Observation and analysis of optical free induction decay in the CH3F ν4 band

Chemical Physics Letters 692 (2018) 106–110

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Research paper

Observation and analysis of optical free induction decay in the CH3F m4 band Yusuke Okabayashi 1, Yuki Miyamoto, Jian Tang, Kentarou Kawaguchi ⇑ Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530, Japan

a r t i c l e

i n f o

Article history: Received 11 November 2017 In final form 5 December 2017 Available online 7 December 2017

a b s t r a c t Optical free induction decay (FID) signals of the CH3F m4 band were observed by using a cw-OPO infrared laser coupled with a Stark switching method. The observed signals have been Fourier transformed to obtain the Lorentz functions and the widths have been analyzed to determine the pressure-broadening coefficients for rR(0,0), rQ(1,0), rR(1,0), rR(1,1), and pP(2,1) to be 1/(pT2 p) = (46.1 ± 2.1), (31.6 ± 3.6), (21.8 ± 2.5), (25.2 ± 4.0), and (26.5 ± 1.8) MHz/Torr, where T2 is the transverse decay time. The value of r R(0,0) is larger than that determined from a recent pressure-broadening measurement by 39 ± 12%. The difference is explained by collision induced reorienting transitions (DM = ±1, DJ = 0). Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Coherent transient phenomena are caused by interaction of radiation with resonant level systems and are competing with relaxation processes. Studies of relaxation are important for purposes of making coherent states. Coherent transient phenomena were first studied in nuclear magnetic resonance in the radio frequency region, as free induction decay (FID) [1] and spin echo [2]. FID signals of NH3 in the microwave region were first observed by Dicke and Romer [3] by using pulsed and continuous microwave radiation. After the experiment, many studies on FID have been reported, leading to the development of the field of Fourier transform microwave spectroscopy [4]. Recently, remarkable application of FID is developed for discrimination of chiral compounds in the microwave region, as reported by Patterson et al. [5] and Grabow [6]. So far the method is only applied to gas-phase molecules. In infrared region, the method may become applicable to liquid and solid phases. Optical FID has been studied extensively in both infrared and visible regions by using cw lasers with Stark switching [7] or frequency switching techniques [8]. The methods take advantage of the use of the heterodyne detection which observes beat signals between weak transient emission (FID) and strong cw laser radiation. The Stark switching technique is applicable to only polar

molecules, but it is easy to control the width and separation of the Stark pulses. The first infrared FID was reported on NH2D with the Stark switching technique by utilizing accidental coincidence between the molecular transition frequency of (v2, J, M) = (1, 5, 5) – (0, 4, 4) and the CO2 laser P(20) frequency in the 10 lm region [7]. Here v2 is a vibrational quantum number, J is an angular momentum quantum number, and M is a magnetic quantum number. It allowed the determination of the FID time of 0.1 ls at one pressure point. As described later, the decay time of FID depends on laser power (i.e. Rabi frequency), so investigation of laser power dependence is necessary for getting the intrinsic decoherence time, which is one of the motivations in the present study. Duxbury et al. [9] reported observations of FID signals of nitrous oxide by using a current modulated quantum cascade laser, where power dependence of FID signals was clearly recognized. Transient spectroscopy has been applied for the determination of the transverse and/or longitudinal decay time T2 and T1 of CH3F. Jetter et al. [10] reported a time-resolved infraredmicrowave double resonance experiment for the 13CH3F m3 qR (4,3) transition to obtain 1/(pT1 p) = 30.4 ± 0.8 MHz/Torr in the ground state, where p is the pressure. Brewer and Shoemaker [11] reported 1/(pT2 p) = 31 MHz/Torr from a photon echo experiment by using the same m3 band transition. Berman, Levy and Brewer [12] reported

1=ðpT 2 pÞ ¼ 1=ðpT 1 pÞ ¼ 28:3MHz=Torr ⇑ Corresponding author. E-mail addresses: [email protected] (Y. Okabayashi), miyamo-y@cc. okayama-u.ac.jp (Y. Miyamoto), [email protected] (J. Tang), okakent@cc. okayama-u.ac.jp (K. Kawaguchi). 1 Present address: National Institute of Advanced Industrial Science and Technology, Umezono 1-1-1, Tsukuba, Ibaraki 305-8506, Japan. https://doi.org/10.1016/j.cplett.2017.12.009 0009-2614/Ó 2017 Elsevier B.V. All rights reserved.

