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.

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, 023008, (2008).

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

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.

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

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

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

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

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!

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

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.

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 632.27979(59) B 0.2119401(79) 0.211931 d 0.00739(92) T0(A 2P) 11946.31531(46) 11946.30900 135BaF: rms: =0.00188 cm-1 Parameter Fitted Values (cm-1) Isotopic scaled (cm-1) X2Σ+ bF 0.07205(41) 0.06939 A 2P(v=0) A 632.27826(80) B 0.212275(11) 0.212314 d 0.00661 T0(A2P) 11946.30339(64) 11946.293969

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

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

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 .

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