- Email: [email protected]
Hyperfine structure in the B-X transition of the iodine molecule near the head of the 12-0 band, by laser spectroscopy of a pure iodine supersonic jet
Volume 30, number I
OPTICS COMMUNICATIONS
July 1979
HYPERFINE STRUCTURE IN THE B - X TRANSITION OF THE IODINE MOLECULE NEAR THE HEAD OF THE 12-0 BAND, BY LASER SPECTROSCOPY OF A PURE IODINE SUPERSONIC JET S. CHURASSY, G. GRENET *, M.L. GAILLARD and R. BACIS Laboratoire de Spectrorn~trie Ionique et Moldculaire (associd au C.N.R.S.}, Universitd Claude Bernard, Lyon 1, France Received 26 March 1979
Crossing a pure iodine supersonic jet with the output beam of a tunable monomode dye laser, we carried out a systematic high resolution survey of band-heads in the B-X transition of iodine. Working out the specific example of the 12-0 band head, we show that despite thek apparent complexity, HFS patterns observed in transitions between low J levels can be interpreted rather easily when proper account is taken of the theory of second order effects. The high density of the beam allows the observation under high resolution of faint lines, such as AF = 0 and even AF = - A J transitions, which permits the determination of eQq' and eQq" independently.
1. Introduction The hyperfine structure of the molecular iodine B - X system has been intensively investigated during the past few years, either by laser saturated absorption [ 1] or by molecular beam laser induced fluorescence spectroscopy [2]. Initially limited to accidental coincidence with gas laser lines, this type of work,is currently extended to the spectral range of c.w. tunable dye lasers using mainly Rhodamine 6 G [3]. It must be pointed out however that in the experiments carried out so far, whether in a cell or in an effusive molecular beam, the rotational temperature was sufficiently high to prevent the observation under good experimental conditions of transitions starting from low J " levels. On the contrary, the degree of rotational cooling which can be achieved even on a relatively simple supersonic beam machine strongly favors the laser excitation of transitions near the band heads. An additional advantage of the supersonic beam configuration over ordinary effusive beam source is the large increase in beam density which simplifies the data * Permanent address: Institut de Physique Nucl6aire, Universit~ Claude Bernard, Lyon I (France).
acquisition procedure on laser induced fluorescence signal. In our experiment, we obtained rotational temperatures as low as 90 K thus being able to carry out the analysis of the band heads with a signal to noise ratio of 100 for the strongest hyperfine lines, with 0.04 second of sampling time. The theoretical interpretation includes hyperfine interactions to second order, and we will report the typical results obtained in the case of the 12-0 band.
2. Apparatus The supersonic iodine beam is generated from a heated stainless steel oven. The nozzle is designed on the principles which were previously successful for the production of alkali dimers [4,5]. It consists o f a stainless steel convergent cone (60 °) ended by a circular aperture of 0.5 mm diameter. The nozzle is independently heated and kept at a temperature substantially higher than the oven temperature in order to prevent clogging. Erosion for repeated runs o f several hours seems to be unimportant, even when the iodine generating pressure reaches several hundred torrs in the oven. 41
Volume 30, number 1
OPTICS COMMUNICATIONS
The expansion chamber and the interaction chamber are separately pumped by 280 l/s diffusion pumps and the jet is surrounded by copper shields cooled at liquid nitrogen temperature. Due to the efficiency of cryogenic pumping for pure iodine, the use of a skimmer is not essential, at least for the type of rotational cooling which was deemed necessary in our experiment. In the second chamber, a set of liquid nitrogen cooled slits collimates the beam with a ratio of 130 thus narrowing the beam Doppler width in crossed beam geometry below the laser spectral width. The laser used in the experiment is a modified type 580 Spectra-Physics dye cell laser, working with Rhodamine 6 G. The free running spectral line width of 40 MHz is reduced down to 5 MHz by active servolooping on an external 25 cm confocal Fabry-Perot. Both the laser and the reference F.P. are enclosed in a vacuum tank and the wavelength is tuned by pressure scanning of the entire instrument. With this setup, continuous tuning range of 30 GHz without mode jump is routinely achieved. Coarse laser wavelength measurement is carried out with a 1.65 m spectrograph with 0.3 cm -1 resolution. The beam fluorescence in the interaction region is
•
,
h.
