High-Resolution Laser Spectroscopy of the A3Π1←X1Σ+ System of IBr with a Titanium:Sapphire Ring Laser

Journal of Molecular Spectroscopy 214, 132–143 (2002) doi:10.1006/jmsp.2002.8589

High-Resolution Laser Spectroscopy of the A3 Π1 ← X 1Σ+ System of IBr with a Titanium : Sapphire Ring Laser Tokio Yukiya, Nobuo Nishimiya, and Masao Suzuki Department of Electronic and Computer Engineering, Tokyo Institute of Polytechnics, Iiyama 1583, Atsugi-City, Kanagawa 243-0297, Japan Received December 29, 2001

The vibrotational absorption spectra of the A ← X electronic transition of I79/81 Br were measured in the 11 330- to 13 220-cm−1 region using a Ti:sapphire ring laser. The P-, Q-, and R-branch lines of the rotational states from J = 10 to 100 belonging to the v  ← v  = (3∼20) ← (1∼6) bands were assigned. The P- and R-branch lines, unlike the Q-branch lines, were split into the doublet by the nuclear quadrupole coupling effect of the I atom. The quadrupole coupling constants of eQq0 and eQq2 in the A state were estimated to be −0.030 ± 0.018 and −0.062 ± 0.018 cm−1 , respectively, by using the first order perturbation theory. The unperturbed line positions for the rotational lines higher than J = 20 were determined. The Dunham coefficients of the X state were determined by the least squares fitting method using the pseudo vibrotational transition wavenumbers obtained by calculating the combination differences between the electronic spectral lines assigned and the far infrared vibrotational lines reported by Nelander et al. (7). The spectroscopic constants of T v  , Bv  , Dv  , and H v  of the A state were determined suitable C 2002 Elsevier Science (USA) for the vibrational states from v  = 3 to 20 by using a least squares fitting procedure. 

Although the laser spectrometer is useful for the analysis of the rovibrotational bands because of its high resolving power, the measurements have seldom been done since the tuning range is rather narrower than that of a Fourier transform spectrometer or a grating spectrometer. The preliminary measurement using a GaAs laser done by one of the authors was extended by replacing the laser source with a Ti:sapphier ring laser in 1995 (8, 9). It was, however, difficult to assign the bands from the higher vibrational states of v  = 5 and 6 in the X state to states lower than v  = 6 in the A state. Clevenger et al. reported that the T v  and Bv  terms of the A state deviate from the (v + 1/2) polynomial fitting based on the analysis of the β ← A transition (10). In this paper we report the measurement of the P, Q, and R branches in the region from 11 330 to 13 220 cm−1 , where the nuclear quadrupole splittings at the order of the Doppler width were corrected in the P and R branches by a simple method useful for the higher rotational branches. The range of observed vibrational levels of the A state was extended down to v  = 3 and that of the X state up to v  = 6. The Dunham constants for the X state without correlation to the parameters of the A state were determined by the least squares fitting method using the combination differences calculated from the A ← X line wavenumbers and those reported by Nelander et al. (7). The spectroscopic constants at the A state are given by the constants of Tv , Bv e/ f , Dv , and Hv , instead of the terms of the Dunham polynomial.

1. INTRODUCTION

The vibrotational band spectrum of IBr in the A ← X system in the near infrared wavelength region was first observed by W. G. Brown in 1932 (1). Since then the spectroscopic constants have been improved by using a grating spectrometer, a Fourier transform spectrometer, or a laser spectrometer. The measurement by L. E. Selin in 1962 revealed the rovibrational band structure of the A ← X system and the spectroscopic constants were determined using the spectral lines belonging to the v  = 9∼32 states in the A state (2). Tieman and Moeller determined the rotational parameters and the nuclear quadrupole coupling constants of I and Br atoms for the X state by using a microwave spectrometer (3). Since the rovibrational spectroscopic constants for the X state can also be determined from the electronic vibrotational spectrum, the constants determined from the B ← X system by Weinstock and Preston (4) were sometimes used with those from microwave spectroscopy. Campbell and Bernath measured the rovibrational spectrum of the X state in the far infrared wavelength region in 1993 and the spectroscopic constants were determined (5). Appadoo et al. measured the rovibrational lines of the A ← X system by using a high resolution Fourier transform spectrometer in 1994 (6). They assigned the lines belonging to the v  ← v  = (6∼29) ← (1∼4) and determined the Dunham coefficients of the X and A states. Nelander et al. recently improved the accuracy of the spectroscopic constants at the X state by the measurement of the fundamental and the hot bands of v = 2 ← 1 and 3 ← 2 by using a synchrotron source (7).

2. EXPERIMENTAL

The experimental setup modified from that given in our previous report (9, 11) is schematically shown in Fig. 1, where a ring-type titanium sapphire laser (Coherent 899-21) pumped by

Supplementary data for this article may be found on IDEAL (http:// www.idealibrary.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa-hp.htm). 0022-2852/02 $35.00  C 2002 Elsevier Science (USA) All rights reserved.

132

133

LASER SPECTROSCOPY OF IBr

Osc. Coaxial Line PD Absorption Cell (White Cell)

Lock-in Amp.

