Analysis of the D2O absorption spectrum near 2.5 μm

JOURNALOFMOLECULARSPECTROSCOPY

123, 126-134(1987)

Analysis of the D20 Absorption A. D. BYKOV,* V. S. MAKAROV,t

Spectrum near 2.5 pm

N. I. MosKALENKo,t 0. AND 0. V. ZoTovt

V.

NAUMENKO,*

0.N.ULENIKOV,*

*The Institute ofAtmospheric Optics, Siberian Branch, USSR Academy of Sciences, Tomsk 634055, USSR; and YThe Kazan State University, Kazan 420008, USSR The D20 absorption spectrum recorded with a selective modulation Girard spectrometer in the region of 3690-4190 cm-’ (resolution -0.07 cm-‘) has been analyzed. Based on the fitting of experimental data the spectroscopic parameters of the vibrational state (0 I 1)have been determined and the parameters of the vibrational states (110)and (030) have been estimated. o 1987 Academic

Press, Inc.

1. INTRODUCTION

The analysis of vibration-rotation absorption spectra of the isotopic species of water vapor is of great interest for investigating the dynamics of molecular vibrations and rotations, for determining the intramolecular potential function, for studying the role of deuterium in interstellar molecules as an indicator of chemical reactions, and for analyzing the content of these isotopic species in different media using laser techniques. This paper deals with the analysis of the DzO absorption spectrum near 2.5 pm. The DzO spectrum in this region was studied earlier in Ref. (1) using classical grating spectrometers with spectral resolution between 0.25 and 0.3 cm-‘. However, the investigation of the D20 spectrum at higher resolution is of interest. 2. EXPERIMENTAL

DETAILS

In this paper the D20 absorption spectrum has been recorded using an apparatus which is a modified setup of the instrument described in Ref. (2), and which is based on a selective modulation Girard spectrometer with a focal length F = 200 cm. A globar was used as a source of continuous radiation. The recording was carried out with a dry-ice-cooled PbS photoresistor. The measurements were made with a grating spectrograph with 300 grooves/mm used in the second order. The resolution was around 0.07 cm-‘. The centers of the DzO lines were determined with reference to the HZ0 and HDO absorption lines whose centers were taken from Refs. (3, 4). The accuracy of the line centers is -0.04 cm-’ relative to the Hz0 and HDO lines. The spectra were recorded using a multipass gas cell with an optical path length of 800 cm at temperatures in the interval 293-300°K. The partial pressures of D20, HDO, and HZ0 in the gas mixtures were varied, depending on the measurement temperature, in the ranges of 1.78-2.82, 19-66, and 4-13 Pa, respectively, for the three species. About 1400 absorption lines were recorded in the investigated spectral range 3690-4190 cm-‘. 0022-2852187 $3.00 Copyri%t

0

1987 by Academic

AU rights of nzpraduction

126 Press, Inc.

in any form reserved.

