Abstract
Analytical studies with the TBRE ensemble, supplemented by numerical calculations with realistic interactions show that for large particle numbers, the bivariate cumulants (k rs ) defined for the Hamiltonian operator (H) and theJ z operator, are very small; ∥k rs ∥≲0.3 for 3≦r+s≦6. As a result the expansions around a bivariate normal density are meaningful for the fixed-M densities (ρ(E,M)). We adopt a bivariate Edgeworth expansion forρ(E,M) and give a compact form for the same. Finally using thisρ(E,M) (which also define fixed-J densities uniquely), new series expansions are given for fixed-M (and hence for fixed-J) averages of the powers ofH and also for the spin cut-off factors.
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Work supported in part by the U.S. Department of Energy
The author thanks Prof. J.B. French for provoking his interest on the subject of bivariate distributions and also for many useful discussions.
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Kota, V.K.B. Bivariate distributions in statistical spectroscopy studies: Fixed-J level densities, fixed-J averages and spin cut-off factors. Z Physik A 315, 91–98 (1984). https://doi.org/10.1007/BF01436213
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DOI: https://doi.org/10.1007/BF01436213