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

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

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

Experimental Setup Supersonic-jet Fourier transform microwave spectrometer located at Leibniz Universität Hannover 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

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 Elsevier, 2009

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

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

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

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

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.

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 ⊥

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

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 [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, [25] P.M. Rupasinghe. Private Communication, 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.

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