ð1Þ

by the following three methods: (i) optical nutation of CH3F m3 qR(4,3) using a CO2 laser and Stark switching, (ii) Coherent Raman-beat effect, and (iii) Optical Carr-Purcell echoes. They concluded that the determined values by three methods are in agreement within a 3% uncertainty. 13

Y. Okabayashi et al. / Chemical Physics Letters 692 (2018) 106–110

107

The T2 value is also obtained by pressure-broadening experiments, because the following relation is known,

bp ¼

1

pT 2

ð2Þ

where bp is given by FWHM, and b is the pressure-broadening coefficient [13]. Cartlidge and Butcher [14] reported the coefficients 21–31.8 MHz/Torr for the CH3F m4 band transitions with J = 5–13 and K = 1–4, where K is the angular momentum quantum number along with the molecular axis, and they analyzed the observed linewidths by assuming the Voigt profile. The coefficients are also reported to be 42.1 MHz/Torr for the m3 two photon transition of (m3, J, K) = (2,3,1) – (0,1,1) [15], and 34.4–37.5 MHz/Torr for the m3 q Q(1,1), qR(2,0), qR(2,1), and qR(2,2) transitions [16,17]. In the ground state, a microwave pressure-broadening experiment by Gilliam et al. [18] reported the coefficient 40 MHz/Torr (FWHM) for the (J, K) = (1,0) – (0,0) pure rotational transition. These values for the b coefficient determined from the pressure-broadening experiments are consistent with 1/(pT2 p) or 1/(pT1 p) determined by transient spectroscopy in the case of the ground and v3 = 1 states. Brechignac reported the pressure-broadening parameters of the Stark-split components of the CH3F R(1,1) line at 2866.7 cm1, where the individual Stark components are found to be broader than the zero-field line [19]. Although there are many studies on transient phenomena concerning the ground and v3=1 states, experiments using coherent sources on the m 4 band have not been reported, presumably because of a lack of high-power cw laser in the 3 lm region. Recently, we observed the Lamb-dip spectra of eight transitions of the CH3F m4 band, and derived the pressure-broadening coefficients [20]. In the present study, we report measurements of FID signals for determination of the relaxation time in the CH3F m4 band by using a cw OPO laser and the Stark switching method. Use of a tunable infrared source has an advantage to measure low J transitions with a few Stark components, and measurements of power dependence of FID lead to the determination of the decay time and understanding of the decay process. 2. Experimental The experimental setup used in the present study is shown in Fig. 1. It is similar to that of Brewer and Shoemaker [7] who used a CO2 laser system as the source. A cw-OPO laser with a spectral width of about 0.8 MHz was used to cover the 3 lm infrared region in the present experiment. The cw-OPO laser has a bow-tie-type cavity, and a PPLN crystal is pumped by a fiber laser (iPG PHOTONICS YAR-25 K-LP-SF) which is seeded by a DFB laser (KOHERAS Y10-PM). The typical output of the OPO laser in the 3 lm region was 200 mW in the case of 6–8 W pumping power of the fiber laser. The OPO laser beam was focused by a CaF2 lens with a focal length of 300 cm at the center of a Stark cell to get a higher power density. The Stark electrodes were composed by a pair of aluminum plates (40 cm  4 cm  0.6 cm) with a separation of 0.500 ± 0.001 cm, mounted inside a Pyrex glass tube with 41 cm length and 6.5 cm inner diameter. The sample pressure was measured by a capacitance manometer (MKS Baratron 626A01TCE). The Stark switching pulse with a duration of 0.75 ls, a repeating rate of 100 kHz and a rise time of about 50 ns was generated up to 200 V by a fast switching circuit of DC voltage. The wave form is supplied by an arbitrary waveform generator (Agilent 33250A) which was controlled by a LabVIEW program. The Stark field was set to be perpendicular to the polarization of the laser beam, so only transitions with DM = ±1 selection rules were observed when the quantum axis was taken along the applied Stark field. The transmitted laser beam and coherent transient signal resulted in

