Scattering and pair production by a potential barrier

TL;DR

This paper analyzes scattering and electron-positron pair production in a one-dimensional potential using the S-matrix formalism, classifying solutions by frequency sign and providing explicit wave function sets for various potentials.

Contribution

It introduces a detailed classification of Dirac solutions and explicit wave functions for scattering and pair production in external potentials within the S-matrix framework.

Findings

Explicit orthonormal wave functions for various potentials

Relation between wave function norm and asymptotic amplitude

Influence of virtual vacuum processes on scattering phases

Abstract

Scattering and electron-positron pair production by a one-dimensional potential is considered in the framework of the $S-$matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogoliubov transformation relating the in- and out-states are given. We show that the norm of a solution of the wave equation is determined by the largest amplitude of its asymptotic form when $x_3\to \pm\infty$. For a number of potentials we give the explicit expressions for the complete in- and out-sets of orthonormalized wave functions. We note that in principle virtual vacuum processes in external field influence the phase of wave function of scattered particle..