Positron annihilation in $e^+ -$H collision above the Positronium formation threshold

摘要

A long-standing problem to account for the electron-positron annihilation inpositron Hydrogen scattering above the Positronium formation threshold has beenresolved by the use of the three-body Faddeev formalism. The multichannelthree-body theory for scattering states in presence of a complex absorbingpotential is developed in order to compute the direct $e^+ e^-$ annihilationamplitude, the amplitude of Positronium formation and respective crosssections. A number of $e^+ e^-$ direct annihilation cross sections andPositronium formation cross sections in the energy gap between Ps$(1s)$ andH$(n=2)$ thresholds are reported for both the positron-Hydrogen incomingchannel as well as the proton-Positronium incoming channel.