Hyperfine structure of muonic lithium ions

A. P. Martynenko ; A. A. Ulybin

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 2, pp. 270-282.

Résumé

On the basis of perturbation theory in fine structure constant $\alpha$ and the ratio of electron to muon masses we calculate recoil corrections of order $\alpha^4 (M_e/M_\mu)$, $\alpha^4 (M_e/M_\mu)^2\ln(M_e/M_\mu)$, $\alpha^4 (M_e/M_\mu)^2$, $\alpha^5(m_e/m_\mu)\ln(m_e/m_\mu)$ to hyperfine splitting of the ground state in muonic lithium ions $(\mu\ e\ ^6_3\mathrm{Li})^+$ and $(\mu e\ ^7_3\mathrm{Li})^+$. We obtain total results for the ground state small hyperfine splittings in $(\mu\ e\ ^6_3\mathrm{Li})^+$ $\Delta\nu_1=14153.03$ MHz and $\Delta\nu_2=21571.26$ MHz and in $(\mu\ e\ ^7_3\mathrm{Li})^+$ $\Delta\nu_1=13991.97$ MHz and $\Delta\nu_2=21735.03$ MHz which can be considered as a reliable estimate for a comparison with future experimental data.

Détail

Keywords: quantum electrodynamics, hyperfine splitting, quasipotential method.

Bibliographie

[1] Martynenko A. P., Ulybin A. A., “Hyperfine structure of muonic lithium ions”, The 4nd International Conference “Mathematical Physics and its Applications”, Book of Abstracts and Conference Materials, eds. I. V. Volovich; V. P. Radchenko, Samara State Technical Univ., Samara, 2014, 240–241 (In Russian)

[2] Pohl R., Antognini A., Nez F. et al., “The size of the proton”, Nature, 466 (2010), 213–217 | DOI

[3] Antognini A., Kottmann F., Biraben F., Indelicato P., Nez F., Pohl R., “Theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen”, Annals of Physics, 331 (2013), 127–145, arXiv: [physics.atom-ph] 1208.2637 | DOI | Zbl

[4] Lakdawala S. D., Mohr P. J., “Hyperfine structure in muonic helium”, Phys. Rev. A, 22:4 (1980), 1572–1575 | DOI

[5] Lakdawala S. D., Mohr P. J., “Calculation of the muonic $^3\mathrm {He}$ hyperfine structure”, Phys. Rev. A, 24:4 (1981), 2224–2227 | DOI

[6] Lakdawala S. D., Mohr P. J., “Perturbation-theory calculation of hyperfinr structure in muonic helium”, Phys. Rev. A, 29:3 (1984), 1047–1054 | DOI

[7] Huang K.-N., Hughes V. W., “Theoretical hyperfine structure of the muonic $^3 \mathrm {He}$ and $^4\mathrm{He}$ atoms”, Phys. Rev. A, 26:5 (1982), 2330–2333 | DOI

[8] Borie E., “On the hyperfine structure of neutral muonic helium”, Z. Physik A, 291:2 (1979), 107–112 | DOI

[9] Drachman R. J., “Nonrelativistic hyperfine splitting in muonic helium by adiabatic perturbation theory”, Phys. Rev. A, 22:4 (1980), 1755–1757 | DOI

[10] Chen M.-K., “Correlated wave functions and hyperfine splittings of the $2s$ state of muonic $^{3,4}\mathrm{He}$ atoms”, Phys. Rev. A, 45:3 (1992), 1479–1492 | DOI

[11] Yakhontov V. L., Amusia M. Ya., “Hyperfine splitting computation in the $1s^{(e)}_{1/2}2s^{(\mu)}_{1/2}$ state of the exotic $(^4\mathrm{He}^{2+}{-}\mu^-e^-)^0$ and $(^3\mathrm{He}^{2+}{-}\mu^-e^-)^0$ atoms”, J. Phys. B: At. Mol. Opt. Phys., 27:16 (1994), 3743–3765 | DOI

[12] Frolov A. M., “Properties and hyperfine structure of helium-muonic atoms”, Phys. Rev. A, 61:2 (2000), 022509 | DOI

[13] Frolov A. M., “Hyperfine splitting in the ground states of the lithium-muonic ions and in the $2^3S$ states of the lithium-muonic atoms”, Phys. Let. A, 357:4–5 (2006), 334–338 | DOI

