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Cs$_2$ Rydberg-ground molecules consisting of a Rydberg, $nD_{J}$ (33 $\leq$$n$ $\leq$ 39), and a ground state atom, 6$S_{1/2} (F=$3 or 4$)$, areinvestigated by photo-association spectroscopy in a cold atomic gas. We observevibrational spectra that correspond to triplet $^T\Sigma$ and mixed$^{S,T}\Sigma$ molecular states. We establish scaling laws for the energies ofthe lowest vibrational states vs principal quantum number and obtainzero-energy singlet and triplet $s$-wave scattering lengths from experimentaldata and a Fermi model. Line broadening in electric fields reveals thepermanent molecular electric-dipole moments; measured values agree well withcalculations. We discuss the negative polarity of the dipole moments, whichdiffers from previously reported cases.

Cesium $nD_{J}$+$6S_{1/2}$ Rydberg molecules and their permanent electric dipole moments