Laser-induced-fluorescence Fourier transform spectrometry of the XOg+ state of I2: Extensive analysis of the BOu+ → XOg+ fluorescence spectrum of 127I129I and 129I2

JOURNAL OF MOLECULAR

SPECTROSCOPY

116,458-498 (1986)

Laser-Induced-Fluorescence Fourier Transform Spectrometry of the X0: State of I*: Extensive Analysis of the SO,’ - X0: Fluorescence Spectrum of 1271’2gl and 12’12 D. CERNY,* R. BACKS,* AND J. VERGEst *Laboratoire de SpectromBrie Ionique et Moltkulaire, Universite’Claude Bernard (Lyon I), 43, Boulevard du 11 Novembre 1918, 69622 Vilkurbanne Cedex, France; and tLaboratoire Aime’Cotton(CNRS II), Bdtiment 505. 91405 Orsay Cedex. France An extensive rotational analysis of the vibrational levels of the X0,+ state of ‘*71’291 (5 G u’ G 110) and ‘9, (4 < u” G 108) has been done from laser-induced-fluorescence analyzed with a Fourier transform spectrometer. The usual Dunham relationships are checked. For the range explored the lines can be recalculated with an accuracy better than 0.010 cm-’ and even 0.005 cm-’ for low J values. Checks are done from absolute hype&me measurements. o 1986 Academic Fws, Inc. I.

INTRODUCTION

Numerous spectroscopic works have been devoted to the study of the BO:-X0: transition of the ‘*‘I2 molecule (see references in the previous part of this article (1) that we shall call paper I). There have also been several spectroscopic studies of this transition for the ‘2912molecule. One ofthe aims was to clarify the vibrational assignment of various electronic transitions or line determinations (2-9). Other studies were devoted to the hypetine structure which was compared to ‘*‘I2 (10-13) or used for the identification of lines as secondary reference standards for locking lasers at 5 14.5 (14-25), 618 (16-19), or 633 nm (20-22). By contrast very few spectroscopic studies have been devoted to the 1271’291 isotopic molecule. Two vibrational levels of the BO: state were observed in Ref. (5) and some hyperfine structure in the 633-nm range in Ref. (21). But for both the ‘27I129Iand L29I2isotopic species nothing has been done about the nonthermally populated vibrational levels of the ground state, mainly for the levels close to the dissociation limit where various perturbations may occur (paper I). So in order to complement and make clear the results obtained at the dissociation limit of and the ground state of the ‘*‘I2 molecule, we have undertaken the study of 12711291 129I2X0: state from laser-induced-fluorescence (LIF) analyzed with a Fourier transform spectrometer (FTS). Our main aims were an analysis of this state as close as possible to the dissociation limit, a comparison of the isotopic relations, and a determination of the usual long-range parameters for these two isotopes. It is now known from a priori calculations that all of the nine states dissociating at the same dissociation limit as the X0,+ state are bound (23,24). The main perturbations of the X state can occur due to interaction with the alg (D, = 406.0 cm-‘) and the a’0: states (0, = 243.8 cm-‘) (I, 25). The bottom of these wells are close to the u” = 84-85 and 2)”= 88-89 levels of the 12’12X state, respectively, so in our isotope 0022-2852/86 $3.00 Copyist 0 1986 by Academic Press, Inc. All ri&s of reproduction in any form rcservd.

458

B -

X SPECTRUM OF ‘27I’29IAND ‘29I2

459

studies, perturbations may occur from the related levels up to the dissociation limit. But smaller perturbations due to hyperfine mixing could occur at much lower vibrational levels since it is experimentally known that A’2u and A 1u are strongly bound: D,(A’2u) = 2505.7 cm-’ - u”(XO,+) N 57-58 (26) and D,(Alu) = 1639.8 cm-’ u”(XOi) N 66-67 (7, 27. 28). The electronic levels going to the BO: state dissociation limit are expected to be bound (23, 24, 26) and some hyperfine perturbations have recently been found and analyzed (13. 29). So in order to eliminate safely the influence of possible perturbations, we have compared potential curves, long-range behavior, etc., for the three isotopes studied, from separate analysis of their fluorescence spectra. The results of the extensive study of the ‘*‘I2 X0: state have been given in paper I. In the present paper referred to as II, we determine the rotational parameters of both isotopes and compare the determined values of those obtained from ‘*‘I*. In the following paper (to be referred to as III), we will examine and compare the long-range behavior of the three isotopes.’ 11. EXPERIMENTAL

DETAILS

The data are obtained in the same conditions as those reported in paper I. The laser-induced-fluorescence of I2 analyzed with a high-resolution Fourier transform spectrometer was obtained from multimode Kr+ (520.832 nm) or Ar+ (5 14.532 and 50 1.7 16 nm) excitation lines (Fig. 1). In order to have a good signal to noise ratio the entire spectral range of the fluorescence (0.5 - 1.35 pm) was obtained from five recordings for both isotopes. They are reported in Table I. The full-width half maximum (FWHM) of the apparatus function is of the order of 0.020 cm-’ in the visible to 0.010 cm-’ in the infrared; the FWHM of nonapodized recorded lines decreases from 0.030 to 0.0 15 cm-’ (Table I). The enlargement due to the hyperfine structure is lower than in ‘*‘I2 (see Sect. V) and the shift between the center of gravity G and the maximum M of a recorded line (see paper I, Sect. II) was neglected. III. FITTING PROCEDURE

AND ANALYSIS OF THE DATA

The J levels used in the fits for the X0; vibrational levels are shown in Figs. 2a ( ‘271’291) and b (‘2912).For ‘27I129Ithe range 30 < U”< 40 is poorly defined: this is also

true for some low u” levels (5-6 in ‘271’291 and for some levels with U” < 30 in ‘2912). The number of lines of each transition used in the fits are noted in Tables IIa (‘271’291) and b (‘2912). The fitting procedure is the same as in paper I. The fits were done in five groups (‘271’291,Fig. 3a) and eight groups (‘2912,Fig. 3b). Care has been taken to keep the same origin for all groups. With that aim, the data of the 9” = 7 and 72 levels ( r271’291) and V” = 6 and 73 (‘2912)were used in all the fits (Figs. 3a and b). For every group we found that the parameters of these reference levels had the same value to within less

‘Paper III: “Laser-Induced-Fluorescence Fourier Transform Spectrometry of the X0,+ State of 12: Tests of the Long-Range Behavior for Three Isotopes of I*,“ R. Bacis, D. Cemy. and F. Martin, J. Mol. Spectrosc.. submitted for publication.

460

CERNY, BACIS, AND VERGES

ul 127

0.100cm-' u t

45

'23

19429.73d

(501.716

nm)

L

5

34

(520.632

129 12

12

11

1942 '9.73cm-' (514.532

nm)

"Ill)

Lu

6 ,769 f

t 19194.71cm-'

I

6

1L Iw ,

12

129

t 19926.04cm-'

I

(514.532

I

"m)

13

t 19926.04cm-' (501.716

nm)

PIG. I. Lines excited from Kr+ or Ar” multimode laser line. Only lines from which the fluorescence was analyzed are reported. The height of bars is proportional to the observed relative Iluorescence intensities. The wavenumbers of excited lines are calculated from our determined parameters: 1271'291:

from 5 14.532 nm Ar+ (19429.73 cm-‘) 1 P22 (49-l) 19429.812cm2 P57 (51-1) 19429.819 cm-’ 3 R65 (45-O) 19429.861 cm-’

from 501.716 nm Ar+ (19926.04 cm-‘) 4 R 7 (61-O) 19925970cm-’ 5 P 6 (61-O) 19926.001 cm.-’ 6 R24 (62-O) 19926.055 cm-’

from 520.832 nm Kr+ (19194.71 cm-‘) 1 Rlll(43-0) 19194.595 cm-’ 2 R 71(40-O) 19194.651 cm-’ 3 Rl43(48-0) 19194.777 cm-’ 4 P149 (50-O) 19194.803 cm-’

‘2912: from 5 14.532 nm Ar+ (19429.73 cm-‘) 5 Rl03(49-0) 19429.658 cm-’ 6 Rl09(50-0) 19429.716 cm-’ 7 R 67(52-l) 19429.776 cm-’ 8 P 16 (49-l) 19429.810 cm-’ 9 R 43(50-l) 19429.838 cm-’

from 501.716 nm Ar+ (19926.04 cm-‘) 10 P21 (62-O) 19925.894 cm-’ 11 R31(63-0) 19925.914 cm-’ 12 R54(70-0) 19926.064 cm-’ 13 P52 (69-O) 19926.131 cm-’

than 2 SD (see Appendixes Ia and b) which ensure the homogeneity of the results. The G(u”) origin was fixed at G(u” = 7, J = 0) = 1568.1707 cm-’ (‘271’291)and G(u” = 6, J = 0) = 1357.884 1 cm-’ (L2912)calculated from isotopic relations from Luc and Gerstenkorn’s preliminary results on the X0,’ state of 12’12(v” = O-19) (see Appendix II). By doing this, we have defined the same origin of energy values for 1271’291 and ‘29I2to be that of ‘27I2(the u” = - l/2 level of the X0,’ state), which will allow a convenient way of comparing the behavior of the three isotopes. Checks from isotopic relations and direct determinations show that the differences in origin given in that way are negligible for the three isotopes (see Sect. IV).

B -

X SPECTRUM

461

OF ‘2’I’29I AND ‘32

TABLE I Full-Width Half Maximum (FWHM) of the Nonapodized Apparatus Function (Resolution) and of the Nonapodized Recorded Lines (I mK = 0.001 cm-‘) 127I1291

range

0.5

t.O 0.7

excitation 1 ine

514.532

resolution

0.0398

recorded line

pm

nm

cm-1

60 I&

0.5

to

I.1 urn

501.716

to

1.05

519.532

cm-1

0.0093

14 to

nm

0.8

0.015

20 UK

urn

nm

cm

I to

1.25 wl

5(11.71b nm

-I

0.0093

25 nK

cm

-I

1.25 to

1.33 WI

501.716

0.013

14 mK

nm

cm-'

20 nii

129 I2 range

0.54

t0

excitation line

520.832

resolution

0.0265

recorded 1 ine

0.9

nm

cm-’

40 0x

urn 0.7

to 0.8

501.716

0.0206

urn

nm

cm-’

30 Ia

0.8

to 0.98

520.832

0.0179

nm

cm-’

28 nx

pm

0.9

to

520.632

1.3 w

nm -I

0.0137

cm

20 to

22 I&

0.9

to

I.3 um

501.716

0.0093 15 IN (v’ 25 UK (v’ 30 ax (v’

nm

cm-’ = 62,631 = 69) = 70)

The iterative fitting procedure was done in the same way as for “‘12 as explained in paper I and for similar reasons. The results of the last iteration are gathered in Tables IIIa and b for the X0: state and Tables IVa and b for the BO: state. The expansion parameters of the 12’12as determined by Gerstenkom and Luc, used for isotopic relation calculations, are reported in Appendixes II and III. The Y, values (30) were calculated in the usual manner because the experimental fits cannot give these constants as explained in Appendix IV. The expansion parameters obtained from the last fit are reported in Tables Va (1271’291) and b (12912). As already noted at the start of this section, the examination of the data at our disposal (Figs. 2a and b) shows that almost no (or no) fluorescence lines were recorded for 0 c D”4 4 and 30 < U”< 39 in 127I129I and 0 < ~1”< 3 in 12912.Careful comparison of the experimental parameters with the parameters calculated from isotopic relations shows an excellent agreement for levels close to this range (see Sect. IV). Then in the determination of the expansion parameters of Tables Va and b the above-mentioned nonexperimentally determined constants were replaced by the isotopic calculated ones from the relations given in Appendix I for 0 < t? % 4 (1271’291) and 0 < D”< 3 (‘2912). It should be noted that a preliminary determination of the expansion parameters using only experimental values allows us to recalculate the missing rotational constants with a good accuracy; in most cases the recalculated constants are the same as the isotopic calculated ones to within 2 averaged SD. Moreover, we have not reported the standard deviations on the expansion parameters of Tables V, because from our point of view

462

CERNY, BACIS, AND VERGES

J’a 100 _

50 _

J 100

II I ’

50 1

:l’I IllI T

T

613

65

70

FIG. 2. (a) J values for lines used in the fits of the transitions involving a given uNlevel (‘271’2g1 molecule). (b) J values for lines used in the fits of the transitions involving a given u” level (lB12 molecule).

they do not have a clear significance here, these parameters being only effective constants allowing the calculation of G(u), B(u), etc., within the experimental precision. This needs a higher number of decimal places than those defined by the standard deviations. Moreover, these effective constants change within more than 2 SD when for instance one changes the number of terms in the polynomial expansion or uses a lower range of data. For example, for ‘*‘12, Y10 = 212.8520 cm-’ with 14 terms or 212.8612 cm-’ (15 terms in Table Vb) with 0 < u” 6 88 levels and Y,o = 212.8478 cm-* (3 terms) or 2 12.85 17 cm-’ (4 terms) with 0 f z)” < 10 levels only, the rms deviation for recalculated G(u”) values being the same (~0.002 cm-‘) in the four examples. In all fits relative to the BOZ state, as noted in Table IV, all nondetermined parameters in a given u’ level were held fixed to the value calculated from isotopic relations and Gerstenkom’s data. For clarity we recall briefly the iterative fitting procedure. The first iteration is made in the following way: the first fit is done with the parameters of X0: without standard deviations in Table III held fixed to zero. This gives a first X0,’ RKR curve for each isotope. From this first RKR curve we calculate the centrifugal distorsion constants

B -

150

463

X SPECTRUM OF ‘271’291 AND ‘2912

b

J

100

50

l’l:l:‘:l

5

10

15

20

1 1

: ill ’;lll:l:.:l:; I

30

25 1

35 I

40 I

1 1 1

::

: 45 1

55 I

50 1

* v”

150 J

/I

1oc

II I/l,’ I i

50

1 ::

60

1

I

65

70

I’ ’ 1’1i III( 1

1

75

60 FIG.

85

:I

I’ ‘:

II 1:

,

90

I

95

1

100

106

*

VW

2-Continued.

