Ultracold Thermalization of ${}^7$Li and ${}^{87}$Rb

We report on measurements of cross-species thermalization inside a magnetically trapped spin-polarized mixture of ${}^{87}$Rb and ${}^7$Li atoms with both atoms in their respective low field seeking magnetic substates |F=2,m_F=2\right>. Measurement of the thermalization velocity in the ultracold regime below $10\mu$K allows for the derivation of the absolute value of the pure triplet s-wave scattering length governing the interaction. We find $\mathrm{\mid }{a}_{7,87}\mathrm{\mid }=(59\pm 19)a_{\mathrm{B}}$. We propose to study both species in the condensed regime to derive the sign of $a_{7,87}$. In this context, we present numerical solutions to the coupled Gross-Pitaevskii equation based on the hypothesis of a positive sign. According to the simulations, phase separation of the Li and Rb |2,2\right> clouds occurs along with a mean-field stabilization allowing for larger atom numbers of condensed ${}^7$Li atoms before collapse sets in. Observation of this mean-field stabilization would directly fix the sign of $a_{7,87}$. We discuss our results in the light of this proposal.