Properties of cold collisions of ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ atoms and of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ atoms in relation to Bose-Einstein condensation

We have determined properties of cold ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ singlet and triplet bound states. We predict positive scattering lengths for the ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ singlet potentials, as well as for the ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ triplet potential, and a negative value for ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$+${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ triplet scattering. From a study of the magnetic field dependence we conclude that ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the $f=1\mathrm{}$, $m_f=-1\mathrm{}$ hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.