40

ABSORPTION SPECTRUM

NEAR 2.5 pm

127

3. THE ANALYSIS OF THE SPECTRUM

(1) To assign the D20 absorption lines, the HZ0 and HDO lines have been preliminary extracted from the spectrum (the total band intensities of the HzO, HDO, and D20 absorption bands, which appear in the region under study are given in Table I). Assignments of the Hz0 lines were made based on the data from Ref. (3). Assignments of the HDO lines were made based on the data from Ref. (4). In the last case the rotational levels of the HDO vibrational states (00 l), (1 lo), and (030) were used as initial data. Since, however, the rotational levels of these vibrational states are not reported in Ref. (4) for all values of the quantum number T (in particular, when J 2 9), then the inverse spectroscopic problem has been preliminary solved (that is the rotational and centrifugal constants have been determined) for the above vibrational states of the HDO molecule. In this case, the energy levels from Ref. (4) were used as initial data. As can be seen from the analysis for the state (001) it is sufficient to use the model of an isolated vibrational state, while for the states (110) and (030) it is necessary to take into account the Fermi resonance.’ The obtained band centers, rotational, centrifugal, and resonance constants are given in Table II. The values u = { zi(Ey’C _ ,777P)2/N} ‘j2 characterizing the accuracy of reproduction of the initial energy levels for all three vibrational states (OOl), (1 lo), (030) are presented in Table II.2 These results allowed one to calculate the transitions to the states [JT) which were not observed in Ref. (4). The spectral lines remaining after such an analysis were assigned to the D20 molecule. (2) The spectrum of the DzO molecule in the region under study is caused by transitions from the ground vibrational state to the rotational sublevels of the state (0 11). This state, together with (030) and ( 1 lo), forms the second triad of interacting vibrational states of the D20 molecule. The results relevant to the second triad of H20 are presented in Ref. (5). These data were used here as the initial ones to estimate, based on isotopic relations, the rotational and centrifugal constants of the states under study. This enabled one to obtain a sufficiently good initial approximation for analyzing the spectrum and for solving the inverse problem. There is one more problem whose solution is necessary for the correct analysis of the spectrum: the lines of the bands vI + u2 and, in particular, of the band 3v2 of D20 are weak and are not observed in the spectrum. At the same time, the rotational levels of the vibrational states (110) and (030) can affect the positions of the v2 + v3 band lines observed in the spectrum. In view of this, one should take into account the presence of the Fermi resonance (between the states ( 110) and (030)) and of the Coriolis resonance (between the states (1 lo), (030), and (01 l)), or, at least, one should consider the errors in the determination of the (0 11) state parameters caused by the absence of information on the states (030) and (110). (a) Estimation of the rotational and centrifugal parameters. To calculate the

’ Strictly speaking, from the symmetry point of view, when simultaneously considering the (110) and (030) states of HDO, the Coriolis-type interaction should also be taken into account in a resonance block. However, it is not difficult to show that in the case considered the Coriolis-type interaction parameters can be omitted. This results only in small variations of rotational constants of the states (110)and (030). 2 It should be noted that for the purpose of this paper the parameters of Table II give a sufficiently good reproducibility of the initial data.

BYKOV ET AL.

128

TABLE I Total Band Intensities of H20, HDO, and D20 from the Region of 3690-4180 cm-’ Molecule

Band

WO

$3 J 1+

$2

332

36.0@

7.9P)

0.748)

ED0

0.114

0.26&

H20

33

H20

242

A20

32 + $3

D20

3, + 32

D20

332

D20

From Ref. b From Ref. ’ Calculated d From Ref.

86.85')

SB

HLIO

$1

a

SA

(in cm-*atm-‘)

9.726b) 214.675') 1.76eb) 5.696')

~L04~)

0.261')

0.211~)

0.0013c)

(4). (8). from Eq. (4). (9).

rotational and centrifugal parameters relative to the states (030), (1 lo), and (011) of the DzO molecule, we used the following isotopic relations: B:(D20) = Bo,(DzO) +A”‘K{B:(H20)

- B:(H20)},

(1)

A”(D20)=Ao(D20)+A1’2K2{A”(H~0)-Ao(H~0)},

(2)

W(D20) = H’(D20) +A”2K3{W(H20)

(3)

- H”(H20)},

where B, is any of the constants A, B, C, A is any of the constants AK, AJK,AJ, &, aJ; H is any of the constants HK, HKJ, HJK, HJ, hK, h_,K,h,; the index 0 denotes the parameters of the ground vibrational state; the index v stands for an excited state. The values A and K (the mean values of Axx and K, (Km = 1 - JtJ&)) are the parameters of isotopic relations (for the determination of these parameters, see, e.g., Ref. (6)). For the H20 molecule mo % mH. As a result, the relations A x (mD - mH)/mD, K = (mD - mH)/mD are fulf%d. These values of the parameters A and K were used for calculating the rotational and centrifugal constants. The values of the parameters which are given in Table VI without standard deviations were obtained using the isotopic relations (l)-(3) and remained fixed in calculations. As an illustration of the accuracy of the estimates obtained using Eqs. ( 1)-( 3), Table III gives a comparison between calculated and experimental spectroscopic parameters for the first-triad vibrational states of the D20 molecule. (b) Estimation of the total band intensities. The total band intensities of the D20 molecule occurring in the interval 3680-4180 cm-’ can be estimated using the isotopic relation ~WW’(D20)=

A("'+"Z+"3-')~2~"IV2"3(H20)~o'o(D20)/~010(H20).

