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Particle scattering and vacuum instability by exponential steps S. P. Gavrilov, D. M. Gitman, A. A. Shishmarev

By: Gavrilov, Sergey PContributor(s): Gitman, Dmitri M | Shishmarev, A. AMaterial type: ArticleArticleSubject(s): вакуумная неустойчивость | Дирака уравнения | Клейна-Гордона уравнения | неоднородное электрическое полеGenre/Form: статьи в журналах Online resources: Click here to access online In: Physical Review D Vol. 96, № 9. P. 096020-1-096020-17Abstract: Particle scattering and vacuum instability in a constant inhomogeneous electric field of particular peak configuration that consists of two (exponentially increasing and exponentially decreasing) independent parts are studied. It presents a new kind of external field where exact solutions of the Dirac and Klein-Gordon equations can be found. We obtain and analyze in- and out-solutions of the Dirac and Klein-Gordon equations in this configuration. By their help we calculate probabilities of particle scattering and characteristics of the vacuum instability. In particular, we consider in details three configurations: a smooth peak, a sharp peak, and a strongly asymmetric peak configuration. We find asymptotic expressions for total mean numbers of created particles and for vacuum-to-vacuum transition probability. We discuss a new regularization of the Klein step by the sharp peak and compare this regularization with another one given by the Sauter potential.
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Particle scattering and vacuum instability in a constant inhomogeneous electric field of particular peak configuration that consists of two (exponentially increasing and exponentially decreasing) independent parts are studied. It presents a new kind of external field where exact solutions of the Dirac and Klein-Gordon equations can be found. We obtain and analyze in- and out-solutions of the Dirac and Klein-Gordon equations in this configuration. By their help we calculate probabilities of particle scattering and characteristics of the vacuum instability. In particular, we consider in details three configurations: a smooth peak, a sharp peak, and a strongly asymmetric peak configuration. We find asymptotic expressions for total mean numbers of created particles and for vacuum-to-vacuum transition probability. We discuss a new regularization of the Klein step by the sharp peak and compare this regularization with another one given by the Sauter potential.

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