Pressure-broadening of water lines in the THz frequency region: improvements and confirmations for spectroscopic databases G. Cazzoli, C. Puzzarini Dipartimento di Chimica “G. Ciamician”, Università di Bologna G. Buffa G. Buffa IPCF-CNR and Dipartimento di Fisica "E. Fermi", Pisa 10th International HITRAN Conference — June, 2008

OUTLINES 1) Experimental set-up: The THz spectrometer The THz spectrometer 2) Theoretical calculations: The semiclassical approach The semiclassical approach 1) Experimental details: The THz spectrometer The THz spectrometer 2) Theoretical calculations: The semiclassical approach The semiclassical approach 3) Experiment & Theory: Results Results 3) Experiment & Theory: Results Results

1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure

FREQUENCY RANGE LMSB (2) GHz (from fundamental to the 6th harmonic) GHz (8th harmonic) GHz (8th harmonic) (3) THz (9th harmonic) THz (12th harmonic) THz (12th harmonic) (1) GHz (wave-guide Stark cell – P band) (3) THz (9th harmonic) THz (12th harmonic) THz (12th harmonic)

BLOCK DIAGRAM of the THz SPECTROMETER MULTIPLIER SYNTH 10 kHz-1 GHz MULT fSfS nfSnfS MIX MULT SYNCR ref: 20 MHz RF OSCILL GHz f RF 20 MHz 73 MHz |f G - mf RF | GUNN P. SUPPLY and SYNCR ref: 73 MHz |f RF - nf S | HP8642A SYNTH MIX corr fGfG Ge DETECTOR PREAMPL 10 MHz freq. standard ref GUNN DIODES CELL FUNCTION GENERATOR 300 Hz CHOPPER LOCK-IN AMPLIFIER  FREQUENCY MODULATION TECHNIQUE 2x frequency modualtion

BLOCK DIAGRAM of the THz SPECTROMETER MULTIPLIER SYNTH 10 kHz-1 GHz MULT fSfS nfSnfS MIX MULT SYNCR ref: 20 MHz RF OSCILL GHz f RF 20 MHz 73 MHz |f G - mf RF | GUNN P. SUPPLY and SYNCR ref: 73 MHz |f RF - nf S | HP8642A SYNTH MIX corr fGfG Ge DETECTOR PREAMPL 10 MHz freq. standard ref GUNN DIODES CELL FUNCTION GENERATOR 300 Hz CHOPPER LOCK-IN AMPLIFIER  AMPLITUDE MODULATION TECHNIQUE chopper frequency revolution

(3) EXPERIMENTAL SET-UP in the THz REGION Quartz cell (1cm long)THz scource (gunn + multiplier) Chopper Bolometer The THz SPECTROMETER

(3) EXPERIMENTAL SET-UP in the THz REGION The THz SPECTROMETER THz scource Cell

1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure

AMPLITUDE MODULATION TECHNIQUE Natural line profile Lambert-Beer law I = I 0 exp[  ( - 0 )L]

LINE SHAPE ANALYSIS To retrieve COLLISIONAL HALF-WIDTH  L : by fitting the observed line profiles – natural line profiles - directly to the chosen line profile model (Voigt profile, Galatry profile, Speed Dependent Voigt profile, … …) Residuals: Residuals: Obs. – Calc.

SOURCE MODULATION TECHNIQUE FREQUENCY MODULATION (sine wave): (t) = ( - 0 ) +  cos  m t (t) = ( - 0 ) +  cos  m t  = modulation depth  = modulation depth  m = modulation frequency K(x, y, z) = Voigt, Galatry or SP-Voigt or … function Line profile expanded in a cosine Fourier series. 2nd harmonic detection: 2nd harmonic detection: a 2 (  ) = 2/   K(x,y,z) cos 2  d  a 2 (  ) = 2/   K(x,y,z) cos 2  d  0 Validity: Absorption  6% I = I 0 [1-  ( - 0 )L]

LINE SHAPE ANALYSIS COLLISIONAL HALF-WIDTH  L : by fitting the observed line profiles to a model that explicitly accounts for frequency modulation [Cazzoli & Dore JMS 141, 49 (1990); Dore JMS 221, 93 (2003)]. Residuals: Residuals: Obs. – Calc.

