The Two-Body Random Ensemble in Nuclei

Abstract

Combining analytical and numerical methods, we investigate properties of the two-body random ensemble (TBRE). We compare the TBRE with the Gaussian orthogonal ensemble of random matrices. Using the geometric properties of the nuclear shell model, we discuss the information content of nuclear spectra, and gain insight in the difficulties encountered when fitting the effective interaction. We exhibit the existence of correlations between spectral widths pertaining to different quantum numbers. Using these results, we deduce the preponderance of spin-zero ground states in the TBRE. We demonstrate the existence of correlations between spectra with different quantum numbers and/or in different nuclei.

16 pages, 13 figures

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Cited by in corpus (14)

• Random Matrices and Chaos in Nuclear Physics
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Random Matrices and Chaos in Nuclear Spectra
• A new puzzle for random interaction
• Strong Linear Correlation Between Eigenvalues and Diagonal Matrix Elements
• Lowest Eigenvalues of Random Hamiltonians
• Abundance of Ground States with Positive Parity
• Nuclear Masses, Chaos, and the Residual Interaction
• A smooth transition towards a Tracy-Widom distribution for the largest eigenvalue of interacting $k$-body fermionic Embedded Gaussian Ensembles
• Level Repulsion in Constrained Gaussian Random-Matrix Ensembles
• Lowest eigenvalue of the nuclear shell model Hamiltonian
• Model space truncation in shell-model fits
• Correlations between spectra with different symmetry: any chance to be observed?
• Eigenvalues correlations and the distribution of ground state angular momenta for random many-body quantum systems