Localization of the essential spectrum for relativistic $N$-electron ions and atoms

Abstract

The HVZ theorem is proven for the pseudorelativistic $N$-electron Jansen-Hess operator $(2\le N\le Z)$ which acts on the spinor Hilbert space $\mathcal{A}(H_1({\mathbb{R}}^3)\otimes {\mathbb{C}}^4{)}^N$ where $\mathcal{A}$ denotes antisymmetrization with respect to particle exchange. This 'no pair' operator results from the decoupling of the electron and positron degrees of freedom up to second order in the central potential strength $\gamma =Z{e}^2$.