Collisional properties of sympathetically cooled $^{39}$K
We report the experimental evidence of the sympathetic cooling of $^{39}$K with $^{87}$Rb down to 1 $μ$K, obtained in a novel tight confining magnetic trap. This allowed us to perform the first direct measurement of the elastic cross section of $^{39}$K below 50 $μ$K. The result obtained for the triplet scattering length, $a_T = -51(7)$ Bohr radii, agrees with previous results derived from photoassociation spectra and from Feshbach spectroscopy of $^{40}$K.