Calculations and first quantitative laboratory measurements of O2 A-band electric quadrupole line intensities and positions 16O2 b(1) ← X (1) PQ(11) magnetic dipole hot band line S=2.87×10-27 cm molec-1 =12934.5516 cm-1 16O2 NO(21) electric quadrupole line S=3.70×10-30 cm molec-1 =12934.7490 cm-1 David A. Long, Mitchio Okumura, Caltech Charles E. Miller, Herbert M. Pickett, JPL Daniel K. Havey, Joseph T. Hodges, NIST, Gaithersburg

The O2 A-band: ← N must be odd for 16O2 and 18O2 intensity (10-25 cm molec.-1) PP,PQ RR,RQ |Δ J |= 0,1 |Δ J |= 0,1 |Δ J |= 2 Sband, MD~2.23×10-22 cm molec.-1 HITRAN 2008 |Δ J |= 2 PO RS intensity (10-30 cm molec.-1) Sband, EQ~1.8×10-27 cm molec.-1 N must be odd for 16O2 and 18O2 We will use the notation ΔNΔJ (N ΄΄) NO TS

Electric quadrupole transitions in the O2 A-band Overlap with MD transitions TS transitions first observed in the solar spectra of Brault (JMS, 1980). TS(9) line was observed in the laboratory by Naus et al (PRA, 1997). Present study has quantitatively measured nine transitions. Eight have not previously been observed. intensity (10-30 cm molec.-1) Brault * 12900 13000 13100 13200 13300 wave number (cm-1)

Why should we care about such weak transitions? A-band is widely utilized to determine optical pathlength and surface pressure via remote sensing EQ transitions have been observed in solar spectra. Can reach 1% absorbance. Can bias A-band remote sensing retrievals. High-resolution MD lineshape studies. A benchmark for ultra-sensitive techniques. Computational models. Figure from Yang et al. JQSRT, 2005

Frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) Leff~25 km FSR = c/2L = 200MHz frequency TEM00 TEM01

Spectral scans (mode jumping) dq 1. lock to local mode 2. acquire ring-down data 3. unlock laser 4. tune to next mode detuning

Electric quadrupole line position calculations: uncertainties less than 3 MHz Positions based on simultaneous fit to ground ( ) and excited state ( ). Utilized a fit to an ensemble of literature positions for the ν=0 and ν=1 levels of the ground state to determine lower state parameters: Raman: Rouillé et al. JMS, 1992; Millot et al. JMS, 1996; Brodersen et al. JMS, 2003; Brown et al., JMS, 2000. Microwave: Yu et al. JMS, 2005; Golubiatnikov et al. JMS, 2003; Endo et al. Jpn. J. Appl. Phys., 1982; Park et al. JQSRT, 1996. Far-infrared: Zink et al., JMS, 1987. FS-CRDS A-band MD positions of Robichaud et al. (JMS, 2008) used to determine upper state parameters. Positions were tied to 39K D1 and D2 transitions; uncertainties < 1MHz. Precise knowledge of EQ positions and probe laser frequency allowed us unambiguously locate EQ transitions and average over narrow spectral windows.

Short-term measurement statistics: ring-down time averaging Relative standard deviation in the ring-down time, στ/τ, <0.2%, facq~10 Hz → εNEA~2.5×10-10 cm-1 Hz -1/2 After 5s averaging, rms baseline=1.1×10-10 cm-1 Δtacq

Long-term measurement statistics: averaging of complete spectra After 10 h of averaging, observe steady reduction in baseline noise with an ns-1/2 dependence. Long-term averaging led to a reduction in detection limit by a factor of 10. Minimum rms baseline ~ 1.8×10-11 cm-1 → detection limit ~ 2.5×10-31 cm molec.-1. μ=0.46

Increase in signal-to-noise ratio with spectra averaging N.B. Middle and top spectra are offset vertically. NO(19) EQ transition S = 6.36×10-30 cm molec.-1

Spectra averaging with FS-CRDS does not lead to non-physical lineshapes SNR=18,000:1 Measured PP(21) MD line near the Doppler limit. Measured Doppler width agreed with calculated value to within 143 kHz (1/6000) on average with a standard deviation of 379 kHz. Center frequency agreed to 200 kHz. ns=1 ns=28

Examples of final electric quadrupole spectra: can resolve ultraweak lines in the wings of strong features 16O18O PP(11) MD line S=1.54×10-26 cm molec.-1 =13088.3092 cm-1 16O2 TS(5) EQ line S=2.05×10-29 cm molec.-1 =13179.9239 cm-1 16O2 NO(5) EQ line S=2.12×10-29 cm molec.-1 =13088.1529 cm-1

Lorentzian width utilized in Voigt profiles SNR of EQ spectra too low to retrieve wL. Set wL = 2γp. Utilized empirical J-dependent correlation of Yang et al. (JQSTR, 2005): with experimental FS-CRDS MD parameters of Robichaud et al. (JMS, 2008).

Observed linearity between peak area and O2 number density NO(5) NO(13) NO(15) NO(17) NO(19) NO(21) Solid lines are: (not a linear fit)

Uncertainty analysis Three dominant sources of uncertainty: 1) lineshape (self-broadening coefficient (γ) and use of Voigt profile) 2) ring-down cavity’s base losses 3) total losses (base plus absorption) Systematic uncertainties: 2.8-4.9% Random uncertainties: 2.3-9.9% Total uncertainties: 4.1-11% Observables which should not contribute: measurements of the cavity FSR, spectra’s frequency axes, sample temperature, pressure, and number density.

Electric quadrupole line intensity calculations Matrix elements of the transitions moments were derived using spherical tensor relations with Hund’s case (b) basis The three transition moments (M1, Q1, Q3) were then determined through a simultaneous fit to FS-CRDS MD and EQ measurements Transition Moments Band Intensities Sband, MD=2.25(2)×10-22 cm molec.-1 and Sband, EQ=1.8(1)×10-27 cm molec.-1 M1 Q1 Q3 0.06868(8) Bohr-magnetons 0.0124(4) Debye Å 0.00783(23) Debye Å

Electric quadrupole line intensity calculations: comparison to present measurements NO PO RS TS MAD(Present,Calc) = 5% which is within our average uncertainty Indicates that our measurements show the expected J and branch dependences

Electric quadrupole line intensity calculations: comparison to Brault NO TS PO RS Brault, JMS 1980. MAD(Brault,Calc) = 15% consistent with quadrature sum of uncertainties. Brault’s measurements are systematically low relative to calculations.

Take home points Frequency-stabilized cavity ring-down spectroscopy was utilized to quantitatively measure nine electric quadrupole transitions in the O2 A-band. Eight of these transitions have never before been measured Intensities ranged from S ~ 3×10-30 to 2×10-29 cm molec.-1 Uncertainty in S = 4.1-11% Detection limit of 2.5×10-31 cm-1 molec.-1 This level of sensitivity was possible due to: High reflectivity mirrors (R = 99.997%) Precise knowledge of EQ line positions Long-term averaging of entire spectra Long-timescale frequency stability

Funding D. A. Long: D. K. Havey: Research Funding: