Calculation of the van der Waals force between a spherical particle and an infinite cylinder

Formulae for the van der Waals attraction energy and force between a spherical particle and an infinite cylinder are derived by the method of additive summation of the pair interactions described by the potential of the general form Um=−αmρ−m. The formula of Rosenfeld and Wasan for the non-retarded vdW force between a sphere and a cylinder (m=6) is confirmed and the compact expression for the retarded force (m=7) is obtained. The comparison is given for the forces of the retarded vdW interaction between a sphere and a cylinder, another sphere, a row of spheres and a half-space. Also, the compact formulae for the energy of the vdW interaction of a point-like particle (atom, molecule) with a sphere and a cylinder are derived for the case of arbitrary m.