pressure-broadening of water lines in the thz frequency region: improvements and confirmations for...

Pressure-broadening of water lines Pressure-broadening of water lines in the THz frequency region: in the THz frequency region:

improvements and confirmations improvements and confirmations for spectroscopic databasesfor spectroscopic databases

G. Cazzoli, G. Cazzoli, C. PuzzariniC. PuzzariniDipartimento di Chimica “G. Ciamician”, Università Dipartimento di Chimica “G. Ciamician”, Università

di Bolognadi Bologna

G. BuffaG. BuffaIPCF-CNR and Dipartimento di Fisica "E. Fermi", PisaIPCF-CNR and Dipartimento di Fisica "E. Fermi", Pisa

10th International HITRAN Conference 10th International HITRAN Conference — 22-24 June, 2008— 22-24 June, 2008

OUTLINESOUTLINES

1) Experimental set-up:1) Experimental set-up: The THz spectrometerThe THz spectrometer

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

1) Experimental details:1) Experimental details: The THz spectrometer The THz spectrometer

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

3) Experiment & Theory:3) Experiment & Theory: ResultsResults3) Experiment & Theory:3) Experiment & Theory: ResultsResults

1) Experimental details:1) Experimental details: The THz spectrometerThe THz spectrometer - set upset up - techniquestechniques - procedure - procedure

1) Experimental details:1) Experimental details: The THz spectrometerThe THz spectrometer - - set upset up - techniquestechniques - procedure - procedure

FREQUENCY RANGE covered @ LMSBFREQUENCY RANGE covered @ LMSB

(2) 50-600 GHz (from fundamental to the 6th harmonic) (2) 50-600 GHz (from fundamental to the 6th harmonic) + 600-800 GHz (8th harmonic)+ 600-800 GHz (8th harmonic)

(3)(3) 1.0-1.2 THz (9th harmonic) 1.0-1.2 THz (9th harmonic) + 1.33-1.6 THz (12th harmonic)+ 1.33-1.6 THz (12th harmonic)

(1) 8-120 GHz (wave-guide Stark cell – P band) (1) 8-120 GHz (wave-guide Stark cell – P band)

(3) 1.0-1.2 THz (9th harmonic) (3) 1.0-1.2 THz (9th harmonic) + 1.33-1.6 THz (12th harmonic)+ 1.33-1.6 THz (12th harmonic)

BLOCK DIAGRAM of the 1.0-1-6 THz SPECTROMETER

MULTIPLIER

SYNTH10 kHz-1 GHzMULT fS

nfS

MIXMULT

SYNCRref: 20 MHz

RF OSCILL3.7- 7.6 GHz

fRF

20 MHz

73 MHz|fG - mfRF |

GUNN P. SUPPLY and

SYNCRref: 73 MHz

|fRF - nfS|

HP8642ASYNTH

MIX

corr

fG

GeDETECTOR

PREAMPL

10 MHzfreq. standard

ref

GUNNDIODES CELL

FUNCTIONGENERATOR

300 Hz

CHOPPERCHOPPER

LOCK-INAMPLIFIER

FREQUENCY MODULATION TECHNIQUEFREQUENCY MODULATION TECHNIQUE

2x frequency modualtion2x frequency modualtion

BLOCK DIAGRAM of the 1.0-1-6 THz SPECTROMETER

MULTIPLIER

SYNTH10 kHz-1 GHzMULT fS

nfS

MIXMULT

SYNCRref: 20 MHz

RF OSCILL3.7- 7.6 GHz

fRF

20 MHz

73 MHz|fG - mfRF |

GUNN P. SUPPLY and

SYNCRref: 73 MHz

|fRF - nfS|

HP8642ASYNTH

MIX

corr

fG

GeDETECTOR

PREAMPL

10 MHzfreq. standard

ref

GUNNDIODES CELL

FUNCTIONGENERATOR

300 Hz

CHOPPERCHOPPER

LOCK-INAMPLIFIER

AMPLITUDE MODULATION TECHNIQUEAMPLITUDE MODULATION TECHNIQUE

chopper frequency revolutionchopper frequency revolution

(3) EXPERIMENTAL SET-UP (3) EXPERIMENTAL SET-UP in thein the THz REGION THz REGION

Quartz cell (1cm long) THz scource (gunn + multiplier)

