MPEJ Volume 8, No. 3, 30 pp. Received: Dec 7, 2001. Accepted: Jul 3, 2002. Jakubassa-Amundsen D.H. The essential spectrum of relativistic one-electron ions in the Jansen-Hess model ABSTRACT: 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 $mc^2$ to infinity when the nuclear charge is below the critical value $Ze^2 \approx 1.006.$ 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 $Z$. http://www.maia.ub.es/mpej/Vol/8/3.ps http://www.ma.utexas.edu/mpej/Vol/8/3.ps http://mpej.unige.ch/mpej/Vol/8/3.ps