Role of collisions in creation of overlapping Bose condensates

We study the elastic scattering length and inelastic decay rate associated with collisions of [Formula Presented] and [Formula Presented] atoms in different hyperfine states: one with atoms in the [Formula Presented] and one with atoms in the [Formula Presented] state. For Na the real part of the [Formula Presented] scattering length for 22〉+1-1〉 collisions is predicted to be positive and equal to 65±5 Bohr length units [Formula Presented] for small B. The zero-temperature low-field decay rate is of the order of a typical exchange rate: [Formula Presented]=(1.5±0.7)[Formula Presented] [Formula Presented] [Formula Presented], showing that a two-condensate experiment is not feasible for a Na gas sample in a static magnetic trap. For the case of Rb atoms the present knowledge of the singlet interaction does not allow a similar calculation. The extreme suppression of [Formula Presented] demonstrated by a recent experiment is shown to be very restrictive for the value of the singlet accumulated phase.