Reduction Relations for the Third and the Fourth Moments of Energy Spectra in a Many-Particle Configuration

Abstract

The third and fourth moments of energy spectra in a many-particle configuration are completely related to two-particle matrix elements, so that neither c.f.p. nor explicit diagonalization of any matrix is needed to evaluate these moments. Recah algebra and reduction relations for c.f.p. are well used. We confine ourselves, for simplicity, to jⁿ and j₁^n₁j₂^n₂ configurations of identical particles.