ChopperBolometer

The 1.0-1.6 THz The 1.0-1.6 THz SPECTROMETERSPECTROMETER

(3) EXPERIMENTAL SET-UP (3) EXPERIMENTAL SET-UP in thein the THz REGION THz REGIONThe 1.0-1.2 THz The 1.0-1.2 THz SPECTROMETERSPECTROMETER

THz scourceTHz scource

Cell Cell


1) Experimental details:1) Experimental details: The THz spectrometerThe THz spectrometer - set upset up - - techniquestechniques - procedure - procedure

AMPLITUDE MODULATION TECHNIQUEAMPLITUDE MODULATION TECHNIQUE

1146550 1146600 1146650

Frequency (MHz)

Self-broadening: J = 72,5 - 8

1,8

residuals x 3

Natural line Natural line profileprofile

Lambert-Beer Lambert-Beer lawlaw

II = = II00 exp[ exp[((--00))LL]]

LINE SHAPE ANALYSISLINE SHAPE ANALYSISTo retrieve To retrieve COLLISIONAL HALF-WIDTH COLLISIONAL HALF-WIDTH LL:: by fitting the observed line profiles – natural line profiles - by fitting the observed line profiles – natural line profiles - directlydirectly to the chosen line profile model (Voigt profile, to the chosen line profile model (Voigt profile, Galatry profile, Speed Dependent Voigt profile, … …)Galatry profile, Speed Dependent Voigt profile, … …)

1146550 1146600 1146650

Frequency (MHz)


1,8

residuals x 3

Residuals:Residuals:Obs. – Calc.Obs. – Calc.

SOURCE MODULATION TECHNIQUESOURCE MODULATION TECHNIQUEFREQUENCY MODULATIONFREQUENCY MODULATION (sine wave): (sine wave):

((tt)) = = (( - - 00)) + + cos cos mmtt

== modulation modulation depthdepth mm== modulation modulation frequencyfrequency

K(x, y, z) K(x, y, z) = Voigt, Galatry or SP-Voigt or … function= Voigt, Galatry or SP-Voigt or … function

Line profile expanded in a cosine Fourier Line profile expanded in a cosine Fourier series.series.

2nd harmonic detection:2nd harmonic detection: aa2 2 (() = 2/) = 2/ K(x,y,z) cos 2K(x,y,z) cos 2

dd

00301805 301810 301815 301820 301825

O3: 301.8 GHZ line

O2-broadening

T = 296 K

40.4139.5240.1342.5447.2

FREQUENCY (MHz)

Validity:Validity: Absorption Absorption 6% 6%

II = = II00 [1- [1- ((--00))LL]]

LINE SHAPE ANALYSISLINE SHAPE ANALYSISCOLLISIONAL HALF-WIDTH COLLISIONAL HALF-WIDTH LL:: by fitting the observed line profiles to a by fitting the observed line profiles to a model that model that explicitly accounts for frequency modulationexplicitly accounts for frequency modulation [Cazzoli & Dore JMS 141, 49 (1990); Dore JMS 221, 93 (2003)].

301805 301810 301815 301820 301825

O3: 301.8 GHZ line

O2-broadening

T = 296 K

40.4139.5240.1342.5447.2

FREQUENCY (MHz)

Residuals:Residuals:Obs. – Calc.Obs. – Calc.


1) Experimental details:1) Experimental details: The THz spectrometerThe THz spectrometer - set upset up - techniquestechniques - - procedureprocedure

LINE SHAPE ANALYSIS:LINE SHAPE ANALYSIS:Which line Which line profile model?profile model?

301805 301810 301815 301820 301825

Frequency (MHz)

Voigt profileVoigt profile301805 301810 301815 301820 301825

Frequency (MHz)

Galatry profileGalatry profile

The 301.8 GHz line of OThe 301.8 GHz line of O33 broadened by N broadened by N22

LINE SHAPE ANALYSIS:LINE SHAPE ANALYSIS:Which line Which line profile model?profile model?