(4)

129

DzO ABSORPTION SPECTRUM NEAR 2.5 pm TABLE I1 Spectroscopic Parameters for the States (OOI), (1 IO), and (030) of HDO (in cm-‘) (001)

(110)

3707.4667

J A

(030) 4128.2017

4117.2276

22.37bb78~o.ooo81

25.11234$0.0021

31.9578g&0.0024

B

9.091445~O.OOOl7

9.058b087~0.000b2

9.4953b47~0.000b7

C

b.328b47&.ooo12

b.2133717~0.00083

b.1b497g4$.ooo79

AK102

1.1bt3b7,+o.oo82

2.0232&0.014

9.0b13,+o.011

Qo4

8.7143&o.091

410~

3.b928+o.017

3.4415&0.087

5.8437go.079

SK103

1.94e57~o.021

3.08429+ob4

9.148,go.o76

QO4

1.2080b.&0.0033

1.58,~0.11

yo4

0.487,,$0.035

l.04107~o.039

1.147go.51

11.873$0.45

1.8bo&0.21

10.00277~0.09b

[email protected]

-0.023+0.41

-5.10,&0.023

H,lOb

1.bo55+13

-2.b57&1.9

15.B7&3.7

HJ108

3.3g2po.72

0.5227+0.48

&105

1.b87b9@054

l.177$o.34

%‘05

12

%JIOb

o.bo5g0.

IglO7

-l.98,($0.54

wo7

3.8b7~l.8 -75.0441+o.9a

[email protected]¶

o.58925?;o.074

L&o*

4 lb.b80?;l.3

-1.0227$.4b

-

1.5g~l.o

Lz108

1.277k0.b

lK107

-1.423+0.13

PKIO’O

1.4b&2.7

Po=22.0874

FK10=-EL1254,@0.0048

G 103 B 0 < IEC’ -Eesl<10-2

-0.

1417~0.

12

2.4&1.9 F,103.3.4E04+o.18

7.7

8.3

7.4

128

164

82.6

%

06.7

Fg102.-3.74

83

I$

92.8

%

In the calculations, the data for the I&O-molecule band intensities are taken from Ref. (10). The 40 total band intensities for the bands vI + v2, v2 + v3, and 3v2 are given in Table I. The calculations show that the vl + v2 band intensity is about 6 of the intensity of the strong band v2 + v3 (the corresponding absorption coefficients in the line peaks are of order 10-3-10-4 cm-‘). The 312 band intensity is approximately 1000 times weaker than that of the band v2 + v3. (c) Estimation ofre.sonance e&3x In light molecules such as D20, accidental Coriolis, Fermi, or Darling-Dennison resonances significantly affect the molecular spectra. The Fermi and Coriolis resonances are usually taken into account for the states of the type under consideration. The rotational levels of the second triad of the D20 molecule can be described by the following effective operator: H=

C u.3=5,6,7

&&)@l,

(5)

BYKOV ET AL.

130

TABLE III Rotational and Centrifugal Parameters for the States (lOO), (020), and (001) of DzO, Calculated by Eqs. (l)-(3) (in cm-‘) (020)

(100) A

15.180')

B

7.180

7.196

7.402

7.383

7.245

C

4.779

4.784

4.734

4.740

4.793

4.795

0.88

0.88

2.19

2.29

0.84

0.86

&lo*

-0.14

-0.15

-0.24

-0.24

-0.15

-0.15

4103

0.33

0.31

0.37

0.37

0.31

0.32

&Co3

0.34

0.34

1.30

1.65

0.33

0.35

6,103

0.12

0.12

0.15

0.15

0.13

0.13

0.14

0.16

0.88

1.0

0.14

0.15

-0.19

-0.25

-0.63

-0.25

-0.26

0.62

0.78

A,ro*

I$(104 %105 I-I,107

0.43

15.152b)

0.64

18.143a)

(001)

18.142b)

-0.99

1.06

14.887a)

14.984b) 7.241

%105

0.31

0.36

1.07

2.22

0.36

0.37

hJ107

0.21

0.33

0.52

0.48

0.32

0.39

From Ref. (7). b Calculated using Eqs. (I )-(3). Rotational and Centrifugal parameters of Hz0 from Ref. (5) were used as the initial ones. a

where

- S;t-{ J: , J:,,} - 2S$J2J$, + H;J: + Hft;J:J’ + H&J;( J2)2 +H:(J2)3+hK(J:,J&}

f.

