Coupled channel effects on resonance states of positronic alkali atom

Yamashita, Takuma; Kino, Yasushi

doi:10.1140/epjd/e2017-80542-6

“…In the present calculation, we consider a Schrödinger equation (H − E ν )Ψ ν = 0 where the fourbody Hamiltonian H contains kinetic energy operators (separated from the center-of-mass motion) and all inter-particle Coulomb potential energy operators. We adopt a Gaussian expansion method (see reviews [17][18][19] and our recent calculations [20][21][22][23][24]) for the four-body wave function Ψ ν . The Ψ ν is expanded in terms of Gaussian basis functions ϕ il (r) = N il r l exp(−r 2 ) (N il is a normalization constant) and spherical harmonics as follows:…”

Section: Theorymentioning

confidence: 99%

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

Yamashita

¹

,

Niiyama

²

,

Yasuda

³

et al. 2022

J. Phys.: Conf. Ser.

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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 dtμ 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.

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“…An investigation on weights of the wavefunction by Stegeby and Piszczatowski [29] suggests an intriguing aspect on the mechanism and structure of the resonance states and admits further studies. In the present paper, we investigate the role of the inter-particle correlations, 'positron-antiproton and electron-proton' and 'positron-electron and antiproton-proton' correlations, in the HH resonance states by analyzing the energy levels by a coupled channel study [27,31,32] using GEM. We use simple coupled-channel trial wavefunctions due to the limit of computation cost, and calculate resonances by a complex scaling method [33].…”

Section: Introductionmentioning

confidence: 99%

Coupled channel study of antihydrogen-hydrogen molecular resonance state

Yamashita¹,

Kino²

2018

3rd China-Japan Joint Workshop on Positron Science (JWPS2017)

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We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron-antiproton and electron-proton correlations as well as positron-electron and antiprotonproton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen-hydrogen configuration, and the other is a positronium-protonium configuration. The antihydrogen-hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium-protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen-hydrogen dissociation threshold with its lifetime 16 (2) fs.

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“…An investigation on weights of the wavefunction by Stegeby and Piszczatowski [29] suggests an intriguing aspect on the mechanism and structure of the resonance states and admits further studies. In the present paper, we investigate the role of the inter-particle correlations, 'positron-antiproton and electron-proton' and 'positron-electron and antiproton-proton' correlations, in the HH resonance states by analyzing the energy levels by a coupled channel study [27,31,32] using GEM. We use simple coupled-channel trial wavefunctions due to the limit of computation cost, and calculate resonances by a complex scaling method [33].…”

Section: Introductionmentioning

confidence: 99%

Coupled channel study of antihydrogen-hydrogen molecular resonance state

Yamashita

¹

,

Kino

²

2018

JJAP Conf. Proc.

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0

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We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron-antiproton and electron-proton correlations as well as positron-electron and antiprotonproton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen-hydrogen configuration, and the other is a positronium-protonium configuration. The antihydrogen-hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium-protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen-hydrogen dissociation threshold with its lifetime 16 (2) fs.

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Coupled channel effects on resonance states of positronic alkali atom

Cited by 7 publications

References 71 publications

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

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

Coupled channel study of antihydrogen-hydrogen molecular resonance state

Coupled channel study of antihydrogen-hydrogen molecular resonance state

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