1. Spectroscopy in support of parity nonconservation measurements: the A2Π-X2Σ+(0,0) of Barium Monofluoride
Anh T. Le, Sarah Frey and Timothy C. Steimle Department of Chemistry and Biochemistry Arizona State University, Tempe,AZ 85287
Colan Linton
Dept. Phys., University of New Brunswick, Fredericton, NB, Canada
The 65th International Symposium
on Molecular Spectroscopy, June 2010
Funded by: NSF-Exp.

2. Motivation
Provide needed spectroscopic parameters for 137BaF and 135BaF in support of proposed experiment1 for measuring the P-odd nuclear spin-dependent parity non-conservation (NSD-PNC) effect resulting from the interaction of the anapole moment of nucleus with the unpaired electron of the X2S+ state.
A2P-X2S+ Band System
LIF
Detection S
NSD-PNC
Mixing
1.D. DeMille, S.B. Cahn, D. Murphree, D. A. Rahmlow and M.G. Kozlov, Phys. Rev. Lett, 100, , (2008).

3. Effective Hamiltonian
“Traditional” terms
Parity non-conservation terms
WAkA =Anapole moment -electron spin interaction
WSks =scalar electron - nuclei interaction
Wdde = electric dipole moment of electron, de, with effective electric field, Wd

4. Background 3.17(15) Previous work - 138BaF Previous work – 137&135BaF
% abundance
Nucl. Spin I
Mag. Mom
(nucl. Magneton)
Quad.mom
(Barns)
Dipole moment (Debye)
134Ba
1.42
X2Σ+
3.17(15)
135Ba
6.59
3/2
+0.838
0.160
136Ba
7.85
137Ba
11.23
+0.937
0.245
A2Π 1.306(11)
138Ba
71.70
19F
100
1/2
+2.628
Previous work - 138BaF
Numerous studies : Effantin et al, Ernst et al, Bernath et al
Previous work – 137&135BaF
137BaF X2Σ+:
Ryzlewicz et al Chem Phys. 71, 389 (1982) Microwave Rot. spectrum of X2S+
135BaF: No previous work
Goals: 1. Determine if existing parameters for 138BaF &137BaF can predict optical spectra and if not determine new parameters. 2. Predict Zeeman tuning of X2S+ & A2P.

5. Energy levels of the X2S+ 137BaF (Ryzlewicz et al )
Levels of interest in parity
Non-conservation experiments
Case bbJ
Limit
J=N+1/2
J=N-1/2
Case bbS
Limit
G(=I+S) 1 2
Spin-rotation
splitting
Mag. Hyf.
splitting

6. Experimental method A2P1/2-X2S+ ~11630 cm-1 A2P3/2-X2S+ ~12260 cm-1
PMT
Gated photon counter
skimmer
Ablation laser
Reagent
&
Carrier
Single freq. tunable laser radiation
Metal target
Pulse
valve
Well collimated
molecular beam
Rot.Temp.<10 K Ba
Absolute calibration .002 cm-1
Relative calibration .0001cm-1
A2P3/2-X2S+ ~12260 cm-1
A2P1/2-X2S+ ~11630 cm-1

7. Observation: QP21(6.5)&Q2(5.5) A2P3/2X2S+
QP21(6.5) 138BaF
Q2(5.5) 138BaF
Energy levels for 137BaF
Note
Observed
137BaF a
G=1 b
G=2
136BaF
135BaF
138BaF predicted
LIF signal
137BaF predicted1
1 A2P3/2: hyf. =0 & iso. scaled fine structure a b
135BaF predicted2
2 A2P3/2: hyf=0,X2S+ hyf. iso. scaled
Wavenumber

8. Observation: R1(1.5) A2P1/2X2S+
138,136,134BaF
G=2
G=1
137BaF
135BaF
LIF signal
137BaF predicted1
1 A2P1/2 hyperfine =0 & iso. scaled fine structure
135BaF predicted2
2 A2P1/2 hyperfine=0, bF(X2S+) scaled
Wavenumber
Energy levels for 137BaF

9. General conclusions from observations
a) The scaled 137BaF hyperfine parameters of the X2S+ state are not sufficient for predicting 135BaF.
b) The parameters, A, B, and T00 for the A2P state need to be slightly altered from those given by isotopic relationships.
c) The hyperfine structure for the A2P1/2 spin component has to be considered.
Need to fit the optical spectrum!

10. Analysis of observed 135BaF and 137BaF A2P-X2S+ spectra.
Effective Hamiltonian for X2S+:
16x16 matrix representation in a sequentially coupled Hund’s case (abJ) basis set Ybasis= |nL|(SS)J(JI1)F1(F1I2)FW
Effective Hamiltonian for A2P:
32x32 matrix representation in a sequentially coupled Hund’s case (abJ) basis set Ybasis= |nL|(SS)J(JI1)F1(F1I2)FW

11. Analysis (cont.) 137BaF 135BaF
The 90 precisely measured optical transition wavenumbers.
All the parameters for the X2Σ+(v=0) state were held fixed. The A, B, d(137Ba) and T00 parameters of the A2P(v=0) state were varied.
135BaF
The 60 precisely measured optical transition wavenumbers
The bF parameter of the X2Σ+(v=0) state was varied.
The A, B, and T00 parameters of the A2P(v=0) state were varied and d was scaled.

12. Results 135BaF: rms: =0.00188 cm-1 137BaF: rms: = 0.00181 cm-1
Parameter
Fitted Values (cm-1)
Isotopic scaled (cm-1)
A 2P(v=0) A
(59) B
(79) d
(92)
T0(A 2P)
(46)
135BaF: rms: = cm-1
Parameter
Fitted Values (cm-1)
Isotopic scaled (cm-1)
X2Σ+ bF
(41)
A 2P(v=0) A
(80) B
(11) d
T0(A2P)
(64)

13. Observation: R1(1.5) A2P1/2X2S+
Obs. G=1
137BaF a b c d
135BaF
Old 137BaF predicted
LIF signal
New 137BaF predicted
Old 135BaF predicted
New 135BaF predicted
Energy levels for 137BaF
Wavelength

14. Zeeman prediction
We have used the field-free parameters to predict the magnetic field tuning of the low-J lines for the X2S+ state. The effective Hamiltonian
was taken as:
A 64 x 64 matrix representation of HZee + Hfield-free operator was constructed in a sequentially coupled Hund’s case (abJ ) basis set and
numerically diagonalized to give the energies. gs=2.002, gl used Curl’s relationship. The results are:
Region of interest

15. Summary
1. First analysis of the A2P-X2S+ band system of 135BaF, 137BaF
2. Identification of the optimum optical transition to use in the proposed PNC experiment.
3. Predicted the Zeeman tuning of the X2S+ state of 137BaF .

16. Colan Linton
Tim Steimle
Sarah Frey
Fang Wang
Xiujuan Zhuang
Thank you