Many-body atomic potentials in Thomas-Fermi theory

Rafael Benguria; Elliott H. Lieb

doi:10.1007/3-540-27056-6_23

Many-body atomic potentials in Thomas-Fermi theory

Rafael Benguria, Elliott H. Lieb

Mathematics

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

Abstract

Many-body atomic potentials, ε, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ε(1, 2) ≡ E(1, 2) - E(1) - E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (-1)ⁿ for all co-ordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ε's, when truncated at the n-body terms, has the sign (-1)ⁿ⁺¹.

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	317-328
Number of pages	12
ISBN (Print)	3540420835, 9783540222125
DOIs	https://doi.org/10.1007/3-540-27056-6_23
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1007/3-540-27056-6_23

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title = "Many-body atomic potentials in Thomas-Fermi theory",

abstract = "Many-body atomic potentials, ε, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ε(1, 2) ≡ E(1, 2) - E(1) - E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (-1)n for all co-ordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ε's, when truncated at the n-body terms, has the sign (-1)n+1.",

author = "Rafael Benguria and Lieb, \{Elliott H.\}",

year = "2005",

doi = "10.1007/3-540-27056-6\_23",

language = "English (US)",

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pages = "317--328",

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T1 - Many-body atomic potentials in Thomas-Fermi theory

AU - Benguria, Rafael

AU - Lieb, Elliott H.

PY - 2005

Y1 - 2005

N2 - Many-body atomic potentials, ε, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ε(1, 2) ≡ E(1, 2) - E(1) - E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (-1)n for all co-ordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ε's, when truncated at the n-body terms, has the sign (-1)n+1.

AB - Many-body atomic potentials, ε, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ε(1, 2) ≡ E(1, 2) - E(1) - E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (-1)n for all co-ordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ε's, when truncated at the n-body terms, has the sign (-1)n+1.

UR - https://www.scopus.com/pages/publications/84892328098

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M3 - Chapter

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SN - 3540420835

SN - 9783540222125

SP - 317

EP - 328

BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

Many-body atomic potentials in Thomas-Fermi theory

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