M IBr

M

GP-IB Bus

PD Lock-in Amp.

M I2 BS

M

PD Lock-in Amp.

BS

Confocal Cavity PD

BS

Lock-in Amp.

Power Monitor L

Wave Meter

Opt. Fiber

BS +

Ti:Al 2O 3 Laser

Ar Ion Laser

Function Generator

M Laser Controller

Sweep signal

PC

Etalon Driven Signal

Servo Amp.

BRF Driven Signal

D/A Local Bus

FIG. 1.

Experimental setup.

an argon ion laser (Coherent Innova 90) was used as a radiation source. A small part of the laser power was extracted from the main beam and detected by a PIN photodiode at the power monitoring pass. The lock-in detected signal was subtracted from the absorption signal to reduce the interference noise mainly introduced from the laser source. Since the wavenumber region lower than 12 000 cm−1 contains the lines of the A ← X electronic transitions of I2 , the absorption signals of I2 were recorded by introducing the beam to another reference cell filled with I2 vapor. We compared the IBr lines recorded with the pure I2 spectrum to avoid incorrect assignments for the weaker P- and R-branch lines. The lengths and diameters of the absorption and reference cells of Pyrex were 1.5 m and 4 cm, respectively. The substances were purified by a conventional sublimation technique in vacuum and were filled into the absorption and the reference cell, respectively, at a saturated vapor pressure at room temperature. Each of the effective pass lengths was made 12 m by using the multipass techniques shown in the figure. Almost all the measurements were done at room temperature. It was, however, necessary to heat the cell to a temperature around 100◦ C to measure the lines from the v  = 5 and 6 in good S/N . The wavenumber was measured using a wavelength meter (Anritsu MF9630A). The wavenumber of the line center was in-

terpolated with the fringe signals generated by a confocal Fabry– Perot interferometer of 25 cm, which were calibrated against the wavelength meter. The accuracy of the wavenumber measurement was estimated to be 0.005 cm−1 and that of the line splitting obtained from the wavenumber intervals of the fringe markers to be ±0.0005 cm−1 (9). The laser frequency was modulated by a sine wave of small amplitude applied to the galvo motor used for the frequency tuning of the laser. The modulation frequency was set at 13 Hz in consideration of the response time of the galvo motor. A modulation width of 100∼200 MHz was found to be preferable. The second derivatives of the absorption signals and that of the interference noise in the radiation source were detected by two conventional lock-in amplifiers and were sent to a personal computer through a GP-IB bus line together with the data from the wavelength meter and the fringe signals. Then we processed the signals of the continuous tuning ranges of about 1 cm−1 according to the method schematically shown in Fig. 2. The trace (b) of the interference noise was first subtracted from the trace (a) showing the absorption signal. In this subtraction the amplitude ratio and the offset voltage of the signal recorded by the power monitoring pass were used as fitting variables to give the residuals of the interference noise minimum. We further reduced the short term noise still left in the absorption signal shown in the

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make the peak intensities duplicate at the overlapping region. The absorption lines from the 11 660- to 11 663-cm−1 region thus detected are shown in Fig. 3, which shows that the P- and R-branch lines were clearly detected as doublets although they were much weaker than the Q-branch lines. Some of the lines were assigned to be the Q-branch lines of the A ← X system of I2 , which was contained as an impurity by decomposition of IBr. The lines of IBr and I2 belonging to rotational states higher than J = 100 were not taken into consideration in this analysis. Each line marked by the symbol × in the figure may be assigned as one of these higher rotational lines because the lines of the A ← X system of Br2 and those of the B ← X systems of I2 and IBr fade away in the wavenumber region concerned. The spectral band systems for I79/81 Br assigned in the wavenumber region from 11 333 to 13 300 cm−1 are summarized in Table 1 with the bands reported in Refs. (2, 6). In case only the Q-branch lines were assigned, the letter Q is given as shown at some of the bands. The total number assigned in 67 bands was approximately 11 000.

3. RESULTS AND DISCUSSION

Elimination of the interference noise in a radiation source.

(a) Spectral Lines and Correction of the Nuclear Quadrupole Hyperfine Splitting by I Atom

trace (c) using a Fourier transform smoothing technique and obtained the trace (d), in which the weaker hyperfine components of the P and R branches can clearly be seen. The improvement of S/N attained by this method was estimated to be 46 dB. The absorption signals of every tuning range were compiled using the frequency calibrated fringe signals for the reference of the wavenumber scale and the amplitudes were adjusted to

109 85 83

67

36

34

41

39

38

36 64

78 78

x

30 40 58 66

32

61

75 80

75

I2 24–2Q(51)

I2 20–1Q(90)

87 35 63

62 73

x

85

33

61

81

I 79Br I 81Br

31

x

I2 33–0Q(30)

32 37 59

x

I2 35–3Q(44)

83

I2 29–2Q(85)

6" 6" 6" 5" 4"

I2 37–3Q(53)

, 10, 9 , 8 , 6 , 4

It was not difficult to distinguish the Q-branch lines in the dense spectrum since those belonging to the rotational lines higher than J = 10 were not split by the nuclear hyperfine effect and their intensities were several times stronger than those of the P- and R-branch lines. Almost all the P- and R-branch lines

I2 23–2Q(36)

FIG. 2.

x

x

-1

11660.0 11660.5 11661.0 11661.5 11662.0 11662.5 11663.0 cm FIG. 3.

