234,302 research outputs found
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
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
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
Coulomb corrections to bremsstrahlung in electric field of heavy atom at high energies
The differential and partially integrated cross sections are considered for
bremsstrahlung from high-energy electrons in atomic field with the exact
account of this field. The consideration exploits the quasiclassical electron
Green's function and wave functions 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 up over the final-electron states are independent of screening
in the leading approximation over a small parameter ( is
a screening radius, is the electron mass, ). Bremsstrahlung from
an electron beam of the finite size on heavy nucleus is considered as well.
Again, the Coulomb corrections to the differential probability are very
susceptible to the beam shape, while those 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 ( is the electron energy) and
are obtained.Comment: 13 pages, 4 figure
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