A general hamiltonian H of electrons in finite concentration, interact
ing via any two-body coupling inside a crystal of arbitrary dimension,
is considered. The electron motion is described in the Hilbert space
S-phi, spanned by a basis of Slater determinants of one-electron Bloch
wave functions. The diagonal part of H in the Slater determinant basi
s is called H-D. Electron pairs of total momentum K and projected spin
zeta = 0, +/-1 are considered in this work. The Schrodinger equation
(H - epsilon)psi = 0 is shown to include a class of solutions psi, eps
ilon such that (H-D - epsilon)psi = 0. It is also shown that this clas
s of eigenvectors cannot sustain any kind of long-range order and that
the associated two-body correlation functions, accordingly, decay as
power laws.