Observed spectral lines around 11 660∼11 663 cm−1 .

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LASER SPECTROSCOPY OF IBr

TABLE 1 Observed Band System of I79/81 Br 0

1

2

X State (v'') 3

4

5

6

Q Q Q P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R Q Q

P, Q, R Q Q P, Q, R P, Q, R P, Q, R Q

A State ( v ' )

0 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 31 32

Q P, Q, R P, Q, R Q Q

Q P, Q, R P, Q, R Q P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R Q Q

P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R

By Selin (2)

P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R P, Q, R Q Q

By Appadoo et al. (6)

Note. The bands surrounded with the dotted line are those by Selin (2) , those with the broken line by Appadoo et al. and the shaded letters P, Q, R are the branches assigned by this work, where the letter Q means that the P and R branches are not included in the assignments.

were split into the doublet of 0.028 ± 0.003 cm−1 , which was wider than the Doppler width. The values are almost equal to those observed for ICl (12). We considered that the nuclear hyperfine effect of the Br atom and its v dependence on the I atom may be ignored. The correction for the nuclear hyperfine effects was done according to the same method given in Ref. (12). The energy shift at the A state is given by 

e/ f E HF(A)

 C   = , J , I ) −eQq0 + Y (F J  (J  + 1)     1 − 2ρ 2 3 ± eQq2 , [1] × 1−   J (J + 1) 2 a 2 



and that at the X is  E HF(X ) =

a  2



C  + Y (F  , J  , I )[−eQq0 ], J  (J  + 1)

[2]

where C is given by the term of F(F + 1) − J (J + 1) −

I (I + 1), a is the nuclear magnetic coupling constant, eQq0 and eQq2 are the nuclear quadrupole coupling constants, and ρ is the mixing factor with the singlet state considered to be approximately zero. The positive sign in Eq. [1] is for the e level and the negative is for the f level. Y (J , I , F) is the Casimir function and is given by

Y (F, J, I ) =

3C(C + 1) − 4J (J + 1)I (I + 1) . 8I (2I − 1)(2J − 1)(2J + 3)

[3]

Although the nuclear hyperfine splitting at the rotational state J splits into 2I + 1 components, the difference between Casimir’s functions of J and J + 1 decreases rapidly at the rotational states higher than J = 20 and approximately converges to the three values independent of J , that is, for F = J ± 5/2 to Y (J , I , F) = 0.125, for F = J ± 3/2 to Y (J , I , F) = −0.025, and for F = J ± 1/2 to Y (J , I , F) = −0.100. The hyperfine lines may be given by Eq. [4] since the shift by the nuclear magnetic constants given by the first term in Eqs. [1] and [2] decreases

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YUKIYA, NISHIMIYA, AND SUZUKI

(a)

(b) J+ - 5/2

79

I Br12-4Q(28) Simulation

I81Br12-4P(26) Simulation

J+ - 3/2 J+ - 1/2 J+ - 1/2

J+ - 5/2

A.U.

A.U.

J+ - 3/2

Error

12567.2791

0.002cm-1

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 cm

Error

12568.5261

0.002 cm-1

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06

-1

cm-1

FIG. 4. Line profiles of the Q(28) and P(26) lines in the v = 12 ← 4 band. The line profiles of traces (a) and (b) were calculated using Eqs. [5] and [6], respectively.

rapidly with J ,   1 ν P,R/Q (F) = ν(J ) + Y (F, J, I ) −eQq0 ± eQq2 + eQq0 . 2 [4] The hyperfine splitting was difficult to resolve for the Qbranch lines and was estimated to be almost equal to or narrower than the Doppler width of 0.008 cm−1 , but for the P- and Rbranch lines it was detected as a doublet having a J independent value of 0.028 ± 0.003 cm−1 . This means that the splitting between the F = J ± 3/2 and the J ± 1/2 component could not be resolved. The eQq0 and eQq2 for the A state were determined using the equations      5 1 ν Q = Y J  , I, F = J  ± − Y J  , I, F = J  ± 2 2   1 × −eQq0 − eQq2 + eQq0 ≤ 0.008 cm−1 , [5] 2 and ν

P,R

   5 = Y J  , I, F = J  ± 2 



 Y J , I, F = J  ± 32 + Y J  , I, F = J  ± 12 − 2   1 × −eQq0 + eQq2 + eQq0 2 −1

= −0.028 ± 0.003 cm .

