1. The 61 th International Symposium on Molecular Spectroscopy. ‘06 Funded by: NSF- Exp. Phys. Chem Mag. Hyperfine Interaction in 171 YbF and 173 YbF Timothy C. Steimle, Tongmei Ma Arizona State University, USA & Colan Linton University of Brunswick, Canada

2. Motivation for Magnetic Hyperfine studies of YbF 1)Insight into f-block bonding & chemistry. Mag. hyf. interactions probe valence electrons: H= b F (I  S) + c(3I z S z - I  S)+…. b F (Fermi Contact)  Prob. of finding un-paired electron in vicinity of nuclei with non-zero spin c(Dipolar)  spatial coordinates r&  of unpaired electrons.

3. Motivation for Magnetic Hyperfine studies of YbF (cont.) 2) Needed in scheme to test of elementary particle physics beyond the standard model via measurement of electric dipole moment of electron, d e. d e Requires effective electric field of unpaired electron, W d W d is calculated using highly accurate  theory b F & c (Exp.) b F & c (calc. using  theory ) Most accurate test of  Theory

4. -1- NucleusIsotopeNatural Abundance (%) Spin(h/2  ) Magnetic moment (  N ) Elect. quadrupole moment(10 -24 cm 2 ) Yb 170 3.50 171 14.31/2+0.49367 172 21.90 173 16.15/2-0.67989+0.28 174 31.80 176 12.70 F100.01/2+2.682 Nuclear Properties for Yb and F Many Isotopologues !

5. 1.Barrow & Chojnicki “ Analysis of Optical …” J. Mol Spec. (1975) 2.Lee & Zare “ Chemiluminescence of YbCl & YbF“ J. Mol Spec. (1977) 3.Van Zee et al “ESR of YbF at 4K” JPC (1978). 4.Dunfield et al (New Brunswick group) “ Laser Spectroscopy…” J. Mol Spec. (1995). 5.Dickinson,Coxon,Walker&Gerry “ FTMW spectroscopy…”,JCP (2001). Previous Spectroscopic Studies YbF Ref. 4  Fine structure A 2  & X 2  parameters for 172 YbF, 174 YbF & 176 YbF Ref. 5  Precisely determined Fine and hyperfine parameters for 172 YbF, 174 YbF & 176 YbF for X 2   Ref. 3  Hyperfine parameters for 171 YbF, in matrix C. Linton Int. Sym. On Mol. Spectrosc. 1995

6. -2- Previous Spectroscopic Studies System Ed Hind’s Group 1.Sauer et al “Anomalous spin-rotation coupling in the X 2  +...” PRL (1995) 2.Sauer, et al “Laser-rf double resonance of 174 YbF in the X 2  + state: Spin- rotation, hyperfine interactions, and the electric dipole moment.” JCP (1996). 3.Sauer,et al “ Perturbed hyperfine doubling in the A 2  ½...” JCP (1999) 4.Tarbutt,et al “ A jet beam source of cold YbF radicals.” J Phys. B (2002) 5.Hudson, et al. “Measurement of the Electron Electric Dipole Moment Using YbF Molecules.” Phys. Rev.Lett. (2002), 6.Condylis et al “Stark shift of the A 2  1/2 state in 174 YbF ”. JCP (2005) G. Meijer’s group (Collaboration w/Hind’s) 1.Tarbutt et al “Slowing Heavy, ground-state molecules…” PRL, 92, (2004).

7. Electronic Structure predictions for YbF 1.Dolg, M. et al ‘A combination of quasirelativistic pseudopotential and ligand field…” Theo Chim Acta (1993). 2.Wang, et al, “ Density Functional calculation…” J Chem Phys. (1995). 3.Titov, etal “P,T-odd spin-rotational Hamiltonian for YbF.” PRL (1996). 4.Quiney, “Hyperfine and PT-odd effects in YbF 2  ” J Phys B (1998), 5.Parpia, “Ab initio calculation of the enhancement of the electric dipole moment of an electron in the YbF molecule.” J Phys B (1998) 6.Liu et al “Fully relativistic DFT….” JCP (1998). 7.Mosyagin, et al “Electric dipole moment of the electron in the YbF molecule.” J Phy. B: (1998) 8.Titov, et al. “ Two-step method for precise calculations of core properties in molecules” Int. J. Q. Chem. 104 (2005) 9.Nayak et al “Ab initio calculation of the P,T-odd effect in YbF” Chem Phys. Lett. (2006).

