The effect of the long-wavelength approximation on the one-photon transition rates for heavy quarkonia

A simple model of the one-photon transitions in heavy quarkonia is presented based on a quark-antiquark Hamiltonian with spin-dependent potential terms. qq-bar bound state wavefunctions are obtained treating the whole Hamiltonian nonperturbatively, including the tensor term. The one-photon transition rates are calculated using these wave functions and a non-relativistic electromagnetic current density operator. All the relevant terms in the multipole decomposition are taken into account and the results are compared with those obtained after performing the long-wavelength limit as well as with results given by other authors. (author)