Small-energy three-body systems. V. threshold laws when Wannier theory fails

We investigate cases of Coulombic systems near the break-up threshold for which the Wannier model holds, but not Wannier theory. Making use of the classical trajectory method, we derive threshold laws for a model system of fractional charge (Z= 1/4 au) nucleus and electrons, and a real (though perhaps impractical) system of two beryllium nuclei and an antiproton. For the first system we find the threshold law of the form exp(- lambda / square root E), where E is the total energy, and for the second one a number of characteristic features above the classical threshold have been obtained. Finally we investigate numerically a realistic case of an electron and two beryllium nuclei and discuss some general features of the ionization probability above the classical threshold.