ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
The self-consistent relativistic Thomas-Fermi theory of heavy positive ions with N electrons and nuclear charge Ze is shown to lead to a chemical potential μ which has the scaling property \documentclass{article}\pagestyle{empty}\begin{document}$$ \mu = Z^{4/3} F\left( {N/Z;\;\varepsilon /Z^{2/3} } \right), $$\end{document} with ∊ = α2Z2, α being the fine structure constant. Combining this with the Layzer-Bahcall expansion for the total energy E(Z, N), namely, \documentclass{article}\pagestyle{empty}\begin{document}$$ E(Z,N) = Z^2 \sum\limits_{n = 0}^\infty {\sum\limits_{m = 0}^\infty {E_{mn} (N)\varepsilon ^m Z^{ - n} } } $$\end{document} it is proved that the coefficients Enm (N) at large N have the asymptotic behavior Nn-2m/3#1/3. The corresponding result for the scaling of the relativistic Thomas-Fermi energy is \documentclass{article}\pagestyle{empty}\begin{document}$$ E_{{\rm TF}} (Z,N) = Z^{7/3} F_1 (N/Z;\varepsilon /N^{2/3} ). $$\end{document} Scaling properties of the higher order terms in Enm (N) and E(Z, N) are also proposed.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560200311
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