Calculation of moments of spectral density distributions in finite-dimensional N-electron spin-adapted spaces

This paper reports a calculation of moments of spectral density distributions which are used in statistical theory of spectra of many-electron systems. The procedure lead to formulae which are fit for computer evaluations. The method is based on the determination of spin-adapted traces of powers of the Hamiltonian operator, represented in a finite-dimensional antisymmetric and spin-adapted Hilbert space. A whole study of the traces which appear in this problem is described.