Abstract
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|.
Original language | English (US) |
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Title of host publication | The Stability of Matter |
Subtitle of host publication | From Atoms to Stars: Fourth Edition |
Publisher | Springer Berlin Heidelberg |
Pages | 471-484 |
Number of pages | 14 |
ISBN (Print) | 3540420835, 9783540222125 |
DOIs | |
State | Published - 2005 |
All Science Journal Classification (ASJC) codes
- General Physics and Astronomy