The effective Hamiltonian for the ground state of 207 Pb 19 F and the fine structure spectrum Trevor J. Sears Brookhaven National Laboratory and Stony Brook University RA th OSU Spectroscopy Symposium June 23, 2011 Support: Department of Energy Basic Energy Sciences and EPSCoR, Deutsche Forschungsgemeinschaft and Land Niedersachsen Richard Mawhorter, Benjamin Murphey, Alexander Baum, T. ZH Zhang, P. M. Rupasinghe, C. P. McRaven, N. E. Shafer-Ray, Lukas D. Alphei and Jens- Uwe Grabow

Introduction PbF has a 2 Π ground electronic state with the 2 Π 1/2 component lower. The fine structure splitting is about 8276 cm -1 *. There are multiple known excited electronic states, some of which are predissociative. But it is the lowest rotational levels of the ground state of 207 Pb 19 F that are of interest for a potential e-EDM measurement. *Ziebarth et al. J. Mol. Spec (1998)

Experimental Data Obtained in a pulsed FT MW spectrometer with an ablation supersonic nozzle source [Hannover]. A transition in 208 Pb 19 F between levels shown. Line is doubled due to axial Doppler effect in the spectrometer

Effective Hamiltonian Transitions observed in 204 Pb, 206 Pb, 207 Pb, and 208 Pb isotopomers. All have 19 F, with I=1/2 Even isotopes have I(Pb)=0, 207 Pb isotope I(Pb)=1/2 Fit all data to the effective Hamiltonian for 2 Π molecules H SR contains spin-orbit, rotation, spin-rotation, Λ-doubling… H HF-1 contains usual Frosch and Foley hfs Hamiltonian (2 nuclei for 207 Pb 19 F). Additional terms in H HF-2 were found to be needed to reproduce the high precision data for 207 Pb 19 F. These include a nuclear spin- spin dipolar interaction, and terms representing a J 2 dependence of H HF-1.

Hyperfine Terms Combinations of components of the hyperfine interaction tensor are related to the Frosch and Foley constants a, b, c and d. Preliminary analysis of the 207 PbF microwave data found the observed-calculated residuals were always greater than those for the even isotopes. Checked by writing two independent codes using different coupling schemes:

Smaller Hyperfine Terms The first term is a nuclear spin-rotation one for each nucleus, needed because of the precision of the data even though only low-J lines were observed. The second term is the nuclear spin-spin dipolar coupling The last term can be viewed as a spin-rotational (Ω- dependent) correction to I.J, or alternatively a centrifugal distortion (J 2 ) of I.S.

Data Fitting Deal with the even Pb isotope data first and determine the 19 F – dependent hyperfine terms. There is a weak isotopic trend with the Pb mass. Include data (lower precision) from the infrared work of Ziebarth et al. to determine spin-orbit and higher order spin-rotational and Λ-doubling terms Fix the 19 F terms from even isotope analysis and fit the 207 Pb 19 F data, including the infrared data as for the even isotopes. Data fit to expected precision and t 0 comes out close to expected on the basis of the nuclear magnetic moments and the PbF bond length!.

Fine Structure Spectrum? Promised a report on the experimental measurement of the low-J part of this spectrum Planned to do this using an ECDL-based spectrometer referenced to a frequency comb. Slit jet ablation source designed and constructed, but experiment has not yet begun  Maybe next year!

Conclusions and Acknowledgements The accuracy and precision of the FTMW data required the inclusion of additional small terms in the zero field effective hyperfine Hamiltonian in order for it to reproduce the experiment. Now the energy levels are known to extremely high precision and Stark/Zeeman experiments for P- and T- violation effects can be designed. I’m very grateful to all my collaborators, especially Neil Jens and Richard and their students for their inspiration and help.