Distribution of spectral widths and preponderance of spin-0 ground states in nuclei

Abstract

We use a single j-shell model with random two-body interactions to derive closed expressions for the distribution of and the correlations between spectral widths of different spins. This task is facilitated by introducing two-body operators whose squared spectral widths sum up to the squared spectral width of the random Hamiltonian. The spin-0 width is characterized by a relatively large average value and small fluctuations while the width of maximum spin has the largest average and the largest fluctuations. The approximate proportionality between widths and spectral radii explains the preponderance of spin-0 ground states.

arXiv comment4 pages, 4 eps figures

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Cited by in corpus (18)

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• Random Matrices and Chaos in Nuclear Spectra
• The Two-Body Random Ensemble in Nuclei
• A new puzzle for random interaction
• SU(N) Wigner-Racah algebra for the matrix of second moments of embedded Gaussian unitary ensemble of random matrices
• Origin of chaos in the spherical nuclear shell model: role of symmetries
• Patterns of the ground states in the presence of random interactions: nucleon systems
• Strong Linear Correlation Between Eigenvalues and Diagonal Matrix Elements
• Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI
• Emergence of symmetry from random n-body interactions
• Lowest Eigenvalues of Random Hamiltonians
• Behavior of shell-model configuration moments
• Abundance of Ground States with Positive Parity
• Regularities with random interactions in energy centroids defined by group symmetries
• Energy Centroids in the presence of random interactions
• Energy Centroids of Spin $I$ States by Random Two-body Interactions
• Lowest eigenvalue of the nuclear shell model Hamiltonian
• Eigenvalues correlations and the distribution of ground state angular momenta for random many-body quantum systems