Deeply bound (24$D_J$ + 5$S_{1/2}$) $^{87}$Rb and $^{85}$Rb molecules for eight spin couplings

We observe long-range $^{85}$Rb and $^{87}$Rb (24$D$+5$S_{1/2}$) Rydberg molecules for eight different spin couplings, with binding energies up to 440~MHz and sub-percent relative uncertainty. Isotopic effects of the molecular binding energies arise from the different masses and nuclear spins. Because the vibrational states involve different spin configurations and cover a wide range of internuclear separations, the states have different dependencies on the $s$-wave and $p$-wave scattering phase shifts for singlet and triplet scattering. Fitting the spectroscopic data, we comprehensively determine all four scattering length functions over the relevant energy range as well as the zero-energy scattering lengths of the two $s$-wave channels. Our unusually high temperature and low density (180 $\mu$K, 1 $\times$ 10$^{11}$ cm$^{-3}$) suggest that the molecule excitation occurs through photoassisted collisions.