Atomic energies from the largehyphen;dimension limit

摘要

Analytic approximations to nonrelativistic atomic ground state energies are obtained from the first two terms of the 1/Dexpansion for theNhyphen;electron atom. These two terms describe the equilibrium structure (Drarr;infin; limit) and normal mode oscillations (1/Dterm) of a completely symmetricNhyphen;dimensional configuration of localized particles. The connection between these largehyphen;Dresults and real atoms is established through the vibrational state, which is restricted by antisymmetry requirements atD=3. Convergence considerations lead us to consider three different approximations, depending on whether all, none, or part of the results obtained from the 1/Dterm are used (in addition to those obtained from theDrarr;infin; limit); the maximum errors are respectively about 8percnt;, 3percnt;, and 1percnt;. In all three approximations the dependence of neutral atom energies on the nuclear chargeZis roughlyZ12/5for physicalZ(as observed for real atoms) and roughlyZ7/3for very largeZ(in agreement with the known asymptotic result). The best approximation, which utilizes the 1/Dterm up to lowest nonvanishing order in 1/Z, is comparable in accuracy to singlehyphen;zgr; Hartreendash;Fock calculations.