Abstract
The Tucson-Melbourne two-pion exchange three-nucleon force is split into a reducible part mediated by \ensuremath{\Delta} excitation and an irreducible part not mediated by \ensuremath{\Delta} excitation. The triton binding energy is calculated. The irreducible part of the Tucson-Melbourne force is taken into account in the calculation. Its reducible part is discarded, but regenerated by the explicit treatment of the \ensuremath{\Delta} isobar in a coupled-channel approach. The remaining irreducible part of the Tucson-Melbourne force makes a nonnegligible contribution to the triton binding energy. The strong dependence of the triton binding energy on the cutoff parameter for the \ensuremath{\pi}NN vertex in the Tucson-Melbourne force is considerably reduced.
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