301810 301811 301812 301813 301814 301815 301816

301.8 GHz line of O3:

O2-broadening at T=240 K

PO2

= 201.8 mTorr

Frequency (MHz)

EXP VP obs-calc (VP) obs-calc (SDVP) obs-calc (GP)

(a)

(b)

(c)

(d)

LINE SHAPE ANALYSIS:LINE SHAPE ANALYSIS:Which line Which line profile model?profile model?LINE SHAPE ANALYSIS:LINE SHAPE ANALYSIS:Which line Which line profile model?profile model?Galatry vs Speed-dependent Voigt profileGalatry vs Speed-dependent Voigt profile

0 200 400 600 800 1000

0

500

1000

1500

2000

2500

3000

3500

4000

rela

xatio

n rate

(kH

z)

PO2

(mTorr)

317.2 GHz line of O3:

O2-broadening at T=240 K

SDV rate in blue (SDVP)

2 rate in blue (SDVP)

rate in red (GP)

RETRIEVAL PARAMETERSRETRIEVAL PARAMETERS

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200

1400

1600

L (kH

z)

Pperturb (mTorr)

PRESSURE BROADENING COEFFICIENT PRESSURE BROADENING COEFFICIENT

:: by a weighted linear fit of linear fit of LL against against PP

perturbperturb

00

L L == 0 0 + + perturbperturb P Pperturbperturb

Lorentzian halfwidthLorentzian halfwidth

Broadening due to absorberBroadening due to absorber

0 100 200 300 400 5006.552

6.554

6.556

6.558

6.560

6.562

6.564

6.566

6.568

Fre

quency (M

Hz)

Pperturb

(mTorr)

RETRIEVAL PARAMETERSRETRIEVAL PARAMETERS

PRESSURE SHIFT COEFFICIENT sPRESSURE SHIFT COEFFICIENT s:: by a weighted linear fit of linear fit of against against PP

== 0 0 + s+ sperturbperturb P Pperturb perturb

Transition frequencyTransition frequency

Frequency at PFrequency at Ppertubpertub = 0 = 0ss

00

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

THEORETICAL DETAILSTHEORETICAL DETAILS

COLLISIONAL RELAXATIONCOLLISIONAL RELAXATION described within the IMPACT APPROXIMATION by the EFFICIENCY FUNCTION EFFICIENCY FUNCTION PP.

For a line i f PP = 1 - < i | S | i ><f | St | f >

S = scattering matrix, H0 = Hamiltonian of internal degrees, V = collisional interaction, O = time ordering operator.

SEMICLASSICAL APPROXIMATIONSEMICLASSICAL APPROXIMATION (impact parameter bb, relative velocity v, internal state of perturber r): PP = = PP((b,v,rb,v,r)).

The linewidth linewidth and lineshift lineshift ss: real and imaginary parts of PP:

r = population of level r, f(v) = Maxwellian velocity distribution, n = perturber density.

dtetVeOS tiHtiH

// )(exp 00

1

r

rdb r v b bP dv v vf n is00

2) , , ( ) (

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - theo & exp results:- theo & exp results: detailed comparisondetailed comparison

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - - HH22O: which linesO: which lines - theo & exp results:- theo & exp results: detailed comparisondetailed comparison

JJ = 3 = 31,21,2 - 3 - 30,30,3** (1.097 THz) (1.097 THz) JJ = 1 = 11,11,1 - 0 - 00,00,0

(1.113 THz) (1.113 THz) JJ = 7 = 72,52,5 - 8 - 81,81,8

(1.147 THz) (1.147 THz) JJ = 3 = 31,21,2 - 2 - 22,12,1** (1.153 THz) (1.153 THz) JJ = 6 = 63,43,4 - 5 - 54,14,1** (1.158 THz) (1.158 THz) JJ = 3 = 32,12,1 - 3 - 31,21,2** (1.163 THz) (1.163 THz) JJ = 8 = 85,45,4 - 7 - 76,16,1