[6]

Using −0.0918469 cm−1 for the nuclear quadrupole coupling

constant of I at the X state reported by Tieman and Moeller (3) the eQq0 and 1/2eQq2 for the A state were determined to be −0.030 ± 0.018 cm−1 and −0.062 ± 0.018 cm−1 , respectively. The eQq0 is almost equal to that of ICl while 1/2eQq2 decreased in comparison with −0.071 ± 0.015 cm−1 of ICl although the change 0.009 cm−1 is smaller than the uncertainties. The line profiles were then calculated and compared with the observed ones. The results for the Q (28) of I79 Br and the P (26) of I81 Br at 12568 cm−1 are shown in Figs. 4a and 4b where the profiles shown by the dotted lines are those calculated with the parameters determined. The linewidth of 0.010 cm−1 was based on the modulation width and the eQq0 and 1/2eQq2 values varied within the error limits of 0.018 cm−1 . The small discrepancies are comparable with the accuracy of the measurement. The unperturbed line positions were then calculated for the P- and R-branch lines using the nuclear quadrupole coupling constants given above. The rotational levels belonging to the e-levels up to J = 100 assigned from v  = 3 to 20 at the A state are summarized in Fig. 5 with the symbols × and
for 79 Br and 81 Br species, respectively. The symbols + and ∗ are for the f levels. The lines belonging to lower rotational states than J = 10 were omitted from the analysis because the line intensities were not strong enough to make assignments of the hyperfine structures and further, a high J approximation could hardly be used. The tables of the observed and calculated line wavenumbers for all the bands studied have been placed in the Depository of Unpublished Data and are available from the Editorial Office upon request. (b) Dunham Coefficients of the X State First we tried to determine the Dunham coefficients suitable for the X and A states by using a least squares fitting procedure like that used in the analysis done by Appadoo et al. (6).

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LASER SPECTROSCOPY OF IBr

100

80

J

60

40

20 79

Q

0 2

79

PR

81

4

Q

81

PR

6

8

10

12

14

16

18

20

v FIG. 5.

Rotational levels assigned at the A state.

The standard deviations, however, were rather greater than the accuracy of the wavenumber measurement. This means that the Dunham expansion is not suitable for representing the energy levels of both the X and A states. Then we tried to get the spectroscopic constants of the X state using the spectral data in the far infrared region reported by Nelander et al. (7) and those of the pseudo rotation–vibration transition wavenumbers of the S, Q, and O branches at the X states calculated by the combination differences given as

parentheses and the Y03 and Y13 were of almost the same order. The Y03 and Y13 terms were constrained to those calculated by the relation given by Tyuterev et al. (13) and the Y22 term was omitted from the fitting. The result by the second fitting is listed in the column shown as Set II. One can see that the standard errors in the Y40 and Y31 are decreased because the lines belonging to the vibrational states up to v  = 6 were included. We consider the values listed in Set II reasonable although the accuracy in the centrifugal distortion constants was not improved.

S(v1 ← v2 , J ) = P(v1 ← v1 , J + 2) − R(v1 ← v2 , J ) for J = +2 [7a] Q(v1 ← v2 , J ) = Q(v1 ← v1 , J ) − Q(v1 ← v2 , J ) for J = 0 [7b] O(v1 ← v2 ,

J) =

P(v1 ← v1 ,

J) −

R(v1 ← v2 ,

J − 2)

for J = −2. [7c]

(c) Spectroscopic Constants at the A State The coefficients of the power expansion for the A state were then calculated by the polynomial form of J (J + 1) while those for the X state were by (v + 1/2){J (J + 1)}. Using the following equation the spectroscopic constants were calculated using a least squares fitting procedure, ν(v  , J  ; v  , J  ) e/ f

By using the 10 791 lines of the rovibrational transition wavenumbers at the X state thus obtained we determined the Dunham coefficients by a mass-reduced least squares fitting procedure. The results are shown in the second and third columns in Table 2. The values of Appadoo et al. and those of Nelander et al. are listed for comparison in the fourth and fifth columns. The first one shown as Set I was obtained using all the constants in the table as fitting parameters. Although the rotational lines up to J = 100 are included in our fitting, the Y22 value was 5 times smaller than the standard error given in the

= Tv + Bv {J  (J  + 1) − 2 } − Dv  {J  (J  + 1) − 2 }2   1  X v  + + Hv  {J  (J  + 1) − 2 }3 − Y,m 2 ,m × {J  (J  + 1)}m ),

[8] f

where the effective rotational constant Bv splits into Bv = Bv −  qv /2 and Bve = Bv + qv /2 owing to the type doubling. The results of a least squares fitting are listed in Tables 3 and 4 for I79 Br and I81 Br, respectively. The Dunham coefficients for

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YUKIYA, NISHIMIYA, AND SUZUKI

TABLE 2 The Dunham Coefficients for the X States of I79 Br and I81 Br Set I

Set II

Ref. (6)a

Ref. (7)b

268.680 523 (66) −0.816 173 (43) −1.528 2 (108) 0.685 (89) 5.683 270 6 (172) −1.969 23 (24) −4.572 (63) −4.73 (57) −1.016 71 (309) −4.572 (63) −0.87 (454) −1.93 (161) 1.09 (215)

268.680 526 (64) −0.816 173 (43) −1.527 9 (108) 0.682 (89) 5.683 274 8 (95) −1.969 29 (13) −4.585 (46) −4.67 (56) −1.017 72 (74) −4.998 (69) −1.327d −5.692d

