Kato's theorem and ultralong-range Rydberg molecules

We consider nonadiabatic coupling in the “trilobite”-like long-range Rydberg molecules created by perturbing degenerate high-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>ℓ</a:mi></a:math> Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular nonadiabatic coupling. We find that the gap between the trilobite potential curve and neighboring “butterfly” or “dragonfly” potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>s</b:mi></b:math>-wave radial wave function. This is an unanticipated outcome of Kato's theorem.