(CDC) together with G(u) and B(u) of the X0; state using Hutson’s method (31, 32). In the second iteration we make a second fit with the CDC (Hutson’s) constants held fixed at their smoothed values from the first iteration. We then determine a second RKR curve and a second set of Hutson’s constants. In the third iteration we obtain the results given in Tables III which correspond to the third fit, the fixed constants coming from the second set of Hutson’s constants. This third iteration gives RKR curves reported in Tables Via and b, and finally from these RKR curves we calculated again a third set of Hutson’s constants as a check of the convergence of the iterations. We have shown in Figs. 4a and b the differences between this third set of constants and the experimental determinations. We have reported in paper I various causes that can introduce differences between recalculated G(v) from an RKR curve and experimental values Gexp. The lack of precise data is an important point which is clearly shown here. We can see from Figs.

464

CERNY, BACIS, AND VERGES TABLE IIa ‘2711291 BO: + X0, Transition: Number of Lines in Each Transition ~‘-1)”Used in the Fits”

a,)

45

49

51

61

62

I

6

(14)

14 9

7

(68)

42

8

(40)

19

9

(69)

35

II

10

(42)

I

2:

I:

11

(56)

1

12

(48)

I

15

5

7

8

18

3

2

4

11

16

7

2 15

14

21

(35)

I

19

4

6

4

2

22

(27)

1

6

2

5

6

*

23

(26)

1

11

3

4

5

3

24

(17)

I

6

2

2

5

2

) 29 30

(6)

1

(2)

2

2

2

2

51

(28)

4

15

9

52

(64)

42

8

14

53

(22)

5

II

6

54

(60)

42

9

9

55

(20)

9

9

2

56

(68)

42

15

II 2

57

(28)

I8

8

58

(93)

1

43

14

19

59

(30)

I

25

3

2

51

61

62

2

9

13

10

(40)

12

15

5

6

2

(95)

40

8

15

20

12

45

14

16

20

10 9

(63)

64 65

(

2

6

19 7

49 29

63

8

9

66

(10)

67

(105)

2

8

68

(48)

15

2

6

16

69

(74)

38

15

I2

6

3

70

(95)

36

2

14

27

16

71

09)

14

13

2

4

6

72

(113)

45

17

19

21

II

73

(54)

5

10

22

17

74

(74)

40

21

II

75

(99)

42

8

19

19

II

76

(63)

II

6

5

26

15

77

(95)

54

22

13

2

4

78

(83)

30

4

17

20

12

2

79

(100)

34

10

6

29

21

80

(104)

55

18

10

10

11

81

(55)

18

7

23

5

2

82

(107)

42

5

13

28

19

83

(117)

59

12

2

26

18

84

(62)

17

14

18

4

9

85

(22)

13

7

2

26

17

2

25

22

17

13

86

(62)

87

(77)

I 19 14

14

88

(44)

14

89

(45)

22

19

90

(39)

8

l9

91

(35)

92

(64)

2

93

(53)

2

94

(39)

2

95

(10)

96

(4)

98

(20)

4 10 ~

2

25

10

25

20

17

13

22

16

2

I7

18

5

5 2

2 20

99

(4)

4

100

(4)

4

101

(15)

13

102

(14,

14

2

103

(26)

22

104

(21)

15

4 6

105

(16)

12

4

106

(20)

15

5

107

(15)

9

6

108

(7)

5

109

(8)

4

110

(4)

4

4

B -

X SPECTRUM

OF ‘27I’29IAND ‘*‘I2

465

TABLE IIb ‘2912

Bo:

-

X0; Transition: Number of Lines in Each Transition ~‘4’ Used in the Fits”

4a and b that G,,, - G(u) is most often positive and less than 0.090 cm-’ for 1271’291 and 0.040 cm-’ for ‘29I2 where the determinations are more precise. The agreement set of data. is still better in ‘27I2 (see paper I) where we have a more comprehensive

466

CERNY, BACIS, AND VERGES a

v’ 62

-

61

-

FIG. 3. (a) Scheme of the tluorescence transitions related to the global fitting procedure. The whole set of lines was fitted in five groups. In every group the five v’ levels are involved and also 1)”= 72 and 7* (reference level). For the other v” levels we have: groupI:fromu;= group 2: from v; = group 3: from VT= group 4: from v; = group 5: from v; =

5tov ‘; = 14 to II; = 42 to I$ = 64 to vz = 87 to ul =

28 (109 bands, 976 lines, rms = 3.05 mK) 42 excepting 32 < v” < 37 (95 bands, 671 lines, rms = 2.14 mK) 64 (95 bands, 1220 lines, rms = 1.25 mK) 87 (125 bands, 1863 lines, rms = 1.45 mK) 110 excepting1)”= 97 (63 bands, 765 lines, rms = 3.07 mK).

* G term held fixed in the fit. rms = root mean square deviation between observed and calculated lines. (b) Scheme of the tluorescence transitions related to the global fitting procedure. The whole set of lines was fitted in eight groups. In every group the ten v’ levels are involved and also u” = 73 and 6* (reference level). For the other v” levels we have: group group group group group group group group

1: from 2: from 3: from 4: from 5: from 6: from 7: from 8: from

u’i = v; = VT= u; = v’; = v; = 0’; = u’[ =

4 to 15 to 27 to 39 to 51 to 63 to 76 to 89 to

u; = v5 = v’$= vi = v; =

17 (62 bands, 589 lines, rrns = 1.43 mK) 27 (56 bands, 5 15 lines, rms = 1.18 mK) 39 (93 bands, 766 lines, rms = 1.26 mK) 51 (105 bands, 827 lines, rms = 2.10 mK) 63 (94 bands, 1118lines, rms = 1.31 mK). vl = 76 (125 bands, 2086 lines, rms = 1.55 mK) us = 88 (115 bands, 1810 lines, rms = 2.40 mK) us = 108 excepting U" = 97 and v,” = 105 (54 bands, 364 lines, rms = 2.36 mK).

G term held fixed in the fit. rms = root mean square deviation between observed and calculated lines. *

The relatively poorer recalculated G(V) values in 12’1’291 are due to two factors: (i) the precision of data is lower [rms deviations are less than 0.0031 cm-’ for ‘27I129Iand 0.0024 cm-’ for lz912in the various fits (Figs. 3)]; (ii) the absence of data in the

B -

X SPECTRUM

OF ‘27I’29I AND

I*912

467

FIG. 3-Continued.

30 < 2rx< 39 range (for ‘271’291) . Nevertheless it is easy to see that the differences in calculated G(u) - G(v + 1) are in excellent agreement with the measured values. This is also true for recalculated B(v) or D(u) which are found within the experimental errors (Figs. 4) except for a few high u” values. The differences in H (Fig. 5) or L calculated in the second and third iterations are small, showing that the convergence of the iterations cannot be improved given the present data. Finally, some slight perturbations appear in some recorded lines which have been eliminated in the fits (in 0” = 102, 105 for ‘27I’29Iand u” = 91, 92, 103, 105 for ‘2912). In contrast to 12’12,we had insufficient data to allow us to deperturb the related levels. The good rms deviations for the various groups of fits (Fig. 3) ensure that the possible perturbations have little influence on the experimental G and B values, and the good recalculated G(u) values for high u levels encourage us to undertake a long-range analysis for both isotopes (paper III). IV. ISOTOPIC

RELATIONS

The G(v) and B(u) values of both isotopes in the X0; and BO: states can be calculated from the usual polynomial expansion (33) as reported in Appendixes II and III. The relationship between the Dunham coefficients Yklfor the different isotopic molecules is then given approximately by yki

=

bl

-k + 21 ukl 2

(1)

where p is the reduced mass of the molecule and ukl is isotopically invariant. It is known that this approximation is inadequate for high-precision measurements. The

468

CERNY, BACKS, AND VERGES TABLE IIIa Parameter? of the ‘271’291 X0,+ State (in cm-‘) G

B x 10

Dx

-Lx1019 ('78) 0.61

5

1156.8213 (404) 0.3644779 (174) 0.4301

6

1363.1218 (294) 0.3633422 (51) 0.4635

0.66

(4') 0.46’5

(66) 0.66

I

7'

1568.1707

8

1771.9495

(40) 0.3610101 (80) 0.5060

(102) 0.71

9

'974.4587

(32) 0.3597940 (76) 0.4539

(90) 0.71

'0

2'75.6743

(32) 0.3585696 (78) 0.3893

(98) 0.75

11

2375.6045

(34) 0.3573699 (76) 0.4233

(90) 0.78

12

2574.2'75

(31) 0.3561817 (80) 0.4695

(106) 0.82

13

2771.5203

(35) 0.3549582 (76) 0.4729

(90) 0.84

14

2967.4926

(22) 0.3537125 (66) 0.4927

(83) 0.91

15

3162.1304

(26) 0.3524835 (66) 0.5339

(81) 0.94

16

3355.4'52

(22) 0.35'2493 (67) 0.5691

(89)

1.00

'7

3547.3434

128) 0.3499416 (66)

0.4785

(81)

1.06

18

3737.8945

(24) 0.3486789

(68) 0.5030

(92)

1.12

19

3927.0603

(29) 0.3473974 (66) 0.5202

(82)

1.17

20

4114.8258

(26) 0.3460965 (70) 0.5146

(99)

1.23

21

4301.1768

(30) 0.3447964 (68) 0.5368

(87)

1.30

22

4486.1006

(32) 0.3434736 (75) 0.5366

(104)

1.33

23

4669.5844

(37) 0.3421228 (75) 0.5177

(11')

1.41

24

4851.6058

(39) 0.3407891 (86) 0.5454

(144)

1.46

25

5032.1586

(42) 0.3393849 (86) 0.4642

(142) 1.54

26

5211.2155

158) 0.3380664

27

5388.77'2

(66) 0.3366544 (117) 0.5538

(218) 1.66

28

5564.8040 (129) 0.3352259 (180) 0.5473

(342) 1.73

29

5139.2927

(86) 0.3338070 (39) 0.5728

1.81

30

5912.1973

(29) 0.3324164 (65) 0.5807

1.91

3'

6083.6738

(29)

0.3306487 (67) 0.5891

2.00

0.3621626

(109) 0.5913

-

a

lo8

-

(202)

1.59

-1 The origin of the vu1levels was fixed from G(v" = 7, J = 0) - 1568.1707 cm 7 I k ; p = 0.9961126. calculated from the isotopic relation Gi(v") = 1 pk YkO(vM + $ k=l '27 The YkO coefficients are determined from I2 and are given in Appendix II. The number in parenthesis is the uncertainty in the last digits typed in upright characters and corresponds to two standard deviations. The digits given in italic characters correspond to a much higher precision than the standard deviation, but due to correlation effects they are needed in order to recalculate the measured lines with the precision noted in Figure 3-a. Parameters without uncertainty were determined from the R K R curve and Hutson's program (31.32) (see text) and held fixed in the fit.

b

For levels v" = 7 and 72 the reported parameters and errors (two SD) are the average of the results from the 5 groups of fit (given in Figure 3-a and in Appendix I-a).

* The values marked with * are calculated from a logarithmic extrapolation from the parameters of the preceding v" levels.

