A Simple Model for the Non-Retarded Dispersive Force between an Electrically Polarizable Atom and a Magnetic Polarizable One

It is well known that for the case of two neutral but electrically polarizable atoms the consideration or not of retardation effects on the dispersive van der Waals force between them leads essentially to different power laws for the forces; while the retarded force is proportional to $1/r^8$, where $r$ is the distance between the atoms, the non-retarded force is proportional to $1/r^7$. Here we consider the (repulsive) dispersive force between an electrically polarizable atom and a magnetically polarizable one and show that, in contrast to the previous case, a quite unexpected result appears, namely: while the retarded force is still proportional to $1/r^8$, the non-retarded force is proportional to $1/r^5$. We employ a semiclassical method based on the fluctuating dipole model for both atoms.