Quantum Effect on Collisions in Electron-positron Plasmas

Abstract

Quantum effects on the electron-positron scattering are investigated in electron-positron plasmas. The corrected Kelbg potential, taking into account the quantum effects, is applied to describe the electron-positron interaction potential in electron-positron plasmas. The Bom approximation is considered to obtain high-energy electron-positron scattering cross sections. The results show that the differential electron-positron scattering cross sections increase with increasing thermal de Broglie wavelength, i.e., decreasing plasma temperature. The differential electron-positron scattering cross sections decreases with increasing collision energy. It is also found that the quantum effects on the differential scattering cross section are small for forward and backward scattering angles.Key words: Electron-positron Plasmas; Electron-positron Collisions.Atomic collision processes [1 -4] in plasmas have been of great interests since these processes can be used for plasma diagnostics. Collision processes in volving positrons and electrons have received much attention since these processes have many applica tions in atomic, plasma physics, and astrophysics [5,6 ]. Electron-positron collisions can also contribute to the collective effects for the bremsstrahlung in the case of electron-positron collisions. Such mass-sym metrical plasma systems may be observed in lab oratory [7,8 ] and astrophysical [5,6 ] plasmas. In weakly coupled plasmas, the collision processes have been investigated using the Debye-Hückel potential with various methods depending on the collision sys tems [9, 10]. The plasmas described by the DebyeHiickel model are called ideal plasmas since the av erage energy of interaction between particles is small compared to the average kinetic energy of the par ticles [11]. However, in the region of partial degen eration and strong coupling, the interaction potential differs from a pure Coulomb or screened Coulomb potential because of the strong coupling and quantum effects of nonideal particle interaction. In the present paper we investigate quantum effects on high-energy electron-positron collisions in a mass-symmetrical pair plasma. An effective potential model called the corrected Kelbg potential [12], including the classi cal effect as well as the quantum-mechanical effect such as the Heisenberg principle and the Pauli ex clusion principle is applied to describe the interaction potential in electron-positron plasmas. The first-order Bom approximation is applied to obtain the differen tial scattering cross section as a function of the thermal de Broglie wavelength, scattering angle, and collision energy.For a potential scattering, the differential scattering cross section der [ 1 1 ] is defined bŷwhere dJ? is the differential solid angle and /( J ? ) is the scattering amplitude. The Bom approxima tion is known to be very reliable to describe ini tial and final states of the collision system for highenergy collisions, i.e., E » Ry where E(= p v 2/2) is the collisions energy, p the reduced mass of the collision...