Integrated Lennard-Jones Potential between a Sphere and a Thin Rod

A compact analytical form is derived via an integration approach for the interaction between a sphere and a thin rod of both finite and infinite lengths, with each object treated as a continuous medium of materials points interacting by the Lennard-Jones 12-6 potential. Expressions for the resultant forces and torques are obtained. Various asymptotic limits of the analytical sphere-rod potential are discussed.