In heavy nuclei, the structure generating the slow-neutron resonance spectrum extends downward in energy to ~(1–2) MeV excitation and, of course, upward as well until particle emission becomes significant, thereby generating an Embedded Gaussian Orthogonal Ensemble (EGOE) spectrum built on a secular mean-density function. In this extended chaotic domain, principles and methods for the calculation of one-point quantities (e.g., level densities, spin-cutoff factors, occupancies, etc.,) have been well developed during the last several years. The economy and the resultant generic forms follow from the dominance of unitary symmetries, central limit theorems, and quantum chaos. In this paper, techniques used for level densities are illustrated by a detailed study of several heavy nuclei, the input data being taken from the observed low-lying spectrum and the far-separated neutron-resonance spectrum, this in itself saying much about long-range spectral rigidity. Explicit forms for the interacting particle state densities, expectation values, and expectation-value densities of operators in Hamiltonian eigenstates are given. Extension of the formalism to two-point functions that deal with spectral fluctuations, transition strengths, and analysis of measures for broken symmetries and which involve the same formal structure is indicated; higher order correlation functions are of little immediate interest because they define quantities only rarely measurable.PACS Nos.: 21.10Ma, 21.60Cs, 24.60–k, 24.60.Lz
Level densities of
Ge74,76
from compound nuclear reactions