July 1979
detected by a combination of color filter and photomultiplier working in the photon counting mode. The signal from the beam is recorded simultaneously with the reference peaks from a 75 cm confocal FabryPerot and with the fluorescence light from a room temperature iodine cell.
3. Experiment and results 3.1. Molecular beam Each 30 GHz scan in the Rhodamine 6 G range usually exhibits several rotational lines (fig. 1) which can be identified by reference to the "Atlas du spectre de la mol6cule d'iode" [6] together with the accurate molecular constants derived by Luc [7]. The recorded fluorescence from the room temperature iodine cell provides relative intensities for molecules at thermal equilibrium at 300 K while comparison with the intensities of the same transitions in the beam fluorescence gives a direct measurement of beam rotational and vibrational temperature, assuming Boltzmann distribution [5]. Three experiments are
lu,lJil IllLl, till LllIll L
J
~: ~I 0
I
I
I
I
I 5
I
~I
I
1
GHz I 10
Fig. 1. Part of the recording of 14-0 band, in the supersonic beam (upper trace) and in a cell at room temperature (lower trace). Rotational cooling in the beam is illustrated by strong reduction of signal for high J transitions together with enhancement for f'trst J transitions, such as P(1) which is very weak in the cell. This recording corresponds to the third experiment of table 1.
42
Volume 30, number 1
OPTICS COMMUNICATIONS
carried out in the 14-0 band head region. Five lines, namely R(5) (14-0), R(135) (16-0), P(93)(15-0), R(74) (19-2) and R(88) (17-1) were used as "thermometers". The results summarized in table 1 clearly display the cooling achieved with increasing generating temperature. Supersonic beam properties are generally described in term of a Mach number M which is related to the thermodynamic beam temperature T and generating temperature T O by the relation [8] To/T = 1 + ~1 (y - 1)M 2 (1) Since T is related to the velocity distribution of the particles in the beam, it is not directly measured. However, under the assumption of complete thermal equilibrium between the rotational and translational degrees of freedom, the relation (1) with T = T R gives M with a good approximation. The resulting Mach number values given in table 1 were calculated with the usual assumption 3' = 7/5 which is rigorously valid only for diatomic molecules with inactive vibrational energy transfer [9]. In the case of iodine significant vibrational cooling occurs, and thus the M values obtained should be considered only as lower limits. Once the Mach number is known, calculations based on the ideal isentropic flow theory lead to the beam density. In the case of Mach 4.3, we obtain a theoretical flux of 1020 mol/sec/ster which probably overestimates the experimental value and corresponds to a gain of 104 over a room temperature effusive source of same aperture. Nevertheless, the experimentally achieved beam density is sufficient to'provide of the order of 108 photons/sec/ster for the strongest hyperfine lines in the detection window 600 to 660 nm, with 20 mW of incident laser power.
Table 1 Rotational and vibrational temperatures in the supersonic iodine beam for three different oven (generating) temperature, and associated Mach numbers calculated from relation (1) with T = TR and ~ = 7/5 Generating temperature To (K)
Rotational temperature TR (K)
Vibrational temperature Tv(K)
Estimated Mach number
330 390 430
160 140 90
200 180 160
2.3 3 4.3
July 1979
3.2 Hyperfine structure As a typical example, we carried out a complete analysis of the 12-0 band from R(0) to R(6). The fluorescence line on the room temperature cell recording in fig. 2 is in fact the superposition of the first five rotational lines of the 12-0 transition. The corresponding hyperfine structure exhibits over 70 well resolved components. The HFS pattern of the transitions arising from such low J levels is noticeably different from the more familiar pattern of 15 or 21 main lines which correspond to the selection rule AF = AJ between high J levels. In our case transitions with AF = 0 and even AF --- - A J have sizeable intensities. As a consequence, we decided to use the labels p, q, r for the hyperfine components by analogy with the convention followed in rotational transitions. In fig. 2, the label is followed by the F " value and preceded by the J " value (standing for R (J")) thus providing a compact characterization of each HFS line. The identification and theoretical interpretation of the spectrum is based on a parametric analysis up to second order in perturbation [10]. The model bamiltonian for the hyperfine structure in iodine consists of four terms: H~-HNE Q +HIR +HTs S + H s s S
(2)
which represent respectively the quadrupolar, spinrotation, tensorial spin-spin and scalar spin-spin interaction. For a full second order treatment, the hamiltonian is developed on the subspace spanned by the state vector arising from the J and J -+ 2 levels. This model leads to a description of the hyperfine interaction in terms of four parameters, classically referred as eQq, C1, d and 6. The first step of the numerical treatment is the determination of hierarchy of the perturbations in formula (2). Whereas the situation is already well understood for high J levels, it was not clear a priori that the ordering of decreasing importance suggested by formula (2) would still prevail near the band heads. It must be pointed out that this part of the analysis relies only on the relative magnitude of the HFS splittings and thus depends only on the relative precision of the measured frequency intervals. The experimental limit is set by: (i) the accuracy of the line centre determination which is estimated to be better than a 1/5 of the line width. 43
Volume
30, number
1
OPTICS COMMUNICATIONS
~T t
pb# o
II
gb~, ~,do
J S.
