Balinsky A.A., Evans W.D.
Stability of one-electron molecules in the Brown-Ravenhall model
(61K, LaTex 2e)

ABSTRACT.  In appropriate units, the Brown-Ravenhall Hamiltonian for a
system of $1$ electron relativistic molecules with  $K$ fixed
nuclei having charge and position $Z_k, R_k$,
$k=1,2, \ldots,K$, is of the form $\bB_{1,K}=
\Lambda_+ \bigl( D_0 + \alpha V_c\bigr) \Lambda_+ $,
where $\Lambda_+ $ is the projection onto the
positive spectral subspace of the free Dirac operator
$D_0$ and $V_c= - \sum_{k=1}^K \frac{\alpha Z_k}{\lmod \bx-R_k
\rmod}  + \sum_{k<l, \ k,l=1}^K \frac{\alpha Z_k Z_l}{\lmod
R_k-R_l \rmod} $, with $\alpha$ Sommerfeld's fine
structure constant. It is proved that for $\alpha
Z_k \leq \alpha Z_c = \frac{2}{\pi /2 + 2/ \pi}$ ,  $k=1,2,
\ldots,K$,  \ $\bB_{1,K} \geq \operatorname{const} \cdotp K$.