Dirac operators with a spherically symmetric δ-shell interaction

Abstract

Dirac operators with a contact interaction supported by a sphere are studied restricting attention to the operators that are rotationally and space-reflection symmetric. The partial wave operators are constructed using the self-adjoint extension theory, a particular attention being paid to those among them that can be interpreted as δ-function shells of scalar and vector nature. The class of interactions for which the sphere becomes impenetrable is specified and spectral properties of the obtained Hamiltonians are discussed.