8. Experimental approach YbF skimmed molecular beam: Pulse Valve /Ablation Source SF 6 (2%) + Ar Plasma Pulse Valve 355 nm Nd:YAG Pulse Laser Yb Rod -3-

9. Molecular Beam LIF Spectrometer -4- (Or Pulsed dye) Or Box car

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

12. High-resolution LIF spectra of YbF: P 12 (4) branch feature of (0,0) band of A 2  1/2 - X 2  + transition 176 YbF 174 YbF 172 YbF 170 YbF 171 YbF G=0 G=1 173 YbF G=3 G=2

13. X 2   : Case b  S with two nuclear spin 173 Yb(I=5/2)F G = 2 & 3 171 Yb(I=1/2)F G = 0 & 1 A 2  : Case a  J with two nuclear spin 173 Yb(I=5/2)F F 1 = J-5/2.. J+5/2; F=F 1  1/2 171 Yb(I=1/2)F F 1 = J-1/2.. J+1/2; F=F 1  1/2

14. Electronic transitions for P 12 (4) of 171 YbF -7- X2+X2+ A 2  1/2

15. Energy Levels for P 12 (4) of 173 YbF -8- A 2  1/2 X2+X2+

16. What has been measured o P 12 (N) N= 2-11, 15 R 1 (N) N= 3-6, 10,15 170 YbF 171 YbF 172 YbF 173 YbF 174 YbF 176 YbF #32 123 34 149 32 34

17. Known or Estimated Molecular Constants for the X 2  + State of YbF (MHz) -9- Parameter 170 YbF 171 YbF 172 YbF 173 YbF 174 YbF [a] 176 YbF B 7250.0611 7246.3390 7242.1231 7237.9298 7233.8271 7225.7150 D (  10 3 ) 7.176 7.171 7.167 7.163 7.159 7.151  -13.44792 -13.44000 -13.43218 -13.42440 -13.14679 -13.40174 b F (F) 170.65878 170.58234 170.45900 170.36031 170.26374 170.07280 c (F) 85.6010 85.5052 85.5007 85.4512 85.4208 85.3070 FTMW Fitting procedure Isotopic relationships

18. State Parameter 170 YbF 171 YbF 172 YbF 173 YbF 174 YbF 176 YbF X 2  + b F (Yb) 0.241(2) -0.0657(3) c (Yb) 0.014(1) -0.00440 [b] eQq 0 (Yb) -0.0345(3) A 2  T 0 (-18700) 88.913(4) 88.899(2) 88.875(3) 88.860 88.845 88.811 B 0.24583(2) 0.24839(6) 0.24825(4) 0.2481 [a] 0.24797(4) 0.24769(5) (p+2q) -0.3978(3) -0.3976 [a] -0.3974(2) -0.3972 [a] -0.3971(1) -0.3966(1) d (Yb) 0.0360(3) -0.0107(7) eQq 0 (Yb) -0.0365(5) Std. dev. 0.00320 0.00305 0.00214 0.00235 0.00228 0.00216 -10- Fitting procedure Transition wavenumbers fitted directly to standard 2-spin hamiltonian operator. X 2  + :  D,  b F (F) &  c(F) for all isotopologues held fixed to the scaled FTMW values. ESR 0.254 ESR 0.010

19. Modeling spectra-Results for o P 14 (4) Calc

20. Future work: Optical Zeeman Spectroscopy 171 YbF G=0 O P 12 (4) {

21. Horn antenna Pump/Probe Double resonance Precise pure rotational spectroscopy

22.  A 2  1/2 -X 2  + (0,0) band of YbF was recorded at near-natural linewidth limit.  Magnetic hyperfine parameters for both ground and excited states of 171 YbF and 173 YbF were obtained.  Optical Zeeman measurements in progress. Concluding Remarks Thank you !