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The breakdown of Efimov universal relations between resonances andinterference features in ultracold $^{40}$K-$^{87}$Rb mixtures has sparked muchdiscussion. In this study, we investigate the atom-dimer elastic scattering andthree-body recombination (TBR) rates with $J=0$ symmetry for a$^{87}$Rb-$^{87}$Rb-$^{40}$K system to understand the mechanisms underlyingthis breakdown. We use the R-matrix propagation method in a hypersphericalcoordinate frame with the Lennard-Jones model potential describing theinteractions between atoms. We extract the atom-dimer scattering length, crosssections and three-body recombination rates with a finite intraspeciesscattering length. An atom-dimer elastic scattering resonance at negativeinterspecies scattering length is found, which is due to the presence of thenear-threshold trimer state at the atom-dimer threshold ($^{40}$K +$^{87}$Rb$^{87}$Rb). In addition, we predict an Efimov recombination minima atpositive interspecies scattering length, which is outside the range of previousmeasurements. Our calculations show that the breakdown of the universalrelations predicted by zero-range theory can be attributed to the effectiverange corrections and finite intraspecies scattering length. The presentresults help elucidate the universal relations between Efimov features as wellas the importance of finite-range corrections for mixed systems.

Universal Three-Body Physics for Ultracold $^{87}$Rb-$^{40}$K Mixtures with Finite-range Interactions