Efimov effect in a D-dimensional Born-Oppenheimer approach

Author(s)

Rosa, D. S. ^[1] ; Frederico, T. ^[2] ; Krein, G. ^[1] ; Yamashita, M. T. ^[1]

Affiliation

^[1] Univ Estadual Paulista, Inst Fis Teor, UNESP, Rua Dr Bento Teobaldo Ferraz 271, Bloco 2, BR-01140070 Sao Paulo, SP - Brazil

^[2] Inst Tecnol Aeronaut, BR-12228900 Sao Jose Dos Campos, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS; v. 52, n. 2 JAN 28 2019.
• Web of Science Citations: 2

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/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. (AU)

• FAPESP's process: 13/01907-0 - São Paulo Research and Analysis Center
• Grantee: Sergio Ferraz Novaes
• Support type: Research Projects - Thematic Grants
• FAPESP's process: 16/01816-2 - Dimensional transition in Few-Atom Systems
• Grantee: Marcelo Takeshi Yamashita
• Support type: Regular Research Grants
• FAPESP's process: 17/05660-0 - Theoretical studies of the structure and reactions of exotic nuclei and many-body systems
• Grantee: Brett Vern Carlson
• Support type: Research Projects - Thematic Grants