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 $Z$.