B + X SPECTRUM

469

OF ‘*7I’291AND ‘*912

TABLE IIIa-Continued

V”

G

B x

10

Dx

-Hx10'5

10'

-Lx1019

I 38

7236.9611

(86)

0.3199454

(188)

0.6614

3.17

39

7394.8038

(22)

0.3184377

(50)

0.6739

3.42

40

7550.9218

(28)

0.3167469

(55)

0.6870

41

7705.2186

(64)

0.3150028

(96)

0.6346

3.68 (166)

3.95

42

7857.6639

(55)

0.3133084

(31)

0.7009

(42)

4.26

cl.05

43

8008.2221

(25)

0.3115622

(31)

0.7372

(64)

4.59

0.06

B x

G

44

8156.8738

(46)

45

8303.5849

(20)

46

8448.3198

(33)

f

10

Dx

108

-HxlO

1'

LX10

0.3097711

(25)

0.7665

(31)

0.493

0.3079278

(26)

0.7666

(56)

0.529

0.08

0.3060607

(18)

0.7911

(22)

0.569

0.09

47

8591.0462

(18)

0.3041543

(24)

0.8201

(50)

0.610

0.10

8731.7279

(24)

0.3022005

(15)

0.8307

(16)

0.655

0.12

49

8870.3288

(16)

0.3002103

(22)

0.8551

(48)

0.703

0.13

SO

9006.8123

120)

0.2981694

(14)

0.8699

(14)

0.754

0.15

51

9141.1383

(16)

0.2960924

(23)

0.8989

(47)

0.809

0.16

52

9273.2698

(18)

0.2939670

(14)

0.9373

(16)

0.870

0.18

53

9403.1652

(18)

0.2917887

(24)

0.9681

(48)

0.936

0.21

54

9530.7839

(16)

0.2895600

(14)

1.0039

(15)

1.008

0.23

55

9656.0860

(20)

0.2872628

(28)

1.0195

(54)

1.086

0.26

56

9779.0268

(14)

0.2849183

(13)

1.0555

(14)

1.173

0.29

57

9899.5641

(20)

0.2825147

(27)

1.0952

(50)

1.268

0.32

58

10017.6538

(12)

0.2800476

(12)

1.1290

(14)

1.374

0.35

59

10133.2554

(26)

0.2775045

(22)

1.1511

(34)

1.490

0.39

60

10246.3212

(12)

0.2749184

(12)

1.2180

114)

1.618

0.44

61

10356.8115

(18)

0.2722336

(18)

1.2405

(30)

1.759

0.49

62

10464.6824

(12)

0.2694944

(14)

1.2939

(21)

1.915

0.55

63

10569.8924

(12)

0.2666872

(13)

1.3687

(16)

2.086

0.61

64

10672.4000

(13)

0.2637921

(18)

1.4159

(31)

2.275

0.69

(30)

65

lC772.1675

(16)

0.2608171

(24)

1.4656

10869.1514

(92)

0.2578477

(18)

1.5183

-t&i1023

0.07

48

66

1'

2.483

0.77

0.03

2.712

0.87

0.04

67

10963.3302

(18)

0.2546288

(23)

1.5959

(27)

2.964

0.98

0.04

68

11054.6593

(16)

0.2514097

(26)

1.6693

(37)

3.241

1.12

0.05

69

11143.1114

(16)

0.2481034

(24)

1.7400

(30)

3.547

1.28

0.06

70

11228.6635

(16)

0.2447090

(24)

1.8201

(30)

3.885

1.46

0.08

71

11311.2917

(20)

0.2412232

(32)

1.8940

(54)

4.259

1.67

0.09

7Zb

11390.9786

(21)

0.2376427

(42)

1.9742

(47)

4.674

1.93

0.11

73

11467.7111

(16)

0.2339893

(26)

2.0694

(42)

5.135

2.23

0.13

74

11541.4804

(17)

0.2302450

(24)

2.1797

(29)

5.652

2.59

0.16

75

11612.2835

(16)

0.2264009

(23)

2.2755

(28)

6.232

3.02

0.20

76

11680.1224

(16)

0.2224643

(26)

2.3742

(36)

6.887

3.54

0.25

introduction of correction terms was given originally by Dunham (30) and Van Neck (34). Such corrections were discussed later on, and after allowing for the breakdown of the Born-Oppenheimer approximation, cast in a form suitable for use in fitting

470

CERNY,

BACIS,

AND VERGES

TABLE IIIa-Continued

Y”

B x

G

10

Dx

IO7

-kixlO'

-LxlO'

+x1023

77

11745.0031

(16)

0.2184604

(24)

0.25274

(29)

0.7631

0.0418

0.31

78

11806.9385

(16)

0.2143482

(24)

0.26537

(30)

0.8483

0.0497

0.39

79

11865.9464

(16)

0.2101327

(24)

0.27595

(30)

0.9464

0.0594

0.50

80

11922.0463

(16)

0.2058519

(26)

0.29353

(5’)

0 .941(3f

0.0715

0.65

81

11975;2671

(18)

0.2014505

(25)

0.30549

(34)

1.193

0.0862

0.82

82

12025.6373

(16)

0.1969774

(24)

0.32444

(28)

1.345

0.1034

1.03

83

12073.1915

(16)

0.1924041

(25)

0.345’9

(46)

1 .358(3(

0.1304

1.84

84

12117.966

(17)

0.1877208

(25)

0.36403

(32)

1.784

0.1944

3.08 4.50

85

12160.00'3

(20)

0.1829140

(37)

0.38128

(87)

2.136

0.2034

86

12199.3364

(16)

0.1780276

(46)

0.40151

(48)

2.251

0.1603

5.97

87

12236.0160

(16)

0.1730176

(25)

0.44357

(36)

2.729

0.4903

9.16

0.3221

88

12270.0855

(39)

0.1677432

(120)

0.4'504

(133)

3.361

89

12301.5838

(36)

0.1625408

(57)

0.51288

('1)

3.993

0.83

90

12330.5572

(38)

0. ‘57’295

(63)

0.58476

(14)

4.929

0.57

91

12357.0656

(38)

0.1513290

(20)

0.65387

(25)

5.795

1.15

92

12381.1617

(35)

0.1457819

(44)

0.65956

(67)

6.455

1.02 1.24

93

12402.9’67

(36)

0.1398776

(57)

0.71060

('2)

7.465

94

12422.4680

(38)

0.1338801

(65)

0.69783

(18)

8.423

1.95

95

12439.9695

(74)

0.1280322

(60)

0.80312

(78)

9.358

1.97

96

‘2455.6067

(59)

0.122267

(91)

0.836

110.51

2.9

98

12481.9664

(40)

0.111288

(34)

0.948

116.07

6.4

99

'2492.9783

(15)

0.104985

(23)

1.025

!0.89

9.0

100

'2502.6770

(13)

0.099474

(20)

1.121

16.96

13.8

101

12511.1691

(42)

0.094103

(16)

1.240

$5.07

20.1

102

12518.5445

(43)

0.086153

(31)

1.383

1i6.40

31.1

103

12524.8491

(40)

0.082186

(34)

1.4375

(48)

f52.91

51.1

104

12530.1720

(41)

0.076247

(37)

1.5900

(5')

105

12534.6326

(45)

0.068760

(53)

1.7129

(75)

106

12538.1748

(40)

0.063637

(82)

2.344*

1;77.3

279.

107

12541.0259

(45)

0.056996

(86)

2.630*

2f i5.2

479.*

108

12543.2189

(54)

0.049755

(12)

2.951*

3f i3.0*

813.*

109

‘2544.8244

(66)

0.042683

(15)

3.350*

5111.0*

410.*

110

‘2545.9628

(‘71

0.035843

(27)

3.802*

7(38.0*

400.*

I17.77

1:z5.0

86.8 147.

data from several isotopes (35,36). The order of magnitude of the corrective terms to Uk, is mJM, where me is the electron mass and it4 the nuclear mass (-4 X lop6 in the present case). This means that the correction to the most precise experimental term ( Yio) is of the order of 0.00 1 cm-’ (= 1 mK), that is to say about 1 SD. Moreover we have seen in the discussion of the previous section that changing the range or the number of terms of the expansion can give changes within more than 2 SD, that is to say in Yro changes of the order of 5-10 mK. This can be seen in comparing three precise results obtained from “‘I* X0,’ FIS measurements: Yio = 2 14.5 186 cm-’ (0 c u” d 9) [Ref. (37)], YiO= 214.5268 cm-’ (0 G 0” G 19) (see Appendix II), and

E + X SPECTRUM

471

OF ‘27I’29IAND ‘29I2

TABLE IIIb Parameters’ of the lz912X0: State (in cm-‘) Dx

-

lo8

H x

4

945.5916

(41)

0.3628259

(17)

0.45304

(67)

5

1152.3564

(58)

0.3616882

(18)

0.45806

(69)

0.591

Sb

1357.8841

0.3605287

(17)

0.46096

(58)

0.639

10

15

-lx1020

0.593

7

1562.1603

(50)

0.3593809

(17)

0.46372

(65)

0.643

8

1765.1884

(31)

0.3582099

(16)

0.46584

(62)

0.697

9

1966.9434

(51)

0.3570361

(17)

0.46847

(64)

0.698

10

2167.4257

(30)

0.3558534

(16)

0.47128

(61)

0.751

11

2366.6208

(60)

0.3546653

(18)

0.47534

(66)

0.772

12

2564.5213

(30)

0.3534676

(18)

0.47914

(61)

0.814

13

2761.1162

(86)

0.3522602

(20)

0.48262

(75)

0.829

14

2956.3944

(30)

0.3510472

(16)

0.48793

(60)

0.886

15

3150.3522

(72)

0.3498004

(90)

0.48510

(26)

0.904

16

3342.9618

(25)

0.3485711

(14)

0.49158

(55)

0.945

17

3534.2249

(82)

0.3473257

(102)

0.49620

(300)

0.986

18

3724.1307

(25)

0.3460621

(14)

0.49856

(57)

1.035

19

3912.6572

(94)

0.3447949

(22)

0.50377

(84)

1.076

20

4099.7962

(26)

0.3435143

(14)

0.50826

(55)

1.135

21

4285.525

(25)

0.3422443

(60)

0.52182

(220)

1.196

22

4469.8566

(26)

0.3409174

(14)

0.51892

(58)

1.263

23

4652.7492

(26)

0.3395983

(63)

0.52403

(24)

1.332

24

4834.1996

(30)

0.3382597

(14)

0.52707

(58)

1.401

25

5014.1774

(36)

0.3369344

(67)

0.53699

26

5192.6939

(36)

0.3355630

(15)

0.54336

(60)

1.572

27

5369.7115

(45)

0.3341878

(120)

0.55136

(670)

1.666

28

5545.2192

(38)

0.3327944

(14)

0.55687

(60)

1.765

1.501

a The

origin

of

calculated

the

from

The

Yko

The

number

v”

the

in

are

and

correspond

lines

with

Parameters program

determined

the

is

corresponds

correlation

noted

text)

standard

are

= 6, 7

=

127

I2

uncertainty

in

and

C(v”

Gi(v”)

higher

they

uncertainty (see

from

from

two

a much

precision

(31,321

the

to

to effects

without

fixed

relation

parenthesis

characters

to

was

isotopic

coefficients

characters due

levels

= 0)

+ $

and

are

in

in

the

given

last

order

digits The

than

in

1357.8841

I

pk YkO(v”

deviations.

needed

=

1 k=l

precision

Figure

J

the

to

k

cm-’

; p = 0.992210.

Appendix

II

typed

upright

digits

in

given

standard

in

italic

deviation,

recalculate

the

but

measured

3-b.

were

determined

held

fixed

in

from the

the

R K R curve

and

Hutson’s

fit.

b For of c

The

levels the

level

tive *

The

v”

9’

constants values

meters

= 6 and

results

of

from =

103

is

because

marked the

73 the

the

with

preceding

reported

8 groups

perturbed the

data

* are 9’

of

and

and

the

given

constants

did

not

allow

a deperturbation

from

in

e,-ro,-s

(given

calculated levels.

parameters fit

Figure

a logarithmic

(two

3-b have

SD)

and to

in be

are

the

average

Appendix

I-b).

considered

as

effec-

analysis. extrapolation

from

the

para-

CERNY, BACIS, AND VERGES

472

TABLE IIIb-Continued

V”

B x

G

10

DX

I----

10'

-HxlO

15

-Lx10

20

29

5719.1822

(140)

0.3314305

(40)

0.59018

(220)

30

5891.6315

(27)

0.3299576

(14)

0.57116

(58)

1.978

0.216

31

6062.4974

(28)

0.3285140

(14)

0.57986

(64)

2.080

0.243

32

6231.7773

(26)

0.3270503

(14)

0.58798

(58)

2.202

0.243

33

6399.4515

(29)

0.3255660

(14)

0.59677

(65)

2.333

0.278

34

6565.4968

(28)

0.3240607

(14)

0.60523

(58)

2.468

0.310

35

6729.8924

(29)

0.3225350

(14)

0.61552

(65)

2.608

0.349

36

6892.6141

(30)

0.3209852

(14)

0.62522

(58)

2.759

0.364

37

7053.6385

(29)

0.3194142

(14)

0.63697

(65)

2.932

0.397

B x

10

i: x

106

1.863

-HxlO

14

-Lx1019

38

7212.9401

(32)

).3178168

(14)

0.64792

(59)

0.3109

0.0448

39

737c.4954

(29)

I.3161951

(14)

0.66123

(65)

0.3305

0.0475

40

7526.2810

(50)

I.3145523

(22)

0.68127

(88)

0.3518

0.0537

41

7630.2618

(42)

I.3128668

(22)

0.68973

(97)

0.3743

0.0571

42

7832.4105

(49)

).3111607

(22)

0.70551

(88)

0.4008

0.0585

43

7982.7006

(40)

I.3094211

(21)

0.72005

(90)

0.4298

0.0680

44

8131.1023

(46)

3.3076491

(22)

0.73687

(88)

0.4595

0.0755

45

8277.5803

(39)

3.3058455

(21)

0.75504

(69)

0.4933

0.0780

46

8422.1042

(51)

3.3040067

(22)

0.77403

(90)

0.5315

0.0853

47

9564.6417

(40)

D.3021308

(21)

0.79435

(89)

0.5726

0.0949

48

8705.1742

(59)

3.3001748

(23)

0.80058

(91)

0.6174

0.105

49

8843.6167

(43)

3.2982500

(22)

0.83446

(91)

0.6660

0.117

50

8980.0659

(110)

3.2960417

(311

0.77953

(120)

0.7186

0.129

51

9114.2070

(40)

3.2942101

(13)

0.88431

(58)

0.7764

0.142

0.3

52

9246.2662

(170)

3.2921120

(40)

0.90703

(160)

0.8390

0.160

0.4

53

9376.1277

(136)

0.2899453

(36)

0.92368

(300)

0.9064

0.181

0.4

54

9503.7250

(71)

3.2877638

(23)

