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Zeeman effect of the hyperfine structure levels in H- and Li-like lead

Zeeman effect of the hyperfine structure levels in H- and Li-like lead. D. L. Moskovkin 1 , V. M. Shabaev 1 , and W. Quint 2 1 Department of Physics, St. Petersburg State University, Oulianovskaya 1, Petrodvorets, St. Petersburg 198504, Russia

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Zeeman effect of the hyperfine structure levels in H- and Li-like lead

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  1. Zeeman effect of the hyperfine structure levels in H- and Li-like lead D. L. Moskovkin1, V. M. Shabaev1, and W. Quint2 1Department of Physics, St. Petersburg State University, Oulianovskaya 1, Petrodvorets, St. Petersburg 198504, Russia 2Gesellschaft f¨ur Schwerionenforschung, Planckstrasse 1, D-64291 Darmstadt, Germany dlmos@pcqnt1.phys.spbu.ru

  2. Abstract The fully relativistic theory of the Zeeman splitting of the 1s and 2s hyperfine-structurelevels in hydrogen- and lithiumlike Pb-207, respectively, is considered for the magnetic fieldmagnitude in the range from 1 to 10 T. The second-order corrections to the Breit – Rabiformula are calculated and discussed. The results can be used for a precise determinationof the nuclear magnetic moment, hyperfine structure (HFS), and electronic gj-factor of leadfromg-factor experiments. dlmos@pcqnt1.phys.spbu.ru

  3. We consider a hydrogen- or lithiumlike Pb-207 in the ground state. The ion is placed in ahomogeneous magnetic field B directed along the z axis. μ = < I I|μz|II > is the nuclear magnetic moment I = ½ is the nuclear spin z gI = μ/(μNI) is the nuclear g factor B µ dlmos@pcqnt1.phys.spbu.ru

  4. Zeeman effect of the HFS levels MF=+1 F′ = 1 ΔEmag ~ 5*10-4 eV B = 1 – 10 T MF=0 MF=-1 207Pb ΔEHFS(1s)=1.22 eV (H-like lead) 1s, 2s ΔEHFS(2s)=0.20 eV (Li-like lead) I =1/2 F = 0 MF=0 ΔEHFS = E(F′) − E(F) ΔEmag = E −½ [E(F) + E(F′)] For light ions ΔEmag~ΔEHFS For 207Pb81+ and 207Pb79+ΔEmag<<ΔEHFS dlmos@pcqnt1.phys.spbu.ru

  5. The Breit – Rabi formula for Pb-207 dlmos@pcqnt1.phys.spbu.ru

  6. The individual contributions to the coefficients dlmos@pcqnt1.phys.spbu.ru

  7. The diagrams contributing to the Breit – Rabi formula coefficients dlmos@pcqnt1.phys.spbu.ru

  8. The idea of taking into account the interaction of the valent electron with the closed (1s)2 electron shell. dlmos@pcqnt1.phys.spbu.ru

  9. dlmos@pcqnt1.phys.spbu.ru

  10. Corrections to the Breit – Rabi formula for H- and Li-like Pb-207 dlmos@pcqnt1.phys.spbu.ru

  11. The numerical results dlmos@pcqnt1.phys.spbu.ru

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  14. dlmos@pcqnt1.phys.spbu.ru

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