V. M. Strakhovenko

High-energy expansion of Coulomb corrections to the e + e − photoproduction cross section

First correction to the high-energy asymptotics of the total

HIGH-ENERGY PHOTON SPLITTING ON HEAVY ATOMS

e^+e^-

Quasiclassical green function in an external field and small-angle scattering processes

photoproduction cross section in the electric field of a heavy atom is derived with the exact account of this field. The consideration is based on the use of the quasiclassical electron Green function in an external electric field. The next-to-leading correction to the cross section is discussed. The influence of screening on the Coulomb corrections is examined in the leading approximation. It turns out that the high-energy asymptotics of the corresponding correction is independent of the photon energy. In the region where both produced particles are relativistic, the corrections to the high-energy asymptotics of the electron (positron) spectrum are derived. Our results for the total cross section are in good agreement with experimental data for photon energies down to a few

Coulomb corrections to bremsstrahlung in the electric field of a heavy atom at high energies

MeV

Charge asymmetry in the differential cross section of high-energy e + e − photoproduction in the field of a heavy atom

. In addition, the corrections to the bremsstrahlung spectrum are obtained from the corresponding results for pair production.

CROSS SECTION OF HIGH-ENERGY PHOTON SPLITTING IN THE ELECTRIC FIELDS OF HEAVY ATOMS

Various differential cross sections of high-energy photon splitting in the electric fields of heavy atoms are calculated exactly in the parameter \al. The consideration is based on the quasiclassical approach applicable for small angles between all photon momenta. The expressions obtained are valid for arbitrary transverse momenta of final photons . The detailed investigation of the process is performed taking into account the effect of screening . The exact cross section turns out to be noticeably smaller than the result obtained in the Born approximation.

Simple analytical representation for the high-energy Delbruck scattering amplitudes

A representation is obtained for the quasiclassical Green functions of the Dirac and Klein-Gordon equations allowing for the first nonvanishing correction in an arbitrary localized potential which generally possesses no spherical symmetry. This is used to obtain a solution of these equations in an approximation similar to the Furry-Sommerfeld-Maue approximation. It is shown that the quasiclassical Green function does not reduce to the Green function obtained in the eikonal approximation and has a wider range of validity. This is illustrated by calculating the amplitude of small-angle scattering of a charged particle and the amplitude of Delbrück forward scattering. A correction proportional to the scattering angle was obtained for the amplitude of charged particle scattering in a potential possessing no spherical symmetry. The real part of the Delbrück forward scattering amplitude was calculated in a screened Coulomb potential.

Analytical calculation of Coulomb corrections to e+ e- pair production at intermediate photon energies

We consider the differential and partially integrated cross sections for bremsstrahlung from high-energy electrons in an atomic field, with this field taken into account exactly. We use the semiclassical electron Green function and wavefunctions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed over the final-electron states are independent of screening in the leading approximation in the small parameter 1/mrscr (rscr is the screening radius and m is the electron mass, ℏ = c = 1). We also consider bremsstrahlung from a finite-size electron beam on a heavy nucleus. The Coulomb corrections to the differential probability are also very susceptible to the beam shape, while the corrections to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters mε (ε is the electron energy) and 1/mrscr are obtained.

Erratum: High-energy expansion of Coulomb corrections to the e{sup +}e{sup -} photoproduction cross section [Phys. Rev. A 69, 022708 (2004)]

First quasiclassical correction to the differential cross section of high-energy electron-positron photoproduction in the electric field of a heavy atom is obtained with the exact account of the field. This correction is responsible for the charge asymmetry A in this process. When the transverse momentum of at least one of the produced particles is much larger than the electron mass m, the charge asymmetry can be as large as tens percent. We also estimate the contribution ˜ A to the charge asymmetry coming from the Compton-type diagram. For heavy nuclei, this contribution is negligible. For light nuclei, ˜ A is noticeable only when the angle between the momenta of electron and positron is of order of m/! (! is the photon energy) while the transverse momenta of both particles are much larger than m.