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Hyperfine structure in the B3Π0+u state of Br2 and the influence of the perturbing 1u state
JOURNAL
OF MOLECULAR
SPECTROSCOPY
150,
52 l-526 (1991)
Hyperfine Structure in the 83110+UState of Br2 and the Influence of the Perturbing 1, State P. Lru, ’ J. KIECKH&ER,
AND E. TIEMANN
Institut fir Atom- und Molekiilphysik, Vniversittit Hannover. 3000 Hannover, F.R. Germany Using Doppler-free polarization spectroscopy, the hyperfme structure of the E-X system of 79Br2was measured for the levels B’II,+,, u’ = 16-28, and X’ZBf, u” = 1, 2. Besides the nuclear electric quadrupole coupling, the magnetic spin-rotation interaction was analyzed, which varies strongly with the vibrational energy of the electronically excited state. This behavior originates from a perturbing repulsive state R = l., the potential of which can be estimated in this way. 0 1991 Academic Press. Inc. INTRODUCTION
The knowledge about the hyperline structure (hfs) of the B3JI,,+u-X1ZB system of the bromine molecule is relatively poor. Hyperfine studies of the vibrational levels o = O-3, 4, and 7 of the ground state and u = 1 l-14, 16, and 17 of the excited state have been reported in Refs. ( l-4) and the nuclear quadrupole coupling (eqQ) and spin-rotation interaction (CsR) are analyzed. The CsR parameters of the B state are known with low accuracy only because rotational levels with J < 16 have been measured showing small line splittings or shifts caused by this interaction. Eng and LaTourette (I) and Siese et al. (4) observed an increasing spin-rotation constant with increasing V’ levels, which motivated us to start systematic investigations to higher vibrational levels. In the case of IBr (5) and I2 (6) a comparable dependence of the interaction is explained by a coupling of the B state with two states 1: and 1’: sharing the B state dissociation limit. In the present work we investigate hfs of the 79Br2molecule by high resolution laser polarization spectroscopy and we will concentrate on high rotational levels (J = 658 I ) of the vibrational levels u = 16-28 of the B311o+ustate in order to get precise data on the magnetic interaction. EXPERIMENTAL
DETAILS
In the conventional setup for the polarization spectroscopy ( 7) a tunable cw ring dye laser (CR 699 Coherent pumped by an Innova 100 Coherent Ar+ laser) with a bandwidth of about 1 MHz is applied. In the wavelength range of 605-540 nm, Rhodamine 6G and Rhodamine 110 are used with output powers between 270 and 300 mW. The pump beam is mechanically chopped with f = 1.3 kHz and circularly polarized by a X/4 plate. The crossed polarizers for the probe beam have an extinction ’ On leave from University Ninxia, 75002 1 Yinchuan, China. 521
0022-2852/91 $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form resewed.
522
LIU, KIECKH&ER, 7g 6% P (66) F-J:
-200
AND TIEMANN
(27-l) 0
2 1 -1-2
0
0
200
v
9 (MHz)
FIG. 1. Typical record of a rotational line 79Br2P( 66) (27- 1) of the B-X transition. The solid line indicates the simulated structure.
