Potassium scattering lengths and prospects for Bose-Einstein condensation and sympathetic cooling

We have determined the scattering lengths for collisions between the different isotopes of two potassium atoms in singlet and triplet molecular states of ${\mathrm{K}}_2$. We show that for the two bosonic species ${}^{39}\mathrm{K}$ and ${}^{41}\mathrm{K}$ the scattering lengths are positive, hence, leading to stable condensates. The fermionic isotope ${}^{40}\mathrm{K}$ also has positive scattering lengths, but the triplet value is nearly zero, hence, a quasi-non-interacting fermionic gas. We also give results for the interspecies collisions. We conclude that double condensates of ${}^{39}\mathrm{K}$ and ${}^{41}\mathrm{K}$ are possible for purely spin-polarized atoms, and sympathetic cooling between the bosonic ${}^{39}\mathrm{K}$ and the fermionic ${}^{40}\mathrm{K}$ will be efficient due to low spin-flip rates and a sizable interspecies scattering length.