Quantum and semiclassical analysis of long-range Rydberg molecules - art. no. 042508

A recent study suggests the existence of highly polar and nonpolar long-ran ge Rydberg molecules under temperature and density conditions representativ e of those found in atomic Bose-Einstein condensates. The electronic wave f unctions of these Rydberg molecules are characterized by an elliptically sh aped nodal structure. We use a combination of quantum and semiclassical met hods to explore this unique nodal structure and its correlations with the B orn-Oppenheimer potential curves of the molecules. We demonstrate a special "quasiseparability" that arises in elliptic coordinates at certain internu clear separations and give a semiclassical interpretation of this in terms of quantized Einstein-Brillouin-Keller orbits.