205,548 research outputs found
DRA method: Powerful tool for the calculation of the loop integrals
We review the method of the calculation of multiloop integrals suggested in
Ref.\cite{Lee2010}.Comment: 6 pages, contribution to ACAT2011 proceedings, Uxbridge, London,
September 5-9, 2011, typos are correcte
Relativistic Coulomb Green's function in -dimensions
Using the operator method, the Green's functions of the Dirac and
Klein-Gordon equations in the Coulomb potential are derived for
the arbitrary space dimensionality . Nonrelativistic and quasiclassical
asymptotics of these Green's functions are considered in detail.Comment: 9 page
Electron-positron pair production in ion collisions at low velocity beyond Born approximation
We derive the spectrum and the total cross section of electromagnetic
pair production in the collisions of two nuclei at low relative
velocity . Both free-free and bound-free pair production is
considered. The parameters are assumed to be small
compared to unity but arbitrary compared to ( are the charge
numbers of the nuclei and is the fine structure constant). Due to a
suppression of the Born term by high power of , the first Coulomb
correction to the amplitude appears to be important at . The effect of a finite nuclear mass is discussed. In contrast to the
result obtained in the infinite nuclear mass limit, the terms
are not suppressed by the high power of and may easily dominate at
sufficiently small velocities.Comment: 9 pages, 1 figur
Quasiclassical Green function in an external field and small-angle scattering
The quasiclassical Green functions of the Dirac and Klein-Gordon equations in
the external electric field are obtained with the first correction taken into
account. The relevant potential is assumed to be localized, while its spherical
symmetry is not required. Using these Green functions, the corresponding wave
functions are found in the approximation similar to the Furry-Sommerfeld-Maue
approximation. It is shown that the quasiclassical Green function does not
coincide with the Green function obtained in the eikonal approximation and has
a wider region of applicability. It is illustrated by the calculation of the
small-angle scattering amplitude for a charged particle and the forward photon
scattering amplitude. For charged particles, the first correction to the
scattering amplitude in the non-spherically symmetric potential is found. This
correction is proportional to the scattering angle. The real part of the
amplitude of forward photon scattering in a screened Coulomb potential is
obtained.Comment: 20 pages, latex, 1 figur
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