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

Angular distributions in J/ψ→ppˉπ0(η)J/\psi\to p\bar{p}\pi^{0}(\eta) decays

The differential decay rates of the processes $J/\psi\to p\bar{p}\pi^{0}$ and $J/\psi\to p\bar{p}\eta$ close to the $p\bar{p}$ threshold are calculated with the help of the $N\bar{N}$ optical potential. The same calculations are made for the decays of $\psi(2S)$. We use the potential which has been suggested to fit the cross sections of $N\bar{N}$ scattering together with $N\bar{N}$ and six pion production in $e^{+}e^{-}$ annihilation close to the $p\bar{p}$ threshold. The $p\bar{p}$ invariant mass spectra is in agreement with the available experimental data. The anisotropy of the angular distributions, which appears due to the tensor forces in the $N\bar{N}$ interaction, is predicted close to the $p\bar{p}$ threshold. This anisotropy is large enough to be investigated experimentally. Such measurements would allow one to check the accuracy of the model of $N\bar{N}$ interaction.Comment: 10 pages, 8 figure

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

New quantum-mechanical phenomenon in a model of electron-electron interaction in graphene

A quantum mechanical model of two interacting electrons in graphene is considered. We concentrate on the case of zero total momentum of the pair. We show that the dynamics of the system is very unusual. Both stationary and time-dependent problems are considered. It is shown that the complete set of the wave functions with definite energy includes the new functions, previously overlooked. The time evolution of the wave packet, corresponding to the scattering problem setup, leads to the appearance of the localized state at large time. The asymptotics of this state is found analytically. We obtain the lower bound of the life time of this state, which is connected with the breakdown of the continuous model on the lattice scale. The estimate of this bound gives one a hope to observe the localized states in the experiment.Comment: 10 pages, 2 figure