Transcript OSU-TJS-2.ppt

The effective Hamiltonian for the
207
19
ground state of Pb F and the fine
structure spectrum
Trevor J. Sears
Brookhaven National Laboratory and Stony Brook
University
RA-06 66th OSU Spectroscopy Symposium June 23, 2011
Richard Mawhorter, Benjamin Murphey, Alexander Baum, T. ZH Zhang, P. M.
Rupasinghe, C. P. McRaven, N. E. Shafer-Ray, Lukas D. Alphei and JensUwe Grabow
Support: Department of Energy Basic Energy Sciences
and EPSCoR, Deutsche Forschungsgemeinschaft and
Land Niedersachsen
Introduction
PbF has a 2Π ground
electronic state with
the 2Π1/2 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 207Pb19F that are of
interest for a potential e-EDM
measurement.
*Ziebarth et al. J. Mol. Spec. 191 108 (1998)
Experimental Data
Obtained in a pulsed FT MW
spectrometer with an ablation
supersonic nozzle source
[Hannover]. A transition in
208Pb19F between levels shown.
Line is doubled due to axial
Doppler effect in the spectrometer
Effective Hamiltonian
•Transitions observed in 204Pb, 206Pb, 207Pb, and 208Pb
isotopomers. All have 19F, with I=1/2
•Even isotopes have I(Pb)=0, 207Pb isotope I(Pb)=1/2
•Fit all data to the effective Hamiltonian for 2Π molecules
H eff  H SR  H HF 1  H HF  2
HSR contains spin-orbit, rotation, spin-rotation, Λ-doubling…
HHF-1 contains usual Frosch and Foley hfs Hamiltonian (2 nuclei
for 207Pb19F).
Additional terms in HHF-2 were found to be needed to reproduce
the high precision data for 207Pb19F. These include a nuclear spinspin dipolar interaction, and terms representing a J2 dependence
of HHF-1.
Hyperfine Terms
H HF 1  I Pb . Aˆ .S   I F . Aˆ .S 
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 207PbF 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:
I Pb  I F  I ; I  J  F
I Pb  J  F1; F1  I F  F
Smaller Hyperfine Terms
H HF  2 cPb I Pb .J  cF I F .J
 .n)( I F .n)  ( I Pb .I F )]
 t0 [3( I Pb
 (d C ( Pb) I Pb .J  d C ( F ) I F .J )( J .S )
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 (Ωdependent) correction to I.J, or alternatively a centrifugal
distortion (J2) of I.S.
Data Fitting
Deal with the even Pb isotope data first and determine the 19F
– 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 19F terms from even isotope analysis and fit the
207Pb19F data, including the infrared data as for the even
isotopes.
cPb  36.8(1) kHz
d C ( Pb)  7(2) kHz
t0  2.2(6) kHz
Data fit to expected precision and t0
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 Tviolation 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.