2,318 research outputs found
High-energy photoproduction cross section close to the end of spectrum
We consider the cross section of electron-positron pair production by a
high-energy photon in a strong Coulomb field close to the end of electron or
positron spectrum. We show that the cross section essentially differs from the
result obtained in the Born approximation as well as form the result which
takes into account the Coulomb corrections under assumption that both electron
and positron are ultrarelativistic. The cross section of bremsstrahlung in a
strong Coulomb field by a high-energy electron is also obtained in the region
where the final electron is not ultrarelativistic.Comment: 20 pages, 4 figure
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
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
Relativistic corrections to the electromagnetic polarizabilities of compound systems
The low-energy amplitude of Compton scattering on the bound state of two
charged particles of arbitrary masses, charges and spins is calculated. A case
in which the bound state exists due to electromagnetic interaction (QED) is
considered. The term, proportional to , is obtained taking into
account the first relativistic correction. It is shown that the complete result
for this correction differs essentially from the commonly used term
, proportional to the r.m.s. charge radius of the system. We
propose that the same situation can take place in the more complicated case of
hadrons.Comment: 19 pages, LaTe
Small-angle scattering and quasiclassical approximation beyond leading order
In the present paper we examine the accuracy of the quasiclassical approach
on the example of small-angle electron elastic scattering. Using the
quasiclassical approach, we derive the differential cross section and the
Sherman function for arbitrary localized potential at high energy. These
results are exact in the atomic charge number and correspond to the leading and
the next-to-leading high-energy small-angle asymptotics for the scattering
amplitude. Using the small-angle expansion of the exact amplitude of electron
elastic scattering in the Coulomb field, we derive the cross section and the
Sherman function with a relative accuracy and ,
respectively ( is the scattering angle). We show that the correction of
relative order to the cross section, as well as that of relative
order to the Sherman function, originates not only from the
contribution of large angular momenta , but also from that of . This means that, in general, it is not possible to go beyond the accuracy
of the next-to-leading quasiclassical approximation without taking into account
the non-quasiclassical terms.Comment: 12 pages, 3 figure
Corrections to the energy levels of a spin-zero particle bound in a strong field
Formulas for the corrections to the energy levels and wave functions of a
spin-zero particle bound in a strong field are derived. General case of the sum
of a Lorentz-scalar potential and zero component of a Lorentz-vector potential
is considered. The forms of the corrections differ essentially from those for
spin-1/2 particles. As an example of application of our results, we evaluated
the electric polarizability of a ground state of a spin-zero particle bound in
a strong Coulomb field.Comment: 7 pages, 1 figur
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