BINDING-ENERGIES OF WEAKLY BOUND SYSTEMS FROM COMPLEX DIMENSIONAL SCALING

In the limit of infinite spatial dimension D, the particles of a system become perfectly localized at the minimum of an effective potential surface. Perturbation theory in 1/D has been used successfully to predict binding energies and electronic structure in the physical three-dimensional space. For weakly bound systems which are neutral if one particle is removed the large dimensional approach has not been applicable because the effective potential surface exhibits a saddle point rather than a global minimum. We show that the extension to complex dimensional scaling can theoretically handle this situation and gives good practical estimates for the binding energies of three-particle Coulomb systems, calculated here as an application of the new method.