Four-body variational calculation of a hydrogen-like atom involving an excited muonic molecule

• Published in: Journal of physics. Conference series Vol. 2207; no. 1; pp. 12035 - 12040
• Main Authors: Yamashita, Takuma, Niiyama, Motoaki, Yasuda, Kazuhiro, Kino, Yasushi
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.03.2022
• Subjects: Electrons; Energy levels; Induced polarization; Perturbation theory; Physics; Reaction kinetics; Resonance
• DOI: 10.1088/1742-6596/2207/1/012035
• ISSN: 1742-6588

Abstract We report a four-body variational calculation of a hydrogen-like atom consisting of an excited muonic molecule consisting of d, t, and μ, and a ground state electron. Due to the compact size of the muonic molecule dtμ, it behaves as a quasi-nucleus for the electron; however, the system is actually a resonance state because the de-excitation energy of dtμ is sufficient to ionize the electron. We calculate resonance energy levels of the four-body system dtμe using a Gaussian expansion method and a stabilization method. Our best calculation results in a four-body energy of –100.159 88 a.u. which is in good agreement with the value estimated by the first order perturbation theory [Harston et al. Zeitschrift für Physik D 22, 635 (1992)]. We indicate that implementation of the electron-induced polarization of dt μ will be indispensable for the further precise determination of the resonance energy. The present result is the first step towards a full four-body calculation of the muonic molecule under the presence of the electron, which is of importance for development of a muon catalyzed fusion kinetics model.