(1.168 THz) (1.168 THz) JJ = 7 = 74,44,4 - 6 - 65,15,1

(1.173 THz) (1.173 THz) JJ = 8 = 85,35,3 - 7 - 76,26,2

(1.191 THz) (1.191 THz) JJ = 6 = 63,33,3 - 5 - 54,24,2

(1.542 THz) (1.542 THz)

HH22O: THz pure rotational lines investigatedO: THz pure rotational lines investigated

Self-broad:Self-broad:amplitude modulationamplitude modulation

NN22- - && O O22-broad -broad frequency modulationfrequency modulation

Self-broad:Self-broad:amplitude modulationamplitude modulation

NN22- - && O O22-broad -broad frequency modulationfrequency modulation

Cazzoli et al. JQSRT 2008 Cazzoli et al. JQSRT 2008

Cazzoli et al. JQSRT submitted Cazzoli et al. JQSRT submitted **Cazzoli et al. JQSRT in preparation Cazzoli et al. JQSRT in preparation

HH22O: THz pure rotational lines investigatedO: THz pure rotational lines investigated

JJ = 3 = 31,21,2 - 3 - 30,30,3** (1.097 THz) (1.097 THz) JJ = 1 = 11,11,1 - 0 - 00,00,0

(1.113 THz) (1.113 THz) JJ = 7 = 72,52,5 - 8 - 81,81,8

(1.147 THz) (1.147 THz) JJ = 3 = 31,21,2 - 2 - 22,12,1** (1.153 THz) (1.153 THz) JJ = 6 = 63,43,4 - 5 - 54,14,1** (1.158 THz) (1.158 THz) JJ = 3 = 32,12,1 - 3 - 31,21,2** (1.163 THz) (1.163 THz) JJ = 8 = 85,45,4 - 7 - 76,16,1

(1.168 THz) (1.168 THz) JJ = 7 = 74,44,4 - 6 - 65,15,1

(1.173 THz) (1.173 THz) JJ = 8 = 85,35,3 - 7 - 76,26,2

(1.191 THz) (1.191 THz) JJ = 6 = 63,33,3 - 5 - 54,24,2

(1.542 THz) (1.542 THz)

What was available for these lines? What was available for these lines?

- experimental values for 1- experimental values for 11,1 1,1 - 0- 00,00,0 (N (N22 && O O2 2 ) ) - calculated and/or extrapolated data for otherscalculated and/or extrapolated data for others - - experimental values for 1experimental values for 11,1 1,1 - 0- 00,00,0 (N (N22 && O O2 2 ) ) - calculated and/or extrapolated data for others calculated and/or extrapolated data for others

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - theo & exp results:- theo & exp results: previous exp dataprevious exp data

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - - theo & exp results:theo & exp results: previous exp dataprevious exp data

0 100 200 300 400 500 600 7000

2

4

6

8

10

12

14Self - broadening: 19.72(46) MHz/Torr

L (M

Hz)

H2O pressure (mTorr)

EXPTHEO

HITRAN

JJ = 1 = 11,11,1 – 0 – 00,00,0 transition of H transition of H22OO

T = 297 KT = 297 K

Cazzoli et al. JQSRT 2008Cazzoli et al. JQSRT 2008

0 100 200 300 400 500 600 7000.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

N

L (M

Hz)

N2 partial pressure (mTorr)

N2 - broadening:

4.38(15) MHz/Torr

Gasster et al JOSA B 1988

EXPTHEO


T = 297 KT = 297 K


0 100 200 300 400 500 600 7000.0

0.4

0.8

1.2

1.6

2.0

2.4

Gasster et al JOSA B 1988

O2 - broadening:

2.40(12) MHz/Torr

NL (M

Hz)

O2 partial pressure (mTorr)

EXP

THEO


T = 297 KT = 297 K


SelfSelf NN22 OO22 AirAir

297 K297 K ExpExp TheTheoo

ExpExp TheTheoo

ExpExp TheTheoo

ExpExp TheTheoo

This This workwork

19.72(4619.72(46))

19.819.8 4.38(154.38(15))

4.24.2 2.40(122.40(12))

2.52.5 3.96(133.96(13))

3.83.8

Gasster Gasster et al.et al.