Fig. 1. Block diagram for observing infrared transient signals with the Stark switching method.

a heterodyne beat signal, which was detected by an infrared mercury-cadmium-telluride (MCT) detector (Vigo PVI-3TE-4, the time constant of 20 ns) followed by a preamplifier (MIPDC-F-100, a bandwidth of DC-100 MHz). Two ND filters with attenuation factors of 1/2 and 1/3 were used for measurements of power dependence of FID signals. Another ND filter with attenuation of 1/100 was always used in front of the detector to avoid saturation of the detector. The power was measured in front of the cell for each measurement. CaF2 plates are used as windows of the cell, so the power inside the electrodes was estimated to be 94% of the measured value in front of the cell. The detected signal was displayed and accumulated by a digital storage oscilloscope (Agilent DSOX-2014A, bandwidth 100 MHz). A homemade slit-scan beam profiler was used for measurements of beam diameters at distances of 176 cm and 335 cm from the lens. The latter position corresponded to the center of the Stark cell. The horizontal and vertical 1/e2 half widths were 1.18 mm and 1.65 mm at the 176 cm point, respectively, while those at 335 cm are 0.63 mm (2rh) and 1.43 mm (2rv). So we assumed a homogeneous size inside the Stark cell and the cross section of S = 0.63  1.43  p mm2 = 2.83  106 m2, which was used for estimating the laser electric field amplitude. 3. Observed transient signals and analysis The rR(0,0), rQ(1,0) rR(1,0), rR(1,1), and pP(2,1) transitions of the CH3F m4 band were utilized in the present measurements of FID signals. The transition wavenumbers are taken from the report of Giguere and Overend [21], and listed in Table 1. The energy levels of Stark components of rR(0,0) are shown in Fig. 2. The + and  signs in v4 = 1 indicate the parity of the l-type doubling of the J = 1 and K(=|k|) = 1 levels, corresponding to wave functions of {|k = 1, l = 1> ± |k = 1, l = 1>}/(2)1/2. The rR(0,0) transition is allowed to the higher component of the l-type splitting in the absence of the electric field. On the other hand, the upper level of the rQ(1,0) transition is the lower l-type doubling component. The splittings of the l-type doubling have been accurately determined to be 32.103 MHz, and 96.394 MHz for (J, K) = (1,1) and (2,1), respectively, by infrared radio-frequency (IR-RF) double resonance [22] and is smaller than the Doppler width of 190 MHz. An example of observed FID signals for rR(0,0) is shown in Fig. 3 (a), where the optical nutation signal is overlapped with the

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0 V/cm

106 V/cm

M’=±1

v4=1,J’=K’=l=1 −

M’=0

+

M’=0 M’=±1 r

R(0,0)

+

M=0 J=K=0

Fig. 2. Rotational energy levels for the infrared free induction decay of the CH3F m4 R(0,0) transition. The transition wavenumber is 3010.751 cm1, and the energy separation of the l-type doublet is 32 MHz for J0 = K0 = 1, l = 1. The + and – signs in v4 = 1correspond to wavefunctions {|k = 1, l = 1> + |k = 1,l = 1>}/ (2)1/2 and {|k = 1,l = 1> - |k = 1, l = 1>}/(2)1/2, respectively, at zero field. The energy levels at electric field of 106 V/cm are also shown, where the Stark shift of M0 = ±1 is observed as a beat signal in FID.

r

(a) 0.000

absorption

-0.002

-0.004

-0.006

-0.008 -0.2

0.0

0.2

time ( µ sec)

0.4

0.6

(b)

Arbitrary Units

200

100

Experimental

0

Theory 25

30

35

Frequency (MHz)

40

Fig. 3. (a) Observed FID signal in the CH3F m 4 rR(0,0) transition by applying the Stark pulse of 106 V/cm, overlapped with the slowly varying nutation signal. The sample pressure is 20 mTorr and the OPO laser power is 125 mW. The upper figure shows the waveform of the applied Stark field. (b) Fourier-transform spectrum of Fig. 3-(a). Only the FID portion of the spectrum is shown with the center frequency of 33.728 (3) MHz and the Lorentzian line width of 3.76(1) MHz.

