TITLE
The muonic helium atom as a classical three-body problem

AUTHORS
T.J.Stuchi$^1$, A.C.B.Antunes$^1$ and M.A.Andreu$^2$.
1) Instituto de F\'{\i}sica, Universidade Federal do Rio de Janeiro,
Caixa Postal 68.528, 21945-970 Rio de Janeiro, RJ, Brazil.
e--mail: tstuchi@if.ufrj.br
2) Dept. Matem\`atica Aplicada i An\`alisi, Univ. Barcelona,
Gran Via 585, 08007--Barcelona (Spain).
e--mail: mangel@maia.ub.es

ABSTRACT: 
We study the classical problem of the muonic helium atom, a helium atom
with one of its electrons  replaced by  a muon. Firstly, we establish 
the connection of the model with the one-dimensional frozen planetary 
approximation of the helium atom and find that there is classically 
stable motion for the configuration alpha--electron--muon, and no stable
motion for the alpha--muon--electron configuration. After that, we
introduce the restricted muonic helium problem, a model for the movement
of an electron in the potential of the alpha/muon pair moving in a
circular orbit. In this model, the equilibrium points, their associated
Lyapunov families of periodic orbits and their stability parameters have
been studied. The most interesting feature is the stability of the Halo
orbits, for a range of energy values. The vicinity of the alpha particle
is also studied examining Poincar\'e sections for increasing energy 
values showing an increase of the chaotic motion. 