**

(6)

are Watson-type Hamiltonians, and the operators of resonance interaction have the form h5,6= F$‘*@J;+ F:5,6)J2+ F$?‘J&, h5,, = iC$?‘)Jy+ Cyi7’{J,, J,}, he,’ = iCry7’Jy+ C$‘)( J,, J,},

(7)

where J& = J: - Jc; {A, B} = AB + BA. Here the vibrational index is u = 5 for (030), v=6for(llO),andv=7for(Oll). The constants C, and C,, of the first triad of interacting states of D20 given in Ref. (7) can be used as an initial approximation for the resonance constants C, and C,-, since, as seen from Ref. (5, I I), for Hz0 they depend weakly on the vibrational quantum number v2. A similar situation ought to be observed for the D20 molecule. For the constants F!5*6’and Fyg6’ the main part of the dependence on v2 is determined as {(v2 + 1)(v2 + 2)) 1’2.Th erefore, the initial values for these parameters can be obtained using the data from Ref. (7) by simple calculation. The constants FL’*@and Fy,@ thus

DzO ABSORPTION SPECTRUM

131

NEAR 2.5 pm

TABLE IV Some Strongly Interacting Rotational Sublevels for D2W (011)

J

‘A

(110)

KC

‘A

(030)

‘C

‘A

C011,110, JQKC s KAK;:

CO11,030,

011 ,dBx K

mAKC*KAKC

ilc (cm

KC

-0.60

75

361

0.28

75

262

0.29

-0.60

85

462

0.41

-1.09

a5

363

0.41

-1.09

95

563

0.56

-1.77

95

464

0.59

-1.91

102

9

3

7

0.27

-0.31

105

6

6

4

0.74

-2.66

105

5

6

5

0.97

-3.51

114

a

5

6

-0. lb

115

7

b

5

0.94

115

6

6

6

101

9

0.77 -3.64

2.93 b

-11.60 0.65

5

- EIK& aHex Ct$$&b = ((JK,K&o~l,~,,,IJGG)V(E ,K~K= is determined from the conditions C’$$$?K:,

d 1. A@&,

1

-0.36

The absence of resonance interactions

are the shifts of the energy levels caused by

resonance interactions.

obtained were used for evaluating the Fermi-resonance effect on the position of energy levels. The changes of constants caused by the absence of contribution independent of J, in the operator h5,6were also taken into account. The estimates of resonance effects on the energy-level positions were made using the scheme described in Ref. (12). A calculation showed that the resonance effects on vibration-rotation levels of the states (01 l), (1 lo), and (030) can be neglected for the states with a small value of the quantum number J (J < 5), since the corresponding corrections are smaller than 0.03 cm-‘, that is, do not exceed the experimental errors. For most of the levels with J > 5 the resonance effects are also sufficiently small. The levels which are strongly affected by the Coriolis resonance are given in Table IV. These levels were introduced in the fitting at the second stage only, and the parameters of resonance interaction were determined based on these perturbed levels. (d) Spectrum assignment: Determination of spectroscopic constants. The assignment of the spectrum was made in two steps. At the first step for the lines with small values of a quantum number J the conventional combination differences method was used. While the quantum number J increases, the efficiency of the method of combination differences decrease. Therefore at the second step the spectral line assignment was carried out simultaneously with the solution of the inverse spectroscopic problem (i.e., simultaneously with the determination of rotational and centrifugal constants).

BYKOV ET AL.

132

TABLE V Energy Levels for the States (011) and (110)of D20 (in cm-‘) J

'A KC

0

0

Ee~'(O1l)

102

J

KA %

Eexp*(Oll)

IO*

J

KA

Kc

Eexp~(Oll)

