1. 2007 November 23dlmos@pcqnt1.phys.spbu.ru 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 2 Gesellschaft f¨ur Schwerionenforschung, Planckstrasse 1, D- 64291 Darmstadt, Germany

2. 2007 November 23dlmos@pcqnt1.phys.spbu.ru Abstract The fully relativistic theory of the Zeeman splitting of the 1s and 2s hyperfine- structure levels in hydrogen- and lithiumlike Pb-207, respectively, is considered for the magnetic field magnitude in the range from 1 to 10 T. The second-order corrections to the Breit – Rabi formula are calculated and discussed. The results can be used for a precise determination of the nuclear magnetic moment, hyperfine structure (HFS), and electronic g j -factor of lead from g-factor experiments.

3. 2007 November 23dlmos@pcqnt1.phys.spbu.ru We consider a hydrogen- or lithiumlike Pb-207 in the ground state. The ion is placed in a homogeneous magnetic field B directed along the z axis. z B µ μ = is the nuclear magnetic moment I = ½ is the nuclear spin g I = μ/(μ N I ) is the nuclear g factor

4. 2007 November 23dlmos@pcqnt1.phys.spbu.ru Zeeman effect of the HFS levels ΔE HFS = E(F′) − E(F) ΔE mag = E − ½ [E(F) + E(F′)] For light ions ΔE mag ~ ΔE HFS For 207 Pb 81+ and 207 Pb 79+ ΔE mag << ΔE HFS F′ = 1 F = 0 M F =+1 M F =-1 M F =0 ΔE HFS (1s)= 1.22 eV (H-like lead) ΔE HFS (2s) =0.20 eV (Li-like lead) B = 1 – 10 T ΔE mag ~ 5*10 -4 eV 1s, 2s 207 Pb I =1/2

5. 2007 November 23dlmos@pcqnt1.phys.spbu.ru The Breit – Rabi formula for Pb-207

6. 2007 November 23dlmos@pcqnt1.phys.spbu.ru The individual contributions to the coefficients

7. 2007 November 23dlmos@pcqnt1.phys.spbu.ru The diagrams contributing to the Breit – Rabi formula coefficients

8. 2007 November 23dlmos@pcqnt1.phys.spbu.ru The idea of taking into account the interaction of the valent electron with the closed (1s) 2 electron shell.

9. 2007 November 23dlmos@pcqnt1.phys.spbu.ru

10. 2007 November 23dlmos@pcqnt1.phys.spbu.ru Corrections to the Breit – Rabi formula for H- and Li-like Pb-207

11. 2007 November 23dlmos@pcqnt1.phys.spbu.ru The numerical results

12. 2007 November 23dlmos@pcqnt1.phys.spbu.ru

13. 2007 November 23dlmos@pcqnt1.phys.spbu.ru

14. 2007 November 23dlmos@pcqnt1.phys.spbu.ru