Random matrix analysis of the monopole strength distribution in ²⁰⁸Pb

We study statistical properties of the 0⁺ spectrum of ²⁰⁸Pb 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 Δ₃(L) which is shifted towards the random matrix limit of the Gaussian orthogonal ensembles.