FID beat signal. Two transitions from the ground state with J = K = M = 0 to M0 = +1 and M0 = 1 of J0 = (k0 l0 ) = 1 have the same Stark shifts, where it is noted that the matrix element of the Stark effect is not zero between two l-type doublet states. The Stark field amplitude of 106 V/cm was used in the present experiment, so the beat frequency corresponding to the Stark shift was expected to be 33 MHz by using the permanent electric dipole moment of 1.8332 (23) D in the v4 = 1 state [22]. The Stark shift should be larger than several times of the homogeneous width (FWHM) for avoiding the effect of the original spectral line. According to our Lamb dip measurements [20], the homogeneous width originating from pressure broadening and power broadening reaches 5–6 MHz in relatively high pressure region. The Lorentz function for the homogeneous width has a value of 1/17 of the peak value at the position of 2 times of FWHM, so the Stark shift is set to be more than 4 times (24 MHz) of FWHM for two Lorentz functions. Higher frequency region is also limited by the response time of the IR detector used, so the 33 MHz shift is adopted. The lower energy Stark components with M0 = ±1 in Fig. 2 are shifted downward by 33 MHz from the zero field position and have a character of the upper l-type doublet state. Therefore, the beat frequency related to the lower M0 = ±1 levels is expected to be 65 MHz, which is a sum of the l-type doublet splitting and the Stark shift. The upper and lower levels at the Stark field are expressed as 0.815 |> + 0.579|+> and 0.579 |> + 0.815|+>, respectively, where |> and |+> correspond to the l-type doublets of Fig. 2, and the coefficients are determined by diagonalization of the 2  2 energy matrix including the Stark effect. By considering the mixing of wavefunctions, the intensity of the 65 MHz beat is estimated to be half of the 33 MHz beat signal, but the frequency is out of the detector response frequency (50 MHz). Therefore, the beat signal was observed with the only one frequency, as shown in Fig. 3(a). Forty-five FID signals for the rR(0,0) line were recorded at various laser powers from 11 mW to 168 mW and CH3F sample pressures from 5 mTorr to 66 mTorr. In the analysis of the observed FID data, we used a theoretical model derived by Brewer [23], Brewer and Shoemaker [7], and Hopf et al. [24]. We adopt the following notation for the Bloch equations in a coordinate frame rotating at the laser angular frequency X [23],

du u þ Dv þ ¼0 dt T2

ð3Þ

dv v  Du  vw þ ¼0 dt T2

ð4Þ

dw ðw  w0 Þ ¼0 þ vv þ dt T1

ð5Þ

where u, v, w denote the components of a Bloch vector R which represents the state of the molecule, T1 is the longitudinal relaxation time, T2 is the transverse relaxation time, the Rabi angular frequency v = l12E0/⁄, and D = X + kvz + x21, and w0 is the occupation probability difference in the absence of external radiation. The infrared laser field e = E0cos X t is assumed to be linearly polarized, and l12 is the transition dipole matrix element. kvz is the Doppler shift and x21 is the molecular transition angular frequency. The initial condition is derived from the steady-state solution of the Bloch equations, because molecules interact with the laser field for long enough to reach the steady state before the Stark pulse is applied. The solution can be derived from the Bloch equations by setting the time derivatives equal to zeros, as follows,

uð0Þ ¼  vð0Þ ¼

v

Dvw0 v2 T 1 =T 2 þ D2 þ 1=T 22

2T

vw0 =T 2 1 =T 2

þ D2 þ 1=T 22

ð6Þ ð7Þ

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" wð0Þ ¼ w0 1 

v

v2 T 1 =T 2 2T

1 =T 2

# ð8Þ

þ D2 þ 1=T 22

By applying the Stark field at time t = 0, the molecular transition frequency is shifted and becomes off-resonant with the laser frequency, where the v value is assumed to be zero. The FID beat intensity is obtained by velocity averaging, as follows,

ðE2T Þbeat ¼ E0 Q 12 ðtÞ cos½dx12 ðt  /Þ;

ð9Þ

where ET is the total field of the field associated with the induced polarization and the laser field with the amplitude E0, dx12 the beat angular frequency corresponding to the Stark shift, / the initial phase, and

!

h i p3=2 NLl212 E0 w0 1 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1  exp ðD1 =kgÞ 2 e0 uh v T1T2 þ 1 

