Using computer simulations we investigate the microscopic structure of the
singular director field within a nematic droplet. As a theoretical model fo
r nematic liquid crystals we take hard spherocylinders. To induce an overal
l topological charge, the particles are either confined to a two-dimensiona
l circular cavity with homeotropic boundary or to the surface of a three-di
mensional sphere. Both systems exhibit half-integer topological point defec
ts. The isotropic defect core has a radius of the order of one particle len
gth and is surrounded by free-standing density oscillations. The effective
interaction between two defects is investigated. All results should be expe
rimentally observable in thin sheets of colloidal liquid crystals.