Degenerate Wannier Theory for Multiple Ionization

It is shown that the cross section for multiple breakup of a system into charged fragments near the threshold energy $\epsilon =0\mathrm{}$ follows a power law modified by logarithmic correction terms if the system possesses degenerate normal mode frequencies about the fixed point of the equilibrium configuration. For more than two identical particles, e.g., a multielectron atom, this will be the generic case since the equilibrium configuration is highly symmetric. The modified threshold law is derived using consistently the properties of the classical monodromy matrix about the fixed point to formulate the threshold cross section.