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The study of Efimov features and their relationships in $^{40}$K-$^{87}$RbMixtures has generated extensive discussion, yet the discrepancy between Efimovuniversality predictions based on the zero-range approximation and experimentalobservations remains unresolved. In this study, we investigate the three-bodycollision properties with $J=0$ symmetry for a $^{87}$Rb-$^{87}$Rb-$^{40}$Ksystem on both sides of Rb-K scattering length to understand the mechanismsunderlying this discrepancy. Our approach employs the R-matrix propagationmethod within a hyperspherical coordinate frame, utilizing the Lennard-Jonesmodel potential to describe atom interactions. We predicts the existence ofthree-body shape resonances at large negative Rb-K scattering lengths, whichleads to the enhancement of three-body recombination rates. On the positiveRb-K scattering length side, we find an Efimov recombination minimum beyond therange of previous measurements. These Efimov features, combined withexperimental observations of the atom-dimer Efimov resonance, offer anopportunity to test the universality of Efimov features. Our study demonstratesthe influence of finite-range effects and non-resonant intraspecies scatteringlength in $^{40}$K-$^{87}$Rb mixtures, providing valuable insights into theuniversal relations between Efimov features in heteronuclear systems.

Investigation of Efimov Features and Universality in $^{87}$Rb-$^{40}$K Mixtures with finite-range interaction