[14] Korobov V. I., “Coulomb three-body bound-state problem: Variational calculations of nonrelativistic energies”, Phys. Rev. A, 61:6 (2000), 064503 | DOI

[15] Pachucki K., “Hyperfine structure of muonic helium”, Phys. Rev. A, 63:3 (2001), 032508 | DOI

[16] Krutov A. A., Martynenko A. P., “Ground-state hyperfine structure of the muonic helium atom”, Phys. Rev. A, 78:3 (2008), 032513 | DOI

[17] Krutov A. A., Martynenko A. P., “Hyperfine structure of the ground state muonic $^3\mathrm{He}$ atom”, Eur. Phys. J. D, 62:2 (2011), 163–175, arXiv: [hep-ph] 1007.1419 | DOI

[18] Krutov A. A., Martynenko A. P., “Hyperfine structure of the excited state $1s_{1/2}^{(e)}2s_{1/2}^{(\mu)}$ of the muonic helium atom”, Phys. Rev. A, 86:5 (2012), 052501 | DOI

[19] Landau L. D., Lifshits E. M., Kvantovaia mekhanika (nereliativistskaia teoriia) [Quantum Mechanics: Nonrelativistic Theory], Nauka, Moscow, 1989, 768 pp. (In Russian)

[20] Sobel'man I. I., Introduction to the theory of atomic spectra, International Series in Natural Philosophy, 40, Pergamon Press, Oxford, 1972, xvi+609 pp. | DOI

[21] Mohr P. J., Taylor B. N., Newell D. B., “CODATA recommended values of the fundamental physical constants: 2010”, Rev. Mod. Phys., 84:4 (2012), 1527–1605 | DOI

[22] Stone N. J., “Table of nuclear magnetic dipole and electric quadrupole moments”, Atomic Data and Nuclear Data Tables, 90:1 (2005), 75–176 | DOI

[23] Hameka H. F., “On the use of Green functions in atomic and molecular calculations. I. The Green function of the hydrogen atom”, J. Chem. Phys., 47:8 (1967), 2728–2735 ; | DOI | DOI

[24] Bethe H. A., Salpeter E. E., Quantum mechanics of one- and two-electron atoms, A Plenum/Rosetta Edition, New York, 1977, xii+370 pp. | DOI

[25] Fock V. A., Nachala kvantovoi mekhaniki [Principles of Quantum Mechanics], Nauka, Moscow, 1976, 376 pp. (In Russian)

[26] Eides M. I., Grotch H., Shelyuto V. A., “Theory of light hydrogenlike atoms”, Physics Reports, 342:2–3 (2001), 63–261 | DOI | Zbl

[27] Arnowitt R., “The hyperfine structure of hydrogen”, Phys. Rev., 92:4 (1953), 1002–1009 | DOI | Zbl

[28] Huang K.-N., Hughes V. W., “Theoretical hyperfine structure of muonic helium”, Phys. Rev. A, 20:3 (1979), 706–717 | DOI

[29] Chen M.-K., “Hyperfine splitting for the ground-state muonic $^3\mathrm{He}$ atom-corrections up to $\alpha^2$”, J. Phys. B: At. Mol. Opt. Phys., 26:15 (1993), 2263–2272 | DOI

[30] Martynenko A. P., “2S Hyperfine splitting of muonic hydrogen”, Phys. Rev. A, 71:2 (2005), 022506, arXiv: hep-ph/0409107 | DOI

[31] Martynenko A. P., “Theory of the muonic hydrogen-muonic deuterium isotope shift”, J. Exp. Theor. Phys., 101:6 (2005), 1021–1035, arXiv: hep-ph/0412250 | DOI

[32] Martynenko A. P., “Hyperfine structure of the S levels of the muonic helium ion”, J. Exp. Theor. Phys., 106:4 (2008), 690–699, arXiv: [hep-ph] 0710.3237 | DOI

[33] Martynenko A. P., “Fine and hyperfine structure of P-wave levels in muonic hydrogen”, Atom. Nuclei, 71:1 (2008), 125–135, arXiv: hep-ph/0610226 | DOI

[34] Faustov R. N., Martynenko A. P., Martynenko G. A., Sorokin V. V., “Radiative nonrecoil nuclear finite size corrections of order $\alpha(Z\alpha)^5$ to the hyperfine splitting of S-states in muonic hydrogen”, Phys. Let. B, 733 (2014), 354–358, arXiv: [hep-ph] 1402.5825 | DOI