0.96093

(22)

0.9065

0.203

0.5

55

9629.0361

(571

0.2855142

(161

0.99029

(8)

1.0586

0.231

0.5

56

9752.0135

(59)

0.2832140

(181

1.02927

(17)

0.9053

(50)

0.260

0.7

57

9872.6177

(60)

D.2808490

(19)

1.06298

(16)

1.0177

(43)

0.289

0.8

58

9990.8031

(58)

0.2784221

(18)

1.09522

(16)

1.2728

(45)

0.326

0.8

59

10106.5277

(61)

0.2759362

(18)

1.13751

(16)

1.2738

(43)

0.370

1. 0

60

10219.749;

(58)

0.2733813

(18)

1.17763

(15)

.4282

(40)

0.417

1.3

61

10330.4250

(62)

0.2707565

(19)

1.21927

(16)

1 .6233

(43)

0.467

1.5

62

10438.5102

(58)

0.2680651

(16)

1.26471

(15)

.8458

(40)

0.525

1.8

63

10543.9739

(58)

0.2652772

(18)

1.29667

(14)

2 .4249

(40)

0.590

2.1

64

10646.7464

(59)

0.2624693

(16)

1.38157

(14)

1 .7238

(40)

0.662

2.6

65

10746.8214

(59)

0.2595519

(16)

1.43805

(14)

.9034

(39)

0.742

3.0

66

10844.1488

(59)

0.2565537

(16)

1.49600

(14)

2.1689

(40)

0.836

3.5

67

10938.6936

(59)

0.2534755

(16)

1.55936

(14)

2.3983

(40)

0.946

4.1

68

11030.4229

(60)

0.2503147

(16)

1.62636

(15)

2.6596

(40)

1.070

5.0

69

11119.3056

(59)

0.247072

7 (16)

1.70017

(14)

2.8790

(39)

1.211

6.0

70

11205.3171

(59)

0.2437431

(16)

1.77863

(14)

3.0738

(40)

1.376

7.0

71

11288.4345

(591

0.2403173

116)

1.84665

(141

3.7467

(40)

1.572

a.4

(61)

B -

473

X SPECTRUM OF 12’1’291AND I2912 TABLE IIIb-Continued

V-I

Dx

B x lo

G

10'

-

1013'

Ii x

-Lx1o17

-Mx10z3

72

11368.6364

(58)

0.2368202

(II5)

0.194028

(14)

0.35054

(38)

0.0181

1.100

79

11445.9151

(53)

0.2332151

(2(If

0.201365

(13)

0.48587

(34)

0.0208

1.122

74

11520.247a

(59)

0.2295404

(115)

0.211042

(11)

0.55113

(64)

0.0241

I.150

75

11591.6416

(59)

0.2251746

(lt5)

0.222032

(14:

0.55396

(39)

0.0281

I.184

76

11660.0938

(39)

0.2219161

(lf5)

0.232192

(14:

0.61111

(38)

0.0329

I.227

77

11125.6019

(78)

0.2179808

(21b)

0.244449

(22)

0.10131

(58)

0.0388

I.283

78

117aa.19i4

(80)

0.2139435

(21i)

0.256652

(22)

0.77702

(58)

0.0460

1.355

79

lla47.a65a

(78)

0.2098272

(21i)

0.210301

(22)

0.85486

(60)

0.0547

I.450

a0

11904.6511

(78)

0.2056140

(2:3)

0.284326

(20)

0.96129

(56)

0.0656

I.575

81

11958.5698

(80)

0.2013035

(2li)

0.298595

(22)

1.11379

(58)

0.0790

8.741

a2

12009.6520

(18)

0.1969047

(21i)

0.314722

(22)

1.27377

(58)

0.0960

I.969

a3

12051.9395

(78)

0.1923534

(21i)

0.326161

(22)

1.63951

(59)

0.1175

.2ao

a4

12103.4340

(80)

0.1878147

(21b)

0.350653

(22)

1.73612

(60)

0.1445

.610

a5

12146.2092

(80)

0.1931087

(21i)

0.310138

(22)

2.09703

(62)

0.1784

.2ao

86

12186.2931

(78)

0.1782929

(2~i)

0.391370

(22)

2.56837

(58)

0.2387

.1611

a7

12223.7263

(78)

0.1733716

(21b)

0.418873

(22)

2.81252

(60)

0.3661

.470

aa

12258.5669

(85)

0.1682221

(2Li)

0.433035

4.126ll

(77)

0.3662

-310

a9

12290.8333

(64)

0.162886

(lO(1)

0.46030

(27) (440)

3.436

0.411 0.968

90

12320.5910

(64)

0.156846

(3f1)

0.31378

(28)

4.486

91

12347.8420

(110)

0.152330

(26(1)

0.61944

(250)

5.299

92

12372.7107

(84)

0.146180

(ll[

0.36052

(130)

93

12395.1666

(76)

0.141874

94

12415.4150

(140)

0.13528

(21

)

0.8630

95

12433.6540

(690)

0.12919

(64

)

0.76091

)I

(a:5)

38.1 6.846

0.66902 (780)

0.621 (20.2)

1.31 0.990

7.94

1.48

8.64

2.11

96

12449.9120

(820)

0.12321

(11

)

0.80665

9.88

2.35

98

12471.3320

(140)

0.11225

(16

)

0.90707

14.26

5.39

99

12488.8240

(280)

0.10691

(93

)

1.0616

(660)

17.98

100

12499.0010

(210)

0.10126

(19

)

1.1430

(530)

23.64

101

12501.9420

(140)

0.09564

(15

)

1.1744

32.52

18.5

102

i2515.7280

(600)

0.08997

(190

)

1.3947(1.300)

$3.28

26.2

7.78 12.2

103(

12522.7180

(120)

0.01611

(13

)

1.4055

53.45

32.0

104

12528.0670

(620)

0.01909

(200

)

2.1544C1.400)

62.76

46.1

106

12536.7750

1540)

0.06610

(170

)

2.4576C1.160)

141.2*

101."

107

12539.9330

(590)

0.05919

(190

) ,2.6378(1.300)

199.0"

155."

108

12542.3580

(150)

0.05294

(21

) 13.4600'

269.0*

219.*

Y,O = 214.5208 cm-’ (0 G 0” G 89) (Table IV of paper I). Then, only very precise data for the first vibrational levels of isotopes of Iz could allow us to calculate the corrections to relation (1) in the X0: state. We think that they could be obtained from LIF FTS, but the related spectra were not recorded because they were of no practical importance to the long-range analysis (paper III). The precision obtained from the approximation (1) was checked directly by comparison with our data. An example is given for some X0: vibrational levels (v” -C20)

474

CERNY, BACIS, AND VERGES TABLE IVa Parameter9 of the ‘27I’29IBO: State

(cm-‘)

G

v’

B x

lO’(cm-‘)

DxlO’(cm-‘)

-H~lO’~krn-‘)

-1

-LxlO”(cm

0.086

0.205 I

I

/

I

51

19821.199

(17)

19821.1960

61

0.15716

I

(10)

0.379

0.15713

20033.9068

(22)

20033.9019

62

I

0.11605

(56)

20047.7266

0.22109

0.2342

0.326

0.649

0.78012

1.7886

5.3

0.90452

2.2797

7.3

(10)

0.11610

20047.7339

(17)

0.373

0.11168

(13)

0.63

0.11174

(10)

0.69

a For

each

global

v' vibrational

fits

uncertainty

The

values

level

(given

in

in

last

digits

second

row

in

the

the

Figure

the 3-a

first and

and

are

in

row

is the

Appendix

corresponds

calculated

average

I-a). to

from

value

The

two

standard

isotopic

determined

number

in

from

the

parenthesis

is

five the

deviations.

relations

(see

G(v’

= - $)

Appendix

III).

In

15 particular

:

Gi(v’)

= 15 769.0588

15 769.0588 When non

there

were

determined

= Te + p2

insufficient constants

+

CY,B, -

excited were

held

1 k=I

pk

Yoi)

levels fixed

yko(v’

is to

at

the

+

the

i)“,

distance

detemine value

the given

parameters in

the

second

^ G(v” of

= - ;).

a given

v’,

the

row.

in Table VII where it is seen that the constants calculated from ‘27I2 of Luc and Gerstenkorn’s polynomial expansion are in excellent agreement with our direct determination. This allows us to suppose that fixing the common origin for the tree isotopes (Sect. IV) has introduced an error which is lower than 2 SD. For the low t)” levels of the ‘27I’291and 12912isotopes, this corresponds to an error less than 0.004 cm-‘. We have also checked our directly determined G(v”) values with those calculated from isotopic relations from the results for ‘27I2(Table IV of paper I). Examples are given in Fig. 6 where one can see that for the range 0 < 0” < 85 the differences between isotopically calculated and experimentally determined constants do not differ by more than 2 SD. The agreement is better for B constants than for G constants. The best way of comparing results for different isotopes is to introduce the mass-

B -

475

X SPECTRUM OF ‘27I’29IAND ‘*‘I2 TABLE IVb Parameters’ of the ‘29I2Xl: State

20044.4511

63

20057.3466

(96)

20113.0183

69

0.0310

0.131580

0.152

0.155633

0.189

0.184486

0.237

0.2610

0.38

2.08

6.

2.66

9.

(22)

0.80

0.107595

0.7150

0.991

0.0807707

1.095

2.760

0.076196

1.185

3.347

(52)

20113.0183 70

(75)

0.107608

20057.3439

0.038803

20119.1712

13.5

90.

19.2

140.

(54)

20119.1716

-

I

a For

each

eight is

The

v’

vibrational

global

the

fits

uncertainty

values

in

level

(given in

the

in the

second

the

first

Figure

3-b

last

row

row

digits

are

and and

is in

the

average

Appendix

corresponds

calculated

from

to

: Ci(v’) =

particular

15 769.0589

+

1

pk YkO(V’

The

two

isotopic

15 In

value

1-b).

determined number

standard

relations

I

+ 7’

k

from

in

the

parenthesis

deviations.

(see

Appendix

III).

*

k=l with Wha the

the

same

there non

origin

were

determined

as

in

insufficient constants

Table

IV-a

excited were

(C(v” levels

held

fixed

= - +u. to at

determine the

value

the

parameters

given

in

the

of

a given

second

v’,

row.

reduced vibrational quantum number v = (v’ + $)/pLf as shown by W. G. Stwalley (38). Following King (5), we use relative values as 17= (u” + 4)~ with p = 1 (“‘I*), p = 0.9961126 (‘271’291),and p = 0.9922 10 (‘2912).Then we can directly compare the

476

CERNY, BACKS, AND VERGES TABLE Va Expansion’ Parameter Coefficients of the 1*71’2gI X0, State (in cm-‘)

k C" 1 2 3 4 5 6 7 8 9 10 1, 12 13

%co

(0 4 Y”E

871

k

-0.26, C-02) O.Z13697,655 c+031 -0.608925708 (too) 0.,40,,,7 C-04) -0.174184231, C-03) 0.13**416,548 C-04, -0.69772557779 C-06) 0.246944545764c-071 -0.601209414147l-09) 0.1006204863338(-10) -0.1,36056*6001*~-12) 0.824632555609C-15) -0.34611578069,C-17) 0.63603802597 t-20)

0 1 * 3 4 5 6 I 8 9 10 1, 12 13

?41

(0 : "" I 87)

0.3707827 C-01) -0.1114639 C-03) -0.1066429 C-05) 0.20665506 C-06) -0.297629828 C-07) 0.24913,0*56 ~-OB~ -0.13311582486c-091 0.4,30,529680C-11) -0.11‘*405819 C-12) 0.18.9171795856(-14) -0.*080403,,441~-161 0.,4,6*405,04*~-181 -".60,*54,68,,C-2,) 0.11004114964C-23)

k 0 1 2 3 4 5 6 7 8 9 10 1, 12

dk

(0 I Y" 6 87)

-0.83500954 (+Ot) 0.*18,7*3 C-02) 0.7011603 C-04) -0.73769209 C-05) 0.776913826 C-06) -0.4168501498C-07) 0.12281815136(-08) -0.16*375*55*3~-10~ -0.7522464626c-131 0.590,893639*(-14) -0.86334319766(-16) 0.56,9480,64*(-18) -0.,4596008,04(-20)

k 0 1 * 3 4 5 6 7 8 9 10 I, 12 k 0 1

k

C" I 2 3 4 5 6 7 8 9 10 I, 12

YkO

(83 < "" 6 109)

-0.1*,,034* c*o31 0.829939512 (+o*) -0.1562844228 (to*) 0.42816336826 (*ol) -0.82208265734 C+OO, 0.106*378031680(*00) -0.947500053659C-02) 0.589066538,9,6(-03) -0.2542535535377~-04) 0.746,**389,996~-06) -0.,1*08969661*6~-071 0.,58*5,36453,,(-09) -0.78290087540 C-12)

lo*

(+f(““))

-,E,\(V”

+

k

Yk,(83 t Y" .' 109)

k

0 1 * 3 4 5 6 7 8 9

0.1612998 C-01) 0.38534941 C-02) -0.161233864 C-02) 0.3252709130C-03) -0.3928612830C-04) 0.29540232251(-05) -0.13934519845(-06) 0.40068878493(-08) -0.6415384380C-10) 0.4381135405C-12)

0 I * 3 4 5 6 7 :

4)” far 65 $ v"

4, (83 s 1" 6 109)

-0.632285 (+ol) -0.12035543 (*oI) 0.5101368, (+00) -0.,163446839~+oo~ 0.,6200886,6(-0,) -0.14466174374~-0*~ 0.8456569225C-04) -0.3**34*,*063~-051 0.7,*7,51386C-0,) -0.10589693347(-08) 10 0.633035901 C-11)

* 3 4 5 6

0 : 3 4 5 6

hk

(0s "" s 109)

-0.153189 (a*) 0.347156 t-011 -0.6943128 (-02) 0.117099216 (-02) -0.1046367690(-03) 0.5642081429C-05) -0.19549729148(-06) 0.44959555431(-08) -0.69264984623(-10) 0.705,,,65860(-12) -0.4556‘464,*,(-14) 0.168656,,3,4(-161 -0.2723668299C-19) lk

(0 s Y" < 109)

-0.2158269 (*O*) 0.165944 t-0,) 0.,*3068*0(-02) -0.46156305(-04) 0.9**8*009(-06) -0.86655895(-081 0.3**17593~-10~

-0.532468581 (+05) 0.4275367158(~24) -0.14*81**6134(+03) 0.*5389480432(*01) -0.*53,6*84*61~-0,) 0.13455313115(-03) -0.2970817469C-06)

< 87 (from third iterarioo).