coefficient of about 10 +. The transmitted intensity is observed by a photodiode ( Siemens BPW 34) and a lock-in amplifier (PAR 128 A). The residual Doppler width due to the finite crossing angle of the two laser beams is about 5 MHz for Br2. The cell is filled with bromine at a pressure of 0.15 Torr. For an absolute frequency calibration the absorption spectrum of ‘*‘I2(8) is recorded simultaneously with the bromine fine structure, and the assignment of the vibrationrotation quantum numbers is carried out with molecular constants determined by Gerstenkom and Luc (9). To get a relative frequency calibration the hfs is recorded along with markers of a Fabry-Perot interferometer having a free spectral range of 150 MHz. HYPERF’INE ANALYSIS
The hfs of a rotational line is given by the nuclear quadrupole interaction and the spin-rotation interaction for the ground state and the excited state in the usual manner ( ZO) . The line shift by the spin-rotation interaction is given by
z&,=+{F(F+1)-.Q.Z+
l)-z(z+
l)),
(1)
where Z is the total nuclear spin (I = 0, 1, 2, 3 for Z( Br) = 3/2) and F is the total angular momentum. This interaction becomes significant for high rotational levels. The number of hfs lines depends on the isotopic combination ( 79Br2,*lBr2 or 79Br81Br). In the case of the B state the homonuclear molecule has 6 or 10 hypertine levels for an odd or even rotational quantum number J, respectively; the molecule 79Br81Brhas 16 levels. We investigated odd rotational levels J between 65 and 8 1 of the isotope 79Br2to get the simplest hfs. The analysis of the spectra uses vibration-rotation parameters from Ref. (9) and hyperfme parameters of the ground state from Ref. (4). The predissociation of the B
B STATE
Br2 HYPERFINE
STRUCTURE
523
state as observed in molecular beam experiments with fluorescence detection (4) will not influence our observation because the expected broadening is smaller than the experimental linewidth. Figure I shows a typical recording of the hfs which is fully resolved into the expected 6 lines with selection rule 0 = AJ; lines with selection rule AF = 0 and AF = -A J are too weak to be observable in our experiment. The two outermost components with F - J = 0 are almost independent of the magnetic interaction because Cs, is small compared to the linewidth, and, therefore, they show directly the nuclear quadrupole coupling. The 4 components in the center are mainly split by the magnetic interaction. Therefore, the fit of such a structure will yield hyperline parameters with very low correlation. Because the hyperhne structure of low vibrational levels with the same value of J shows stronger overlap of lines in the center than that in Fig. 1, the fit of the observations must simulate the overlapping structure to obtain the magnetic constant Csn. The result of such a simulation is included in Fig. 1. For the calculations the two hyperfme parameters eqQ, CSRof the excited state and the linewidth were varied but the hyperfine parameters of the ground state were fixed to the values determined in Ref. (4) by observations of P( 1) lines. The linewidth obtained in the present study is about 8 MHz, which is satisfactory in comparison with a composition of the reduced Doppler width of 5 MHz, the laser width of 1 MHz, and some pressure broadening. The coupling coefficients Cs, and eqQ’ show no dependence upon the rotational quantum number J (the prime indicates the excited state). Table I collects the results of the hyperfine analysis of the vibrational levels u’ = 1628. For each vibrational level the hfs of at least two rotational lines have been investigated and the weighted average of the fits is given here. The error limits are estimated from the fit quality and the linewidth, and should represent about 2 standard deviations. Within the error limit our result of eqQ’ for the 0’ = 16 is comparable to that by Siese et al. (4). But the Cs, value differs by almost three times their estimated error from our value. Siese et al. (4) measured only low rotational levels and therefore, larger errors could be expected. For v’ = 17 the parameters as shown in Table I agree with values obtained by Eng and La Tourette (I ) . DISCUSSION
