We predict the existence of a ubiquitous class of long-range molecular Rydberg states, whose Born-Oppenheimer potential curves are oscillatory in nature. These oscillations reflect the nodal structure of the atomic Rydberg state wave functions. The temperature and density of atoms in a Bose-Einstein condensate are particularly favorable for the laser excitation of ultra-long-range vibrational bound states localized at internuclear distances in the range ${10}^3$– ${10}^5$ a.u. A surprising trilobitelike class of polar homonuclear diatomics should exhibit electric dipole moments in the kilodebye range.

• Received 19 May 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.2458