We consider the possibilities for producing ultracold mixtures of K and Cs and forming KCs molecules by magnetoassociation. We carry out coupled-channel calculations of the interspecies scattering length for $^{39}$KCs, $^{41}$KCs and $^{40}$KCs and
characterize Feshbach resonances due to s-wave and d-wave bound states, with widths ranging from below 1 nG to 5 G. We also calculate the corresponding bound-state energies as a function of magnetic field. We give a general discussion of the combinations of intraspecies and interspecies scattering lengths needed to form low-temperature atomic mixtures and condensates and identify promising strategies for cooling and molecule formation for all three isotopic combinations of K and Cs.
Studies of cold atom collisions and few-body interactions often require the energy dependence of the scattering phase shift, which is usually expressed in terms of an effective-range expansion. We use accurate coupled-channel calculations on $^{6}$Li
, $^{39}$K and $^{133}$Cs to explore the behavior of the effective range in the vicinity of both broad and narrow Feshbach resonances. We show that commonly used expressions for the effective range break down dramatically for narrow resonances and near the zero-crossings of broad resonances. We present an alternative parametrization of the effective range that is accurate through both the pole and the zero-crossing for both broad and narrow resonances. However, the effective range expansion can still fail at quite low collision energies, particularly around narrow resonances. We demonstrate that an analytical form of an energy and magnetic field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length.
