The bounding energy for singlet and triplet states of the negative muonium ion

Authors

  • М. Гайсак Institute of Electron Physics NASc of Ukraine, Ukraine
  • М. Гнатич Institute of Experimental Physics SASc, Slovakia
  • Ю. Федорняк Uzhhorod National University, Ukraine

DOI:

https://doi.org/10.24144/2415-8038.2011.30.240-245

Keywords:

Hyperspherical coordinates method, Adiabatic potentials, Muonium ion, Born-Oppenheimer approach

Abstract

Calculations were performed for two singlet and triplet states of negative muonium ion (µ+e–e–) in the framework of adiabatic hyperspherical approximation. In the Born-Oppenheimer approach scaling non-relativistic Shrödinger equation was solved. Application of Richardson extrapolation equation revealed that in addition to bound singlet state (1s2) one-particle excited states (1s2s) and (1s3s) exist. The affinity energy value for these states is 0.144 and 0.53 eV. Moreover, two bound triplet states - (1s2s) and (2s3s) – exist with affinity energy values equal to 0.115 та 0.050 eV. The energy value of 0.523975 a.u. for the ground state was received while the precise value obtained by M. Frolov in variational method is equal to
0.52505 a.u.

References

Гольданский В.И., Шантарович В.П. Физика ХХ века. Развитие и перспективы. – Москва: Наука, 1984.

Nakatsuji H. // Phys. Rev. Lett. – 2004. – Vol.93. - N3. – P. 030403.

Frolov A.M., Smith V.H.,Jr. // Phys.Rev. – 1994. - №2. - A49.

Рид М., Саймон Б. Методы современной математической физики. – Москва: Мир, 1982. - T.3.

Chattopadhyay R., Das T.K. // Phys. Rev. – 1997. - N2. - A56. – P. 1281.

Barham M., Darewych J. // arXiv: 0706.3017v1 [physics. atom-ph] (2007).

Шехттер Х., Анализ методов дискрети¬зации для обыкновенных дифференциальных уравнений. – Москва: Мир, 1978.

Hylleraas E. // Astrophisica Norvegica. – 1964. – Vol.9. - N 32. – P. 345.

Rau A.R.P. // J. Astrophys. – 1996. - Abstr. 17. – P. 113.

Lin C.D. // Phys. Rept.. – 1995. – Vol.257. – N 1.

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Published

2011-12-31

Issue

Vol. 30 (2011)

Section

Статті

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Copyright (c) 2011 Scientific Herald of Uzhhorod University.Series Physics

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