Abstract
Polyatomic molecules are studied in the limit as the total charge Z becomes infinite with the number of nuclei and their charge ratios fixed. It is shown that, in the Born-Oppenheimer approximation, if such a system has a stable bound state then it is asymptotically neutral in the sense that it satisfies the inequality |Z − N| < C 1Z1−ε where N denotes the number of electrons, C 1 is a positive constant and we can choose ε = 1/7. The proof uses comparisons with Thomas-Fermi theory, as in the proof in [23] of a similar result for diatomic molecules. A critical element in the proof is a demonstration that, for a stable configuration, all internuclear distances are bounded below by C 2 Z (−1/3)(1−ε) for some positive constant C 2.
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Ruskai, M.B., Solovej, J.P. (1992). Asymptotic Neutrality of Polyatomic Molecules. In: Balslev, E. (eds) Schrödinger Operators The Quantum Mechanical Many-Body Problem. Lecture Notes in Physics, vol 403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55490-4_10
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DOI: https://doi.org/10.1007/3-540-55490-4_10
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