Scattering and pair production by a potential barrier

Scattering and electron-positron pair production by a one-dimensional electric barrier is considered in the framework of the S-matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogolyubov transformations relating the in- and out-states are given. We show that the norm of a solution to the wave equation is determined by the largest amplitude of its asymptotic form when x(3) --> +/-infinity. For the Sauter-type potential, 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 an external held influence the phase of the wave function of the scattered particle. (C) 2004 MAIK "Nauka/Interperiodica".