- ;
I'°
gb~
£ •
0
¢b
='==~"~,O :
9 b lv
gJO
o~3 =
L .qv
¢.~,
_4 . - -
6._ /£bl, BO~
j~ ~Jl
E= O
~
8bE
,
9bl
:
¢J¢ 9J¢
;
~bz
9Jl gJE
Eb Z
gJg
gbE
gJ¢ PJl 91~ ~ J¢
O
o~
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'gJ~ I ~
9bl
~
gdl gbl gdl
I~a~
!~,b~ I ~bE ~,d~, ' ~a g
44
~.~ E
July 1979
(ii) the relative accuracy of frequency scale set by the peaks of the reference F.P. Despite good thermal insulation and protection against atmospheric perturbations, it was experimentally observed that the stability of the superinvar mount of F.P. was not sufficient to prevent calibration peak shifts during the measurements, and corresponding variations of the apparent free spectral range were measured to be of the order of 1% over one hour. (iii) further indetermination could arise from nonlinearities in the pressure scanning of the laser wavelength. The resulting uncertainty is estimated to be well below 1 MHz. The overall uncertainty on relative frequency intervals is thus dominated by the error on line centre determination, with an upper bound of 1 MHz. Four optimization procedures were carried out using the numerical simplex method. Results of table 2 show that the best fit to the experimental data is obtained with eQq' and C; for excited state, and eQq"in ground state, C[' being known to be zero for the first v" values. This fit leads to an r.m.s, deviation o of 0.54 MHz for line positions of 130 components. Two standard deviations are typically 1 MHz in eQq' and eQq",and 15 kHz in C~, except for R(0) in which reduced information gives 3 MHz and 50 kHz respectively. Inspection of the fits with successive J" values clearly shows that for R(0) and R(1) the HFS pattern is correctly described within our experimental accuracy by pure quadrupolar interaction while for J" ~> 2 the spin-rotation contribution becomes significant due to the (l.J)' multiplicative factor. It has to be pointed out that eQq' and eQq"are simultaneously and independently determined with a good accuracy. This is an interesting feature of the first rotational transitions for which in contrast of the case of high J value the selection rule AF = AJ no longer holds rigorously. Appearance of AF = 0 and AF = - A J transitions reduces the correlation between the parameters and leads to the determination of each of them rather than their difference, despite a moderate resolution and precision. The absolute determination of the three numerically significant parameters relies on accuracy of the absolute frequency scale of the measurement. The apparent FSR of the reference cavity was measured on the iodine cell fluorescence recordings by peak counting
Volume 30, number 1
OPTICS COMMUNICATIONS
July 1979
Table 2 Optimization for eQq, C1, d and 6 parameters in 12-0 band. All values are given in MHz. o is r.m.s, deviation between measured and calculated line positions 12-0 band
R0
R1
R2
R3
R4
R5
R6
Number of fitted lines
7
15
15
19
20
30
24
-2448 -508 0.56
-2449 -508 0.35
-2450 -512 0.98
-2453 -516 1.07
-2459 -519 1.14
-2453 -520 1.66
-2448 -509 0.97
1.08
-2458 -508 0.062 0.50
-2449 -508 0.032 0.33
-2451 -511 0.063 0.44
-2450 -511 0.049 0.41
-2455 -512 0.051 0.44
-2448 -510 0.045 0.65
-2448 -509 0.039 0.77
0.54
-2449 0.003 -508 0.049 0.35
-2445 0.43 -508 0.23 0.62
-2448 0.19 -510 0.27 1.08
-2462 0.18 -521 0.33 0.69
-2451 0.17 -515 0.05 1.65
-2449 0.03 -505 0.20 0.57
0.91
