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

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.

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

-1- NucleusIsotopeNatural Abundance (%) Spin(h/2  ) Magnetic moment (  N ) Elect. quadrupole moment( cm 2 ) Yb / / F100.01/ Nuclear Properties for Yb and F Many Isotopologues !

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

-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).

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).

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-

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

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

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

X 2   : Case b  S with two nuclear spin 173 Yb(I=5/2)F G = 2 & 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

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

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

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

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 D (  10 3 )  b F (F) c (F) FTMW Fitting procedure Isotopic relationships

State Parameter 170 YbF 171 YbF 172 YbF 173 YbF 174 YbF 176 YbF X 2  + b F (Yb) 0.241(2) (3) c (Yb) 0.014(1) [b] eQq 0 (Yb) (3) A 2  T 0 (-18700) (4) (2) (3) B (2) (6) (4) [a] (4) (5) (p+2q) (3) [a] (2) [a] (1) (1) d (Yb) (3) (7) eQq 0 (Yb) (5) Std. dev 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 ESR 0.010

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

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

Horn antenna Pump/Probe Double resonance Precise pure rotational spectroscopy

 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 !