发表机构
Beijing Institute of Technology（北京理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在双中心Thomas-Fermi-Dirac-von Weizsäcker理论中证明了电离猜想的一个渐近形式，给出了束缚电子数的上界，并指出结果可推广至任意固定核数。
AI 中文摘要
Thomas-Fermi-Dirac-von Weizsäcker模型的电离猜想询问给定核构型能束缚多少个电子。迄今为止，只有单中心情形由Frank、Nam和Van Den Bosch解决，而原始的分子情形仍然悬而未决。我们在双中心情形下推进了这一猜想。我们证明，对于总电荷为$Z$的两个不同原子核，束缚电子数$N$满足$N\le Z+C Z^{153/154}(1+\log Z)^{3/8}$，其中常数与核位置和核电荷无关。证明依赖于与中性Thomas-Fermi密度的比较，以及通过屏蔽势耦合的局部化和外部$L^1$估计。我们的结果可以推广到具有任意固定核数$K$的分子。
英文摘要
The ionization conjecture for the Thomas-Fermi-Dirac-von Weizsäcker model asks how many electrons a given nuclear configuration can bind. So far, only the single-center case has been settled by Frank, Nam, and Van Den Bosch, while the original molecular case has still remained open. We advance this conjecture in the two-center case. We prove that for two distinct nuclei of total charge $Z$, the number $N$ of bound electrons satisfies $N\le Z+C Z^{153/154}(1+\log Z)^{3/8}$, with constants independent of the nuclear positions and the nuclear charges. The proof relies on a comparison with the neutral Thomas-Fermi density and on localization and exterior $L^1$-estimates coupled through the screened potential. Our results could be extended to molecules with any fixed number $K$ of nuclei.
Comments31 pages
