Klein's paradox and the relativistic d-shell interaction in R3

Abstract

Under certain hypotheses of smallness on the regular potential V, we prove that the Dirac operator in Unexpected text node: 'R', coupled with a suitable rescaling of V, converges in the strong resolvent sense to the Hamiltonian coupled with a Unexpected text node: 'd'-shell potential supported on Unexpected text node: 'S', a bounded Unexpected text node: 'C' surface. Nevertheless, the coupling constant depends nonlinearly on the potential V; Klein’s paradox comes into play.