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 K-2. We show that for the two bosonic species K-39 and K-41 the scattering lengths are positive, hence, leading to stable condensates. The fermionic isotope K-40 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 K-39 and K-41 are possible for purely spin-polarized atoms, and sympathetic cooling between the bosonic K-39 and the fermionic K-40 will be efficient due to low spin-flip rates and a sizable interspecies scattering length.