Creation of polar and nonpolar ultra-long-range Rydberg molecules

We predict the existence of a ubiquitous class of long-range molecular Rydb erg states, whose Born-Oppenheimer potential curves are oscillatory in natu re. These oscillations reflect the nodal structure of the atomic Rydberg st ate wave functions. The temperature and density of atoms in a Bose-Einstein condensate an particularly favorable for the laser excitation of ultra-lon g-range vibrational bound states localized at internuclear distances in the range 10(3)-10(5) a.u. A surprising trilobitelike class of polar homonucle ar diatomics should exhibit electric dipole moments in the kilodebye range.