The Origin of Extra Modes in (VO)₂P₂O₇

Recent inelastic neutron scattering experiments on (VO)_2P_2O_7 (VOPO) have seen previously unanticipated sharp peaks in the dynamic structure factor in addition to the pair of triplet modes observed earlier. We argue that the additional features are in essence `shadows' of the previously studied features arising due to umklapp scattering, and suggest experimental tests of this proposal. The basic point is illustrated by some elementary calculations within a strong-coupling expansion for the alternating chain with the right geometry (on which the matrix element for umklapp scattering depends sensitively) taken fully into account.