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Reliability of the Born-Oppenheimer Approximation in Noninteger Dimensions

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Abstract

We address the question of the reliability of the Born-Oppenheimer (BO) approximation for a mass-imbalanced resonant three-body system embedded in noninteger dimensions. We address this question within the problem of a system of currently experimental interest, namely \(^7\)Li\(-^{87}\)Rb\(_2\). We compare the Efimov scale parameter as well as the wave functions obtained using the BO approximation with those obtained using the Bethe-Peierls boundary condition.

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Acknowledgements

This work was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) [Grant nos. 2017/05660-0 and 2019/07767-1 (T.F.), 2023/08600-9 (R.M.F.), 2023/02261-8 (D.S.R.) and 2018/25225-9 (G.K.)], Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [Grant nos. 306834/2022-7 (T.F.), 302105/2022-0 (M.T.Y.), and 309262/2019-4 (G.K.)] and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) [Grant no. 88887.928099/2023-00 (D.S.R.)].

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Author notes

  1. D. S. Rosa, T. Frederico, R. M. Francisco, G. Krein, and M. T. Yamashita these authors contributed equally to this work.

Authors and Affiliations

  1. Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France

    D. S. Rosa

  2. Instituto Tecnológico de Aeronáutica, Pr. Mal. Eduardo Gomes, São José dos Campos, SP, 12228-900, Brazil

    D. S. Rosa, T. Frederico & R. M. Francisco

  3. Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271-Bloco II, São Paulo, SP, 01140-070, Brazil

    G. Krein & M. T. Yamashita

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Rosa, D.S., Frederico, T., Francisco, R.M. et al. Reliability of the Born-Oppenheimer Approximation in Noninteger Dimensions. Few-Body Syst 65, 77 (2024). https://doi.org/10.1007/s00601-024-01946-w

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