The 2)’dependence of the quadrupole coupling constant eqQ’ is roughly only 0.4 MHz or 0.2% per vibrational quantum. But the coupling coefficient Cg varies strongly with the vibrational energy. This energy dependence may be explained by a secondorder coupling of the B state to electronic states with Q = 1u (6). Because the absolute value of Cs, increases strongly with increasing o’, the perturbing states must lie above and not far from the observed vibrational levels. There are two states 1: and 1’: which are degenerate in the region of the atomic asymptote ‘P, ,* + ’ P3,2 and have the same asymptote as the B state. For decreasing internuclear distances we assume a repulsive character of these St = l,, states as in the case of I2 (6), and the potential curves of the 1: and 1’: states may begin to separate from each other. But this will be neglected in the following interpretation. As shown by ViguC et al. (6) the magnetic coupling constant C’s, comes from a crossed second-order contribution of the coriolis operator -2 B* ?* 3, and the magnetic hyperfme interaction a * Ti, * f , where ?,is the electronic angular momentum. Therefore,
524
LIU, KIECKH&ER,
AND TIEMANN
TABLE I Results of the Hypefine Analysis of the 79Br2B% ,,+“-X ‘2: Transition v'
-
a)
“”
eqQ'(MHz)
CSR'
b) (MHz)
C)
rtll,
l- &
Elu(r)
(cm-')
e
16 - 2
180.9
(27)
0.0852
(34)
3.373
0.677
21 595
(137)
17 - 2
179.7
(22)
0.0965
(28)
3.413
0.689
21 259
(88)
18 - 2
180.0
(19)
0.1063
(22)
3.454
0.702
21 057
(57)
19 - 1.2
180.6
(18)
0.1208
126)
3.496
0.714
20 793
(52)
20 - 1,2
181.5
(17)
0.1341
(20)
3.540
0.726
20 622
(33)
21 - 1
183.0
(18)
0.1537
(23)
3.586
0.741
20 417
(28)
22 - 1
183.5
(18)
0.1661
(22)
3.633
0.750
20 332
(23)
23 - 1
184.6
(20)
0.1874
(23)
3.683
0.765
20 201
(19)
24 - 1
182.2
(25)
0.2098
(31)
3.735
0.777
20 095
(20)
25 - 1
183.8
(18)
0.2361
(35)
3.789
0.786
20 005
(13)
26 - 1
185.3
(19)
0.2620
(31)
3.846
0.801
19 932
(12)
27 - 1
185.2
(20)
0.2939
(44)
3.905
0.810
19 863
(14)
28 - 1
184.3
(23)
0.3295
(49)
3.968
0.824
19 811
(12)
a)
Deduced state
and
represent
from the
the
corresponding
fit
result
two standard
A eqQ
deviations
b) CSR"
of the ground
state
c)
energies
respect
All Level
with
of atomic
(10) cnl-1 taken
eqQ"
[g.
= eqQ'
of
the
ground
- eqQ".
The
errors
of the weighted
average.
is set to zero. to 2
asymptote
Br
from ref.
[91.
v=O P3,2+
2
of
the
Pl,2:
ground
Do'=
state.
19 579.691
Csn is proportional to the effective rotational constant and the a constant which may be evaluated from a separated atom model. The second-order interaction is most efficient when both states, i.e., B3110+Uand l,, are nearly degenerate, which takes place at the outermost turning point r for high v levels. Therefore, one writes CsR =
% ( 1 1- 20,
ii2
2PLr2E,,(r)
1 - Eo+u(r)
a,
where CO,and wvare the vibrational frequencies for the minimum of the B state potential and for level o, respectively. ( 1 - w,/2w,) is an estimate of the probability to stay in the right part of the potential, i.e., around the outermost turning point of the semiclassical motion with the RKR potential of the B state for level 2). The values of ( 1 - ~42~4, listed in Table I, should be close to 1 to neglect a contribution of the inner
B STATE Br2 HYPERLlNE
525
STRUCTURE
turning point. The term h */2kr* is the effective rotational constant for the outer turning point and p is the reduced mass of 79Br2. Eo+. (r) is the potential energy of the B state. E,dr) represents the averaged potential energy of both states 1L and 1’:. With the ansatz of the molecular orbitals for B, 1:) and 1’:as in Ref. ( 6)) one calculates a = [9/2 a3/* + 312 allz] where a3/*, alI2 represent the observed magnetic coupling parameters of the *P3 ,2 and *PIlt levels of bromine (II, 12). ViguC et al. (6) replaced in their formula Ed r) by ED for internuclear distances r > 4.5 A in the case of I2 (ED dissociation energy of the B state). We do not use this approximation because the internuclear distance in our investigations extends from 3.4 to 4.0 A only. And more important the observed value Cs, for u = 16 would be a factor 2.3 too small compared to the extrapolated one from the observation of Cs, u = 28 if one uses the simplified formula of Eq. (2). Therefore we derived an estimate of the potential function E,,(r) from using the observed values of C$, and Eq. (2). The results are plotted in Fig. 2 and the energy values E,,(r) are given in Table 1. Figure 2 also shows an overview of other relevant potential functions. From Saute et al. (13) it is known that the repulsive long range potential of both 1L and 1’: states in the case of Br2 and Cl2 can be represented by the multipole expansion expression: E,,(r)
= ED + 2 CJr”.
