Random matrix analysis of the monopole strength distribution in 208Pb

We study statistical properties of the 0(+) spectrum of Pb-208 in the energy region E (x) <= 20 MeV. We use the Skyrme interaction SLy4 as our model Hamiltonian to create a single-particle spectrum and to analyze excited states. The finite-rank separable approximation for the particle-hole interaction enables us to perform the calculations in large configuration spaces. We show that while the position of the monopole resonance centroid is determined by one-phonon excitations of 0(+), the phonon-phonon coupling is crucial for the description of the strength distribution of the 0(+) spectrum. In fact, this coupling has an impact on the spectral rigidity Delta(3)(L) which is shifted towards the random matrix limit of the Gaussian orthogonal ensembles.