$D$-dimensional three-body bound-state problem with zero-range interactions

$D$ -dimensional three-body bound-state problem with zero-range interactions

D. S. Rosa, T. Frederico, G. Krein, and M. T. Yamashita

Phys. Rev. A 106, 023311 – Published 16 August 2022

Abstract

We solved analytically the three-body mass-imbalanced problem embedded in $D$ dimensions for zero-range resonantly interacting particles. We derived the negative energy eigenstates of the three-body Schrödinger equation by imposing the Bethe-Peierls boundary conditions in $D$ dimensions for zero-energy two-body bound states. The solution retrieves the Efimov-like discrete scaling factor dependence with dimension. The analytical form of the mass-imbalanced three-body bound-state wave function can be used to probe the effective dimension of asymmetric cold atomic traps for Feshbach resonances tuned close to the Efimov limit.

Received 24 November 2021
Revised 6 July 2022
Accepted 2 August 2022

DOI:https://doi.org/10.1103/PhysRevA.106.023311

Physics Subject Headings (PhySH)

Atomic & molecular collisions Atomic & molecular structure Bose-Einstein condensates Cold atoms & matter waves Ultracold collisions

Atomic, Molecular & Optical

Authors & Affiliations

D. S. Rosa ¹, T. Frederico ¹, G. Krein ², and M. T. Yamashita ²

¹Instituto Tecnológico de Aeronáutica, DCTA, 12228-900 São José dos Campos, SP, Brazil
²Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271-Bloco II, 01140-070 São Paulo, SP, Brazil

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Issue

Vol. 106, Iss. 2 — August 2022

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