1. HIGH RESOLUTION ROTATIONAL SPECTROSCOPY STUDY OF THE ZEEMAN EFFECT IN THE 2 Π 1/2 MOLECULE PbF Alex Baum, Benjamin Murphy, Richard Mawhorter Trevor J. Sears T. Zh.Yang, P.M Rupasinghe, C.P. McRaven, N.E. Shafer-Ray Lukas D. Alphei & Jens-Uwe Grabow Pomona College, Claremont, CA Brookhaven National Laboratory, Upton, NY University of Oklahoma, Norman, OK Leibniz Universität, Hannover, Germany June 23, 2011

2. Facts about PbF 1.1 unpaired electron 2. 2 Π 1/2 ground state 3. 4 isotopes - 204 Pb 19 F, 206 Pb 19 F, 207 Pb 19 F, 208 Pb 19 F - 19 F  I = ½ - (even) Pb  I = 0 - 207 Pb  I = ½ 4. e-EDM sensitive

3. Why do we like PbF? Very high internal electric field due to heavy nucleus Closely spaced states of opposite parity Small molecular g-factor (g≈0.05) Sensitivity to e-EDM in ground electronic state

4. Experimental Setup Supersonic-jet Fourier transform microwave spectrometer located at Leibniz Universität Hannover - 2-26.5 GHz range - Accurate to within 0.5 kHz Laser Ablation - 20Hz infrared laser pulses ablate lead into ions - Ions combine with fluorine introduced as ~1% SF 6 in Ne buffer gas

5. Experimental Setup 3 pairs of Helmholtz coils Able to produce magnetic fields up to ~4 Gauss From Jens-Uwe Grabow and Walther Caminati. Microwave spectroscopy: Experimental techniques. Frontiers of Molecular Spectroscopy, page p. 383. Elsevier, 2009

6. Zeeman Effect 2J+1 degeneracy of the spatial components of the rotational state with total angular momentum quantum number J lifted under application of a magnetic field Magnitude of splitting proportional to strength of magnetic field Selection rule ΔM J = 0 or +/-1 depending on relative orientation of applied magnetic field to MW electric field J J

7. Example Zeeman Spectra Perpendicular Magnetic Field: ∆M = ± 1 Parallel Magnetic Field: ∆M = 0

8. F = 3/2 → F = 5/2 transition: 207 PbF 22541.912MHz

9. Perpendicular Magnetic Field: ∆M = ± 1 F = 3/2 → F = 5/2 transition: 207 PbF 22541.912MHz

10. g-factor Definition In general, the g-factor relates the magnetic moment of a particle to its associated angular momentum. Examples include: Electron spin g-factor μ S =g e μ B S/ħ where μ B is the Bohr magneton. Nuclear g-factor μ N =g N μ N I/ħ where μ N is the nuclear magneton.

11. Zeeman Effect in 208 Pb 19 F Can approximate θ = 0 and μ N /μ B ∝ m e /m p ≈ 1/1800 ≈ 0 with about 95% accuracy... Goal: Determine G || and G ⊥

12. Zeeman Effect in 208 Pb 19 F With this approximation Now, for an individual quantum state i

16. Conclusions [2] K. I. Baklanov, A. N. Petrov, A. V. Titov, and M. G. Kozlov. Towards the electron EDM search. Theoretical study of PbF. ArXiv e-prints, January 2010. [19] M G Kozlov, V I Fomichev, Y Y Dmitriev, L N Labzovsky, and A V Titov. Calculation of the P- and T-odd spin-rotational hamiltonian of the PbF molecule. Journal of Physics B: Atomic and Molecular Physics, 20(19):4939, 1987. [25] P.M. Rupasinghe. Private Communication, 2010. This is the first experimental determination of the sign, and increases the precision in our knowledge of the value of the body fixed g-factors for PbF by more than an order of magnitude. This knowledge provides a strong foundation for the design of a robust and finely-tuned e-EDM experiment using PbF.

17. Acknowledgements Special thanks to Dr. Richard Mawhorter Dr. Jens-Uwe Grabow Dr. Neil Shafer-Ray Funded by a Sontag Fellowship from Pomona College