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We predict $s-$wave elastic cross-sections $\sigma$ for low-energyatom-molecule collisions with kinetic energies up to 40 mK, for the $^4$Hecollision with weakly bound diatomic molecules formed by $^4$He with $^7$Li,$^6$Li and $^{23}$Na. Our scattering calculations are performed by usingdiatomic and triatomic molecular binding energies obtained from severalavailable realistic models as input in a renormalized zero-range model, as wellas a finite-range one-term separable potential in order to quantify therelevance of range corrections to our predictions. Of particular relevance forpossible experimental realization, we show the occurrence of a zero in $\sigma$for the collision of cold $^4$He on $^4$He$-^{23}$Na molecule below 20 mK. Alsoour results for the elastic collision $^4$He on $^4$He$-^{6,7}$Li moleculessuggest that $\sigma$ varies considerably for the realistic models studied. Asthe chosen molecules are weakly bound and the scattering energies are very low,our results are interpreted on the light of the Efimov physics, which explainsthe model independent and robustness of our predictions, despite somesensitivity on the potential range.

Scattering of cold $^4$He on $^4$He$-^{6,7}$Li and $^4$He$-^{23}$Na molecules