Efimov effect in a D-dimensional Born-Oppenheimer approach

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/R-2 (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/R-2 approaches the limit - (D - 2)(2)/4. We obtained the scaling function for the Cs-133-Cs-133-Li-6 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 E-2(D). 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 root E-2(D)/E-3((N)) = 0.89, where E-3((N)) is the Nth excited three-body binding energy.