We observe ultralong-range blue-shifted Cs molecular states near Rydberg states in an optical dipole trap, where . The accidental near degeneracy of and Rydberg states for in Cs, due to the small fractional quantum defect, leads to non-adiabatic coupling among these states, producing potential wells above the thresholds. Two important consequences of admixing high angular momentum states with states are the formation of large permanent dipole moments, $\sim 15-100,$Debye, and accessibility of these states via two-photon association. The observed states are in excellent agreement with theory. Both projections of the total angular momentum on the internuclear axis are visible in the experiment.

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