Critical phenomena in atomic physics

It is shown that the threshold energy epsilon = 0 for complete break-up of N charged particles represents a fixed point of the dynamical system. Renor malization theory akin to thermodynamical phase transitions is used to dete rmine the exponent beta of the power law for the fragmentation cross sectio n sigma(epsilon) proportional to epsilon (beta) near the fixed point. In th e generic case beta is the ratio of two rate constants expressed in terms o f Liapunov exponents which emerge from the stability analysis of the critic al point. Using the derived low and the well-known high-energy behavior, a universal shape function for direct ionization by charged particles is give n. (C) 2001 Elsevier Science B.V. All rights reserved.