We determine the interspecies $s$-wave triplet scattering length $a_3$ for all K-Rb isotopic mixtures by measuring the elastic cross section for collisions between ${}^{\mathrm{41}}\mathrm{K}$ and ${}^{87}\mathrm{R}\mathrm{b}$ in different temperature regimes. The positive value $a_3=+{163}_{-12}^{+57}{a}_0$ ensures the stability against collapse of binary ${}^{41}\mathrm{K}-{}^{87}\mathrm{R}\mathrm{b}$ Bose-Einstein condensates. For the fermion-boson mixture ${}^{40}\mathrm{K}-{}^{87}\mathrm{R}\mathrm{b}$, we obtain a large and negative scattering length which implies an efficient sympathetic cooling of the fermionic species down to the degenerate regime.

• Received 18 February 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.053202