lo*

3956.03

4

7

5

2

4544.90

-5

11

1

11

4638.67

-1

101

3968.08

4

7

6

2

4642.37

-2

11

1

10

4746.25

6

111

3976.76

2

7

6

1

4642.37

-2

11

2

10

4746.65

5

110

3979.34

1

7

7

1

4760.78

2

11

2

9

4833.73

4

3991.71

0

7

7

0

4760.78

2

11

4

8

4925.70

11

0

8

3

2

0

2

12

0

2

211 2

21

3998.31

0

8

4338.85

-1

11

4

7

4944.03

4006.02

1

818

4338.96

-2

11

5

7

5017.79

6

4031.88

1

817

4412.93

2

11

5

6

5019.35

-4

2

2

0

4032.37

1

8

2

7

4416.57

-9

11

6

6

5133.67

4

3

0

3

4025.97

0

8

2

6

4463.09

-3

11

6

5

5133.67

2

3

13

4030.31

1

8

3

6

4484.51

-2

11

0

4

5363.99

1

3

12

4045.66

1

8

3

5

4501.40

2

11

a

3

5363.99

1

3

2

2

4068.08

1

8

4

5

4555.84

-1

12

0

12

4757.35

1

3

2

1

4070.46

-2

0

4

4

4558.18

1

12

1

12

4757.36

1

3

3

1

4117.49

-3

0

5

4

4635.95

-1

12

1

11

4075.80

-6

3

3

0

4117.55

-3

0

5

3

4636.00

3

12

2

11

4876.02

-7

4

0

4

4070.03

-1

8

6

3

4740.85

-3

12

2

10

4974.99

4

4072.53

-1

0

6

2

4740.85

-3

12

3

9

5047.62

-1

13

4097.74

0

8

7

2

4859.60

2

12

4

9

5073.04

5

4

2

3

4115.91

1

8

7

1

4059.60

2

12

4

8

5100.68

-3

4

2

2

4122.34

0

8

81

4993.17

-4

12

5

8

5153.43

-3

4

3

2

4166.66

0

8

8

0

4993.17

4

12

5

7

5170.36

-6

4

3

1

4167.08

-1

9

0

9

4429.37

2

12

6

7

5257.99

4

4

41

4233.75

2

9

19

4429.44

0

12

6

6

5250.67

-1

4514.96

5

13

0

13

4865.42

1

4518.29

-2

13

1

13

4085.42

2

414 4

4

4

0

4233.79

-1

5

0

5

4123.52

2

918 9

2

8

5

15

4124.69

-2

9

2

7

4577.35

4

13

1

12

5014.51

-9

5

14

4161.46

-2

9

3

7

4592.73

-3

13

2

12

5014.53

0

5

2

4

4175.05

0

9

3

6

4619.87

0

13

2

11

5124.92

3

5

2

3

4100.16

0

9

4

6

4667.23

1

13

3

11

5126.55

7

5

3

3

4220.17

1

9

4

5

4672.59

4

14

0

14

5022.81

4

5

3

2

4229.71

3

9

5

5

4746.51

2

14

1

14

5022.81

4

2

4295.57

0

9

5

4

4756.50

7

14

1

13

5162.34

3

4295.62

0

9

6

4

4051.58

4

14

2

13

5162.39

4

4851.64

1

14

2

12

5283.70

-3

5

4

5

41

5

5

1

4380.22

5

9

6

3

5

5

0

4380.22

5

9

7

3

4970.64

3

14

3

12

5204.59

3

6

0

6

9

7

2

4970.64

3

14

5

9

5514.00

0

6

16

9

8

2

5104.63

4

15

0

15

5169.61

-1

4235.83

-1

9

8

1

5104.63

4

15

1

15

5169.61

-1

4186.60

615

-3

6

2

5

4245.10

-1

9

9

1

5252.13

-1

15

1

14

5319.61

-4

6

2

4

4267.46

-2

9

9

0

5252.13

-1

15

2

14

5319.66

-2

6

3

4

4301.85

1

10

0 10

4529.33

0

16

0

16

5325.62

2

TABLE V-Continued

J KAKC

Ee-(oll)

102

6

3

3

4306.08

10

1 10

4529.38

6

4

3

4369.89

-3

10

1

9

4626.02

3

6

4

2

4370.14

-2

10

2

9

4626.15

4

6

5

2

4452.56

0

10

2

8

4701.12

0

10

3

8

4711.81

0 -4

3

J

Ee~‘(Oll)

‘AKC

102

-3

’

Ee-(011)

