HIGH RESOLUTION ROTATIONAL SPECTROSCOPY STUDY OF THE ZEEMAN EFFECT IN THE 2Π1/2 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. 2Π1/2 ground state

3. 4 isotopes- 204Pb19F, 206Pb19F, 207Pb19F, 208Pb19F- 19F I = ½- (even)Pb I = 0- 207Pb 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

- 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% SF6 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

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 ΔMJ = 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

Parallel Magnetic Field: ∆M = 0

F = 3/2 → F = 5/2 transition: 207PbF22541.912MHz

Perpendicular Magnetic Field: ∆M = ± 1

F = 3/2 → F = 5/2 transition: 207PbF22541.912MHz

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=gNμNI/ħ where μN is the nuclear magneton.

Zeeman Effect in 208Pb19F

Can approximate θ = 0 and μN/μB m∝ e/mp ≈ 1/1800 ≈ 0 with about 95% accuracy...

Goal: Determine G|| and G⊥

Zeeman Effect in 208Pb19F

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 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.

Acknowledgements

Special thanks to

•Dr. Richard Mawhorter•Dr. Jens-Uwe Grabow•Dr. Neil Shafer-Ray

Funded by a Sontag Fellowship from Pomona College