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potential. A change of 1 % in λ leads to a significant change of 75 % in the cross sections. At the minimum of the Na$_{3}$ potential, a change of 1 % corresponds ap- proximately to 10 K. At present, ab initio calculations of PESs cannot be done with such accuracy. Thus it ap- pears that it is difficult to get an accuracy better than two orders of magnitude in the cross sections for Na + Na$_{2}$( v = 1 , j = 0) collisions. However, for v = 2 and 3, the total cross sections show a weaker dependence on the three-body term. The state-resolved cross sections do not show strong dependence on the three-body term, compared to collisions of molecules in v = 1. 

Fig. 20 shows the dependence of the state-to-state cross sections on the three body term for the reaction Na + Na$_{2}$( v = 3 , j = 0) → Na + Na$_{2}$( v$_{f}$ = 2 , 1 , 0 , j$_{f}$ ) at a col- lision energy of 10 $_{−}$9 K. The oscillations in the cross sec- tions, when λ is modified, are due to Feshbach resonances which arise when a triatomic quasibound state (or a vir- tual state) crosses the energy threshold as the strength of the interaction potential is decreased (increased). When such a Feshbach resonance occurs, Cvitaˇs et al. [97] have argued, strong resonant peaks appear in the cross sec- tions if inelastic couplings are weak. In contrast, weak oscillations of one order of magnitude at best appear 

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when inelastic couplings are strong, as in alkali-metal trimer systems. A generalization of this effect has been discussed by Hutson [114]. Larger modifications of the three-body term affect the cross sections significantly. This can also be seen in Fig. 21 for Li + Li$_{2}$ collisions [96] in which the three-body term is excluded from the dy- namics calculation. The state-to-state cross sections ex- hibit a stronger dependence on the three body term. 