1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure

LINE SHAPE ANALYSIS: Which line profile model? Voigt profile Galatry profile The GHz line of O 3 broadened by N 2 LINE SHAPE ANALYSIS: Which line profile model?

Galatry vs Speed-dependent Voigt profile

RETRIEVAL PARAMETERS PRESSURE BROADENING COEFFICIENT  : PRESSURE BROADENING COEFFICIENT  : linear fit of  L against P by a weighted linear fit of  L against P  perturb 0000  L =  0 +  perturb  P perturb Lorentzian halfwidth Broadening due to absorber

RETRIEVAL PARAMETERS PRESSURE SHIFT COEFFICIENT s : PRESSURE SHIFT COEFFICIENT s : linear fit of against P by a weighted linear fit of against P = 0 + s perturb  P perturb = 0 + s perturb  P perturb Transition frequency Frequency at P pertub = 0 s 0

2) Theoretical calculations: The semiclassical approach The semiclassical approach 2) Theoretical calculations: The semiclassical approach The semiclassical approach

THEORETICAL DETAILS COLLISIONAL RELAXATION EFFICIENCY FUNCTION P COLLISIONAL RELAXATION described within the IMPACT APPROXIMATION by the EFFICIENCY FUNCTION P. P For a line i  f P = 1 - S = scattering matrix, H 0 = Hamiltonian of internal degrees, V = collisional interaction, O = time ordering operator. SEMICLASSICAL APPROXIMATIONb SEMICLASSICAL APPROXIMATION (impact parameter b, relative velocity v, internal state of perturber r): P = P(b,v,r) P = P(b,v,r). linewidth  lineshift s P The linewidth  and lineshift s : real and imaginary parts of P:  r = population of level r, f(v) = Maxwellian velocity distribution, n = perturber density.

3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: detailed comparison detailed comparison 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: detailed comparison detailed comparison

J = 3 1, ,3 * (1.097 THz) J = 3 1, ,3 * (1.097 THz) J = 1 1, ,0  (1.113 THz) J = 1 1, ,0  (1.113 THz) J = 7 2, ,8  (1.147 THz) J = 7 2, ,8  (1.147 THz) J = 3 1, ,1 * (1.153 THz) J = 3 1, ,1 * (1.153 THz) J = 6 3, ,1 * (1.158 THz) J = 6 3, ,1 * (1.158 THz) J = 3 2, ,2 * (1.163 THz) J = 3 2, ,2 * (1.163 THz) J = 8 5, ,1  (1.168 THz) J = 8 5, ,1  (1.168 THz) J = 7 4, ,1  (1.173 THz) J = 7 4, ,1  (1.173 THz) J = 8 5, ,2  (1.191 THz) J = 8 5, ,2  (1.191 THz) J = 6 3, ,2  (1.542 THz) J = 6 3, ,2  (1.542 THz) H 2 O: THz pure rotational lines investigated  Self-broad: amplitude modulation  N 2 - & O 2 -broad frequency modulation frequency modulation  Self-broad: amplitude modulation  N 2 - & O 2 -broad frequency modulation frequency modulation  Cazzoli et al. JQSRT 2008  Cazzoli et al. JQSRT submitted * Cazzoli et al. JQSRT in preparation

H 2 O: THz pure rotational lines investigated J = 3 1, ,3 * (1.097 THz) J = 3 1, ,3 * (1.097 THz) J = 1 1, ,0  (1.113 THz) J = 1 1, ,0  (1.113 THz) J = 7 2, ,8  (1.147 THz) J = 7 2, ,8  (1.147 THz) J = 3 1, ,1 * (1.153 THz) J = 3 1, ,1 * (1.153 THz) J = 6 3, ,1 * (1.158 THz) J = 6 3, ,1 * (1.158 THz) J = 3 2, ,2 * (1.163 THz) J = 3 2, ,2 * (1.163 THz) J = 8 5, ,1  (1.168 THz) J = 8 5, ,1  (1.168 THz) J = 7 4, ,1  (1.173 THz) J = 7 4, ,1  (1.173 THz) J = 8 5, ,2  (1.191 THz) J = 8 5, ,2  (1.191 THz) J = 6 3, ,2  (1.542 THz) J = 6 3, ,2  (1.542 THz) What was available for these lines? What was available for these lines? - experimental values for 1 1, ,0 (N 2 & O 2 ) - calculated and/or extrapolated data for others - experimental values for 1 1, ,0 (N 2 & O 2 ) - calculated and/or extrapolated data for others