-2449 -0.040 -509 0.003 0.34
-2449 -0.38 -509 -0.26 0.44
-2452 0.12 -514 0.22 0.93
-2458 -0.002 -516 0.19 0.82
-2452 0.02 -516 0.15 1.58
-2449 0.09 -507 -0.11 0.80
0.91
eaq
I eQq" I eQq' o
eQq + C
eQq" eQq' Ci o
eQq" d"
eQq + d
eQq' d' o
eQq" eQq + a
6"
eQq' 6' o
over wide scans between rotational lines measuoed in ref. [6]. Due to thermal drifts already mentioned, the reproducibility o f the measurements was no better than 1%. This leads to a final accuracy o f 1% on the quadrupolar parameters, while the uncertainty on the spinrotation parameter, whenever defined, is still mainly due to the variance calculated by fit procedure. With such error bars, the slight variations shown in table 2 between different J levels are not o f physical significance.
Overall RMS
molecular spectroscopy. High density of molecules together with rovibrational cooling which can be controlled to any desired value by the generating temperature should permit the analysis of very weak transitions. Moreover the absence of relaxation in the ground state in the collision-free beam medium opens the possibility of ground state preparation in any v", J " and even F " levels. This may become necessary for the unravelling o f the complex patterns expected near the B state dissociation limit, or the examination of the intersection o f the dissociative 1 flu state with u' = 6, 7 B levels.
4. Conclusion The previous discussion clearly shows that the ex. perimental accuracy would greatly benefit from an improvement of the frequency calibration. This can be done by active servo looping o f the F.P. cavity on a reference frequency such as a stabilised He-Ne laser and accurate determination o f its F.S.R. via a lambdameter. Such an experiment is currently in progress with a narrower laser line width (2 MHz). In its present stage, this work illustrates the wide applicability of supersonic beam for high resolution
Acknowledgement We are grateful to Prof. M. Dufay and J. d'Incan for their continuous support during the experiment, and to M. Broyer, J. Vigu6 and F. Hartmann for numerous fruitful discussions.
45
Volume 30, number 1
OPTICS COMMUNICATIONS
References [1] G.R. Hanes and C.E. Dahlstrom, Appl. Phys. Lett. 14 (1969) 382; T.W. Hffnsch, M.D. Levenson and A.L. Schawlow, Phys. Rev. Lett. 26 (1971) 946; M.S. Sorem, M.D. Levenson and A.L. Schawlow, Phys. Lett. 37A (1971) 33; P. Cerez, A. Brillet, S. Hajdukovic and N. Man, Optics Comm. 21 (1977) 332; A. Morinaga and K. Tanaka, Appl. Phys. Lett. 32 (1978) 114; G. Camy, Thesis, Paris (1979). [2] S. Ezekiel and R. Weiss, Phys. Rev. Lett. 20 (1968) 91; D.J. Ruben, S.G. Kukolich, L.A. Hackel, D.G. Youmans and S. Ezekiel, Chem. Phys. Lett. 22 (1973) 326.
46
July 1979
[3] H. Brand, H.H. Schulz and A. Steudel, Phys. Lett. 63A (1977) 235; B. Couillaud and A. Ducasse, Optics Comm. 21 (1977) 199; J. Vigu6, Thesis, Paris (1978). [4] R.J. Gordon, Y.T. Lee and D.R. Herschbach, J. Chem. Phys. 54 (1971) 2393. [5] M.P. Sinha, A. Schultz and R.N. Zare, J. Chem. Phys. 58 (1973) 549. [6] S. Gerstenkorn and P. Luc, Atlas du Spectre d'Absorption de la mol6cule d'iode, Editions du C.N.R.S. (1978). [7] P. Luc, J. Mol. Spect., to be published. [8] T.C. English and J.C. Zorn, Methods of experimental physics, Vol. 3B, Chapter 6, ed. L. Marton (Ac. Press, N.Y., 1974). [9] R. Campargue, Thesis, Paris (1970). [10] M. Broyer, Thesis, Paris (1977).
