Issue Eur. Phys. J. D Volume 54, Number 3, September 2009 Page(s) 575 - 583 Section Atomic Physics DOI 10.1140/epjd/e2009-00191-8 Published online 30 June 2009

Eur. Phys. J. D 54, 575-583 (2009)
DOI: 10.1140/epjd/e2009-00191-8

Geometrical symmetry of atoms with applications to semiclassical calculation of energetic values

A. Popa

National Institute for Laser, Plasma and Radiation Physics, Laser Department, P.O. Box MG-36, 077125 Bucharest, Romania

ampopa@rdslink.ro

Received 1st February 2009 / Received in final form 22 April 2009 / Published online 30 June 2009

Abstract
In previous papers we proved that, for stationary systems, the geometric elements of the wave described by the Schrödinger equation, namely the characteristic surfaces and their normals, are periodic solutions of the Hamilton-Jacobi equation. In this paper we prove that the Hamilton-Jacobi equation admits periodic solutions with the same geometrical symmetries as the wave function of the system in the case of the beryllium, boron, carbon and oxygen atoms. The above property is a reflection of the fact that for a multielectron atomic system the energetically most favorable geometric configuration minimizes the electron electron repulsion, and it leads to a general semiclassical calculation method, which is in principle valid for more complex systems. We show that this property can be used to compute the energetic atomic values, with the help of the central field method which we developed in previous publications. The relative error of our method is of the order , compared with experimental data for the atoms mentioned above. The accuracy of our method is revealed by a comparison between our theoretical data and values resulting from Hartree-Fock methods.

PACS
31.15.xg - Semiclassical methods.
02.40.Yy - Geometric mechanics.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009

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