Balinsky A.A., Evans W.D.
On the virial theorem for the relativistic operator of
Brown and Ravenhall, and the absence of embedded eigenvalues.
(43K, LaTex 2e)
ABSTRACT. A virial theorem is established for the operator
proposed by Brown and Ravenhall as a model for
relativistic one-electron atoms. As a consequence,
it is proved that the operator has no eigenvalues
greater than $\max(m c^2, 2 \alpha Z - \frac{1}{2})$,
where $\alpha$ is the fine structure constant,
for all values of the nuclear charge $Z$ below
the critical value $Z_c$: in particular there are no
eigenvalues embedded in the essential spectrum when
$Z \leq 3/4 \alpha$. Implications for the operators
in the partial wave decomposition are also described.