Scattering parameters for cold-Li-Rb and Na-Rb collisions derived from variable phase theory

We show how the scattering phase shift, the s-wave scattering length and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds for the scattering length and the scattering volume. We show how, in the framework of the variable phase method, Levinson's theorem yields the number of bound states supported by a potential. We report new results from a study of the heteronuclear alkali dimers NaRb and LiRb. We consider $ab$ $initio$ molecular potentials for the X${}^1\Sigma^+$ and $a{}^3\Sigma^+$ states of both dimers and compare and discuss results obtained from experimentally based X${}^1\Sigma^+$ and $a{}^3\Sigma^+$ potentials of NaRb. We explore the mass dependence of the scattering data by considering all isotopomers and we calculate the numbers of bound states supported by the molecular potentials for each isotopomer.