RKR curves (Fig. 7) and B,/p’ values (Fig. 8) where it is Seen that no systematic difference appears. Also it is possible to show the high precision obtained in the calculation of the differences in G values (see Table VIII), which is important for the comparison of extrapolations at long range.

B -

X SPECTRUM

477

OF ‘27I’29IAND ‘29I2

TABLE Vb Expansion’ Parameter Coefficients of the ‘29I2X0: State (in cm-‘)

k % 0 1 2 3 4 5 6

(5,

Y”

s 881

0.76511722 c+o31 -“.,“92”“,,4 ct021 “.263491358”~+“1~ -“.51999,346,(-“11 “.5,52624”91~-“3) -“.,,81953984~-“51 “.82558,,11 C-08)

Some constants were also directly experimentally determined for the BO: state. They are in agreement with the isotopic calculations as is seen in Tables IVa and b. In this comparison we have to remember that fixing some rotational constants in a v

478

CERNY, BACIS, AND VERGES TABLE Via RKR Potential Turning Points’ for the 1271’291 XO,CState

level gives unrealistically small standard deviations in the floated parameters. Indeed the uncertainty in the fixed constants is not taken into account (see also Sect. IV (iv) and Table II in paper I). The direct determination of G(v’) has given T, = 15 769.078 cm-’ (see Appendix IV), which is in perfect agreement with the value obtained from ‘27I2(see Sect. V). V. DETERMINATION

OF LINES IN THE BO:-X0,+

TRANSITION

We have checked the precision of our work in recalculating the position of our recorded lines from the polynomial expansion of Table Va or b for the X0,’ state and

B -

479

X SPECTRUM OF ‘271’291 AND ‘29I2 TABLE VIb

RKR Potential Turning Points’ for the I2912 X0: State d’

G(““)

CC”“)

R -I

(cm

max(l)

)

(Cm-3

%i”

$.bl"'L

.5056?

I::%9 :*::m

2:roaac

2.49369

:A:%: ::::::4

,;gp;:g

10219:lilS 103~0.4158 lC435.5~14 10543.9569 13646.7415 19746.8162 1 .44.1434 1 8 938.6383 11030.4173 11119.~034 11205.3115 1123 .4260 1136 i .63X 114LS.1044

12415.4667 12433.6450 CI9.OOPl L64.&J32 1 077.3246 1 t 488.8131

1 1

from isotopic relations applied to preliminary parameters of Gerstenkom and Luc (Appendix III). For the range of 2)”-C90 where no perturbation was observed and for J -c 100, the wavenumbers of lines are recalculated with an error lower than 0.0 10 cm-’ and even 0.005 cm-’ if J < 35. In the same u” range but with 100 < J < 150 ( 12912), the precision decreases with increasing Jand is generally lower than 0.100 cm-’ for J z 150. For 2)”> 90, the lines observed have J < 35 and the precision is better than 0.005 cm-’ for nonperturbed vibrational levels (for more details about the perturbed 0” levels, see the end of Sect. III). The precision in the recalculations of lines is not as good as the rms deviation of the fits and becomes progressively worse as J increases. The reason is that we used separate global fits (because of our computer limitation) which, when recombining

480

CERNY, BACK, AND VERGES

20

40

60

00

100

\I”

FIG. 4. (a) Comparison of ‘27I’291 XO,Cparameters obtained using Hutson’s program (31, 32) from the RKR curve of Table Via, with the experimental determination (Table IIIa): AG = Gn,,. - GErp, - DExp cm-‘. The symmetrical full lines for All and AD correspond AB = &uUo. - BEXP, AD = Dmm to k2 SD of the experimental determination. (b) Comparison of IT)&X0, parameters obtained using Hutson’s program (31, 32) from the RKR curve of Table VIb, with the experimental determination (Table IIIb): AG AD = Du,,. - l& cm -I. The symmetrical full lines for = GM.,, - G~xpr AB = BuvUan- Ba,,, AB and AD correspond to +2 SD of the experimental determination.

the results in order to determine the expansion parameters, do not allow the correlations between the constants of BO: and X0,’ to be taken fully into account. The interferometric accuracy on the measurements of the main fluorescence lines gives the maximum of these lines to within 0.002-0.003 cm-‘. If we want to recalculate the measured lines with the same accuracy, it is necessary to use the results of the separate global fits. That is why these results have been reported in Appendix I and in Tables III. Now the general relations used in the recalculation of lines (in paper I and in this paper) are in principle valid in the region of the absorption spectrum of iodine (visible). Our determinations have been extrapolated to this region using the preliminary results of Gerstenkom and Luc. This gives another way of checking our general relations: we can compare the wavenumbers they give to the absolute values of some lines determined

B -

481

X SPECTRUM OF ‘271’291 AND ‘29I2

b i AG (10”) 129

-25_

I

I

1

20

60

40

1

I

60

100

Y"

w

FIG. 4-Continued.

127

An (~6’~)

AAH (16’~)

I

129

I

AA”(lO-15I 129

A/AH(r6141

1 AA

10 _ 0

c

I 20

l

1

I

1

I

40

60

I30

100

"“

b

FIG. 5. Comparison of H constants obtained with Hutson’s program in the second and third iteration: AH = Hz - H, cm-‘. H2 = H obtained from the second iteration fit (Table III). H3 = H obtained from the third iteration fit that is to say from the RKR curve (Table VI) of the third iteration results. The symmetrical full lines correspond to +2 SD of the experimental determination.

482

CERNY, BACIS, AND VERGES TABLE VII Typical Comparison of Parameter Experimental Values (First RoWP) and Calculated Values (Second Rowb) (in cm-‘) 127I129I

VT’

B x

G

Of g

x

10

Dx

IO8

-x x

1015

5

1156.8213 1156.8153

(404)

0.364478 0.364497

(174)

0.430 0.461

(178)

0.6126 0.6119

IO

2175.6743 2175.6741

(32)

0.358570 0.358597

(78)

0.389 0.476

(98)

0.7494 0.7498

I5

3162.1304 3162.1289

(26)

0.352483 0.352484

166)

0.534 0.495

(81)

0.9437 0.9378

19

3927.0603 3927.0577

(29)

0.347397 0.347413

(66)

0.520 0.512

(82)

1.172 1.060

129

x o+ g

I2 B x

G

v”

IO

Dx

-H

IO8

x

IO’5

5

1152.3564 1152.3560

(58)

0.361688 0.361671

(18)

0.4581 0.4534

(69)

0.5912 0.5971

IO

2167.4257 2167.4220

(30)

0.355853 0.355842

(16)

0.4713 0.4685

(61)

0.7511 0.7310

I5

3150.3522 3150.3476

(72)

0.349800 0.349802

(90)

0.4851 0.4868

(26)

0.9038 0.9135

I9

3912.6572 3912.6550

(94)

0.344795 0.344794

(22)

0.5038 0.5041

(84)

I .076 1.035

a In

parenthesis

The

H values

program, b

The

were

second

calculated

expansion

: two standard fixed

in

iteration

values

parameters

deviations.

the

fit

to

the

value

obtained

from

Hutson’s

(31.32).

come of

the

from I27

isotopic I2

X0;

relations state

(see

applied

to

the

polynomial

AppendixII).

from hypertine structure measurements. Unfortunately while numerous measurements have been made for “‘12, there are very few for lz912and we have found only an (22). All these absolute isotope meaincomplete measurement of a line for 1271’291 surements have been made for lines coinciding with the 5 14.5~nm Ar+ or 611.8 and 632.8-nm He-Ne laser lines. We have recalculated from our parameters the lines expected to lie in these regions in Fig. 1 (5 14.5 nm) and Table IX. We have compared these recalculations to the absolute values of the expected position of the center of gravity G of the lines calculated from hyperfine measurements. We have also compared some ‘27I2absolute lines from paper I results. In particular we

B -

X SPECTRUM

483

OF ‘271’291 AND ‘2912

5_ .---.____/ 0

’

dB (16’) -\ ‘.

I

0

I

20

I

40

I

60

I

_,

6OV” 0

I

20

t

1

40

60

,

+I

80~”

t

dD(lO-“) \

; /, 0

I

I

20

40

I

60

1

.

60 V ”

FIG. 6. Comparison of the rotational constants of the X0: states calculated (Cal) from isotopic relations and determined from experiment (exp) (polynomial expansion, Tables Va and b) (in cm-‘). l

With isotopic calculations applied to the rotational constants of “‘I2 molecule (polynomial expansion, Table IV in paper I): = G& - G,,, dG 1~~1~~,

(from Table Va)

dB1~~,l~ = L&, - Bcxp (from Table Va), and similar relationships for dG1z911 and

dB1s12 (experi-

mental values from Table Vb). l

With isotopic calculations applied to the rotational constants of ‘271’291 using the mass reduced ratio p,29,,2,_,29= 0.996082, compared t0 eXp&lMtal VaheS ‘2912: dG = G& - G,,, (from Table Vb) dB = &,,, - Be, (from Table Vb) dD = D& - Dcxp(from Table Vb).

The symmetrical full lines correspond to k2 SD of the experimental determination of the related isotope.

have regrouped the various measurements at the 612-nm wavelength of the He-Ne laser because the relative frequency differences between “‘12 and 129I2have been directly measured at this wavelength. They are shown in Fig. 9. The center of gravity G of the

CERNY, BACIS, AND VERGES

1254 5

G(v

1t

cm-’

d 0’

1234

.O

12535 _

A 0

0’

105

. A

12530 _

r’ .o

0

d

.

A

.

.

12525 -

127I2 127

129

A1

I

,o 0 0

129

.

0

12

12520 _

:

> ,

. 102

I __ 3.3

1214

1 ..r ,. 3

12515q

^_

b.3

1 ^_ 0.3

I n.? t9.a

r(A)

FIG. 7. RKR outer limb curve for higher vibration levels of the ground state of the three isotopes of iodine.

1

I

5

P2 .Ol! 5_

+b.

1

1

O*. OQo ‘A

O. -0

,011 O-

Q

O*.

OY 0

A 0

O-n

-0

OY

127 .

12 129

.oo5_

A 127 0

I

OI O*0

12 129

I

l0 0

L 90

100

95

105

110

P (v41/2) FIG. 8. Comparison of B, values of the ground state of the three isotopes of iodine in mass-reduced coordinates (‘*‘I2:p = 1, ‘27112~:p = 0.9961126, ‘*qz:p = 0.9922 10).

