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The European Physical Journal A

Random matrix structure of nuclear shell model Hamiltonian matrices and comparison with an atomic example

Manan Vyas, V. K. B. Kota

Published Jun 16, 2010• 8 citations
Publisher
DOI
10.1140/epja/i2010-10991-1

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Conventional diagonalization methods to calculate nuclear energy levels in the framework of the configuration-interaction (CI) shell model approach are prohibited in very large model spaces. The shell model Monte Carlo (SMMC) is a powerful technique for calculating thermal and ground-state observables of nuclei in very large model spaces, but it is challenging to extract nuclear spectra in this approach. We present a novel method to extract low-lying energy levels for given values of a set of good quantum numbers such as spin and parity. The method is based on imaginary-time one-body density correlation matrices that satisfy asymptotically a generalized eigenvalue problem. We validate the method in a light nucleus that allows comparison with exact diagonalization results of the CI shell model Hamiltonian. The method is applicable to other finite-size quantum many-body systems that can be described within a CI shell model approach.
Nuclear energy levels are usually calculated using conventional diagonalization methods in the framework of the configuration-interaction (CI) shell model but these methods are prohibited in very large model spaces. The shell model Monte Carlo (SMMC) method is a powerful technique for calculating thermal and ground-state observables of nuclei in very large model spaces, but it is challenging to extract nuclear spectra in this approach. We present a novel method to extract within SMMC low-lying energy levels for given values of a set of good quantum numbers such as spin and parity. The method is based on imaginary-time correlation matrices (ITCMs) of one-body densities that satisfy asymptotically a generalized eigenvalue problem. We validate the method in a light nucleus that allows comparison with exact diagonalization results of the CI shell-model Hamiltonian. The method is broadly applicable to quantum many-body systems in other disciplines.
We consider statistical and correlation properties of overlap integrals of internal states and of distortion matrices in a moving basis which depends on global coordinates parametrizing different configurations of a nuclear system (for example, in heavy-ion-induced reactions or in fission). Analytic expressions for the form and scale of correlation damping are obtained. A mixing of simple (shell) states is taken into account within the framework of the model of random matrices. The formalism of the statistical model is modified in order to include explicitly correlations of random matrices corresponding to different configurations of the system.