On the radiative and multiple reflection corrections of the van der Waals force between two particles/atoms: dipolar contribution

Abstract

We present a theoretical formalism based on fluctuational electrodynamics and the Maxwell-stress tensor for describing the impact of radiative and multiple reflections corrections on the van der Waals force between two nanoscale spherical particles and a pair of atoms in the dipolar approximation. Particularly, we examine the van der Waals forces for two metallic particles whose dielectric constant is represented by the Drude model, for two dielectric particles in which their material response has phononic resonances, and for two atoms with dynamic polarizabilities containing a single resonant frequency. For the metallic particles, in relation to the case in which the aforementioned effects are omitted, the van der Waals force is unchanged by the radiative corrections of the polarizabilities, whereas the mechanism of multiple reflections perturbs force about a few percentage points when the spheres nearly touch each other. In contrast to the the metallic case, the radiative corrections of the polarizabilities of the dielectric particles modify peculiarly the van der Waals force in comparison to the case where such corrections are neglected; there is a critical interparticle separation that divides two regimes: when the interparticle separation is smaller (larger) than this critical distance the force with radiative corrections is smaller (greater) than that without these corrections. Moreover, the van der Waals force is practically unchanged when effect of multiple reflections is taken into account. For the atomic case, the deviation of the van der Waals force due to multiple reflections is about a few percentage points when the interatomic separation corresponds to twice the van der Waals radius, and this deviation can reach about seventeen percent at a separation of 2.5 times the atomic radius. This work might have implications concerning the fine-tuning between theoretical and experimental outcomes of the van der Waals forces.