We develop Haag-Ruelle scattering theory for Wigner particles in local relativistic Quantum Field Theory without assuming mass gaps or any other restrictions on the spectrum of the mass operator near the particle masses. Our approach is based on the Reeh-Schlieder property of the vacuum state. It is shown that a strengthened variant of this property, concerning the relative approximation error for single-particle states, implies the existence of scattering states.