Based on the interaction energy of two particles and calculations for hydrogen (1), the constant of the interaction law is calculated for a wide range of atoms. It is done by generalising an approach with quantum mechanical perturbation theory in its dipole approximation for neutral atoms. The atoms are modelled by a meta particle, which has the same dipole moment as the real atom. Two major cases are considered: the general case for symmetric atoms and the self resonance case. The constant is given numerically for mercury.