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One-electron relativistic molecules with Coulomb interaction. (English) Zbl 0946.81522
Summary: As an approximation to a relativistic one-electron molecule, we study the operator \[ H=(-\Delta +m^2)^{1/2}-e^2 \sum ^K_{j=1}Z_j |x-R_j|^{-1} \] with \(Z_j \geq 0, e^{-2}=137.04\). \(H\) is bounded below if and only if \(e^2Z_j \leq 2/\pi\) for all \(j\). Assuming this condition, the system is unstable when \(e^2\sum Z_j >2/\pi\) in the sense that \(E_0=\inf \text{spec} H\to -\infty\) as the \(R_j\to 0\) for all \(j\). We prove that the nuclear Coulomb repulsion more than restores stability; namely \[ E_0+0.069e^2\sum _{i<j} Z_iZ_j|R_i -R_j|^{-1}\geq 0. \] We also show that \(E_0\) is an increasing function of the internuclear distances \(|R_i-R_j|\).

MSC:
81V55 Molecular physics
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