HIGH RESOLUTION ROTATIONAL SPECTROSCOPY STUDY OF THE ZEEMAN

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

Facts about Pb. F 1. 1 unpaired electron 2. 2Π 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

Why do we like Pb. F? • 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 - 2 -26. 5 GHz range - Accurate to within 0. 5 k. Hz Laser Ablation - 20 Hz 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. 383. Elsevier, 2009

Zeeman Effect 2 J+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 ΔMJ = 0 or +/-1 depending on relative orientation of applied magnetic field to MW electric field J J

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

F = 3/2 → F = 5/2 transition: 207 Pb. F 22541. 912 MHz Parallel Magnetic Field: ∆M = 0

F = 3/2 → F = 5/2 transition: 207 Pb. F 22541. 912 MHz Perpendicular Magnetic Field: ∆M = ± 1

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 μS=geμBS/ħ where μB is the Bohr magneton. • Nuclear g-factor • μN=g. NμNI/ħ where μN is the nuclear magneton.

Zeeman Effect in 208 Pb 19 F Goal: Determine G|| and G⊥ Can approximate θ = 0 and μN/μB ∝ me/mp ≈ 1/1800 ≈ 0 with about 95% accuracy. . .

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 Pb. F. Ar. Xiv 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 Pb. F 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 Pb. F 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 Pb. F.

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