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arXiv:nucl-th/9410008 · Physical Review Letters

Chaos vs Thermalization in the Nuclear Shell Model

Mihai Horoi, Vladimir Zelevinsky, B. ALEX BROWN

Published Jun 26, 1995• 112 citations
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Abstract

Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean-field basis to the thermodynamical entropy found from the level density. Mean occupation numbers of single-particle orbitals agree with the Fermi-Dirac distribution despite the strong nucleon interaction.

DOI
10.1103/physrevlett.74.5194

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Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean-field basis to the thermodynamical entropy found from the level density. Mean occupation numbers of single-particle orbitals agree with the Fermi-Dirac distribution despite the strong nucleon interaction.
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Knowledge of the nuclear level density is necessary for understanding various reactions, including those in the stellar environment. Usually the combinatorics of a Fermi gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally used parameters are also compared with standard phenomenological approaches.
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An algorithm for calculating the level density for a given shell-model Hamiltonian without diagonalzation of a huge matrix is presented and explained. The level density is expressed in terms of the moments (traces) of the Hamiltonian over the restricted orbital space. The underlying physics is that of quantum chaos and intrinsic thermalization in closed systems of interacting particles. We show the examples of the approach and briefly discuss the dependence of the level density on the interaction parameters.
A theory of strongly interacting Fermi systems of a few particles is developed.At high excitation energies (a few times the single-particle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-particle basis states by the residual twobody interaction.This regime can be described as many-body quantum chaos.Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy.Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g.rare earths) and multicharged ions, molecules, clusters and quantum dots in solids.The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-particle basis states (determinants) constructed using the shell-model orbital basis.A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix.We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variables such as temperature in an isolated microscopic Fermi system of a few particles.