(3)
They determined the first two non-vanishing expansion coefficients C, and C, for the internuclear distance r > 5 A, resulting in a slightly attractive behavior below 5 A for the two states in question. From our analysis this behavior must change over to repulsive behavior by electron exchange contributions for r g 3.5 A.
E (cm-‘* IO41
2.4 2 p3/2+
2.0 -
pi/2
ti= 2, 1, 6 1.6-
i-
e I’
1
/--
2P3,2f2P
.I’
3/2
1.2 -
I
2.0
4.0
6.0
> r
(iI
FIG. 2. Potential energy curves of Br* . The solid line of the 1u state indicates the potential energy given in Table I; the X and B state are taken from Ref. ( 9).
526
LIU, IUECKHWFER, AND
TIEMANN
To get more information about the potential function of the 1, state in the region r > 4.0 A, hyperfine investigations of 2)’> 28 would be desirable. The 1, state gets closer to the B state, and the perturbation is expected to increase. It is an open question if there are bound levels within the potentials of the 1: and the 1’: states which would hinder the simple application of Eq. (2) for the analysis of C&. For the region r < 3.3 A the perturbation decreases drastically and the spin-rotation constant is almost not detectable in the hyperfme splitting. The main drawbacks of our analysis are certainly the neglect of the separation of the two states 1Land 1 ‘:, the use of a separated atom model for such small internuclear distances, and the approximation of the effective rotational constant with the help of the probability at the right turning point, Other states with Q = 1Ufrom the asymptote to C’s, of B3110+U =p3,2 + ‘P3,= may be also of importance, but their contributions cannot be estimated from known data. RECEIVED: July 23,
1991. REFERENCES
1. R. S.ENG AND J. T. LA TOURETTE,J. Mol. Spectrosc. 52,269-216( 1974). 2. N. BETTIN,H. KN~CKEL,AND E. TIEMANN,Chem. Phys. Lett. 80,386-388 ( 1981). 3. J. B. KOFFEND,R. BACIS,S. CHURASSY,M. L. GAILLARD,J. P. PIQUE,AND F. HARTMANN,Laser Chem. 1, 185-193 (1983). 4. M. SIESE,E. TIEMANN,AND U. WULF, Chem. Phys. Lett. 117,208-213 (1985). 5. M. SIESEAND E.TIEMANN,Z. Phys. D 7, 147-152 (1987). 6. J. VIGUB,M. BROYER,AND J. C. LEHMANN,Phys. Rev. Lett. 42,883-887 (1979). 7. W. DEMTR~DER,“Laser Spectroscopy,”Springer-Verlag,Berlin/Heidelberg/New York, 1981. 8. S. GERSTENKORN ET P. Luc, “Atlas du Spectred’Absorption de la Molecule d’Iode,” Parties1 et 2, LaboratoireAim&Cotton CNRS, Orsay, France, 1977. 9. S. GERSTENKORN AND P. Luc, J. Phys. Les Ulis., Fr. 50, 1417-1432 (1989). 10. M. BROYER,J. VIGUB,AND J. C. LEHMANN,J. Phys. Les Vlis.. Fr. 39,591-609 ( 1978). Il. G. H. FULLER,J. Phys. Chem. Rej Data 5,835-1092 (1976). 12. P. B. DAVIES,B. A. THRUSH,A. J. STONE,AND F. D. WAYNE, Chem. Phys. Lett. 17, 19-21 (1972). 13. M. SAUTE,B. BUSSERY,AND M. AUBERT-FR~CON, Mol. Phys. 51, 1459-1474 ( 1984).
