Funded by: NSF-Exp. Tongmei Ma & Timothy C. Steimle Dept. Chem. & BioChem., Arizona State University, Tempe, AZ,USA Optical Zeeman Spectroscopy of ytterbium monoflouride, YbF Colan Linton Dept. Phys., University of New Brunswick, Frederiction, NB, Canada John Brown & Cleone Butler Physical & Theoretical Chemistry, Oxford University, Oxford, UK The 63 rd International Symposium on Molecular Spectroscopy, June 2008

The “why & how”  Why? The heavy polar molecule, YbF, has been used to set an upper limit on the electric-dipole moment of the electron, d e.  Why? Precise knowledge of the magnetic g-factors are needed for experimental measurement of d e.  How? Analysis of ultra-high resolution Optical Zeeman spectrum. Hudson et al Phys. Rev. Lett. 2002

Approach-Optical Zeeman Spectroscopy 1.Record at near natural linewidth the (0,0) A 2   - X 2  + band of YbF field-free [a]. (Last year OSU) 2.Based upon results of “1”, record and analyze the optical Zeeman effect in the low-J branch features to obtain g-factors for both (v=0) A 2  1/2 and X 2  + states of YbF. [a] : T.C. Steimle, T. Ma and C. Linton, J. Chem. Phys., 127, Well collimated molecular beam Rot.Temp.<10 K Single freq. tunable laser radiation PMT Gated photon counter Metal target Pulse valve skimmer Ablation laser Reagent & Carrier Electromagnet

-5- Electromagnet for Zeeman spectroscopy (50G-1.2kG) Mirror (3kG-4kG) NdFeB permanent magnets

Low-resolution LIF with Pulsed Dye laser O P 12 (4) Next frame

High-resolution LIF spectra of YbF: O P 12 (4) Typical branch feature of (0,0) A 2  1/2 - X 2  + band 176 YbF 174 YbF 172 YbF 170 YbF YbF G=2 G=3 171 YbF G=1(a-h) G=0 (i) ZEEMAN MEASUREMENT: 172 YbF 171 YbF,G=0 174 YbF

Field-free parameters for the v=0 of X 2  + and A 2   states of YbF [a] [a] : T.C. Steimle, T. Ma and C. Linton, J. Chem. Phys., 127,

172 YbF (0,0) A 2   -X 2  + Optical Zeeman Transitions: Selected for Zeeman cm -1 & cm -1

Zeeman Tuning of the O P 12 (2) transition for (0,0)A 2  1/2 -X 2  + of 172 YbF (v=0) X 2  + N=2 (v=0)A 2  1/2 J=0.5 I II I Last slide Note: Significant tuning Mag. Field (G)

171 YbF (0,0) A 2   -X 2  + Optical Zeeman Transitions: O P 12 (4): cm -1 ; O P 12 (3): cm -1 ; O P 12 (2) cm -1 Selected for Zeeman (next slide)

Zeeman Tuning of the O P 12 (2) transition for (0,0)A 2  1/2 -X 2  + of 171 YbF (v=0) X 2  + N=2 (v=0)A 2  1/2 J=0.5 Last slide Mag. Field (G)

Field-free Hamiltonian: X 2  + :8×8 mat.rep.,Hund’s case (a) BN 2 -DN 4 +γN·S+b F (F)I·S+c(F)×(I z S z -1/3I·S) A 2  1/2 :16×16 mat.rep.,Hund’s case (a) T 0,0 +AL z S z +1/2A D [N 2 L z S z +L z S z N 2 ]+BN 2 -DN 4 + ½(p+2q)(e -2i  J + S + +e -2i  J - S - )+aI z L z +b F I·S+c(L z S z - ½I·S)+½d(e -2i  I + S + +e -2i  I - S - ) Analysis Zeeman Hamiltonian A 2  1/2 Four possible parameters; g L, g S,g l’ & g l X2X2 Three possible parameters; g S, g l’ & g l

Analysis-cont’ Diagonalize  eigenvalues & eigenvectors Truncate matrix to include lowest 6 rot. levels 96x96 mat. rep. J=1/2 16x16 J=3/2 16x16 J=5/2 16x16 J=7/2 16x16 J=9/2 16x16 J=11/2 16x16 48x48 mat. rep. N=0 8x8 N=1 8x8 N=2 8x8 N=3 8x8 N=4 8x8 N=5 8x8 X2+X2+ A2A2

Experimental g-factors for YbF State g S g L g l g l ’ X 2  (42) NA (Fix) 0.0(Fix) A 2  1/ (Fix) (92) 0.0(Fix) (54) Rms:10.3 MHz g l (X 2  + ) fixed to Curl relationship Large > 1 > 2.002

A    (v = 0) state: Interpretation of g-factors for YbF Hund’s Case a limit  E Zee = Obs.shift is significant  E Zee (    )= 0 g L =1 & g S =2.00 Fitted g L (=1.101) >1 A    B     E~3000cm -1 Fitted g L > 1 A    B    mixing g l ’ (fitted)= Further evidence of mixing: g l ’ (Curl Relationship)= X    (v = 0) state: Fitted g S (=2.0646(64)) Significantly bigger than Difficult to rationalize-thinking about this!

Concluding remarks The magnetic tuning of the low-J features in the A 2  -X 2  + transition has been precisely determined. The magnetic g-factors in the A 2   state differ significantly from those expected for a pure “ 2  “ state. Thank You !