RIGID-ROTATOR AND FIXED-SHAPE SOLUTIONS TO THE COULOMB 3-BODY PROBLEM

Solutions to the general classical Coulomb three-body problem in the f orm of rigid-rotator and fixed-shape configurations are studied. In th e collinear case, some necessary and/or sufficient conditions for the existence of the so-called charge-symmetrical, (-)(+)(-), and charge-a symmetrical, (-)(-)(+), configurations are stated. These conditions in volve relations between the geometrical and dynamical parameters of th e system under study. The impossibility of the existence of a planar C oulombic rigid rotator is demonstrated. In the two-dimensional case, f ixed-shape solutions are studied analytically, and it is shown that, i n the three-dimensional case, only fixed-shape solutions involving a t riple collision and a static case are possible. Finally, some numerica l experimentation, mostly based upon theoretical predictions of the wo rk, is performed, and new bound (although unstable) rotating-oscillati ng orbits for systems such as the positronium negative ion and helium are found.