268.681 42 (11) −0.816 913 (72) −1.306 0 (150) −1.24 (7) 5.683 258 9 (21) −1.969 58 (22) −4.469 (100) −6.1 (16) −1.017 1 (31) −4.99 (10) — −1.60 (19) —

268.681 076 (37) −0.816 598 (22) −1.4150 (38) — 5.683 255 3 (10) −1.969 037 (65) −4.787 (14) — −1.016 45 (22) −5.081 (43) — −1.69 (17) —

266.627 463 (65) −0.803 748 (42) −1.393 4 (105) 0.665 (86) 5.596 747 7 (170) −1.924 429 (236) −4.434 (61) −4.55 (55) −0.986 00 (300) −5.034 (399) −0.85 (434) −1.83 (155) 1.03 (204)

266.627 467 (63) −0.803 747 (42) −1.493 2 (105) 0.661 (86) 5.596 751 9 (94) −1.924 496 (122) −4.446 (43) −4.50 (54) −0.986 97 (72) −4.810 (66)

266.628 35 (11) −0.804 477 (72) −1.276 2 (150) −1.21 (7) 5.596 736 2(21) −1.924 77 (22) −4.334 (100) −5.9 (16) −0.985 99 (31) −4.80 (12)

266.627 934 (37) −0.804 123 (21) −1.391 0 (36) — 5.596 734 7 (12) −1.924 291 (65) −1.924 291 (65) — −0.986 16 (28) −4.817 (46)

−1.53 (19) —

−1.31 (22) —

I79 Br Y10 Y20 103 Y30 105 Y40 102 Y01 104 Y11 107 Y21 109 Y31 108 Y02 1011 Y12 1013 Y22 1015 Y03 1017 Y13

c

I81 Br Y10 Y20 103 Y30 105 Y40 102 Y01 104 Y11 107 Y21 109 Y31 108 Y02 1011 Y12 1011 Y22 1015 Y03 1017 Y13

c

−1.268d −5.394d

Note. Units are all in cm−1 . Standard deviations for the fittings in both species were 0.0033 cm−1 and errors in parentheses are 1 σ . a The values reported by Appadoo et al. (6 ). b The values reported by Nelander et al. (7 ). The standard errors in the reference are 3 digits. c The value of Y was not included in the fitting because the standard error was 5 times in Set I. 22 d The values were constrained to those calculated using the Eq. [10] in Ref. (13).

the X state in Eq. [8] were constrained to those listed in the column shown as Set II in Table 2. The values of Tv and Bv at the v  = 0∼2 states are those reported by Clevenger et al. (10) and those of Tv , Bv , and Dv at v  = 25∼29 are from Appadoo et al. (6). The coefficients of polynomials in (v + 1/2) were then calculated from these constants using the relations given by

Tv79

+

Bv79

+

qv79

+

Tv81

Bv81

qv81

=

 -max

 

1  1 + ρ Cv v + , 2



=0

 2

=

 -max



1+ρ

 2 +1

 

1  C B v + , 2

[9b]

 2 +1

 

1  , Cq v + 2

[9c]

=0

=

 -max =0



1+ρ

[9a]

Dv79 + Dv81 = Hv79 + Hv81 =

 -max

 

1   , 1 + ρ 2 +2 Cd v + 2

[9d]

 

1   1 + ρ 2 +3 C h v + , 2

[9e]



=0  -max =0



where ρ is the ratio of the reduced masses of I79 Br and I81 Br. We tried to obtain the coefficients of the (v + 1/2) polynomials using a least squares fitting procedure. The results are summarized in Table 5, where the Born–Oppenheimer breakdown effect in the Tv term was estimated to be −0.0063 cm−1 as given in Ref. (6). The maximum order -max in Eqs. [9a]–[9e] were increased one by one by monitoring the standard errors and it was found that the 8th order term was, at least, necessary for Tv , the 7th for Bv ., the 2nd for Dv , and the 3rd for Hv . The deviations from the calculated curves for Tv and Bv are shown in Figs. 6 and 7, in which the broken lines show those calculated using the Dunham constants by Appadoo et al. (6)

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LASER SPECTROSCOPY OF IBr

TABLE 3 The Spectroscopic Constants for the A State of I79 Br v 0 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

Tv

f

Bv e

Bv

12 436.496 (34) 12 568.25 (13)

Dv × 108

Hv × 1013

0.042 126 (16)

σ Ref. (10) Ref. (10)

12 821.604 7 (28) 12 943.176 0 (14) 13 061.184 60 (97) 13 175.511 22(63) 13 286.008 43(68) 13 392.530 63(67) 13 494.924 37(73) 13 593.029 50(82) 13 686.684 61(81) 13 775.726 09(89) 13 860.000 79(84) 13 939.376 6 (10) 14 013.752 0 (10) 14 083.066 2 (15) 14 147.339 0 (16) 14 206.663 9 (18) 14 261.232 4 (19) 14 311.320 4 (51)

0.040 863 2 (26) 0.040 451 8 (17) 0.040 020 9 (11) 0.039 566 24(74) 0.039 089 12(78) 0.038 584 70(78) 0.038 052 21(75) 0.037 485 04(87) 0.036 880 62(87) 0.036 239 12(92) 0.035 552 20(93) 0.034 822 4 (11) 0.034 045 3 (11) 0.033 222 9 (14) 0.032 358 9 (18) 0.031 463 7 (23) 0.030 543 2 (22) 0.029 616 0 (37)

