Angular distribution of high-energy e+e−e^+e^- photoproduction close to the end of spectrum

We consider the differential cross section of electron-positron pair production by a high-energy photon in a strong Coulomb field close to the end of the electron or positron spectrum. When the momentum transfer largely exceeds the electron mass, the cross section is obtained analytically in a compact form. Coulomb corrections essentially modify the cross section even for moderate values of the nuclear charge number $Z$. In the same kinematical region, the angular distribution for bound-free pair production, bremsstrahlung, and photorecombination is also obtained.Comment: 12 pages, 4 figure

High-energy e+e−e^+e^- 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

The Induced Charge Generated By The Potential Well In Graphene

The induced charge density, $\rho_{ind}(\bm r)$, generated in graphene by the potential well of the finite radius $R$ is considered. The result for $\rho_{ind}(\bm r)$ is derived for large distances $r\gg R$. We also obtained the induced charges outside of the radius $r\gg R$ and inside of this radius for subcritical and supercritical regimes. The consideration is based on the convenient representation of the induced charge density via the Green's function of electron in the field.Comment: 12 pages, 2 figures, version published in Phys.Rev.

Screening of Coulomb Impurities in Graphene

We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, $Z|e|/r$, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter $Z\alpha$, where $\alpha$ is the "fine structure constant" of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge $Z_{eff}$, determined by the localized induced charge. We find that an impurity with bare charge Z=1 remains subcritical, $Z_{eff} \alpha < 1/2$, for any $\alpha$, while impurities with $Z=2,3$ and higher can become supercritical at certain values of $\alpha$.Comment: 4 pages, 2 figure

Coulomb corrections to the Delbrueck scattering amplitude at low energies

In this article, we study the Coulomb corrections to the Delbrueck scattering amplitude. We consider the limit when the energy of the photon is much less than the electron mass. The calculations are carried out in the coordinate representation using the exact relativistic Green function of an electron in a Coulomb field. The resulting relative corrections are of the order of a few percent for scattering on for a large charge of the nucleus. We compare the corrections with the corresponding ones calculated through the dispersion integral of the pair production cross section and also with the magnetic loop contribution to the g-factor of a bound electron. The last one is in a good agreement with our results but the corrections calculated through the dispersion relation are not.Comment: 8 pages, 6 figure

Nature of the Darwin term and (Zα)4m3/M2{(Z\alpha)^4 m^3/M^2} contribution to the Lamb shift for an arbitrary spin of the nucleus

The contact Darwin term is demonstrated to be of the same origin as the spin-orbit interaction. The $(Z\alpha)^4 m^3/M^2$ correction to the Lamb shift, generated by the Darwin term, is found for an arbitrary nonvanishing spin of the nucleus, both half-integer and integer. There is also a contribution of the same nature to the nuclear quadrupole moment.Comment: 9 pages, latex, no figure

Induced Current and Aharonov-Bohm Effect in Graphene

The effect of vacuum polarization in the field of an infinitesimally thin solenoid at distances much larger than the radius of solenoid is investigated. The induced charge density and induced current are calculated. Though the induced charge density turned out to be zero, the induced current is finite periodical function of the magnetic flux $\Phi$. The expression for this function is found exactly in a value of the flux. The induced current is equal to zero at the integer values of $\Phi/\Phi_0$ as well as at half-integer values of this ratio, where $\Phi_0=2\pi\hbar c/e$ is the elementary magnetic flux. The latter is a consequence of the Furry theorem and periodicity of the induced current with respect to magnetic flux. As an example we consider the graphene in the field of solenoid perpendicular to the plane of a sample.Comment: 3 pages, 1 figure, version accepted to Phys. Rev.