OPTICS COMMUNICATIONS
July 1979
HYPERFINE STRUCTURE IN THE B - X TRANSITION OF THE IODINE MOLECULE NEAR THE HEAD OF THE 12-0 BAND, BY LASER SPECTROSCOPY OF A PURE IODINE SUPERSONIC JET S. CHURASSY, G. GRENET *, M.L. GAILLARD and R. BACIS Laboratoire de Spectrorn~trie Ionique et Moldculaire (associd au C.N.R.S.}, Universitd Claude Bernard, Lyon 1, France Received 26 March 1979
Crossing a pure iodine supersonic jet with the output beam of a tunable monomode dye laser, we carried out a systematic high resolution survey of band-heads in the B-X transition of iodine. Working out the specific example of the 12-0 band head, we show that despite thek apparent complexity, HFS patterns observed in transitions between low J levels can be interpreted rather easily when proper account is taken of the theory of second order effects. The high density of the beam allows the observation under high resolution of faint lines, such as AF = 0 and even AF = - A J transitions, which permits the determination of eQq' and eQq" independently.
1. Introduction The hyperfine structure of the molecular iodine B - X system has been intensively investigated during the past few years, either by laser saturated absorption [ 1] or by molecular beam laser induced fluorescence spectroscopy [2]. Initially limited to accidental coincidence with gas laser lines, this type of work,is currently extended to the spectral range of c.w. tunable dye lasers using mainly Rhodamine 6 G [3]. It must be pointed out however that in the experiments carried out so far, whether in a cell or in an effusive molecular beam, the rotational temperature was sufficiently high to prevent the observation under good experimental conditions of transitions starting from low J " levels. On the contrary, the degree of rotational cooling which can be achieved even on a relatively simple supersonic beam machine strongly favors the laser excitation of transitions near the band heads. An additional advantage of the supersonic beam configuration over ordinary effusive beam source is the large increase in beam density which simplifies the data * Permanent address: Institut de Physique Nucl6aire, Universit~ Claude Bernard, Lyon I (France).
acquisition procedure on laser induced fluorescence signal. In our experiment, we obtained rotational temperatures as low as 90 K thus being able to carry out the analysis of the band heads with a signal to noise ratio of 100 for the strongest hyperfine lines, with 0.04 second of sampling time. The theoretical interpretation includes hyperfine interactions to second order, and we will report the typical results obtained in the case of the 12-0 band.
2. Apparatus The supersonic iodine beam is generated from a heated stainless steel oven. The nozzle is designed on the principles which were previously successful for the production of alkali dimers [4,5]. It consists o f a stainless steel convergent cone (60 °) ended by a circular aperture of 0.5 mm diameter. The nozzle is independently heated and kept at a temperature substantially higher than the oven temperature in order to prevent clogging. Erosion for repeated runs o f several hours seems to be unimportant, even when the iodine generating pressure reaches several hundred torrs in the oven. 41
Volume 30, number 1
OPTICS COMMUNICATIONS
The expansion chamber and the interaction chamber are separately pumped by 280 l/s diffusion pumps and the jet is surrounded by copper shields cooled at liquid nitrogen temperature. Due to the efficiency of cryogenic pumping for pure iodine, the use of a skimmer is not essential, at least for the type of rotational cooling which was deemed necessary in our experiment. In the second chamber, a set of liquid nitrogen cooled slits collimates the beam with a ratio of 130 thus narrowing the beam Doppler width in crossed beam geometry below the laser spectral width. The laser used in the experiment is a modified type 580 Spectra-Physics dye cell laser, working with Rhodamine 6 G. The free running spectral line width of 40 MHz is reduced down to 5 MHz by active servolooping on an external 25 cm confocal Fabry-Perot. Both the laser and the reference F.P. are enclosed in a vacuum tank and the wavelength is tuned by pressure scanning of the entire instrument. With this setup, continuous tuning range of 30 GHz without mode jump is routinely achieved. Coarse laser wavelength measurement is carried out with a 1.65 m spectrograph with 0.3 cm -1 resolution. The beam fluorescence in the interaction region is
•
,
h.
