Experimental data on the pp → K+ nΣ+ reaction channel are very poor and more information is needed to understand a strange behavior of the energy dependence of the total cross section. Using ANKE inclusive K+ data at 2.85 and 2.95 GeV/c, preliminary values for the total cross-section of Σ+ production in pp interactions has been extracted applying a simple phase space approach. This gives a result roughly one order of magnitude less than that of the recently published exclusive measurement.

scholarly journals Laser-Assisted (e, 2e) Collisions in the Symmetric/Asymmetric Coplanar Geometry

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 40
Author(s):  
Abdelkader Makhoute ◽  
Driss Khalil ◽  
Imane Ajana
Keyword(s):  
Cross Section ◽  
Born Approximation ◽  
Laser Field ◽  
Target Atom ◽  
Wave Functions ◽  
Final States ◽  
Triple Differential Cross Section ◽  
Comprehensive Survey ◽  
Direction Of Polarization ◽  
Target Wave

In this review, we present a comprehensive survey of laser-assisted (e, 2e) reactions. The influence of a laser field on the dynamics of (e, 2e) collisions in atomic hydrogen is analyzed in the symmetric and asymmetric coplanar geometries. Particular attention is devoted to the construction of the dressed (laser-modified) target wave functions, in both the initial and final states. The calculation is performed in the framework of Coulomb-Volkov-Born approximation, where the initial and final electrons are described by Volkov wave functions, while the interaction of the incident electron with the target atom is treated in the first and the second Born approximation. The state of the ejected electron is described by a Volkov/Coulomb-Volkov wave function. A detailed account is also given of the techniques we have used to evaluate the scattering amplitudes. The influence of the laser parameters (frequency, intensity, and direction of polarization) on the angular distribution of the ejected electron is discussed, and a number of illustrative examples are given. The structure of the triple differential cross section in the vicinity of resonances is also analyzed.

Sign in / Sign up

Export Citation Format

Share Document