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  exp t=T 2 1 þ 1 þ v2 T 1 T 2

ð10Þ

where N is the number density of molecules, D1 = X + x21, L the optical path length. The k g in Eq. (10) denotes the Doppler shift, where g is the rms velocity. The decay rate has two contributions (i) a homogeneous part 1/T2 and (ii) an inhomogeneous part originating from the denominator of Eqs. (6) and (7) by velocity integration. The latter expresses a fact that FID is quickened under the Doppler broadened profile due to various velocity components giving different FID frequencies. The vibrational transition moment of the m 4 band was estimated to be 0.086(4) Debye from the intensity data of Russel et al. [25], where the number in the parentheses corresponds to the measurement error of infrared band intensity. The matrix element in the rotational part was calculated by using the direction cosine matrix elements described by Kroto [26]. Table 1 lists the transition dipole moments of the M components causing the FID signals. It is noted that the decay by 1/T2 is caused by elastic and inelastic collisions. The latter is considered as the effect of 1/T1. Generally, T1 may be different from T2 in Eqs. (3)–(5), where two energy levels are assumed. On the other hand, in the present CH3F case we have to consider many rotational levels which are responsible for major collisional decay paths due to 1/T1 [27]. In fact, the relation of T1 = T2 has been reported by Berman et al. [12] for the CH3F ground state. The second exponential function exp(t/s) of Eq. (10) is Fourier-transformed (FT) to give the Lorentz function with FWHM of 1/(ps), where the FID decay rate is given by

1

s

¼

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ 1 þ v2 T 1 T 2 T2

ð11Þ

We transformed the observed FID signals by using the method of Genack and Brewer [27], and an example of results of FT is shown in Fig. 3(b), where the spline interpolation method is applied before FT to obtain a smooth shape. The beat frequency of dx21/2p = 33.923(7) MHz is in good agreement with the Stark shift (33 MHz) of the M0 = ±1 components in the upper state. The power dependence of the widths of the rR(0,0) line is investigated by plotting the observed widths against (1 + v2T1T2)1/2 in one pressure point, as shown in Fig. 4, where the l12 value in v includes the coefficient c0 in Table 1 under the presence of the Stark effect, and T1 = T2 is assumed. The intercept (v = 0) of Fig. 4 corresponds to 2/ (pT2). Similar plots are obtained for 7 pressure point data, and the 1/(pT2) values are plotted in Fig. 5, as a function of the CH3F pressure. The slope gives the pressure-broadening coefficient 1/(pT2 p) = 46.1 ± 2.1 MHz/Torr, and the intercept is determined to be 0.392 ± 0.023 MHz, where the errors denote one standard deviation (r). The value of 0.392 MHz is due to the laser instability, and it was

Fig. 4. Free induction decay rate vs square-root laser-intensity dependence for rR (0,0).

3.0 2.5 FWHM (MHz)

Q 12 ðtÞ ¼

2.0 1.5 1.0 0.5 0.00

0.01

0.02 0.03 Pressure (Torr)

0.04

0.05

Fig. 5. Plot of full width at half maximum (FWHM) corresponding to the relaxation rate (1/pT2 at v = 0) against the CH3F pressure. The error bars denote one standard deviation. The slope and intercept are determined to be 46.1 ± 2.1 MHz/Torr, and 0.392 ± 0.023 MHz, respectively.

estimated to be 0.8 MHz in the Lamb dip measurement [19]. The measurement time in the present FID experiment is shorter than that of the Lamb dip experiment, so the smaller value due to the instability is reasonable. When we take into account the uncertainty of the laser electric field, which corresponds to change of the v value, a better fit is obtained by a smaller v value, resulting in a larger pressure-broadening constant. FID signals were also observed for rQ(1,0), rR(1,0), rR(1,1), and pP (2,1) transitions. In the former 3 transitions, a single beat frequency was observed like as the case of rR(0,0). On the other hand, the FID signal of pP(2,1) was observed with two beat components (M0  M0 = ±1  ±2 and 0  ±1), and stronger M0  M0 = ±1  ±2 component was analyzed. Because of the limited number of data for these transitions, the analysis as shown in Fig. 4 was not carried out. So observed widths were directly fitted to the following formula,

