Quantum and semiclassical analysis of long-range Rydberg molecules

A recent study suggests the existence of highly polar and nonpolar long-range Rydberg molecules under temperature and density conditions representative of those found in atomic Bose-Einstein condensates. The electronic wave functions of these Rydberg molecules are characterized by an elliptically shaped nodal structure. We use a combination of quantum and semiclassical methods to explore this unique nodal structure and its correlations with the Born-Oppenheimer potential curves of the molecules. We demonstrate a special "quasiseparability" that arises in elliptic coordinates at certain internuclear separations and give a semiclassical interpretation of this in terms of quantized Einstein-Brillouin-Keller orbits.