Determination of the scattering length of the a$^3\Sigma^+$ potential of $^{87}$RbCs

We have determined the scattering length of the a$^3\Sigma^+$ potential of $^{87}$RbCs based on experimental observations from the literature and the known value for the long-range dispersion coefficient. Our analysis uses quantum defect theory and analytical solutions of the Schr\"odinger equation for a van der Waals potential. We find that the scattering length is either 700$^{+700}_{-300}$ $a_0$ or 176$\pm$2 $a_0$ with more confidence associated to the first value, where $a_0$=0.05292 nm is a Bohr radius. An independent value of the van der Waals coefficient could not be determined and the best theoretically determined $C_6$ value was used.