14 507.092 (4)

0.025 144 (8)

0.025 192 (8)

8.5 (3)

Ref. (6 )

14 565.813 (4) 14 591.942 (3) 14 615.893 (5)

0.023 602 (5) 0.022 761 (4) 0.021 908 (12)

0.023 630 (5) 0.022 867 (3) 0.021 968 (12)

19.2 (1) 39.6 (1) 48.5 (1)

Ref. (6 ) Ref. (6 ) Ref. (6 )

0.040 454 5 (17) 0.040 025 2 (12) 0.039 571 17(73) 0.039 094 34(79) 0.038 590 13(78) 0.038 058 05(76) 0.037 491 27(86) 0.036 887 21(89) 0.036 246 40(92) 0.035 55987(92) 0.034 831 0 (11) 0.034 055 1 (11) 0.033 233 5 (14) 0.032 370 0 (18) 0.031 476 2 (23)

1.953 (44) 2.056 (54) 2.188 (31) 2.307 (21) 2.473 (21) 2.649 (22) 2.905 (20) 3.142 (23) 3.415(24) 3.800 (24) 4.139 (25) 4.661 (30) 5.203 (28) 5.763 (36) 6.367 (49) 7.058 (78) 7.617 (60) 8.209 (78)

−0.49 (47) −0.48 (23) −0.63 (16) −0.74 (16) −0.99 (18) −0.98 (14) −1.41 (17) −1.88 (18) −2.12 (17) −3.22 (18) −3.39 (23) −4.13 (20) −5.31 (25) −6.53 (34) −7.01 (73) −8.50 (43) −9.21 (48)

0.0024 0.0025 0.0025 0.0020 0.0021 0.0022 0.0023 0.0024 0.0027 0.0024 0.0024 0.0024 0.0023 0.0022 0.0019 0.0018 0.0019 0.0017

Note. Units are all in cm−1 and the errors in the parentheses are 1 σ . The spectroscopic constants for v  = 0 and v  = 25 ∼ 29 are those f  e/ f reported in Refs. (10, 6), respectively. Bv and Bv e at the states v  = 25 ∼ 29 were calculated using the relation of Bv = Bv ± qv /2 in Ref. (6).

FIG. 6. Deviation of Tv from the (v + 1/2) polynomial calculated by using the coefficients in Table 5. The broken lines indicate the deviation from those calculated by the parameter in Ref. (6) and the dotted line in (a) is by the parameter in Ref. (7 ).

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TABLE 4 Spectroscopic Constants for the A State of I81 Br f

v

Tv

0 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

12 435.992 (33) 12 566.546 (33) 12 693.917 (35) 12 818.302 9 (30) 12 939.050 0 (14) 13 056.293 4 (10) 13 169.916 93(65) 13 279.776 44(71) 13 385.731 29(69) 13 487.627 93(74) 13 585.314 54(82) 13 678.631 90(87) 13 767.418 88(86) 13 851.525 88(98) 13 930.822 87(98) 14 005.201 1(12) 14 074.600 3 (17) 14 139.029 2 (15) 14 198.566 5 (16) 14 253.387 0 (15) 14 303.751 4 (53)

0.041 470 (18) 0.041 061 (18) 0.040 748 (43) 0.040 250 2 (23) 0.039 849 5 (16) 0.039 854 1 (16) 0.039 430 2 (12) 0.039 434 9 (12) 0.038 986 84(71) 0.038 991 56(71) 0.038 521 93(74) 0.038 527 04(74) 0.038 029 90(75) 0.038 035 16(74) 0.037 512 50(79) 0.037 518 11(79) 0.036 959 88(90) 0.036 965 90(88) 0.036 372 71(92) 0.036 378 91(94) 0.035 749 66(94) 0.035 756 60(94) 0.035 082 9 (11) 0.035 090 2 (11) 0.034 372 5 (11) 0.034 380 6 (11) 0.033 619 1 (13) 0.033 628 3 (13) 0.032 821 5 (18) 0.032 831 5 (18) 0.031 980 3 (17) 0.031 991 4 (16) 0.031 110 4 (21) 0.031 121 9 (20) 0.030 214 1 (16) 0.029 305 6 (37)

14 500.839 (4) 14 531.633 (8) 14 560.103 (3) 14 586.465 (4) 14 610.849 (7)

0.024 981 (6) 0.024 141 (13) 0.023 353 (4) 0.022 527 (7) 0.021 696 (4)

Bv

Bve

0.025 005 (6) 0.024 169 (13) 0.023 377 (4) 0.022 557 (7) 0.021 710 (4)

Dv × 108

1.877 (37) 1.973 (44) 2.131 (34) 2.233 (19) 2.391 (19) 2.550 (20) 2.800 (21) 3.001 (24) 3.278 (26) 3.645 (26) 3.969 (31) 4.424 (30) 4.949 (34) 5.515 (48) 6.057 (44) 6.725 (65) 7.316 (42) 7.798 (79)