OF MOLECULAR
SPECTROSCOPY
150,
52 l-526 (1991)
Hyperfine Structure in the 83110+UState of Br2 and the Influence of the Perturbing 1, State P. Lru, ’ J. KIECKH&ER,
AND E. TIEMANN
Institut fir Atom- und Molekiilphysik, Vniversittit Hannover. 3000 Hannover, F.R. Germany Using Doppler-free polarization spectroscopy, the hyperfme structure of the E-X system of 79Br2was measured for the levels B’II,+,, u’ = 16-28, and X’ZBf, u” = 1, 2. Besides the nuclear electric quadrupole coupling, the magnetic spin-rotation interaction was analyzed, which varies strongly with the vibrational energy of the electronically excited state. This behavior originates from a perturbing repulsive state R = l., the potential of which can be estimated in this way. 0 1991 Academic Press. Inc. INTRODUCTION
The knowledge about the hyperline structure (hfs) of the B3JI,,+u-X1ZB system of the bromine molecule is relatively poor. Hyperfine studies of the vibrational levels o = O-3, 4, and 7 of the ground state and u = 1 l-14, 16, and 17 of the excited state have been reported in Refs. ( l-4) and the nuclear quadrupole coupling (eqQ) and spin-rotation interaction (CsR) are analyzed. The CsR parameters of the B state are known with low accuracy only because rotational levels with J < 16 have been measured showing small line splittings or shifts caused by this interaction. Eng and LaTourette (I) and Siese et al. (4) observed an increasing spin-rotation constant with increasing V’ levels, which motivated us to start systematic investigations to higher vibrational levels. In the case of IBr (5) and I2 (6) a comparable dependence of the interaction is explained by a coupling of the B state with two states 1: and 1’: sharing the B state dissociation limit. In the present work we investigate hfs of the 79Br2molecule by high resolution laser polarization spectroscopy and we will concentrate on high rotational levels (J = 658 I ) of the vibrational levels u = 16-28 of the B311o+ustate in order to get precise data on the magnetic interaction. EXPERIMENTAL
DETAILS
In the conventional setup for the polarization spectroscopy ( 7) a tunable cw ring dye laser (CR 699 Coherent pumped by an Innova 100 Coherent Ar+ laser) with a bandwidth of about 1 MHz is applied. In the wavelength range of 605-540 nm, Rhodamine 6G and Rhodamine 110 are used with output powers between 270 and 300 mW. The pump beam is mechanically chopped with f = 1.3 kHz and circularly polarized by a X/4 plate. The crossed polarizers for the probe beam have an extinction ’ On leave from University Ninxia, 75002 1 Yinchuan, China. 521
0022-2852/91 $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form resewed.
522
LIU, KIECKH&ER, 7g 6% P (66) F-J:
-200
AND TIEMANN
(27-l) 0
2 1 -1-2
0
0
200
v
9 (MHz)
FIG. 1. Typical record of a rotational line 79Br2P( 66) (27- 1) of the B-X transition. The solid line indicates the simulated structure.
