Abstract
We prove that the interaction among neutral atoms in Thomas-Fermi theory behaves, for large separationl, likeΓl −7. The constant Γ is independent of the atomic nuclear charges, but does depend on the relative positions of the nuclei. We also show that Π is not a simple sum of pair terms, i.e. in TF theory three and higher body terms persist into the asymptotic (inl) region.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lieb, E. H., Simon, B.: The Thomas-Fermi theory of atoms, molecules and solids. Adv. Math.23, 22–116 (1977). See also Brezis, H., Benilan, Ph.: Non-linear problems related to the Thomas-Fermi equation (in preparation); Lieb, E. H., Simon, B.: Thomas-Fermi theory revisited. Phys. Rev. Lett.31, 681–683 (1973); Lieb, E. H.: Thomas-Fermi and Hartree-Fock theory. Proc. Int. Congr. of Math., Vancouver (1974); Lieb, E. H.: The stability of matter. Rev. Mod. Phys.48, 553–569 (1976)
Benguria, R., Lieb, E. H.: Many-body atomic potentials in Thomas-Fermi theory. Ann. Phys. NY110, 34–45 (1978)
Benguria, R., Lieb, E.H.: The positivity of the pressure in Thomas-Fermi theory. Commun. math. Phys.63, 193–218 (1978)
Lee, C. E., Longmire, C. L., Rosenbluth, M. N.: Thomas-Fermi calculation of potential between atoms. Los Alamos Scientific Laboratory report (LA-5694-MS) (1974)
Sommerfeld, A.: Asymptotische Integration der Differentialgleichung des Thomas-Fermischen Atoms. Z. Physik78, 283–308 (1932)
Teller, E.: On the stability of molecules in the Thomas-Fermi theory. Rev. Mod. Phys.34, 627–631 (1962)
Trudinger, N.: Linear elliptic operators with measurable cofficients. Ann. Sc. Norm. Sup. Pisa, Ser. 3,27, 265–308 (1973)
Nirenberg, L.: Non-linear differential equations invariant under certain geometric transformations. Istit. Naz. di Alta Mat. (Bologna), Symp. Math.18, 399–405 (1976)
Casimir, H. B. C., Polder, D.: The influence of retardation on the London-van der Waals forces. Phys. Rev.73, 360–372 (1948)
Roberts, R. E.: Upper- and lower-bound energy calculations for atoms and molecules in the Thomas-Fermi theory. Phys. Rev.170, 8–11 (1968)
Firsov, O. B.: Interaction energy of atoms for small nuclear separations. Zh. Eksp. Teor. Fiz.32, 1464 (1957). English translation: Soviet Phys. JETP5, 1192–1196 (1957)
Kato, T.: Schrödinger operators with singular potentials. Isr. J. Math.13, 135–148 (1973)
Author information
Authors and Affiliations
Additional information
Communicated by J. Glimm
Work partially supported by U.S. National Science Foundation grant MCS 75 21684 A02
Rights and permissions
About this article
Cite this article
Brezis, H., Lieb, E.H. Long range atomic potentials in Thomas-Fermi theory. Commun.Math. Phys. 65, 231–246 (1979). https://doi.org/10.1007/BF01197881
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01197881