Abstract
A nonlocal energy-dependent two-body quasipotential (E2Q) is defined within the framework of the three-body Faddeev formalism. The Fourier transform of this E2Q generates an energy-dependent Yukawa-type local potential. After an appropriate average of the potential with respect to the energy, a variety of local potentials with different ranges are obtained. These include a Yukawa potential, a Van der Waals potential, and a $1/{r}^{2}$ potential. An interesting potential appears in the $\ensuremath{\pi}$$\mathrm{NN}$ system, which gives rise to the one-pion-exchange $\mathrm{NN}$ interaction. It is also found that the Yukawa potential is automatically accompanied by an additional longer-range interaction. This potential could give rise to an infinite number of bound states near the threshold above the deuteron bound state with a more interesting physics than the Efimov effect.
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