July 1979
detected by a combination of color filter and photomultiplier working in the photon counting mode. The signal from the beam is recorded simultaneously with the reference peaks from a 75 cm confocal FabryPerot and with the fluorescence light from a room temperature iodine cell.
3. Experiment and results 3.1. Molecular beam Each 30 GHz scan in the Rhodamine 6 G range usually exhibits several rotational lines (fig. 1) which can be identified by reference to the "Atlas du spectre de la mol6cule d'iode" [6] together with the accurate molecular constants derived by Luc [7]. The recorded fluorescence from the room temperature iodine cell provides relative intensities for molecules at thermal equilibrium at 300 K while comparison with the intensities of the same transitions in the beam fluorescence gives a direct measurement of beam rotational and vibrational temperature, assuming Boltzmann distribution [5]. Three experiments are
lu,lJil IllLl, till LllIll L
J
~: ~I 0
I
I
I
I
I 5
I
~I
I
1
GHz I 10
Fig. 1. Part of the recording of 14-0 band, in the supersonic beam (upper trace) and in a cell at room temperature (lower trace). Rotational cooling in the beam is illustrated by strong reduction of signal for high J transitions together with enhancement for f'trst J transitions, such as P(1) which is very weak in the cell. This recording corresponds to the third experiment of table 1.
42
Volume 30, number 1
OPTICS COMMUNICATIONS
carried out in the 14-0 band head region. Five lines, namely R(5) (14-0), R(135) (16-0), P(93)(15-0), R(74) (19-2) and R(88) (17-1) were used as "thermometers". The results summarized in table 1 clearly display the cooling achieved with increasing generating temperature. Supersonic beam properties are generally described in term of a Mach number M which is related to the thermodynamic beam temperature T and generating temperature T O by the relation [8] To/T = 1 + ~1 (y - 1)M 2 (1) Since T is related to the velocity distribution of the particles in the beam, it is not directly measured. However, under the assumption of complete thermal equilibrium between the rotational and translational degrees of freedom, the relation (1) with T = T R gives M with a good approximation. The resulting Mach number values given in table 1 were calculated with the usual assumption 3' = 7/5 which is rigorously valid only for diatomic molecules with inactive vibrational energy transfer [9]. In the case of iodine significant vibrational cooling occurs, and thus the M values obtained should be considered only as lower limits. Once the Mach number is known, calculations based on the ideal isentropic flow theory lead to the beam density. In the case of Mach 4.3, we obtain a theoretical flux of 1020 mol/sec/ster which probably overestimates the experimental value and corresponds to a gain of 104 over a room temperature effusive source of same aperture. Nevertheless, the experimentally achieved beam density is sufficient to'provide of the order of 108 photons/sec/ster for the strongest hyperfine lines in the detection window 600 to 660 nm, with 20 mW of incident laser power.
Table 1 Rotational and vibrational temperatures in the supersonic iodine beam for three different oven (generating) temperature, and associated Mach numbers calculated from relation (1) with T = TR and ~ = 7/5 Generating temperature To (K)
Rotational temperature TR (K)
Vibrational temperature Tv(K)
Estimated Mach number
330 390 430
160 140 90
200 180 160
2.3 3 4.3
July 1979
3.2 Hyperfine structure As a typical example, we carried out a complete analysis of the 12-0 band from R(0) to R(6). The fluorescence line on the room temperature cell recording in fig. 2 is in fact the superposition of the first five rotational lines of the 12-0 transition. The corresponding hyperfine structure exhibits over 70 well resolved components. The HFS pattern of the transitions arising from such low J levels is noticeably different from the more familiar pattern of 15 or 21 main lines which correspond to the selection rule AF = AJ between high J levels. In our case transitions with AF = 0 and even AF --- - A J have sizeable intensities. As a consequence, we decided to use the labels p, q, r for the hyperfine components by analogy with the convention followed in rotational transitions. In fig. 2, the label is followed by the F " value and preceded by the J " value (standing for R (J")) thus providing a compact characterization of each HFS line. The identification and theoretical interpretation of the spectrum is based on a parametric analysis up to second order in perturbation [10]. The model bamiltonian for the hyperfine structure in iodine consists of four terms: H~-HNE Q +HIR +HTs S + H s s S
(2)
which represent respectively the quadrupolar, spinrotation, tensorial spin-spin and scalar spin-spin interaction. For a full second order treatment, the hamiltonian is developed on the subspace spanned by the state vector arising from the J and J -+ 2 levels. This model leads to a description of the hyperfine interaction in terms of four parameters, classically referred as eQq, C1, d and 6. The first step of the numerical treatment is the determination of hierarchy of the perturbations in formula (2). Whereas the situation is already well understood for high J levels, it was not clear a priori that the ordering of decreasing importance suggested by formula (2) would still prevail near the band heads. It must be pointed out that this part of the analysis relies only on the relative magnitude of the HFS splittings and thus depends only on the relative precision of the measured frequency intervals. The experimental limit is set by: (i) the accuracy of the line centre determination which is estimated to be better than a 1/5 of the line width. 43
Volume
30, number
1
OPTICS COMMUNICATIONS
~T t
pb# o
II
gb~, ~,do
J S.
