Klein’s paradox in the presence of a scalar potential

Abstract

In this paper, we have studied the Klein’s paradox in the presence of both scalar and vector potential barriers. From the corresponding Dirac equation, we have calculated the transmission and reflection coefficients. It is shown that the presence of a scalar barrier the scalar potential widens the gap between positive and negative energies and so the forbidden region. Accordingly, the Klein’s paradox disappears when the scalar barrier exceeds a critical value. Considering the problem within the framework of quantum field theory, we have calculated the related pair creation probability, the mean number of created particles and the probability of a vacuum to remain a vacuum. Then it is shown that the scalar potential cuts down the Klein range and minimizes the creation of particles; the particle creation decreases as the scalar potential increases and ceases definitely when the scalar potential reaches the critical value.