Zero range potential for particles interacting via Coulomb potential: application to electron positron annihilation

The zero range potential is constructed for a system of two particles interacting via the Coulomb potential. The singular part of the asymptote of the wave function at the origin which is caused by the common effect of the zero range potential singularity and of the Coulomb potential is explicitly calculated by using the Lippmann-Schwinger type integral equation. The singular pseudo potential is constructed from the requirement that it enforces the solution to the Coulomb Schr\"odinger equation to possess the calculated asymptotic behavior at the origin. This pseudo potential is then used for constructing a model of the imaginary absorbing potential which allows to treat the annihilation process in positron electron collisions on the basis of the non relativistic Schr\"odinger equation. The functional form of the pseudo potential constructed in this paper is analogous to the well known Fermi-Breit-Huang pseudo potential. The generalization of the optical theorem on the case of the imaginary absorbing potential in presence of the Coulomb force is given in terms of the partial wave series

Production of high energy particles in laser and Coulomb fields and e^+e^- antenna

A strong laser field and the Coulomb field of a nucleus can produce e^{+}e^{-} pairs. It is shown for the first time that there is a large probability that electrons and positrons created in this process collide after one or several oscillations of the laser field. These collisions can take place at high energy resulting in several phenomena. The quasielastic collision e^{+}e^{-} -> e^{+}e^{-} allows acceleration of leptons in the laser field to higher energies. The inelastic collisions allow production of high energy photons e^{+}e^{-}-> 2 gamma and muons, e^{+}e^{-} -> mu^{+}mu^{-}. The yield of high-energy photons and muons produced via this mechanism exceeds exponentially their production through conventional direct creation in laser and Coulomb fields. A relation of the phenomena considered with the antenna-mechanism of multiphoton absorption in atoms is discussed.Comment: 4 page

Optical control of electron spin coherence in CdTe/(Cd,Mg)Te quantum wells

Optical control of the spin coherence of quantum well electrons by short laser pulses with circular or linear polarization is studied experimentally and theoretically. For that purpose the coherent electron spin dynamics in a n-doped CdTe/(Cd,Mg)Te quantum well structure was measured by time-resolved pump-probe Kerr rotation, using resonant excitation of the negatively charged exciton (trion) state. The amplitude and phase shifts of the electron spin beat signal in an external magnetic field, that are induced by laser control pulses, depend on the pump-control delay and polarization of the control relative to the pump pulse. Additive and non-additive contributions to pump-induced signal due to the control are isolated experimentally. These contributions can be well described in the framework of a two-level model for the optical excitation of the resident electron to the trion.Comment: 15 pages, 18 figure