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 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 π = 1 − and 38 with J π = 1 + ) at excitation energies Ex 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 − 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 − levels suggests a sizable collectivity of the PDR indeed.

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

“…8 and 9 that level energies near dynamical U(5) and SO (9) symmetries in the spd -IBA model seem more regular. Similar to the predictions made by J. Enders in [103], the spectra of medium mass nuclei for dipole states seem almost regular, while for the predictions in light nuclei made by B. Dietz in [72], the spectra for negative and positive parity states are almost regular and chaotic, respectively. It is verified that the NNSD is governed by the interplay between the GDR and the pairing interaction for BAE calculated from the spd -IBA model.…”

“…Depending on the details of the chaoticity, some simple distributions have been proposed for describing the spectral statistics of nuclei [72][73][74][75][76][77][78] with less fitting parameters. For example, in what follows we use the socalled Berry-Robnik Distribution (BRD), which interpolates between Poisson statistics with q=1 and GOE with q=0, respectively.…”

Soft breathing modes in neutron-rich nuclei with the subtracted second random-phase approximation

“…[1][2][3][4][5][6][7][8][9] and Refs. [10,11] for review articles) and their complex nature has been extensively discussed and interpreted in terms of oscillations of a neutron skin against a core, mixing of isoscalar and isovector nature, coupling with a toroidal motion, single-particle versus collective behavior, deformation effects (see for instance some recent publications [12][13][14][15][16][17][18][19][20][21][22][23]). Experimental evidence on the existence of low-energy excitations related to a neutron excess was also reported in Refs.…”

Valence-shell dependence of the pygmy dipole resonance: E1 strength difference in Cr50,54

“…with two valence neutron holes, the PDR apparently has its origin in a few-nucleon effect. A statistical analysis [56] had indicated instead, that the PDR states in the stable Cr isotopes might have the properties of a collective mode. This remains an open question which requires further investigation.…”