Counterintuitive long-range interaction potentials

One of the topics where Richard Drachman made strong contributions concerns the long-range interaction between a distant electron and an atom or ion, a subject that always interested me greatly.  In this presentation, I will point out one problem where  the Drachman treatment predicted an energy dependent term[1] in the long-range effective potential that differed from an analogous term that arose in other derivations including my own with Shinichi Watanabe, a puzzling discrepancy that Richard Drachman subsequently resolved by showing that such terms are nonunique.  Other examples of counterintuitive long-range interactions arise in Rydberg electron interactions with an anisotropic ionic core, where Bernard Zygelman predicted a term proportional to the scalar product of two angular momenta that arose from coupling to the open shell core and not from magnetic moment interactions.  Research carried out in my group with graduate student William Clark showed that such terms arise from an adiabatic expansion of the long-range Hamiltonian,[2] and tested experimentally by Steve Lundeen's group. A final counterintuitive type of long-range interaction effect discussed in this presentation is the surprising one that can arise in a system of three or more particles having finite range interactions, called today the Efimov effect.  In some very recent work, we see that long range adiabatic potentials computed in hyperspherical coordinates develop a modification of their long-range interaction when the scattering length or scattering volume is tuned to infinity.  The talk will show examples of this long range modification including that predicted by Vitaly Efimov for three identical bosons, which produces an infinite number of Efimovian bound or resonant states.

[1] R. J. Drachman, J. Phys. B 12, L699 (1979).

[2] W. Clark and C. H. Greene, Rev. Mod. Phys. 71, 821 (1999).