One-electron relativistic molecules with coulomb interaction

Ingrid Daubechies; Elliott H. Lieb

doi:10.1007/3-540-27056-6_33

One-electron relativistic molecules with coulomb interaction

Ingrid Daubechies, Elliott H. Lieb

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

As an approximation to a relativistic one-electron molecule, we study the operator H=(-Δ+m²)^1/2-e² Z _j|x-R_j|^-1 with Z_j0, 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 e²ΣZ_j>2/π in the sense that E ₀=inf spec (H) → - ∞ as the R_j → 0, all j. We prove that the nuclear Coulomb repulsion more than restores stability; namely E₀+0.069e² Z_iZ_j|R _i-R_j|^-10. We also show that E₀ is an increasing function of the internuclear distances |R_i-R _j|.

Original language	English (US)
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	https://doi.org/10.1007/3-540-27056-6_33
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1007/3-540-27056-6_33

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title = "One-electron relativistic molecules with coulomb interaction",

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|.",

author = "Ingrid Daubechies and Lieb, \{Elliott H.\}",

year = "2005",

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T1 - One-electron relativistic molecules with coulomb interaction

AU - Daubechies, Ingrid

AU - Lieb, Elliott H.

PY - 2005

Y1 - 2005

N2 - 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|.

AB - 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|.

UR - https://www.scopus.com/pages/publications/84892268860

UR - https://www.scopus.com/inward/citedby.url?scp=84892268860&partnerID=8YFLogxK

U2 - 10.1007/3-540-27056-6_33

DO - 10.1007/3-540-27056-6_33

M3 - Chapter

AN - SCOPUS:84892268860

SN - 3540420835

SN - 9783540222125

SP - 471

EP - 484

BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

One-electron relativistic molecules with coulomb interaction

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