Chaos and regularity in the spectra of the low-lying dipole excitations of Cr50,52,54

Abstract

Recent high-resolution nuclear resonance fluorescence experiments performed on the even-even Chromium isotopes $^{50,52,54}\mathrm{Cr}$ have lead to the identification (energy, spin, parity, and transition strength) of altogether 108 nuclear levels of spin $J=1$ (70 levels with ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}$ and 38 with ${J}^{\ensuremath{\pi}}={1}^{+}$) at excitation energies ${E}_{x}$ ranging roughly from 4.5 to 9.7 MeV. In this region just above the orbital magnetic-dipole scissors mode, sizable spin-flip magnetic-dipole strength as well as electric-dipole strength belonging to the pygmy dipole resonance (PDR) is expected. Using statistical measures for short- and long-range correlations, we perform an analysis of the fluctuation properties in the subspectra of the energy levels and also of the distributions of their respective dipole transition strengths. We compare the results with those of a random matrix ensemble interpolating between Poisson statistics generally describing the fluctuation properties in the energy spectra of many-body systems with collective, i.e., regular motion of the particles and the Gaussian orthogonal ensemble (GOE) for complex (i.e., chaotic) behavior. This comparison reveals that the spectral properties of the ${1}^{+}$ states are close to the GOE results while those of the ${1}^{\ensuremath{-}}$ states are closer to Poisson. This is confirmed by an analysis of the spectral fluctuations based on the method of Bayesian inference and corroborated by large-scale shell-model and quasiparticle-phonon model calculations, respectively. The nearly Poissonian behavior of the ${1}^{\ensuremath{-}}$ levels suggests a sizable collectivity of the PDR indeed.