Critical phenomena in atomic physics

It is shown that the threshold energy ε=0 for complete break-up of N charged particles represents a fixed point of the dynamical system. Renormalization theory akin to thermodynamical phase transitions is used to determine the exponent β of the power law for the fragmentation cross section σ(ε)∝εβ near the fixed point. In the generic case β is the ratio of two rate constants expressed in terms of Liapunov exponents which emerge from the stability analysis of the critical point. Using the derived low and the well-known high-energy behavior, a universal shape function for direct ionization by charged particles is given.