3.67(103.67(10))

2.99(372.99(37))

3.53(8)3.53(8)

HITRANHITRAN 4.744.74 3.53(8)3.53(8)


Improvements wrt old measurementsImprovements wrt old measurements

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - theo & exp results:- theo & exp results: HITRAN self broadHITRAN self broad

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - - theo & exp results:theo & exp results: HITRAN self broadHITRAN self broad

0 200 400 600 800 10000

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

L (k

Hz)

water pressure (mTorr)


1,8

17.96(34) MHz/Torr

HITRAN

EXP

THEO

Cazzoli et al. JQSRT submitted Cazzoli et al. JQSRT submitted

0 200 400 600 800 10000

2000

4000

6000

8000

10000

12000

14000

16000


6,1

11.12(26) MHz/Torr

L (

kHz)


HITRAN

THEO

EXP


0 200 400 600 800 10000

2000

4000

6000

8000

10000

12000

14000 Self-broadening: J = 74,4 - 6

5,1

11.98(27) MHz/Torr

HITRAN

THEO

EXP


L (

kHz)


0 200 400 600 800 10000

2000

4000

6000

8000

10000

12000

14000

16000

L (

kHz)



4,1

14.97(8) MHz/Torr

HITRAN

THEO

EXP

Cazzoli et al. JQSRT in preparationCazzoli et al. JQSRT in preparation

0 200 400 600 800 10000

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

L (

kHz)


1,2

19.23(11) MHz/Torr

HITRAN


THEO

EXP

Cazzoli et al. JQSRT in preparation Cazzoli et al. JQSRT in preparation

ExpExp TheoTheo

This workThis work JJ = 3 = 31,21,2 - 3 - 30,30,3 21.98(22)21.98(22) 21.5421.54

HITRANHITRAN 18.4018.40This workThis work JJ = 1 = 11,11,1 - 0 - 00,00,0 19.72(46)19.72(46) 19.819.8








HITRANHITRAN 15.1615.16This workThis work JJ = 6 = 63,33,3 - 5 - 54,24,2 17.5617.56

HITRANHITRAN 16.9416.94

What’s the problem? What’s the problem?

SELF-broadeningSELF-broadening

COMPARISONCOMPARISON: : semiclassical calc. (SC) vs HITRAN (assumption*) valuessemiclassical calc. (SC) vs HITRAN (assumption*) values

**dependence of the broadening parameter on dependence of the broadening parameter on J”J”

COMPARISONCOMPARISON: : semiclassical calculations (SC) vs HITRAN (exp*) valuessemiclassical calculations (SC) vs HITRAN (exp*) values

**IR lines: 600-1000 cmIR lines: 600-1000 cm-1-1 (R. A. Toth) (R. A. Toth)

COMPARISONCOMPARISON: : semiclassical calculations (SC) vs EXP* valuessemiclassical calculations (SC) vs EXP* values

**Markov 1994, Cazzoli et al. 2007, Cazzoli et al. 2008 Markov 1994, Cazzoli et al. 2007, Cazzoli et al. 2008

SuggestionSuggestion: : Make use of calculated values when no Make use of calculated values when no reliable experimental data are availablereliable experimental data are available

HITRAN ref. # lines Mean %error #lines with %err > 25%

3 98 8.3 1013 6 43.3 415 15 37.3 823 1 3.7 030 3 6.8 031 2 39.6 236 1 24.7 050 43 14.7 751 1333 37.5 59552 1 76.6 153 3 24.1 1

Ref. 51: Averaged values as a function of Ref. 51: Averaged values as a function of JJ””

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - theo & exp results:- theo & exp results: NN22, O, O22 & air broad & air broad

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - - theo & exp results:theo & exp results: NN22, O, O22 & air broad & air broad

