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We calculate recently observed $d$-wave Feshbach resonance [Phys. Rev. Lett.{\bf 119}, 203402 (2017)] and associated triplet structure in$^{87}$Rb-$^{85}$Rb cold collisions. We resort to a computational techniquecombining some features of close-coupling (CC) and $R$-matrix theory. In thelong-range part, we numerically calculate a pair of base or reference functionsfor each channel ignoring all interchannel couplings, ensuring the linearindependence of these base functions. The short-range part of the wave functionis calculated by CC method. The multichannel wave functions are obtained bymatching the short- and long-range parts at a suitably chosen matching point.We first verify the method by calculating cold collisional properties of$^{85}$Rb and $^6$Li in the presence of external magnetic fields tuned acrossspecific $s$-wave Feshbach resonances and thereby reproducing known results.Our numerical results on the $d$-wave resonance agree reasonably well with theexperimental ones. Furthermore, our method enables one to readily construct thereal space Green functions in order to calculate perturbatively the effects ofany residual inter-channel couplings in the long range.

Calculation of $d$-wave Feshbach resonance in $^{87}$Rb-$^{85}$Rb cold collisions by a multichannel computational method