- ;
I'°
gb~
£ •
0
¢b
='==~"~,O :
9 b lv
gJO
o~3 =
L .qv
¢.~,
_4 . - -
6._ /£bl, BO~
j~ ~Jl
E= O
~
8bE
,
9bl
:
¢J¢ 9J¢
;
~bz
9Jl gJE
Eb Z
gJg
gbE
gJ¢ PJl 91~ ~ J¢
O
o~
•¢j¢
, Cb z
9Jg
'gJ~ I ~
9bl
~
gdl gbl gdl
I~a~
!~,b~ I ~bE ~,d~, ' ~a g
44
~.~ E
July 1979
(ii) the relative accuracy of frequency scale set by the peaks of the reference F.P. Despite good thermal insulation and protection against atmospheric perturbations, it was experimentally observed that the stability of the superinvar mount of F.P. was not sufficient to prevent calibration peak shifts during the measurements, and corresponding variations of the apparent free spectral range were measured to be of the order of 1% over one hour. (iii) further indetermination could arise from nonlinearities in the pressure scanning of the laser wavelength. The resulting uncertainty is estimated to be well below 1 MHz. The overall uncertainty on relative frequency intervals is thus dominated by the error on line centre determination, with an upper bound of 1 MHz. Four optimization procedures were carried out using the numerical simplex method. Results of table 2 show that the best fit to the experimental data is obtained with eQq' and C; for excited state, and eQq"in ground state, C[' being known to be zero for the first v" values. This fit leads to an r.m.s, deviation o of 0.54 MHz for line positions of 130 components. Two standard deviations are typically 1 MHz in eQq' and eQq",and 15 kHz in C~, except for R(0) in which reduced information gives 3 MHz and 50 kHz respectively. Inspection of the fits with successive J" values clearly shows that for R(0) and R(1) the HFS pattern is correctly described within our experimental accuracy by pure quadrupolar interaction while for J" ~> 2 the spin-rotation contribution becomes significant due to the (l.J)' multiplicative factor. It has to be pointed out that eQq' and eQq"are simultaneously and independently determined with a good accuracy. This is an interesting feature of the first rotational transitions for which in contrast of the case of high J value the selection rule AF = AJ no longer holds rigorously. Appearance of AF = 0 and AF = - A J transitions reduces the correlation between the parameters and leads to the determination of each of them rather than their difference, despite a moderate resolution and precision. The absolute determination of the three numerically significant parameters relies on accuracy of the absolute frequency scale of the measurement. The apparent FSR of the reference cavity was measured on the iodine cell fluorescence recordings by peak counting
Volume 30, number 1
OPTICS COMMUNICATIONS
July 1979
Table 2 Optimization for eQq, C1, d and 6 parameters in 12-0 band. All values are given in MHz. o is r.m.s, deviation between measured and calculated line positions 12-0 band
R0
R1
R2
R3
R4
R5
R6
Number of fitted lines
7
15
15
19
20
30
24
-2448 -508 0.56
-2449 -508 0.35
-2450 -512 0.98
-2453 -516 1.07
-2459 -519 1.14
-2453 -520 1.66
-2448 -509 0.97
1.08
-2458 -508 0.062 0.50
-2449 -508 0.032 0.33
-2451 -511 0.063 0.44
-2450 -511 0.049 0.41
-2455 -512 0.051 0.44
-2448 -510 0.045 0.65
-2448 -509 0.039 0.77
0.54
-2449 0.003 -508 0.049 0.35
