Distribution methods for nuclear energies, level densities, and excitation strengths

Abstract

The centroid energies and widths for configurations, both with and without a specification of isospin, are given in compact forms in which the various terms have a clear physical significance. The forms are derived by use of elementary unitary-group methods which lead to an orthogonal symmetry decomposition of the Hamiltonian, in which Hartree-Fock-like terms representing the induced single-particle energies, and other related quantities, enter in a natural way. Appropriate measures for the various terms are given and discussed. The same method is applicable to the more complicated operators encountered when dealing with excitation strengths of various kinds. Some applications are given to determining ground-state energies, orbit occupancies, and low-lying spectra for complicated systems, and comparisons made with shell-model calculations and with experiment. An account, with some elementary applications, is given of a distribution theory of level densities which takes into consideration the shell-model structures and residual interactions; to specify the densities for fixed angular momentum, the configuration distributions are used to derive the energy variation of the J z 2 and J z 4 averages, the first of these fixing the “spin cut-off factor” σ(J), and the second verifying the accuracy of the Gaussian form commonly used. Finally, an introductory account is given of the distributions of single-particle transfer and electromagnetic-transition strengths in large shell-model spaces.