Pair production in the field of atomic electrons

Maximon, L. C.; Gimm, H.

doi:10.1103/physreva.23.172

Cited by 16 publications

(16 citation statements)

References 18 publications

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confidence: 99%

Simple Analytic Expressions for the Total Cross Section for γ-e Pair Production

Haug

1981

Zeitschrift Für Naturforschung A

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The total cross section for pair production by photons in the field of free electrons is fitted to simple analytic expressions in four intervals of the incident photon energy which cover the whole range between threshold and infinity.The knowledge of accurate cross sections for pair production in the field of electrons or positrons (triplet production) is required in evaluations of total photon absorption cross sections [1,2], for calculations of the cross section for pair production in the field of atoms [3], and in astrophysical prob lems [4][5][6]. Compared to the familiar BetheHeitler formulae [7] for pair production in the Coulomb field of a nucleus, the cross section for triplet production, though obtained by straight forward application of quantum electrodynamics, is extremely complicated due to recoil and exchange effects [8]. Haug [9] has succeeded in deriving an expression for the doubly differential cross section for pair production in the field of free electrons in lowest-order perturbation theory (Born approxi mation) without neglecting the Feynman diagrams which describe exchange and the interaction of the incident photon with the initial electron. This lengthy formula has to be integrated numerically for obtaining the total cross section at ■ In order to facilitate the calculation of ot, the total cross sec tion for triplet production has been fitted to simple analytical expressions in four intervals of the photon energy, the fractional error of the approximation being less than 0.3% everywhere, mostly less than 0.1%.The total cross section at is a relativistic in variant ; it is a function of the invariant product of the energy-momentum four-vectors of the incident photon and electron which in the rest system of the target electron reduces to the photon energy k. If

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confidence: 99%

Simple Analytic Expressions for the Total Cross Section for γ-e Pair Production

Haug

1981

Zeitschrift Für Naturforschung A

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“…As can be seen from Fig. 9 of [17] (to which the reader is referred for a more detailed comparison with experiments) the agreement of the total cross section for pairs, computed with the aid of (21) for hydrogen, with experimental data is good.…”

Section: Electron Momentum Distribution In the Laboratory Systemmentioning

confidence: 54%

“…Nevertheless the contributions to the total cross section are approximately equal for q m ^ q ^ 1 and for 1 ^ q ^ q M . This is in contrast to the behaviour of the recoil momentum distributions da% or Jdq according to the Borsellino formula [5,17] (17) the outgoing electrons with q ^ q c can be designated as the recoil electrons and those with q ^ q c as the pair electrons. For large photon energies q c takes values of the order of one (e.g., q c = 0.92 for k = 20, q c = 0.52 for k = 100).…”

Section: Electron Momentum Distribution In the Laboratory Systemmentioning

confidence: 92%

“…previously obtained by Maximon and Gimm [17,18]. shows that the failure of the Borsellino formula for q ^ 1 does not affect the accuracy of the computation of o x (k,Z).…”

Section: Electron Momentum Distribution In the Laboratory Systemmentioning

confidence: 93%

“…According to (17), the first term represents the total cross section for triplet production in the field of free electrons,…”

Section: Electron Momentum Distribution In the Laboratory Systemmentioning

confidence: 99%

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On Energy and Angular Distributions of Electrons in Triplet Production

Haug

1985

Zeitschrift Für Naturforschung A

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The differential cross section of electron pair production in the field of free electrons (triplet production) is derived from the cross section for electron-positron bremsstrahlung exact to lowest order of perturbation theory. It is used to compute energy and angular distributions of the outcoming electrons. The results are compared with previous calculations. In particular, the accuracy of the momentum distribution according to the Borsellino approximation is discussed.

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Compilation of photon cross-sections: some historical remarks and current status

Hubbell¹

1999

X-Ray Spectrom.

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In x‐ray diffraction spectrometry as well as in the many other scientific, engineering and medical disciplines involving photon radiation, x‐ray attenuation coefficients are required as input data. Within a very few years after the discovery of x‐rays by Röntgen in 1895, the transmission of a narrow (parallel) beam of x‐rays through layers of different materials was measured and quantified with respect to photon (x‐ray) energy and atomic number of the material by Barkla and Sadler in 1907. This quantification is in terms of the mass attenuation (or absorption) coefficient µ/ρ (cm2 g−1) which for monoenergetic photons can be defined as or in which x is the mass thickness of the layer in units of g cm−2, I0 is the intensity (e.g. photons cm−2 s−1) of the incident beam, I is the intensity of the transmitted beam (measured with the layer interposed), ρ is the density of the layer in g cm−3 and µ is the linear attenuation (or absorption, µ*) coefficient in cm−1. Current compilations of µ/ρ are derived from theoretical or semi‐empirical values of the most‐probable individual processes according to in which σpe is the atomic photoeffect cross‐section, σincoh> and σcoh are the incoherent (Compton) and coherent (Rayleigh) scattering cross‐sections, respectively, σpair and σtrip are the cross‐sections for electron–positron pair production (creation) in the field of the nucleus and in the field of the atomic electrons (‘triplet’ production), respectively, and the factor 1/uA, where u is the atomic mass unit and A is the relative atomic mass of the target element, converts the σi units from cm2 per atom to cm2 g−1. Since σpair and σtrip have thresholds above 1 MeV, these do not affect the XRS photon energy region, nor does the photonuclear cross‐section σph.n. which has threshold of 5 MeV or higher and is not included in current µ/ρ compilations. In this brief and arbitrarily selective review, a historical account is given of the evolving compilations of µ/ρ from Barkla and Sadler’s work at the beginning of this century, up to the NIST and Livermore compilations as this century comes to its close. For the latter compilations of µ/ρ, some rough estimates of the ‘envelope of uncertainty’ in different ranges of photon energy are given. Copyright © 1999 John Wiley & Sons, Ltd.

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Pair production in the field of atomic electrons

Cited by 16 publications

References 18 publications

Simple Analytic Expressions for the Total Cross Section for γ-e Pair Production

Simple Analytic Expressions for the Total Cross Section for γ-e Pair Production

On Energy and Angular Distributions of Electrons in Triplet Production

Compilation of photon cross-sections: some historical remarks and current status

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