Scaling Properties of Nuclear Giant Resonance Transition Probabilities

Multifractal scaling analysis of nuclear giant resonance transition probability distributions is performed within the approximation which takes into account the one-particle-one-hole (1p-1h) and 2p-2h states. A new measure to determine the fractal dimensions of the spectra is introduced. It is found that chaotic dynamics governing the decay leads to non-trivial multifractal scaling properties. Such a kind of scaling is absent in the case of regular dynamics. The degree of collectivity is another element which worsens the scaling.