Curvature theorem for scattering states in charged systems

Abstract

Under a $(2,N\ensuremath{-}2)$ factorization assumption for many-electron states, a curvature theorem is proposed that relates the zero-separation value and curvature of two-particle positional correlation functions in quantum many-body systems with Coulomb interactions. Unlike the first derivative counterpart, true for all states, the curvature theorem holds for scattering states. It can be used to derive new sum rules for partial structure factors. By way of application, a discussion of the theorem and its possible use in developing a new criterion for the bound-state transition in charged systems is given, and supporting arguments are presented both at the single-particle and many-particle level.