  The vortex-vortex interaction potential in bulk superconductors is calculated
within the Ginzburg-Landau (GL) theory and is obtained from a numerical
solution of a set of two coupled non-linear GL differential equations for the
vector potential and the superconducting order parameter, where the merger of
vortices into a giant vortex is allowed. Further, the interaction potentials
between a vortex and a giant vortex and between a vortex and an antivortex are
obtained for both type-I and type-II superconductors. Our numerical results
agree asymptotically with the analytical expressions for large inter-vortex
separations which are available in the literature. We propose new empirical
expressions valid over the full interaction range, which are fitted to our
numerical data for different values of the GL parameter.