coefficient of about 10 +. The transmitted intensity is observed by a photodiode ( Siemens BPW 34) and a lock-in amplifier (PAR 128 A). The residual Doppler width due to the finite crossing angle of the two laser beams is about 5 MHz for Br2. The cell is filled with bromine at a pressure of 0.15 Torr. For an absolute frequency calibration the absorption spectrum of ‘*‘I2(8) is recorded simultaneously with the bromine fine structure, and the assignment of the vibrationrotation quantum numbers is carried out with molecular constants determined by Gerstenkom and Luc (9). To get a relative frequency calibration the hfs is recorded along with markers of a Fabry-Perot interferometer having a free spectral range of 150 MHz. HYPERF’INE ANALYSIS
The hfs of a rotational line is given by the nuclear quadrupole interaction and the spin-rotation interaction for the ground state and the excited state in the usual manner ( ZO) . The line shift by the spin-rotation interaction is given by
z&,=+{F(F+1)-.Q.Z+
l)-z(z+
l)),
(1)
where Z is the total nuclear spin (I = 0, 1, 2, 3 for Z( Br) = 3/2) and F is the total angular momentum. This interaction becomes significant for high rotational levels. The number of hfs lines depends on the isotopic combination ( 79Br2,*lBr2 or 79Br81Br). In the case of the B state the homonuclear molecule has 6 or 10 hypertine levels for an odd or even rotational quantum number J, respectively; the molecule 79Br81Brhas 16 levels. We investigated odd rotational levels J between 65 and 8 1 of the isotope 79Br2to get the simplest hfs. The analysis of the spectra uses vibration-rotation parameters from Ref. (9) and hyperfme parameters of the ground state from Ref. (4). The predissociation of the B
B STATE
Br2 HYPERFINE
STRUCTURE
523
state as observed in molecular beam experiments with fluorescence detection (4) will not influence our observation because the expected broadening is smaller than the experimental linewidth. Figure I shows a typical recording of the hfs which is fully resolved into the expected 6 lines with selection rule 0 = AJ; lines with selection rule AF = 0 and AF = -A J are too weak to be observable in our experiment. The two outermost components with F - J = 0 are almost independent of the magnetic interaction because Cs, is small compared to the linewidth, and, therefore, they show directly the nuclear quadrupole coupling. The 4 components in the center are mainly split by the magnetic interaction. Therefore, the fit of such a structure will yield hyperline parameters with very low correlation. Because the hyperhne structure of low vibrational levels with the same value of J shows stronger overlap of lines in the center than that in Fig. 1, the fit of the observations must simulate the overlapping structure to obtain the magnetic constant Csn. The result of such a simulation is included in Fig. 1. For the calculations the two hyperfme parameters eqQ, CSRof the excited state and the linewidth were varied but the hyperfine parameters of the ground state were fixed to the values determined in Ref. (4) by observations of P( 1) lines. The linewidth obtained in the present study is about 8 MHz, which is satisfactory in comparison with a composition of the reduced Doppler width of 5 MHz, the laser width of 1 MHz, and some pressure broadening. The coupling coefficients Cs, and eqQ’ show no dependence upon the rotational quantum number J (the prime indicates the excited state). Table I collects the results of the hyperfine analysis of the vibrational levels u’ = 1628. For each vibrational level the hfs of at least two rotational lines have been investigated and the weighted average of the fits is given here. The error limits are estimated from the fit quality and the linewidth, and should represent about 2 standard deviations. Within the error limit our result of eqQ’ for the 0’ = 16 is comparable to that by Siese et al. (4). But the Cs, value differs by almost three times their estimated error from our value. Siese et al. (4) measured only low rotational levels and therefore, larger errors could be expected. For v’ = 17 the parameters as shown in Table I agree with values obtained by Eng and La Tourette (I ) . DISCUSSION
