Sympathetic cooling ofLi6atoms

We use recently measured cold photoassociation and two-photon data to extract the singlet and triplet accumulated radial phases of interacting ground-state lithium atoms. Using the resulting values we predict scattering lengths, Feshbach resonances, and exchange decay rates for cold collisions between ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ atoms that are of interest for the possibility of sympathetic cooling of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and for the coexistence of the bosonic and fermionic quantum-degenerate phases of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. In addition, we calculate scattering lengths and exchange decay rates for cold collisions between identical lithium isotopes in different hyperfine states. These quantities are used to examine the possibilities of coexisting ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ Bose condensates and of evaporatively cooling coexisting ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ subsystems.