B -

X SPECTRUM

485

OF ‘271’291AND ‘29I2

TABLE VIII Comparison. of the Variations in G at Different Vibrational u” Levels l27I129I

v”

IO

I

(-;j;ii-)p,* dG127

212.6950

+,212.6957

20

40

60

80

85

201.3555

187.7907

155.8112

112.2221

54.8688

40.8366

201.3556

187.7912

155.8116

112.2221

54.8688

40.8372

40

60

80

85

129 I2 v”

I

dG127 ( dv” )pv,,

+(Y&,,, dG129

IO

20

212.7021

201.4090

187.9047

156.1008

112.8340

55.7822

41.7467

212.7025

201.4090

187.9046

156.1013

112.8336

55.7825

41.7461

a For

every

G(v”)

isotope,

1

=

G(v”)

(v”

yko

+

and

the

dv”

from

Table

Table those

VIII

the

taken

V-b

for

compares

deduced

vibrational of

data

from quantum

vibrational

from

Table

dG(v”) dv”

derivative

;)“, ac(v”) = 1

kbl with

its

kYkO

are

(v”

written

:

1 k-l

+ y’

k,,l

IV paper

127

I for

12,

from

Table

V-a

for

127112yI

and

129 Iz. dG(v”) dv” 127

12.

number quantum

for It of

different is

easy 127

number

I2 of

integer to

must I29

see be 12,

v”

that(T the with

values

dG127

same

)

for

of the

127I129

value dG -+f

as -!--( 0129 similar relationships

I

129

or P v” or for

of

the

I2

to

the value

v”

127Il29I.

hyperhne structure was calculated assuming the same intensity for every calculated hyperfme line. We have verified, where possible, that this approximation does not give a significant error in the range of J values involved. When hyperhne lines were missing for ‘*‘I*, we have used a total width W(first to last hyperIme component) of 9 10 MHz with G at 0.44 W of the last violet side hyperfine component (G4 of Fig. 9 was estimated in this way). We have determined and checked this approximation from the various hyperhne measurements cited in the references. This is very close to the G position at 4 W/9 used in Ref. (42). The same type of approximation was used for ‘29I2with W = 600 MHz and G at 0.41 W of the last high-frequency line [average of the three measured lines at 612 and 633 nm, used for R67(52-1) and P69( 12-6) (Table X)]. The

CERNY, BACIS, AND VERGES

486

TABLE IX ‘271’291 and lz912Absorption Lines’ in the Range of He-Ne Laser Lines 127Il29

in

the

in

632.81646 nm regionb (15798.027 cm-‘)

P 33(

6-

3)

R 44(20-10)

15798.021

(2.2)

15798.073

(0.003)

Pl48(

7-

the

632.81646 nm regionb_, (15798.002 cm

the

lines

6 Il.8027

16340.675

0)

129

in

I absorption

(0.04)

I2 absorption

in

ntn regionb (16340.616 cm-‘)

lines

the

61 I .8027

)

nm regionb (16340.616 cm-‘)

R 60(

8-

4)

15797.990

(4. I)

P110(10-

2)

16340.658

(5.5)

R107(

0)

16340.594

P 54(

8-

4)

15798.006

(4.2)

Rll3(14-

4)

16340.635

(0.08)

R 45(15-

5)

16340.593

(0.6)

P 69(12-

6)

15798.025

(0.2)

P l4(

I)

16340.610

(7.3)

R 20(

I)

16340.587

(10.0)

P 33(

3)

15798.057

(2.2)

PlO3(16-

5)

16340.596

(0.4)

Pl48(13-

3)

16340.564

(1.0)

6-

7-

6-

7-

(0.07)

a The wavenumbers are

given

in

most

intense

lines

whose

line

b

-I cm

0.060

in

Neon

are

for

nm line

S.J.

Bennett

the

R47 (9-2)

of

(Fig.1

The 632.8

nm line

reference

(22))

of

;

it

of

are

intensity -3 IO

are

our

was

Their

new parameters.

relative

to

the

arbitrarly

R20(7-I)

set

equal

predicted

line, to

intensities

(expected

10.0.

to

be the

We report

only

the

.

than

of

from

given

-I cm

0.045-0.050 the

and we have

reported

Iodine

lines

in

the

range

Ne lines.

Sventitskii Neutral

and Ionized

Atoms

1968 22 Ne. 22 in

‘27 I2

calculated

whose

lines

and N.S. Lines

are

greater

wavenumber

New York

values

are

the

Striganov

These

spectrum)

the

Spectral

The 611.8

the

around

From A.R.

IFI/Plenum,

lines

The intensities

FWM of

Tables

of

absorption

intensities

The Doppler f

of

parenthesis.

line

22 is

Ne is

centered

reference which

Ne is

at

(39)). is

the It

I6 340.6548

-I .

cm

of

the

.

range

of

this

(within

3 MHz) with

Sfriganov’s

value

-I at - 0.003 cm from -1 cm Striganov’s value

centered

I5 798.032

middle

coincides

the is

A line still

is

of too

line Cl too

129 high

explored

by P.

(Fig.9)

centre

high

by 0.0014

I2 P33(6-3) by 0.0012

Cerez

of

nm

(from

and

gravity

of

!

Fig.5

of

nm.

iodine lines recorded with the help of the 3He- 22Ne 633 laser line [Fig. 5 in (22)] were not identified. From our determinations (Table IX) the most intense components (A, B, C, D) are from ‘29I2P33(6-3). The lowest intensity lines in the middle of Fig. 5 are from ‘29I2P69( 12-6) and some lines of relatively high intensity on the lower frequency side correspond to the end of the ‘27I’29IP33(6-3) line. The first components of this line were observed in Ref. (21) from the 3He-20Ne line; so the ‘27I’29Iline was W N 750 MHz average of 12’12and 129I2widths. We have not used all of the numerous absolute measurements from ‘*‘12, but we have compared our values to some of them (Table X) and also with the absolute

B + X SPECTRUM

OF ‘271’291 AND ‘2912

487

FIG. 9. Center of gravity G of iodine lines calculated from hyperfme measurements. The origin (0) of relative frequencies in MHz is the o component of the R47(9-2) ‘*‘I2line. Gl = Center of gravity of R47(9-2) [12’12,calculated from Ref. (39)], Gl is 16 340.6548 cm-’ [R47(9-2) i = 16 340.6581 cm-‘; see references in (40)]. G2 = Center of gravity of Pl 10( 10-2) [‘2912rcalculated from Refs. (18, 19)], G2 is 16 340.6486 cm-’ obtained from frequency separation with the component o of the R47(9-2) transition of 12’12(19). G3 = Center of gravity of RI 13(14-4) [‘2912,calculated from reference (19)], G3 is 16 340.6352 cm-’ obtained from frequency separation with the component o of the R47(9-2) transition of 12’12(19). G4 = Estimated center of gravity of P48( 1l-3) [12’12(800 MHz below the i component of R47(9-2) (18))], G4 is 16 340.631 cm-‘. l Full line: measured range with the lowest and highest observed relative frequency. l Dashed line: calculated nonobserved range. l The hatched lines show the limits of the scanning on gain curve of the laser at 6 12 nm from P. Ctrez and S. J. Bennett (39). of Ref. (40). In the latter case our determinations are shifted by +0.0060 to +0.0072 cm-’ relative to the absolute frequencies in the range 16 340-l 7 360 cm-‘. On the average, these results and those of Table X show that the polynomial expansion and T,used in paper I give absolute values of ‘*‘I2 lines which are on average too high by +0.008 cm-’ in the visible absorption region of the spectrum. An examination of the other results regrouped in Table X shows that the same shift is expected in that range for ‘29I2and 1271’291. Thus it appears that the extrapolation of our data with the preliminary results of Luc and Gerstenkom has given a slight shift in our determination of T,which is too high by +0.008 cm-‘. Nevertheless, for the range of the fluorescence lines we have measured in the present paper, the use of this T,value does not reproduce this shift; the accuracy of our parameters relative to these lines (for instance in Table XI) has been given at the start of this section. Finally, as in Section V of paper I, we have looked for coincidences between possible I2 laser frequencies and the hyperfine lines of the I 1,2-1~,2transition at 1.3 15 pm. The results are shown in Table XI. We see that there are a few coincidences for every atomic line. For instance with the most intense F'= 3 --+ F" = 4 hyperfine line it is possible to use: (i) the 12912P84(33-72) lasing line pumped in the 5300 A (2)” = 0 - v’ = 30) range; (ii) the 127I’29IP72(21-62) pumped in 5560 A (u” = 0 - o’ = 21) or 5630 A (v” = 1 - 2)’ = 21) range. values

488

CERNY, BACIS, AND VERGES TABLE X Comparison of Our Calculated Wavenumbers (Last Column) with the Calculated Center of Gravity of the Line Obtained from Hypertine Measurements

127 12

R 47 (9-Z)

(6 340.65d

16 340.6655(+,0.7)

12912

P 33 (6-3)

I5 798.045 e

I5 lSS.057(+,2. )

129 12

P,,OC10-2)

16 340.6486a

16 340.658 (t9. 1

,271 12g1 2 2

P 33 (6-3)

15 798.013 f

15 798.021 c+!3.)

,2g12 127 12

R113(,4-4)

16 340.635Za

16 340.635

,2912

P 69(,2-6)

15 798.022 g

15 798.025 (+3. )

P 48(,1-3)

16 340.6314a

16 340.6420('10.6)

12712

P 13(43-O)

19 429.8086h

19 429.8,72(+8.6)

127I2

P 33 (6-3)

15 797.97626

I5 797.9841(+ 7.9)

12712

R 15(43-O)

19 429.818Zh

19 429.8264(+8.2)

R127(11-5)

I5 797.9997=

15 798.0084(r8.7)

12912

R 67(52-l)

19 429.7668'

19 429.776 (r9.2)

P 54 (8-4)

15 797.9980d

15 798.006 (t8.0)

12712

P 62(,7-l)

,I 352.2476j

15 352.2539Ct6.3)

127 I2 129 12

(0)

a See Fig.6

d

Calculated

from Table

Estimated from

I”

Fig.5of

of reference

reference

(21,

and k or

n component of

reference

(22).

(22).

VI. CONCLUSION

Our extensive analysis of the vibrational levels of the ground state of ‘271’291and lz912isotopes has allowed us to determine vibrational levels close to the dissociation limit. Their long-range behavior will be compared in paper III. We have checked the usual isotopic Dunham relationships. They allow us to calculate precisely the rotational constants of the three isotopes of iodine (i2’12, L2711291, ‘2912).Using these Dunham parameters for the BO: state and the determined polynomial expansion for the X0,’ state, we obtain the BO:-X0: lines with an accuracy better than 0.010 cm-’ at least for the range 0 d 2)’G 70 for BO: .

5s2

5p5

3

4

1

3

3

3

2

2

F”

5s2 5p

2

cf

++

3

F’

T

2 P,

Iodine

52

?

P3

7602.6245

7602.6903

7602.7145

7603.1429

7603.2837

7603.3495

Ref.

Wavenumbers -1 (cm )

from

transition

(50)

B 0;

R P P R P

R R R P P P R R P P R P P R P

7603.161 7603.159 7603.151 7603.143 7603.124

7602.736 7602.732 7602.716 7602.707 7602.690 7602.690 7602.679 7602.678 7602.677 7602.660 7602,630 7602.619 7602.603 7602.594 7602.594

58(33-72) 66(48-84) 81 i52-87j 58(43-80) 92(42-79) 89(51-86) 48(53-88) 98(21-62) 32(53-88) 62(27-67) 86(27-67) 95(37-75) 49(48-84) 7808-76) 66(52-87)

64(48-84) 64(52-87) 72(21-62) 97(47-83) 80(47-83)

27(53-88) 63(48-84) 96(21-62) 75(38-76) 75(43-80) 85(32-71) 79(52-87) 32(33-72) 54(38-76) 55(33-72)

Identification

P R R R R P R P P R

3.10e3)

I

7603.380 7603.370 7603.360 7603.344 7603.327 7603.323 7603.278 7603.270 7603.263 7603.255

(FCF>

wavenumbers

Calculated

127Il29 +

“lasing

10 7 125 125 41 9 43 9

103 9 9 15 16 11

9 9 10 11 11

9 10 43 15 181 9 103 43 103

for

FCFx

x 0;

lines”

103

Calculated Coincidences of BO: - X0; Lines with Hyperfine 11,2and Related X0,+ - BO: Pumping Band9

TABLE XI

42 42 43 43 47 47 48 48

32 32 33 33 37 37 38 38

21 21 27 27

-c BO:

Band

I 52 0 53 1 53

0 51 1 51 0 52

0 1 0 1 0 1 0 1

0 1 0 1 0 1 0 1

0 1 0 1

X0;

Pumping

-1

382 170 427 214 585 373 620 408

826 614 891 678 130 918 185 972

19 715 19 502 19 743 19 530 19 769 19 556

19 19 19 19 19 19 19 19

18 18 18 18 19 18 19 18

)

band

17 975 17 763 18 470 18 257

(cm

”

I3,2Transitions

for

FCFx

5071 5126 5063 5119 5057 5112

5158 5215 5146 5203 5104 5160 5095 5151

9.3 5.4 8.6 5.4 7.7 5.3

19.1 3.0 18.0 3.5 13.2 5.0 12.2 5.2

31.5 2.3 30.8 1.3 25.7 0.4 24.9 0.7

bands

lo3

5310 5371 5292 5352 5226 5284 5211 5269

pumping

BO:

19.2 36.6 30.8 16.2

+

5562 5628 5413 5476

(L

X (air)

X 0;

5s’

5p5

a

3

2

molecule

is

obtained

2

2

pressure

7603.7145

1

2

At a given

7603.1429

4

3

Ref.

by

the

(50)

mixing

density

7602.6245

7603.6903

7603.2837

7603.3495

from

Wavenumbers -1 (cm )

3

T

2P3

3

5p5

2

5s2

3

u

CL F”

T

transition

P’

‘P,

Iodine

of I2

and

“‘12.

