Efimov effect in a D-dimensional Born–Oppenheimer approach

Abstract

We study a three-body system, formed by two identical heavy bosons and a light particle, in the Born–Oppenheimer approximation for an arbitrary dimension D. We restrict D to the interval 2 < D < 4, and derive the heavy–heavy D-dimensional effective potential proportional to 1/R2 (R is the relative distance between the heavy particles), which is responsible for the Efimov effect. We found that the Efimov states disappear once the critical strength of the heavy–heavy effective potential 1/R2 approaches the limit . We obtained the scaling function for the 133Cs–133Cs–6Li system as the limit cycle of the correlation between the energies of two consecutive Efimov states as a function of D and the heavy-light binding energy ED2. In addition, we found that the energy of the (N + 1)th excited state reaches the two-body continuum independently of the dimension D when , where is the Nth excited three-body binding energy.