The 2)’dependence of the quadrupole coupling constant eqQ’ is roughly only 0.4 MHz or 0.2% per vibrational quantum. But the coupling coefficient Cg varies strongly with the vibrational energy. This energy dependence may be explained by a secondorder coupling of the B state to electronic states with Q = 1u (6). Because the absolute value of Cs, increases strongly with increasing o’, the perturbing states must lie above and not far from the observed vibrational levels. There are two states 1: and 1’: which are degenerate in the region of the atomic asymptote ‘P, ,* + ’ P3,2 and have the same asymptote as the B state. For decreasing internuclear distances we assume a repulsive character of these St = l,, states as in the case of I2 (6), and the potential curves of the 1: and 1’: states may begin to separate from each other. But this will be neglected in the following interpretation. As shown by ViguC et al. (6) the magnetic coupling constant C’s, comes from a crossed second-order contribution of the coriolis operator -2 B* ?* 3, and the magnetic hyperfme interaction a * Ti, * f , where ?,is the electronic angular momentum. Therefore,
524
LIU, KIECKH&ER,
AND TIEMANN
TABLE I Results of the Hypefine Analysis of the 79Br2B% ,,+“-X ‘2: Transition v'
-
a)
“”
eqQ'(MHz)
CSR'
b) (MHz)
C)
rtll,
l- &
Elu(r)
(cm-')
e
16 - 2
180.9
(27)
0.0852
(34)
3.373
0.677
21 595
(137)
17 - 2
179.7
(22)
0.0965
(28)
3.413
0.689
21 259
(88)
18 - 2
180.0
(19)
0.1063
(22)
3.454
0.702
21 057
(57)
19 - 1.2
180.6
(18)
0.1208
126)
3.496
0.714
20 793
(52)
20 - 1,2
181.5
(17)
0.1341
(20)
3.540
0.726
20 622
(33)
21 - 1
183.0
(18)
0.1537
(23)
3.586
0.741
20 417
(28)
22 - 1
183.5
(18)
0.1661
(22)
3.633
0.750
20 332
(23)
23 - 1
184.6
(20)
0.1874
(23)
3.683
0.765
20 201
(19)
24 - 1
182.2
(25)
0.2098
(31)
3.735
0.777
20 095
(20)
25 - 1
183.8
(18)
0.2361
(35)
3.789
0.786
20 005
(13)
26 - 1
185.3
(19)
0.2620
(31)
3.846
0.801
19 932
(12)
27 - 1
185.2
(20)
0.2939
(44)
3.905
0.810
19 863
(14)
28 - 1
184.3
(23)
0.3295
(49)
3.968
0.824
19 811
(12)
a)
Deduced state
and
represent
from the
the
corresponding
fit
result
two standard
A eqQ
deviations
b) CSR"
of the ground
state
c)
energies
respect
All Level
with
of atomic
(10) cnl-1 taken
eqQ"
[g.
= eqQ'
of
the
ground
- eqQ".
The
errors
of the weighted
average.
is set to zero. to 2
asymptote
Br
from ref.
[91.
v=O P3,2+
2
of
the
Pl,2:
ground
Do'=
state.
19 579.691
Csn is proportional to the effective rotational constant and the a constant which may be evaluated from a separated atom model. The second-order interaction is most efficient when both states, i.e., B3110+Uand l,, are nearly degenerate, which takes place at the outermost turning point r for high v levels. Therefore, one writes CsR =
% ( 1 1- 20,
ii2
2PLr2E,,(r)
1 - Eo+u(r)
a,
where CO,and wvare the vibrational frequencies for the minimum of the B state potential and for level o, respectively. ( 1 - w,/2w,) is an estimate of the probability to stay in the right part of the potential, i.e., around the outermost turning point of the semiclassical motion with the RKR potential of the B state for level 2). The values of ( 1 - ~42~4, listed in Table I, should be close to 1 to neglect a contribution of the inner
B STATE Br2 HYPERLlNE
525
STRUCTURE
turning point. The term h */2kr* is the effective rotational constant for the outer turning point and p is the reduced mass of 79Br2. Eo+. (r) is the potential energy of the B state. E,dr) represents the averaged potential energy of both states 1L and 1’:. With the ansatz of the molecular orbitals for B, 1:) and 1’:as in Ref. ( 6)) one calculates a = [9/2 a3/* + 312 allz] where a3/*, alI2 represent the observed magnetic coupling parameters of the *P3 ,2 and *PIlt levels of bromine (II, 12). ViguC et al. (6) replaced in their formula Ed r) by ED for internuclear distances r > 4.5 A in the case of I2 (ED dissociation energy of the B state). We do not use this approximation because the internuclear distance in our investigations extends from 3.4 to 4.0 A only. And more important the observed value Cs, for u = 16 would be a factor 2.3 too small compared to the extrapolated one from the observation of Cs, u = 28 if one uses the simplified formula of Eq. (2). Therefore we derived an estimate of the potential function E,,(r) from using the observed values of C$, and Eq. (2). The results are plotted in Fig. 2 and the energy values E,,(r) are given in Table 1. Figure 2 also shows an overview of other relevant potential functions. From Saute et al. (13) it is known that the repulsive long range potential of both 1L and 1’: states in the case of Br2 and Cl2 can be represented by the multipole expansion expression: E,,(r)
= ED + 2 CJr”.
