One-electron relativistic molecules with coulomb interaction

As an approximation to a relativistic one-electron molecule, we study the operator H=(-Δ+m²)^1/2-e² Z j|x-Rj|^-1 with Zj0, e ^-2=137.04. H is bounded below if and only if e² Z j>2/π, all j. Assuming this condition, the system is unstable when e²ΣZj>2/π in the sense that E 0=inf spec (H) → - ∞ as the Rj → 0, all j. We prove that the nuclear Coulomb repulsion more than restores stability; namely E0+0.069e² ZiZj|R i-Rj|^-10. We also show that E0 is an increasing function of the internuclear distances |Ri-R j|. © 2005 Springer-Verlag Berlin Heidelberg New York.

Duke Scholars

Author Ingrid Daubechies Mathematics