1s

expected

P 92(38-76) P 33(34-73) P 61(53-W) R 56(34-73) R 86(28-68) R 60(49-85) R 74(39-77) P 53(39-77) Rl00(22-63) P 77(48-04)

7603.733 7603.728 7603.699 7603.694 7603.674 7603.668 7603.655 7603.634 7603.609 7603.608

I

P P P R P P

7603.158 7603.147 7603.146 7603.125 7603.125 7603.121

127I129

P 60(2a-68) R 98(22-63) P 100(47-83) P 75(4B-84)

7603.314 7603.299 7603.269 7603.265

to

be

40(49-85) B7(43-80) 84(33-72) 72(39-77) 91(3B-76) 74(22-63)

P R P P R

29(34-73) 71(39-77) 39(49-G) 50(39-77) 52(34-73)

Identification

B 0;

7603.374 7603.355 7603.340 7603.338 7603.331

> 3.10b3)

wavenumbers (FCF

127

I2

Calculated

129

at

most

85 36 10 36 85

for

x

lo3

the

lines”

half

38 a5 84 85 142 10 36 36 3 12

10 20 86 36 38 3

142 3 14 12

“lasing

FCF

TABLE XI-Continued

value

X0;

for

129

0 53 1 53

I2

)

420 208 579 367 614 402 647 436

883 671 946 734 177 965 229 018

056 a44 537 326

-1

since

this

band

19 764 19 552

19 19 19 19 19 19 19 19

1

0 43 43 47 47 48 48 49 49

18 17 18 18

18 18 18 18 19 18 19 19

0 1 0 1 0 1

” (cm

33 33 34 34 38 38 39 39

0 1 0 1 0 1 0 1

1

0 22 1 22 0 28 28

-c BO:

Band

Pumping +

80:

heteronuclear

5058 5113

5148 5205 5106 5162 5097 5153 5088 5144

5294 5354 5277 5336 5213 5271 5199 5257

5537 5603 5393 5455

ct

h (air)

X0;

for

x

8.0 5.3

18.0 3.5 13.2 5.0 12.2 5.2 11.2 5.4

30.8 1.6 29.9 0.8 24.9 0.8 23.5 1.2

21.5 34.8 31.5 13.0

pumping

FCF

bands

lo3

+ + -t + -

+ + + +

*

YOl

19 19 19 19 19

19 19 19 19 19

C(v’

the

stat?.

average

8,:

The

value

held

of

fixed

effects

digits

correlation

Parameters

all

tbc

in

they

= 45)

51)x

10

(33) (28) (31) (65) (77)

x 10

is

fits

fit.

needed

x107

(47) (62) (76) (89)

x107

order

in

to

characters

in

20 20 20 20 20

this

table

recalculate

can

-I

in

found

measured

a much

x

10

upright

in

Table

lines

higher

III-a

with

the

precision

for

the

precision

(33) (21) (24) (21) (29)

X0:

state

noted

standard

corresponds

x 10

(48) (56) (82) (57) (71)

10

two

in

Figure

(37) (23) (12) (63) (74)

3-a.

IV-a

but

standard

Table

deviation,

to

0.2376387 0.2376575 0.2376545 0.2376106 0.237652C

B(v" = 72) x 10

0.1117421 (53) 0.1117328 (72) 0.1117665 (45) 0.1115285(210) 0.1116522(244)

B(v'=62)

0.1647455 0.1648574 0.1648253 0.1648130 0.1648437

B(v’=49)x

and

in

III.

(33) (16) (12) (19) (27)

72)

(41) (30) (31) (83) (97)

62)

49)

section

the

and

in

390.9792 390.9783 390.9783 390.9784 390.9788

C(v"=

047.7320 047.7324 047.7320 047.7388 047.7343

G(v'=

760.0600 760.0552 760.0556 760.0548 760.0552

than

explained

characters

as

11 11 11 I1 11

20 20 20 20 20

19 19 19 19 IV

C(v'=

of Lines Given in Fig. 3a

0.1159997 (94) 0.1160193 (31) 0.1160450* 0.1159774(134) 0.1161839(140)

B(v'=61)

calculated

(34) (15) (11) (21) (29)

(28) (42)

typed

be

to the

digits

cm

033.9083 033.9065 033.9063 033.9066 033.9063

G(v'=61)

0.11932* 0.12024 0.15376 0.11932* 0.11932*

-H(v'=45)x'o'2

1568.1707

last

=

Ia

from Fits of the Five Groups

correspond

the

J = 0)

(75) (91)

(33)

7) x 108

0.46905* 0.47452 0.46905* 0.43462 0.475fid

D(v"=

0.373080* 0.375337 (68) 0.382447 (98) 0.375349(274) 0.383161(254)

D(v'=Sl)

reported

in

45)

Obtained

0.280437* 0.283637 0.278624 0.280091 0.279334

D(v’=

= 7,

uncertainty

G (v”

italic

parameters

the

are

in

the

was

(32) (25) (8) (64) (76)

7) x 10

0.3621694 0.3621741 0.3621690 0.3621274 0.3621732

B(v"=

0.1571222 (37) 0.1571593 (46) 0.1572020 (65) 0.1571121(190) 0.1572156(180)

B(v'=

0.1795382 0.179558fi 0.1795332 0.1795161 0.1795150

B(v’

given

the

parenthesis

The

in

deviations.

The number

of

1568.1707* 1568.1707* 1568.1707* 1568.1707* 1568.1707*

C(v" = 7)

821.2082 (77) 821.1995 (69) 821.1925(106) 821.2041(312) 821.1893(290)

G(v'=

(59) (26) (46) (49) (63)

51)

= 45)

616.4741 616.4726 616.4757 616.4715 616.4825

G origin

110 87 64 42 28

"I'

110 87 64 42 28

“lV

110 87 64 42 28

a The

145,

87 + 64 42 +

range

87 64 42 14 5

range

87 64 42 14 5

range

‘*7I’291Parameters’

APPENDIX

(42) (68)

for

due

to

0.195781(32) 0.199032 (29) 0.198946(14) 0.195022 (74) 0.198332 (88)

D(v"=72)x107

0.691698* 0.658452 (46) 0.691698* 0.585300(121) 0.630707038)

D(v'= 62)x107

0.33836* 0.35604 0.32784 0.33836* 0.33836*

D(v'=49)x107

v”

108 88 76 63 51 39 27 17

89 + 76 + 63 + 51+ 39+ 27 + 15 + 4+

108 88 76 63 51 39 27 17

“I’

range

ranpe

108 88 76 63 51 39 27 17

89 + 26 + 63 + 51-t 3927+ 15, 4+

89 * 76+ 63 * 51+ 39+ 27+ 15 + 4-

“IV

range

(82) (79) (59) (59) (52)

(35) (113) (136)

IV 785.4108 19 785.3720 19 785.3963

50)

0.1605OlP (39) 0.1604833 (25) 0.160495,4 (17) 0.1604977 (20) 0.1604679 (31) 0.1604167 (19) 0.1605018(240) 0.1604L6.9(290)

10

B("' =50)x

IO

(30) (19) (22) (35) (24) (31) (32) (40)

C(v'=

B("' =48)x

0.1957750 0.1957988 0.19S8024 0.1957880 0.1957884 0.1957858 0.1958433 0.1957832

10

0.1679279= 0.1677902 (22) 0.168029:(630) 0.1678224(154) 0.1678621 (40) 0.1678363 (88) 0.1678694 (63) 0.1687529(320)

(86) (74) (65) (83) (54) (62) (65) (85)

B(v' =40)x

720.2798 (40) 720.5729 (43) 720.3162 (654) 720.563OCl.60) 720.4324 (84) 720.4988 (185) 720.4308 (131) 719.5576(3.34)

C(v'=48)

386.3060 386.2982 386.3006 386.3062 386.3074 386.3050 386.2899 386.3100

40)

785.3695 785.3917 785.3937 785.3963 785.4095

19 19 19 19 19

19 19 19 19 19 19 19 19

19 19 19 19 19 19 19 19

C(v'= (17) (12) (27) (51) (13) (46) (47) (57)

(76)

(15) (37)

0.346012 (35) 0.34516-I (22) 0.34727+ (15) 0.347140 (18) 0.34430% (24) 0.338978 (16) 0.345006(170) 0.339953(200)

D(v*=50h107

0.31471; 0.31471 0.31996 0.31561, 0.31471, 0.31471, 0.31471 0.33675

D("'=48h107

0.220265 0.220904 0.223397 0.220736 0.220073 0.220728 0.227462 0.219917

D(v'=40)x,07

13

753.7630 753.7656 753.7510 753.7548 753.7655 753.7600 753.7470 753.7641

(62) (i8) (59) (58) (42) (29) (49) (62)

0.20859 (99) 0.21027 (59) 0.20190 (40) 0.20288 (47) 0.21161 (64) 0.22405 (41) 0.21045(370) 0.22360(440)

-H(~'=50h.l0'~

19 19 19 19 19 19 19 '9

G(v'=49)

0.7124: 0.7124 0.5158 (12) 0.6709,(25) 0.7'24 0.6605 (22) 0.4067 (23) 0.6878 (28)

-H(v'=40)xlO

B(v'=49)xlO

525.9529 526.0400 526.0023 525.9387 526.0231 525.9652 525.9870 525.9339

(71) (33) (26) (34) (67) (37) (44) (54)

(62) (14) (15) (23) (23) (23) (23) (29)

843.6118(600) 843.5967(130) 843.6086 (91) 843.6164(170) 843.5967(390) 843.6038(220) 843.6013(250) 843.6168(300)

G("' =521

0.1640432 0.1641975 0.1642455 0.1642630 0.1641645 0.1641584 0.1642068 0.1641624

19 19 19 19 19 19 19 19

19 19 19 19 19 19 19 19

G(v'=43) (98) (22) (25) (37) (43) (37) (38) (46)

x 10

(28) (48) (32) (72) (19) (10) (12) (14)

~("'=52)xlO~ 0.38559 0.38736 0.38514 0.38258 0.39564 0.38822 0.38710 0.38462

B(v'=52)

0.152847EC260) 0.1528908 (49) 0.1528587 (33) 0.1528366 (69) 0.1529507(170) 0.152886t (96) 0.152883.Z(110) O.l5285lZ(130)

x 10

0.30979 0.23918 0.18306 0.17187 0.23382 0.23307 0.21893 0.23247

(49) (19) (15) (23) (46) (25) (29) (35)

-H("'=49b.1012

0.256081 (36) 0.251038 (86) 0.252215 (97) 0.256290(140) 0.252067(170) 0.255004(140) 0.254236(150) 0.256854(180)

D(v'=43h107

0.299872(114) 0.319541 (45) 0.330496 (36) 0.333258 (53) 0.318094(107) 0.317573 (58) 0.322396 (69) 0.317685 (83)

D("'=49)x107

0.1858323 0.1857065 0.1857523 0.1858582 0.1857388 0.1858198 0.1857932 0.1858755

B(v'=43)

12912 Parameters’ Obtained from Fits of the Eight Groups of Lines Given in Fig. 3b

APPENDIX Ib

VP!

108 88 76 63 51 39 27 17

range

89 + 76 + 63 + 51+ 39+ 27 15+ 4+

z

average

BO+ state. ”

The

value

held

digits

of

fixed

effects

Parameters

the

the

is

fits

x 10

(21) (23) (13) (25) (17) (16) (23) (28)

x 10

fit.

= 6,

italic order

reported

in

in

in

to

last

this

table

recalculate

can

B(vl.63)

be

found

measured

a much

in

in

Table

lines

higher

upright

calculated

the

III-b

with

than

the

X06

(40) (49) (55)

(46) (36) (63) (46)

(80)

state

noted

standard

to

two

in

Figure

119.1701 119.1686 119.1765

119.1702 119.1652 119.1762 119.1734

119.1695

3-b.

IV-b

but

for

due

0.4868* 0.4556 0.4657 0.4989 0.5350 0.4960 0.4153 0.5346

(44) (51) (58)

(46) (35) (69) (47)

(83)

the

to

(56) (39) (39) (20) (16) (31) (39)

-ki(v”=73)x1013

20 20 20

20 20 20

20

C(v' = 70)

standard

Table

deviation,

and

in

III.

0.201122 (52) 0.203208(220) 0.201944(140) 0.200886(150) 0.200091(110) 0.200593 (78) 0.203705(130) 0.199367(160)

D(““=73)xloJ

113.0172 113.0143 113.0231

113.0166 113.0145 113.0237 113.0208

113.0164

C(v' = 69)

corresponds

section

the

and

in

(22) (24) (17) (18) (22) (14) (19) (23)

x 10

precision

for

characters

explained

0.2331998 0.2332381 0.2332198 0.2332113 0.2332047 0.2332061 0.2332415 0.2331994

B(v”=73)

20 20 20

0.798154, 0.714957, 0.714957

(22)

20 20 20

20

0.714957* 0.714957* 0.714957*

0.714957*

D(v'=63)xlO'

precision

as

(54) (80) (59) (58) (41) (29) (46) (58)

(62) (47) (70) (69) (460) (71) (85)

(120)

x 10

= 73)

445.9174 445.9053 445.9122 445.9174 445.9226 445.9172 445.9058 445.9230

typed

-1

I1 11 11 11 11 11 11 11

C(v”

0.1076284 0.107630; 0.1076008 0.1075825 0.1076026 0.1077606 0.1076219 0.1075883

cm

to the

digits

1357.8841

(30) (49) (52) (91) (59) (59) (64)

(140) (98) (74) (91) (80) (240) (86) (100)

correspond

the

=

0.46100* 0.46261 0.45892 0.46159 0.46722 0.45757 0.45750 0.46131

D(v”=6~x108

057.3645 057.3368 057.3451 057.3520 057.3540 057.3412 057.3387 057.3554

G(v' = 63)

J = 0)

20 20 20 20 20 20 20 20

characters

uncertainty

G (v”

needed

in

the

was

0.3605190,(28) 0.3605265 0.3605242 (12) 0.3605315 (12) 0.3605395 (22) 0.3605253 (14) 0.3605257 (15) 0.360537ti (16)

B(v”=6)

0.1117439 0.1118888 0.1119945 0.1119615 0.1119384 0.1120407 0.1119840 0.1119400

B(v'=62)

parawters

the

are

given

in

they

parenthesis

all

correlation

in

of

The

number

= 6)

(110) (120) (79 (120) (84) (72) (110) (130)

62)

1357.8841; 1357.8841, 1357.8841, 1357.8841, 1357.8841, 1357.8841, 1357.8841, 1357.8841

C(v”

044.4652 044.4478 044.4489 044.4556 044.4617 044.4515 044.4441 044.4613

CC+=

deviations.

