On the relationship between single-particle overlap functions, natural orbitals and the one-body density matrix for many-fermion systems

We consider the groundstate of a system of A interacting fermions and construct relationships connecting the asymptotic behaviour of the one-body density matrix with the overlap functions of the eigenstates in the (A−1)-particle system. It is shown that the knowledge of the exact one-body density matrix is sufficient to determine the overlap functions, spectroscopic factors and separation energies of the bound (A−1)-particle eigenstates. We also derive sumrules linking the overlap functions with the natural orbitals of the system.