3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: previous exp data previous exp data 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: previous exp data previous exp data

J = 1 1,1 – 0 0,0 transition of H 2 O T = 297 K Cazzoli et al. JQSRT 2008

J = 1 1,1 – 0 0,0 transition of H 2 O T = 297 K Cazzoli et al. JQSRT 2008

J = 1 1,1 – 0 0,0 transition of H 2 O T = 297 K Cazzoli et al. JQSRT 2008

Self N2N2N2N2 O2O2O2O2Air 297 K ExpTheoExpTheoExpTheoExpTheo This work 19.72(46) (15) (12) (13)3.8 Gasster Gasster et al. 3.67(10) 2.99(37) 3.53(8) HITRAN (8) J = 1 1,1 – 0 0,0 transition of H 2 O Improvements wrt old measurements Improvements wrt old measurements

3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: HITRAN self broad HITRAN self broad 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: HITRAN self broad HITRAN self broad

Cazzoli et al. JQSRT submitted

Cazzoli et al. JQSRT in preparation

ExpTheo This work J = 3 1, , (22)21.54 HITRAN This work J = 1 1, , (46)19.8 HITRAN 4.74 This work J = 7 2, , (34)17.93 HITRAN This work J = 3 1, , (18)21.22 HITRAN This work J = 6 3, , (8)16.27 HITRAN This work J = 3 2, , (11)19.80 HITRAN This work J = 8 5, , (26)11.33 HITRAN This work J = 7 4, , (27)13.03 HITRAN This work J = 8 5, , (8)11.88 HITRAN This work J = 6 3, ,2 17.56 HITRAN What’s the problem? What’s the problem?SELF-broadening

COMPARISON : semiclassical calc. (SC) vs HITRAN (assumption*) values * dependence of the broadening parameter on J”

COMPARISON : semiclassical calculations (SC) vs HITRAN (exp*) values * IR lines: cm -1 (R. A. Toth)

COMPARISON : semiclassical calculations (SC) vs EXP* values * Markov 1994, Cazzoli et al. 2007, Cazzoli et al. 2008

Suggestion: Make use of calculated values when no reliable experimental data are available HITRAN ref.# linesMean %error#lines with %err > 25% Ref. 51: Averaged values as a function of J”

3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: N 2, O 2 & air broad N 2, O 2 & air broad 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: N 2, O 2 & air broad N 2, O 2 & air broad

Cazzoli et al. JQSRT submitted

ExpTheo This work J = 3 1, , (82)4.00 HITRAN 4.13 This work J = 1 1, ,0 3.96(13)3.8 HITRAN3.53(8) This work J = 7 2, , (20)3.13 HITRAN 3.24 This work J = 3 1, , (75)3.77 HITRAN 3.65 This work J = 6 3, , (60)2.80 HITRAN 2.99 This work J = 3 2, , (57)3.77 HITRAN 3.93 This work J = 8 5, , (66)2.07 HITRAN 2.18 This work J = 7 4, , (34)2.42 HITRAN 2.59 This work J = 8 5, , (24)2.18 HITRAN 2.27 This work J = 6 3, , (72)3.28 HITRAN 3.32 Good agreement! Good agreement!AIR-broadening

3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: shift & SD param shift & SD param 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: shift & SD param shift & SD param

Cazzoli et al. JQSRT 2008

Cazzoli et al. JQSRT submitted

Cazzoli et al. JQSRT in preparation

Conclusions  10 pure rotational THz water lines have been experimentally and theoretically been experimentally and theoretically investigated investigated  Good agreement between experiment and SC calculations and SC calculations  Update for HITRAN self broadening parameters is suggested parameters is suggested  Rather accurate experimental results have been obtained have been obtained

Thank you for your attention!

temperature exponent n Least-square fit: ln(X/X 0 ) = n ln(T 0 /T) TEMPERATURE DEPENDENCE TEMPERATURE DEPENDENCE

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