The

20 20 20 20 20 20 20 20

G origin

108 88 76 63 51 39 27 17

89 + 76 .+ 63 + 51 + 39+ 27+ 15 + 4+

a The

v”

range

494

CERNY, BACIS, AND VERGES APPENDIX II

Polynomial Expansion’ Parameter Coefficients of the 12712 X0, State Obtained from 0 < Y”c 19 Levels (The Values of the Coefficients Given in the Table Come from a Private Communication from Gerstenkom and Luc) ‘kl

‘k0

Q

4

+ .214 526 155 + 03

+ .373 682 334 - 001

+ .453 518 as

- 008

- .510 152 790 - 015

- .611 938 186 + 00

- .I13 922 247 - 003

+ .245 172 014 - 010

- .924 728 688 - 017

- .235 606 136 - 03

- .283 866 568 - 006

- .428 646 554 - 013

- .451 982 759 - 017

- .I40 816 912 - 03

- .521 237 377 - 003

+ .I08 340 667 - 012

+ .618 671 293 - 018

+ .943 318 488 - 05

+ .582 010 316 - 010

- .I09 632 90

- 013

- .416 460 060 - 019

- .344 433 981 - 06

- .195 761 456 - 011

+ .554 529 09!3- 015

+ .976 640 426 - 021

+ .490 ns a

344 - 08

G(v") =

1

Y

k:,

(v" + +)",

B(v")

k"

; h (v" + +k : = k:O ' implies that the origin

H(F) This These for

- .103 723 995 - 016

coefficients

comparison

with

were

fitted

expansion

of 'Iables V-a

Ci(v")

7 1

=

ok Yko(v"

of

used

and +

for

=

P6 ; ok hk(v" k=O

1 Y (v"+ k:, k1

the G(v") the

parameters V-b,

’ k, 7)

k=l

Hi(V”)

=

+ 3"

from

Bi(v")

+k,

is C(v"

calculation (Table the = 0'

D(v")

i k=O

with

= - 4)

and

for sane

relations

pk Ykl(v"

PC ‘27~‘2pI)

dk(""

+ i)",

= 0 cm'. isotope

of the

VIII)

usual

= ,lo

parameters v"

levels

of the X0+ State g in the polynomial

: + ;)k,

=

Di(v")

0.9961126,

= p4

f k=O

ok dk(v"

,,('2g,2) = 0.992210.

+ ;)k

B -

X SPECTRUM

OF ‘*7I’29IAND ‘=I2

495

APPENDIX III Expansion’ Parameter Coefficients of the 12’12BO: State from Gerstenkom and Luc’s Data

2

5 6

lk

k 0

k

0.9641549422252 2

-0.28342771S1906 0.8514947485751 -0.14601726116~0

5

0.1555475181‘11

6

-0.10985069~6171 O.‘J139751676406 -0.1624604439117 O.lC1,,42928443 -0.7531666172655 0.88,1566823264

12

-0.84306Lt6292289

x10-'9 I,

0.,,61946390023

Gi(“‘)’

Te +

o*u;- Yo$+

-0.619014726357*

x10-'>

13

0.30743666~5601

x10-"

1*

-0.6211959154851

12

r,u-‘7

1

DkY,,(“’

l

x10-2O

4)”

k=l

0.C”‘)

14

M.(“‘) log

I

“‘0

% 0

-0.*096779,986,2

=

-0.2633300

2 rlOf

496

CERNY,

BACIS,

AND VERGES

APPENDIX

IV

The Dunham coefficients representing the origins of the vibrational levels of the X0,+ state are written following the expression G(u”) = Y&,+ YTO

(1)

and those of the excited BO: state follow (2) These coefficients are determined from a least-squares fit to the G(u”) and G(v’) determined from fits to the measured lines. But then it is impossible to determine Y& and Y&. Indeed the lines L are given by expressions such that L= *,+

Y&-Y&+

Y$(d+$-

Yfi(v’+f)+

**a +rotationalterms.

Only the quantity T, + Yoo B - Y& can be determined directly from experiment. The value of T, can be obtained only after calculation of Y& and Y& from the usual relation (30, 33)

( Yl I)?ylo)2

ym+‘-~+ 01

y20

144(Yo1)3 + 4

+ ”

-*

So in the fits an origin in the ground state is fixed and usually G(v” = 0) = 0 cm-’ is chosen. This implies that (1) is written

For the excited state the usual convention is G(u’ = 0) - G(u” = 0) = T,-,,,,then G(u’)

=

Too

_

q

_

:

.

.

.

+Y,(,+;)+Y?o(U~+;)2+

***.

(4)

For instance, in paper I (Table IV) G(u”) is represented by the relation (3) and the constant C is just -( Y10/2) - (Y20/4) * * - . For BO: , G(d) are represented by (4) and C’ in Table VIIIa (paper I) is TOO - ( Yfo/2) - ( Yfo/4) - * - . From this we can calculate for 12’12Too = 15 724.595 cm-’ (=C’ + 62.6466) and T, = 15 769.095 cm-‘, [=C - Y& - (C + Y&)1. In the present paper we have taken G(v” = - l/2) = 0 cm-’ which gives directly the isotopic Dunham relation. Then fitting the expression G(u”) = C” + z,,Y&u” + 1/2)k to the experimental G(u”) (Tables III) must give C” = 0. We have found -0.0026 cm-’ (12711291) and -0.0029 cm-’ (lz912)which is of the order of the standard error on c”. It is therefore clear that C” has nothing to do with Y”,. In Appendix III the G(u’) have their origin at u’ = -l/2 (as in paper I) but the reported value of T, is 15 769.078 cm-’ which is different from 15 769.076 (10) cm-’ determined from “‘12. This value was calculated from the fits of Tables IVa and b. It is easy to see that in Table IVa this T, value gives a weighted average difference of

B -

X SPECTRUM OF ‘*‘I’291 AND lz912

497

-0.0042cm-’ in isotopic calculated G (second row of G) with respect to the experimental value (first row of G). In Table IVb this difference is f0.0015 cm-‘. That means that the absolute value of the ‘27I’29Ilines would be better recalculated with T, = 15 759.0822 cm-’ and for 12’12with T, = 15 769.0764 cm-’ for the u’ range of BO: levels used in the fits. The various causes of errors in this determination can explain this difference between the two isotopes. We have taken the same value T, = 15 769.078 cm-’ for both isotopes which is a weighted average taking into account the more precise and extended data for ‘2912.This is exactly the same result as in paper I because the difference in 0.002 cm-’ is due to the difference in the calculation of G(v” = -l/2): in paper I (Table IV) we used - 107.1082 cm-’ and here (from Appendix II) - 107.1103 cm-’ giving +0.002 cm-’ in T,.It is shown in Section V of this paper that T,from 12’12in paper I is too high (+0.0083 cm-‘) when using constants of paper I for calculating lines in the range of the absorption spectrum of the BO: - X0,’ transition. The reasons for these small systematic differences in the absolute value of line wavenumbers are not clear (see Sect. V). VII. ACKNOWLEDGMENTS We thank F. Hartmannand J. P. Pique for useful information concerning the hypertine structure of IZ. RECEIVED:

April 23, 1985 REFERENCES

1. F. R. K. K.

2. 3. 4. 5.

6. 7. 8. 9. 10. II. 12. 13.

MARTIN,R. BACIS,S. CHURASSY,AND J. VERGES,J. Mol. Specfrosc.. submitted for publication. L. BROWNAND TH. C. JAMES,J. Chem. Phys. 42,33-35 (1965). WIELAND,J. B. TELLINGHUISEN, AND A. NOBS,J. Mol. Spectrosc. 41,69-83 (1972). K. YEE, J. Chem. Sot. Faraday II 72,2113-2126 (1975). G. W. KING, I. M. LITTLEWOOD, J. R. ROBINS,AND N. T. WIJERATNE,Chem. Phys. 50, 291-299

( 1980). G. W. KING, I. M. LITTLEWOOD, AND J. R. ROBINS,Chem. Phys. 56, 145-146 (1981). K. S. VISWANATHAN, A. SUR, AND J. TELLINGHUISEN, J. Mol. Spectrosc. 86, 393-405 (198 1). J. TELLINGHUISEN, J. Mol. Spectrosc. 94, 23 l-252 ( 1982). K. S. VISWANATHAN AND J. TELLINGHUISEN, J. Mol. Spectrosc. 101, 285-299 (1983). M. KROLLAND K. K. INNES,J. Mol. Spectrosc. 36,295-309 (1970). M. D. LEVEN~~NAND A. L. SZHAWLOW,Phys. Rev. 6A, lo-20 (1972). J. P. PIQUE,F. STOECKEL, AND F. HARTMANN,Opt. Commun. 33,23-25 (1980).

J. P. PIQUE,Th&e Universittde Grenoble, France, 1984, unpublished. 14. F. SPIEWECK, Metrologia 12,43-46 (I 976). 15. F. SPIEWECK, “Opt0 Electronics,”pp. 130-135, IPC SC. and Techn. Press, 1977. 16. J. HELMCKEAND F. BAYER-HELMS, Metrologia 10, 69-71 (1974). 17. K. DXHAO, M. GLKSER,AND J. HELMCKE,IEEE Trans. Instrum. Meas. IM29, 354-357 (1980). 18. P. E. CIDWR AND N. BROWN,Opt. Commun. 34, 53-56 (1980). 19. M. GLKSER,D. KEGUNG,AND H. J. FOTH,Opt. Commun. 38, 119-l 23 ( 198 I). 20. J. D. KNOX AND Y. H. PAO,Appf. Phys. Lett. 18, 360-362 (197 1). 21. M. TEsICANDY. H. PAO, J. Mol. Spectrosc. 57, 75-96 (1975). 22. W. G. SCHWEITZER, JR., E. G. KESSLER, JR., R. D. DESLATTES. H. P. LAYER,ANDJ. R. WHETSTONE.

Appi. Opt. 12,2927-2938 (1973). 23. M. SAUTEANDM. AUBERT-FRECON, Chem. Phys. Left. 86, 59-65 (1982). 24. M. SAUTEAND M. AUBERT-FRECON, J. Chem. Phys. 77,5639-5646 (1982). 25. S. CHURASSY,F. MARTIN,R. BACIS,J. VERGES.AND R. W. FIELD,J. Chem. Phys. 75, 4863-4868 (1981).

498 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

CERNY, BACIS, AND VERGES J. B. KOFFEND,A. M. SIBAI, AND R. BACIS,J. Whys.(Paris) 43, 1639-165 I (1982). R. A, ASHBYANDC. W. JOHNSON,J. MO/. Spectrosc. 84,41-48 (1980). S. GERSTENKORN, P. Luc, AND J. VERGES,J. Phys. B14, L193-L196 (198 I). J. P. PIQUE,F. HARTMANN,R. BACIS,S. CHURASSY,AND J. B. KOFFEND,Phys. Rev. Lett. 52, 267270 (1984). J.L. DuNHAM,~~~~. Rev. 41,721-731 (1932). J. M. HUTSONAND B. J. HOWARD,Mol. Phys. 41, 1113-l 122 (1980). J. M. HUTSON,J. Phys. 814,851-857 (1981). G. HERZBERG,“Spectraof Diatomic Molecules,” Van Nostrand, Princeton,N. J., 1950. J. H. VAN VLECK,J. Chem. Phys. 4,327-338 (1936). P. R. BUNKER,J. Mol. Spectrosc. 68, 367-371 (1977). J. K. G. WATSON,J. Mol. Spectrosc. 80,411-42 I (1980). P. LUC, J. Moi. Spectrosc. 80, 41-55 (1980). W. C. STWALLEY,J. Chem. Phys. 63,3062-3080 (1975). P. CCREZAND S. J. BENNETT,Appl. Opt. 18, 1079-1083 (1979). L. HLOUSEKAND W. M. FAIRBANK,JR., Opt. Lett. 8, 322-323 (1983). S. GER~TENKORN AND P. Luc, Rev. Phys. Appl. 14, 791-794 (1979). J. E. M. GOLDSMITH,E. W. WEBER,F. V. KOWALSKI,AND A. L. S~HAWLOW,Appl. 0p1. 18, 19831987 (1979). A. MORINAGA,Japan. J. Appl. Phys. 23,774-775 (1984). A. MORINAGAAND K. TANAKA,Appl. Phys. Lett. 32, 114-l 16 (1978). D. A. JENNINGS, C. R. POLLOCK,F. R. PETERSEN, R. E. DRULLINGER, K. M. EVENSON,J. S. WELLS, J. L. HALL, AND H. P. LAYER,Opt. Lett. 8, 136-138 (1983). L. A. HACKEL,K. H. CASLETON,S. G. KUKOLICH,AND S. EZEKIEL,Phys. Rev. Lett. 35, 568-571 (1975). CH. J. BORDB,G. CAMY, B. DECOMPS, J. P. DESCOUBES, ANDJ. VIGUE,J. Phys. 42,1393-1411(198 I). G. R. HANES,Appl. Opt. 18, 3970-3974 (1979). C. R. POLLOCK,D. A. JENNINGS, F. R. PETERSEN, J. S. WELLS,R. E. DRULLINGER, E. C. BEATY,AND K. M. EVENSON,Opt. Lett. 8, 133- 135 (1983). E. LUC-KOENIG,C. MORILLON,ANDJ. VERGES,Physica 70, 175-189 (1973).