The essential spectrum of relativistic one-electron ions in the Jansen-Hess model

It is shown that the essential spectrum of the pseudo-relativistic Dirac operator according to Jansen and Hess which includes the Coulomb potential up to second order, extends from mc to infinity when the nuclear charge is below the critical value Ze ≈ 1.006. There is also no singular continuous spectrum in that case, and for small Z no embedded eigenvalues. This work is an extension of investigations by Evans, Perry and Siedentop on the Brown-Ravenhall operator which is of first order in the potential. It is based on the fact, recently proven by Brummelhuis, Siedentop and Stockmeyer, that the spectrum of the Jansen-Hess operator is bounded from below for subcritical charges Z.