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 [Formula Presented]. We show that for the two bosonic species [Formula Presented] and [Formula Presented] the scattering lengths are positive, hence, leading to stable condensates. The fermionic isotope [Formula Presented] 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 [Formula Presented] and [Formula Presented] are possible for purely spin-polarized atoms, and sympathetic cooling between the bosonic [Formula Presented] and the fermionic [Formula Presented] will be efficient due to low spin-flip rates and a sizable interspecies scattering length.