KAKC

16

1

16

lo*

5325.62

2

6

5

1

4452.56

0

6

6

1

4556.22

0

10

3

7

4751.16

6

6

0

4556.22

0

10

4

7

4790.60

3

66

1

4457.42

2

7

0

7

4257.65

2

10

4

6

4801.19

4

66

0

4457.42

2

7

17

4258.22

1

10

6

5

4974.68

9

77

1

4662.63

3

7

16

4319.82

2

10

6

4

4974.83

2

77

0

4662.63

3 3

J KA %

EeIP*

(110) alO*

7

2

6

4325.70

-3

10

7

4

5093.97

-4

86

3

4644.56

7

2

5

4359.41

-1

10

7

3

5093.97

-4

86

2

4644.56

1

7

3

5

4387.43

-1

10

8

3

5228.27

5

87

2

4761.03

-2

4396.64

2

10

8

2

5228.27

5

87

1

4761.03

-2

7

4

4

4456.66

-2

10

9

2

5376.42

-2

97

3

4873.40

-3

7

4

3

4457.53

-2

10

9

1

5376.42

-2

97

2

4073.40

-3

7

5

3

4544.90

-4

11

0 11

4638.66

-1

6

5oo6.83

-1

734

11

6

TABLE VI Rotational and Centrifugal Parameters for (01 I), (I lo), and (030) States of 40 (011)

(110)

3956.066gO.013

J A

3846.849,+0.45 16.280~~0.022

15.98290~0.0031

B

;1,*

3472.65 20.458

7.31305,~O.OOO82

7.344277Lo.oo99

7.429

4.7335o6$o.ooo91

4.7787&0.020

4.694

l.38137;t0.020 3

(030)

l*29104$&030 -1.192,~0.086

-3.099,+0.038

$Y

3.4203&0.036

3.37

6,104

4.117+0.16

7.71

4.59 -2.98 3.90 27.6

SJ104

l.4758~o.o18

1.35

yo5

7.60,+0.42

3.7

37.0

-24.400g0.70

-4.6

-7.2

klO6

1.53

1.1

0.95

21.1,5f.l.l

1.7

1.7

hJ108

4.86G2.7

4.8

%107

-3.5g4g0.26

-2.0

LRJ108

11.907

11.907

1,108

-1.90

-2.70

PKIO”

20.627

20.627

HJ107 %106

c(5*7) re

0.74

lo*.-3.54&l.3

$6.7)

lo.5.796~o.e0

’ The quoted errors are 68% statistical confidence intervals.

-10.7

c~~*7)102=-6.97,+70

(in cm-‘)

BYKOV

134

ET AL.

The experimental values of energy levels obtained in this way are presented in Table V and were used for determining the spectroscopic parameters given in Table VI. Table V also gives the differences (A = E calc.- Eexp.) between the calculated energy levels and the experimental ones. RECEIVED: April 7, 1986 REFERENCES I.W. S.BENEDICT,N. GAILAR, AND E. K. PLYLER, J. Chem. Phys. 24, 1139-l 165 (1956). 2. N. 1. MOSKALENKO,S. 0. MIRUMYANTZ, A. V. AVERIANOVA, 0. V. ZOTOV, ANDYU. A. ILIN, J. Appl. Speczrosc.(in Russian) 19,752-756 (1973). 3. C. CAMY-PEYRET AND J.-M. FLAUD, Mol. Phys. 26,825-855 (1973). 4. R. A. TOTH AND J. W. BRAULT, Appl. Opt. 22,908-926 (1983). 5. C. CAMY-PEYRET AND J.-M. PLAVD, J. Mol. Spectrosc.59,327-337 (1976). 6. A. D. BYKOV, Yu. S. MAKUSHKIN, AND 0. N. ULENIKOV, “Isotope Substitution in Polyatomic Molecules,” Nauka, Novosibirsk, 1985. 7. N. PAPINEAU,J.-M. PLAIJD, AND C. CAMY-PEYRET, J. Mol. Spectrosc 87, 2 19-232 (198 1). 8. J.-M. PLAUD AND C. CAMY-PEYRET, J. Mol. Spectrosc. 55,278-310 (1975). 9. Y. YAMADA AND K. MACHIDA, J. Mol. Spectrosc. 100,234-244 (1983). 10. C. CAMY-PEYRET, J.-M. FLAUD, ANDR. A. TOTH, J. Mol. Spectrosc.67, 117-131 (1977). II. J.-M. FRAUDAND C. CAMY-PEYRET, J. Mol. Spectrosc.51, 142-150 (1974). 12. A.E.CHEGLOKOV,Yu. S. MAKUSHKIN, 0. V. NAUMENKO, AND 0. N. ULENIKOV, J. Mol. Spectrosc.

97, l-8 (1983).