98-436 Balinsky A.A., Evans W.D.

Stability of one-electron molecules in the Brown-Ravenhall model (61K, LaTex 2e) Jun 12, 98

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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 $\alpha Z_k \leq \alpha Z_c = \frac{2}{\pi /2 + 2/ \pi}$ , $k=1,2, \ldots,K$, \ $\bB_{1,K} \geq \operatorname{const} \cdotp K$.

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