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<img src='content_image/388300.jpg'>

The accuracy of the above numerical results depends on N$_{0}$ , the number controlling the total number of basis functions. As an example the values of ζ ( R , t ) are listed in Table 1 to show the dependence. 

<img src='content_image/388313.jpg'>

The convergency shown in this table is satisfying. Thus we conclude that the numerical results obtained by using N$_{0}$ = 20 are accurate enough in qualitative sense. 

A model of a device containing repeating 3-body colli- sions is proposed to study the weak interactions among neutral atoms and molecules. The advantage is twofold. (i) The initial status can be precisely controlled. (ii) The weak effect of the interaction can be accumulated and therefore easier to be detected. Numerical results support that information on interaction can be thereby extracted. 

## V. SUMMARY 

A crucial point in the device is the initial localization of the particles. If they are better localized (by increas- ing ω$_{p}$ ) and/or they are more separated from each other initially (by increasing | a j | ), the repeating 3-body col- lisions would become more explicit and be maintained longer. Furthermore, if H$_{evol}$ has a larger ω , the inter- val between two successive collisions ( ∼ π/ω ) becomes shorter, therefore the evolution would proceed swifter. 

Although the three particles are assumed to be iden- tical bosons, a generalization to fermions and/or distin- guishable particles is straight forward. In principle, the above device could also be used to study the three-body forces if they exist. 

The support from the NSFC under the grant 10874249 is appreciated. 

## Appendix A: Analytical expressions of the time-dependent densities 

The analytical expressions of the time-dependent den- sities are as follows. 

<img src='content_image/388311.jpg'>

<img src='content_image/388312.jpg'>

(iii) For the derivation of ρ$_{θ}$ ( θ, t ), a transformation is made so that r and R are transformed to r, R, θ, and the three Euler angles specifying the orientation of the triangle formed by the three particles. Then, integrating all the degrees of freedom except θ , we have 

## Acknowledgments 