1

sp

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ bp 1 þ 1 þ v2 T 1 T 2 þ 2c1

ð12Þ

where bp is defined by Eq. (2) and c1 corresponds to an offset due to fluctuation of laser frequency during FID observation. In the fitting, we assumed T1 = T2, and used a smaller c1 value than 0.39 MHz of

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Y. Okabayashi et al. / Chemical Physics Letters 692 (2018) 106–110

Table 1 Pressure-broadening coefficients of the CH3F m4 band.a Transition

m

upper 1

(cm R(0,0) r Q(1,0) r R(1,0) r R(1,1) p P(2,1)

)

3010.75 3009.06 3012.47 3019.97 2998.08

M0  M0

1/pT2p (MHz/Torr)

K

Present

Lamb dip

1 1 1 2 0

46.1 31.6 21.8 25.2 26.5

33.1 19.2 24.5 17.5

(2.1) (3.6) (2.5) (4.0) (1.8)

d

(2.3) (2.1) (1.4) (1.4)

|l12|b

coc

(D) ±10 ±10 ±2  ±1 ±2  ±1 ±1  ±2

0.0496 0.0496 0.0511 0.0511 0.0377

0.815 0.815 0.960 0.707 1.0

a

Numbers in parentheses denote one standard deviation. Transition moment matrix element related to the M0  M0 transition. The vibrational transition moment 0.086 D for the m 4 band is used. In the present experimental condition, the Rabi frequency (not angular frequency) is given by |l12|E0/h = 82.0 MHz/(Debye W1/2) |l12| (P)1/2. c Coefficient of the wavefunction of the observed level under the Stark field of 106 V/cm, which depends on the interval of l-type doublet in v4 = 1 [22]. d Pressure-broadening measurements using Stark modulated Lamb dips [20]. Coefficients of 21.4–31.8 MHz/Torr have been reported for other transitions by Voigt profile analyses [12]. b

Fig. 5. The determined pressure coefficients of decay time are listed in Table 1.

coefficient compared with the previous Lamb dip measurement is recognized and attributed to the rotational relaxation with DM = ±1, DJ = 0.

4. Discussion Acknowledgement In the present study, we obtained the pressure-broadening coefficients as listed in Table 1. For comparison, Table 1 also lists the values determined from the pressure-broadening experiments by using the Stark modulated Lamb dip method [20]. The present values for the rQ(1,0), rR(1,0), rR(1,1) transitions are in agreement with those of Lamb dip measurements within three standard deviations. On the other hand, the value of R(0,0) is larger than that obtained from the Lamb-dip experiment [20] by 39 ± 12%. Although the difference is a little bit larger than three standard deviations, a smaller power density gives a larger pressurebroadening coefficient with a smaller standard deviation. So we conclude that there is a difference in the coefficient of rR(0,0) between the present FID and Lamb dip measurements, and consider the reason giving the difference. It is noted that the signal observed in the present experiment is the heterodyne beat between the laser radiation and the FID from the Stark-shifted transition. The rotational energy levels split by the Stark effect, and collisional transitions between different M components occur. Pickett [28], Schwendeman and Amano [29] considered the problems associated with the magnetic degeneracy of the rotational energy levels theoretically. Hoke et al. [30] reported M dependence of T1 for ammonia inversion doublets transitions. Brechignac [19] obtained a broadening coefficient in the CH3F 2m5 band of 15 MHz/Torr with an electric field and 11.4 MHz/Torr in the zero field. This has been explained by the rotational relaxation through the electric dipole type transition DM = ±1, DJ = 0. According to the theoretical approach proposed by Pickett [28], Brechignac [19] estimated a 22% increment compared to the observed 31% ± 19% for the 2m5 qR(1,1) transition. A similar effect on the m 4 band may explain 20–30% difference between FID and Lamb dip experiments. The effect is also expected to appear on rQ(1,0), rR(1,0), r R(1,1), but it is difficult to discuss increment of their widths under the Stark field because of large errors. As summary, the present study reports measurements of power dependences of FID signals to determine the relaxation time of the m4 band of CH3F. A differences in the pressure-broadening

The present study was partially supported by the Grant-in-Aid (Grant No. 21104003) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

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