11.1 (2) 11.1 (4) 13.2 (1) 15.3 (3) 19.0 (6)

Hv × 1013

−0.59 (35) −0.30 (26) −0.58 (14) −0.71 (13) −0.96 (15) −0.98 (16) −1.52 (17) −1.79 (19) −2.04 (19) −3.08 (24) −3.46 (23) −4.10 (25) −4.92 (37) −6.21 (32) −6.94 (54) −7.84 (29) −9.22 (49)

σ Ref. (10) Ref. (10) Ref. (10) 0.0019 0.0024 0.0024 0.0020 0.002 0.0021 0.0023 0.0024 0.0026 0.0024 0.0025 0.0023 0.0023 0.0020 0.0021 0.0020 0.0015 0.0018

Ref. (6 ) Ref. (6 ) Ref. (6 ) Ref. (6 )

Note. Units are all in cm−1 and the errors in the parentheses are 1 σ . The spectroscopic constants for v  = 0 and v  = 25 ∼ 29 are those f  e/ f reported in Refs. (10, 6), respectively. Bv and Bv e at the states v  = 25 ∼ 29 were calculated using the relation of Bv = Bv ± qv /2 in Ref. (6).

FIG. 7. Deviation of Bv from the (v + 1/2) polynomial calculated by using the coefficients in Table 5. The broken lines indicate the deviation from those calculated by the parameters in Ref. (6) and the dotted line in (a) is by the parameters in Ref. (7 ).  C 2002 Elsevier Science (USA)

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TABLE 5 Spectroscopic Coefficients of the (v + 1/2) Expanded Polynomial Parameters

I79 Br

I81 Br

Vibrational terms (l = 0–8 terms; v = 0, 3–20, 25 fitting) 12369.3353 12369.329 Cv0 (Te ) Cv1 (ωe ) 135.2276 134.1942 −1.8143 −1.7866 Cv2 (−ωe xe ) Cv3 (ωe ye ) 5.705 × 10−2 5.57952 × 10−2 Cv4 (ωe z e ) −1.1108 × 10−2 −1.0773 × 10−2 Cv5 9.6547 × 10−4 9.2914 × 10−4 Cv6 −5.0982 × 10−5 −4.8689 × 10−5 Cv7 1.4416 × 10−6 1.3662 × 10−6 Cv8 −1.6107 × 10−8 −1.5149 × 10−8 σ 0.0042 Rotatinal Const. (l = 0–7 terms; v = 0, 4–18, 25 fitting) Cr 0 (Be ) 0.04235567 0.041671084 Cr 1 (−αe ) −4.9452 × 10−4 −4.8327 × 10−4 Cr 2 (γe ) 4.1376 × 10−5 4.0126 × 10−5 Cr 3 −8.5034 × 10−6 −8.1835 × 10−6 Cr 4 8.1759 × 10−7 7.8012 × 10−7 Cr 5 −4.6352 × 10−8 −4.3929 × 10−8 Cr 6 1.3386 × 10−9 1.2589 × 10−9 Cr 7 −1.4894 × 10−11 −1.3901 × 10−11 σ 0.00000197 Centr. Dist. Const. (4th)(l = 0–2 terms; v = 3–20 fitting) Cd0 (De ) 2.2428 × 10−8 2.1751 × 10−8 Cd1 (βe ) −1.354 × 10−9 −1.2896 × 10−9 Cd2 2.0909 × 10−10 1.9978 × 10−10 σ 0.1351 × 10−8 Centr. Dist. Const. (6th) (l = 0–3 terms; v = 4–20 fitting) −2.7485 × 10−14 −2.6377 × 10−14 C h0 (He ) constrained C h1 1.3684 × 10−15 2.6796 × 10−15 C h2 −2.0339 × 10−16 −4.444 × 10−16 C h3 −10.298 × 10−17 −8.679 × 10−17 σ 3.3591 × 10−14

-type Doubling Const. (l = 0–2 terms; v = 5–18 fitting) 5.3117 × 10−6 5.2308 × 10−6 Cq0 Cq1 −3.1329 × 10−7 −3.0617 × 10−7 Cq2 3.7174 × 10−8 3.6051 × 10−8 σ 0.3101 × 10−6

Uncertainty

0.0099 0.0254 0.0149 3.885 × 10−3 5.447 × 10−4 4.385 × 10−5 2.026 × 10−6 4.990 × 10−8 5.065 × 10−10 4.677 × 10−6 1.147 × 10−5 5.552 × 10−6 1.158 × 10−6 1.251 × 10−7 7.299 × 10−9 2.178 × 10−10 2.593 × 10−12 0.889 × 10−9 1.655 × 10−10 6.798 × 10−12

3.902 × 10−15 5.689 × 10−16 1.978 × 10−17 3.925 × 10−7 7.053 × 10−8 2.918 × 10−9

Note. Units are all in cm−1 . The numbers of the fitting are selected to make the uncertainties at the last column and the standard deviation σ as small as possible. The C h0 (He ) was constrained to the calculated one using Eq. [10] in Ref. (13) to converge the polynomial to minimum at v  = 0. See the text.

and the dotted lines those by Clevenger et al. (10). One can see the observed values stagger out at the lower vibrational states of v  = 4∼5 and deviate greatly from the higher state than v  = 25. This means that some local perturbations from other electronic states have to be taken into consideration at the potential minimum and the higher vibrational states around v  = 20 at the A state. We consider that the spin rotational coupling effect between the A and the A state may perturb the vibrational states lower than v  = 5 and those higher than v  = 20. The RKR potential and the G v values of the A state reported by Radzykewycz et al. (14) indicate that the differences between v  (A) = 2∼7 and v  (A ) = 9∼14 are close to each other with v  = 7.

