Role of collisions in creation of overlapping Bose condensates

We study the elastic scattering length and inelastic decay rate associated with collisions of Na-23 and Rb-87 atoms in different hyperfine states: one with atoms in the \f=2, m(f)=2] and one with atoms in the \f=1, m(f)=-1] state. For Na the real part of the a((22)+(1-1)) scattering length for \22] + \1-1] collisions is predicted to be positive and equal to 65+/-5 Bohr length units a(0) for small B. The zero-temperature low-field decay rate is of the order of a typical exchange rate: G((22)+(1-1))=(1.5+/-0.7) 10(-11) cm(3) s(-1), 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 G((22)+(1-1)) demonstrated by a recent experiment is shown to be very restrictive for the value of the singlet accumulated phase.