Random matrix analysis of the monopole strength distribution in $^{208}$Pb

TL;DR

This paper investigates the statistical properties of the $0^+$ spectrum in $^{208}$Pb using random matrix theory and Skyrme interactions, highlighting the importance of phonon-phonon coupling for accurate strength distribution modeling.

Contribution

It introduces a detailed analysis of the $0^+$ spectrum in $^{208}$Pb using random matrix theory and emphasizes the role of phonon-phonon coupling in spectral properties.

Findings

Phonon-phonon coupling affects the strength distribution.

Spectral rigidity shifts towards Gaussian orthogonal ensemble predictions.

The centroid of the monopole resonance is determined by one phonon excitations.

Abstract

We study statistical properties of the $0^+$ spectrum of $^{208}$Pb in the energy region $E_x\leq20$ 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 a 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.