Nuclear Structure under Random InteractionsNo Access

SPECTRAL DISTRIBUTION ANALYSIS OF RANDOM INTERACTIONS WITH J-SYMMETRY AND ITS EXTENSIONS

V. K. B. KOTA

Physical Research Laboratory, Ahmedabad, 380009, India

Department of Physics, Laurentian University, Sudbury ON P3E 2C6, Canada

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MANAN VYAS

Physical Research Laboratory, Ahmedabad, 380009, India

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, and

K. B. K. MAYYA

Physical Research Laboratory, Ahmedabad, 380009, India

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https://doi.org/10.1142/S0218301308011951Cited by:10 (Source: Crossref)

Abstract

Spectral distribution theory, based on average-fluctuation separation and trace propagation, is applied in the analysis of some properties of a system of m (identical) nucleons in shell model j-orbits with random interactions preserving angular momentum J-symmetry. Employing the bivariate Gaussian form with Edgeworth corrections for fixed E (energy) and M (J_z eigenvalue) density of states ρ(E,M), analytical results, in the form of expansions to order [J(J+1)]², are derived for energy centroids E_c(m,J) and spectral variances σ²(m,J). They are used to study distribution of spectral widths, J=0 preponderance in energy centroids, lower order cross correlations in states with different J's and so on. Also, an expansion is obtained for occupation probabilities over spaces with fixed M. All the results obtained with spectral distribution theory compare well with those obtained recently using quite different methods. In addition, using trace propagation methods, a regular feature, that they are nearly constant, of spectral variances generated by random interactions is demonstrated using several examples. These open a new window to study regular structures generated by random interactions.

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