Classical Coulomb three-body problem in collinear eZe configuration

Abstract

Classical dynamics of two-electron atom and ions H$^{-}$, He, Li$^{+}$, Be$^{2+}$,... in collinear eZe configuration is investigated. It is revealed that the mass ratio $\xi$ between necleus and electron plays an important role for dynamical behaviour of these systems. With the aid of analytical tool and numeircal computation, it is shown that thanks to large mass ratio $\xi$, classical dynamics of these systems is fully chaotic, probably hyperbolic. Experimental manifestation of this finding is also proposed.Comment: Largely rewritten. 21 pages. All figures are available in http://ace.phys.h.kyoto-u.ac.jp/~sano/3-body/index.htm