0 200 400 600 800 10000

400

800

1200

1600

2000

2400

2800

3200 N2-broadening: J = 7

4,4 - 6

5,1

3.127(34) MHz/Torr

NL (

kHz)

nitrogen partial pressure (mTorr)

THEO

EXP


0 200 400 600 800 10000

200

400

600

800

1000

1200

1400

1600

1800

2000

2200 O2-broadening: J = 6

3,3 - 5

4,2

1.967(66) MHz/Torr

NL (

kHz)

oxygen partial pressure (mTorr)

EXP

THEO


ExpExp TheoTheoThis workThis work JJ = 3 = 31,21,2 - 3 - 30,30,3 3.970(82)3.970(82) 4.004.00


HITRANHITRAN 3.53(8)3.53(8) This workThis work JJ = 7 = 72,52,5 - 8 - 81,81,8 3.508(20)3.508(20) 3.133.13








HITRANHITRAN 3.323.32

Good agreement! Good agreement!

AIR-broadeningAIR-broadening

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - theo & exp results:- theo & exp results: shift & SD paramshift & SD param

3) Experiment & Theory:3) Experiment & Theory: ResultsResults - H- H22O: which linesO: which lines - - theo & exp results:theo & exp results: shift & SD paramshift & SD param

100 200 300 400 500 600 70041.0

41.2

41.4

41.6

41.8

42.0

42.2

42.4

42.6

42.8

43.0

43.2Self - shift: J = 1

1,1 - 0

0,0

-2.52(41) MHz/TorrFre

quency

(M

Hz)

H2O pressure (mTorr)

EXP

THEO

Cazzoli et al. JQSRT 2008 Cazzoli et al. JQSRT 2008

0 100 200 300 400 500 600 700 800

620.5

620.6

620.7

620.8

620.9

621.0

621.1

621.2

621.3

621.4

Self - shift: J = 72,5 - 8

1,8

-1.00(11) MHz/TorrFre

quency

(M

Hz)


EXPTHEO


0 200 400 600 800 100058.45

58.50

58.55

58.60

58.65

58.70

58.75 Nitrogen - shift: J = 85,4 - 7

6,1

0.199(10) MHz/TorrFre

quency

(M

Hz)


THEO

EXP


0 200 400 600 800 10000

100

200

300

400

500

600

700

800 N2 - relax (J =31,2-2

2,1): SD parameter

0.638(32) MHz/Torr 2

(k

Hz)


EXP THEO

Cazzoli et al. JQSRT in preparation Cazzoli et al. JQSRT in preparation

ConclusionsConclusions

10 pure rotational THz water lines10 pure rotational THz water lines have have been experimentally and theoretically been experimentally and theoretically investigated investigated

GoodGood agreement agreement between experiment between experiment

and SC calculations and SC calculations

UpdateUpdate for HITRAN self broadening for HITRAN self broadening parameters is suggested parameters is suggested

Rather accurateRather accurate experimental results experimental results have been obtainedhave been obtained

Thank you for your attention!Thank you for your attention!

temperaturetemperatureexponent exponent nn

n

TT

TXTX

0

00 )()(

Least-square fit:Least-square fit: ln(X/Xln(X/X00) = ) = n n ln(Tln(T00/T)/T)

TEMPERATURE DEPENDENCETEMPERATURE DEPENDENCE

TEMPERATURE DEPENDENCETEMPERATURE DEPENDENCE

Laboratory of Millimetre-waveLaboratory of Millimetre-wave

Spectroscopy of BolognaSpectroscopy of BolognaPRAHA 2006PRAHA 2006

temperaturetemperatureexponent exponent nn

n

TT

TXTX

000 )()(

Least-square fit:Least-square fit: ln(X/Xln(X/X00) = ) = n n ln(Tln(T00/T)/T)

0.0 0.1 0.2 0.3 0.4 0.5-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

O3: 301.8 GHz

O2-broadening

n = 0.684(14)

ln(/ 0)

ln(T0/T)

pressure-broadening of water lines in the thz frequency region: improvements and confirmations for...

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thz frequency region

harmonic slide

procedure procedure

thz region quartz cell

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