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is larger than the coupling between the manifolds [22]. We use the eigenfunctions of the asymptotic Hamiltonian to expand the wave function of the collision complex. Inserting this expansion into the Schr¨ odinger equation leads to a system of close-coupled (CC) differential equations yielding S -matrix elements and transition probabilities between the field-dressed states. To solve the CC equations, we evaluate the matrix elements of the Hamiltonian (1) in the field-dressed basis analytically [23] using the most accurate potentials for the singlet and triplet states of Rb$_{2}$ [24]. Seven photon number states are included in the basis set (3) resulting in 252 coupled equations, which are integrated on a grid of R from 3 to 300 a$_{0}$ with a step size of 5 × 10 − 3 a$_{0}$ . This procedure produces fully converged results at a collision energy of 1 µ K. To evaluate the bound states of the Rb$_{2}$ molecule, we use the asymptotic bound-state model (ABM) [25] properly extended to include the interactions with rf fields. 

Figure 1 shows the magnetic field dependence of near-threshold energy levels of the Rb$_{2}$ molecule in the absence of an rf field [25]. At certain magnetic fields, the asymptotic two- atom scattering states become nearly degenerate with molecular states, giving rise to Fesh- bach resonances [1]. We focus on a mixed-spin resonance that has been detected experimen- tally in an optically trapped mixture of ultracold Rb atoms in the | 1 , 1 〉 ⊗ | 2 , − 1 〉 initial state 

