Efimov effect in a D-dimensional Born-Oppenheimer approach

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2019-01, Vol.52 (2), p.25101
• Main Authors: Rosa, D S, Frederico, T, Krein, G, Yamashita, M T
• Format: Article
• Language: English
• Subjects: cold atoms; Efimov effect; low-dimensional systems; three-body problem
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/1361-6455/aaf346

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 − ( D − 2 ) 2 4 . 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 E 2 D E 3 ( N ) = 0.89 , where E 3 ( N ) is the Nth excited three-body binding energy.