(3)
They determined the first two non-vanishing expansion coefficients C, and C, for the internuclear distance r > 5 A, resulting in a slightly attractive behavior below 5 A for the two states in question. From our analysis this behavior must change over to repulsive behavior by electron exchange contributions for r g 3.5 A.
E (cm-‘* IO41
2.4 2 p3/2+
2.0 -
pi/2
ti= 2, 1, 6 1.6-
i-
e I’
1
/--
2P3,2f2P
.I’
3/2
1.2 -
I
2.0
4.0
6.0
> r
(iI
FIG. 2. Potential energy curves of Br* . The solid line of the 1u state indicates the potential energy given in Table I; the X and B state are taken from Ref. ( 9).
526
LIU, IUECKHWFER, AND
TIEMANN
To get more information about the potential function of the 1, state in the region r > 4.0 A, hyperfine investigations of 2)’> 28 would be desirable. The 1, state gets closer to the B state, and the perturbation is expected to increase. It is an open question if there are bound levels within the potentials of the 1: and the 1’: states which would hinder the simple application of Eq. (2) for the analysis of C&. For the region r < 3.3 A the perturbation decreases drastically and the spin-rotation constant is almost not detectable in the hyperfme splitting. The main drawbacks of our analysis are certainly the neglect of the separation of the two states 1Land 1 ‘:, the use of a separated atom model for such small internuclear distances, and the approximation of the effective rotational constant with the help of the probability at the right turning point, Other states with Q = 1Ufrom the asymptote to C’s, of B3110+U =p3,2 + ‘P3,= may be also of importance, but their contributions cannot be estimated from known data. RECEIVED: July 23,
1991. REFERENCES
1. R. S.ENG AND J. T. LA TOURETTE,J. Mol. Spectrosc. 52,269-216( 1974). 2. N. BETTIN,H. KN~CKEL,AND E. TIEMANN,Chem. Phys. Lett. 80,386-388 ( 1981). 3. J. B. KOFFEND,R. BACIS,S. CHURASSY,M. L. GAILLARD,J. P. PIQUE,AND F. HARTMANN,Laser Chem. 1, 185-193 (1983). 4. M. SIESE,E. TIEMANN,AND U. WULF, Chem. Phys. Lett. 117,208-213 (1985). 5. M. SIESEAND E.TIEMANN,Z. Phys. D 7, 147-152 (1987). 6. J. VIGUB,M. BROYER,AND J. C. LEHMANN,Phys. Rev. Lett. 42,883-887 (1979). 7. W. DEMTR~DER,“Laser Spectroscopy,”Springer-Verlag,Berlin/Heidelberg/New York, 1981. 8. S. GERSTENKORN ET P. Luc, “Atlas du Spectred’Absorption de la Molecule d’Iode,” Parties1 et 2, LaboratoireAim&Cotton CNRS, Orsay, France, 1977. 9. S. GERSTENKORN AND P. Luc, J. Phys. Les Ulis., Fr. 50, 1417-1432 (1989). 10. M. BROYER,J. VIGUB,AND J. C. LEHMANN,J. Phys. Les Vlis.. Fr. 39,591-609 ( 1978). Il. G. H. FULLER,J. Phys. Chem. Rej Data 5,835-1092 (1976). 12. P. B. DAVIES,B. A. THRUSH,A. J. STONE,AND F. D. WAYNE, Chem. Phys. Lett. 17, 19-21 (1972). 13. M. SAUTE,B. BUSSERY,AND M. AUBERT-FR~CON, Mol. Phys. 51, 1459-1474 ( 1984).