The energy moments of spectral distributions are used to investigate the structure of spectroscopic calculations. Eigenvalue distributions are used to predict energy spectra, which are compared with the results of matrix diagonalization. The nature of the corresponding eigenvectors is similarly analyzed. The propagation of moments for scalar and configuration distributions is illustrated throughout the $\mathrm{sd}$ shell. These scalar moments are then used to estimate the trend in theoretical binding energies for these nuclei and in turn are compared with empirical data. Finally, we investigate the dependence of the energy and wave function of the ground state of ${\mathrm{O}}^{16}$ upon the vector space underlying a theoretical calculation. The unrenormalized Kuo-Brown matrix elements are employed in this analysis, and the role of multiple particle-hole excitations is discussed.

• Received 8 May 1970

DOI:https://doi.org/10.1103/PhysRevC.3.117