The plots for the qv and Dv values are shown in Figs. 8 and 9. The broken lines are those calculated using the parameters given by Appadoo et al. (6). The coefficients for the qv terms of v  = 4 to 18 were determined with a better accuracy and they are considered to be still positive at vibrational states lower than v  = 3. The expansion for the centrifugal distortion constant of Dv was up to -max = 2. When the Dv were extended to -max = 3 the standard deviation was not improved and the uncertainties of the lower order terms were rather increased. The De and β e values calculated by the relations given by Tyuterev et al.(13) were 1.659 × 10−8 and 0.702 × 10−9 cm−1 , respectively. The coefficients determined were 35% greater than those of the X state in the De and the sign was opposite in βe .

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FIG. 8. The observed and the calculated type doubling constant qv . The calculated values using the coefficients in Table 5 are shown by solid lines. The broken lines indicate the parameters in Ref. (6) and the dotted line in (a) is from the parameters in Ref. (7 ).

The plot for the Hv is shown in Fig. 10. We first tried to determine the coefficients of  = 0 to 3 or 4 in the (v + 1/2) polynomial. The result, which is given at the footnote under the figure, becomes minimum around v  = 4∼5 and the absolute value at the v  = 0 state increases as indicated by a broken line. As it is considered that the value should converge to H0  He at the lower vibrational states, the C h0 corresponding to the He term was constrained to the calculated one by the relation given by Tyuterev et al. (13) as in the case for the X state. The results are listed in Table 5. The C h1 correspond were calculated to be −0.455 × 10−15 cm−1 using ing to Y13

the relations in Ref. (13) and the sign was opposite in the case of βe . These results seem to support the model that the perturbations between the A and X states or between the A and A states exist systematically at the vibrational states from v  = 5 to 20. These effects are transformed into the {J (J + 1)}2 and {J (J + 1)}3 terms by the second perturbation treatment. The spectroscopic constants determined by the least squares fitting method using a polynomial equation are not Dv and Hv in their intrinsic meaning any more, but effectively correspond to the centrifugal distortion constants. The measurement of the spectral lines belongs

FIG. 9. The observed and the calculated centrifugal distortion constant Dv . The calculated values using the coefficients in Table 5 are shown by solid lines. The broken lines indicate the parameters in Ref. (6) and the dotted line in (a) is from the parameters in Ref. (7 ).

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FIG. 10. The observed and the calculated centrifugal distortion constant Hv . The calculated values using the coefficients in Table 5 are shown by the solid lines. The broken lines indicate the results calculated by including the Ch0 (He ) term as a fitting parameter. The polynomials obtained were Hv = −1.572(0.700) × 10−13 + 0.378(0.200) × 10−13 (v  + 1/2) − 0.325(0.172) × 10−14 (v  + 1/2)2 − 0.249(0.459) × 10−16 (v  + 1/2)3 for I79 Br and Hv = −1.501 × 10−13 + 0.359 × 10−13 (v  + 1/2) − 0.306 × 10−14 (v  + 1/2)2 − 0.233 × 10−16 (v  + 1/2)3 for I81 Br.

to v  = 0∼3 and v  = 20∼25, where the local perturbations are expected to be more remarkable by an accidental degeneracy.

ACKNOWLEDGMENTS The authors are grateful for aid received from the Fund for the Promotion of High-Technology Research Centers of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

4. CONCLUSION

The Doppler limited absorption lines in the A ← X system of I81/79 Br were measured using a ring type Ti:sapphire laser in the 0.8-µm region. About 11 000, P-, Q-, and R-branch lines belonging to v  = 3∼20 at the A state and v  = 1∼6 at the X state were assigned. The splittings caused by the nuclear quadrupole coupling effect by I atom were partially resolved in the P- and Rbranch lines and the unperturbed line positions were determined using an approximation for the high J rotational levels. The nuclear quadrupole coupling constants at the A state of I atom were estimated. The Dunham coefficients for the X state not correlative to the fitting condition of the A state were determined with the joint analysis using the pseudo vibrotational wavenumber by calculating the combination differences and those reported by Nelander et al. (7). The analysis for the A state revealed that the local perturbations of two types, one for vibrational state lower than v  = 3 and the other for that higher than v  = 20, have to be taken into consideration. The effective spectroscopic coefficients in the (v + 1/2) polynomial containing a higher order centrifugal distortion constant of Hv were determined in the vibrational range of v  = 6 to 18. The type doubling constants qv were also determined with their polynomial coefficients.

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