-2445 0.43 -508 0.23 0.62
-2448 0.19 -510 0.27 1.08
-2462 0.18 -521 0.33 0.69
-2451 0.17 -515 0.05 1.65
-2449 0.03 -505 0.20 0.57
0.91
-2449 -0.040 -509 0.003 0.34
-2449 -0.38 -509 -0.26 0.44
-2452 0.12 -514 0.22 0.93
-2458 -0.002 -516 0.19 0.82
-2452 0.02 -516 0.15 1.58
-2449 0.09 -507 -0.11 0.80
0.91
eaq
I eQq" I eQq' o
eQq + C
eQq" eQq' Ci o
eQq" d"
eQq + d
eQq' d' o
eQq" eQq + a
6"
eQq' 6' o
over wide scans between rotational lines measuoed in ref. [6]. Due to thermal drifts already mentioned, the reproducibility o f the measurements was no better than 1%. This leads to a final accuracy o f 1% on the quadrupolar parameters, while the uncertainty on the spinrotation parameter, whenever defined, is still mainly due to the variance calculated by fit procedure. With such error bars, the slight variations shown in table 2 between different J levels are not o f physical significance.
Overall RMS
molecular spectroscopy. High density of molecules together with rovibrational cooling which can be controlled to any desired value by the generating temperature should permit the analysis of very weak transitions. Moreover the absence of relaxation in the ground state in the collision-free beam medium opens the possibility of ground state preparation in any v", J " and even F " levels. This may become necessary for the unravelling o f the complex patterns expected near the B state dissociation limit, or the examination of the intersection o f the dissociative 1 flu state with u' = 6, 7 B levels.
4. Conclusion The previous discussion clearly shows that the ex. perimental accuracy would greatly benefit from an improvement of the frequency calibration. This can be done by active servo looping o f the F.P. cavity on a reference frequency such as a stabilised He-Ne laser and accurate determination o f its F.S.R. via a lambdameter. Such an experiment is currently in progress with a narrower laser line width (2 MHz). In its present stage, this work illustrates the wide applicability of supersonic beam for high resolution
Acknowledgement We are grateful to Prof. M. Dufay and J. d'Incan for their continuous support during the experiment, and to M. Broyer, J. Vigu6 and F. Hartmann for numerous fruitful discussions.
45
Volume 30, number 1
OPTICS COMMUNICATIONS
References [1] G.R. Hanes and C.E. Dahlstrom, Appl. Phys. Lett. 14 (1969) 382; T.W. Hffnsch, M.D. Levenson and A.L. Schawlow, Phys. Rev. Lett. 26 (1971) 946; M.S. Sorem, M.D. Levenson and A.L. Schawlow, Phys. Lett. 37A (1971) 33; P. Cerez, A. Brillet, S. Hajdukovic and N. Man, Optics Comm. 21 (1977) 332; A. Morinaga and K. Tanaka, Appl. Phys. Lett. 32 (1978) 114; G. Camy, Thesis, Paris (1979). [2] S. Ezekiel and R. Weiss, Phys. Rev. Lett. 20 (1968) 91; D.J. Ruben, S.G. Kukolich, L.A. Hackel, D.G. Youmans and S. Ezekiel, Chem. Phys. Lett. 22 (1973) 326.
46
July 1979
[3] H. Brand, H.H. Schulz and A. Steudel, Phys. Lett. 63A (1977) 235; B. Couillaud and A. Ducasse, Optics Comm. 21 (1977) 199; J. Vigu6, Thesis, Paris (1978). [4] R.J. Gordon, Y.T. Lee and D.R. Herschbach, J. Chem. Phys. 54 (1971) 2393. [5] M.P. Sinha, A. Schultz and R.N. Zare, J. Chem. Phys. 58 (1973) 549. [6] S. Gerstenkorn and P. Luc, Atlas du Spectre d'Absorption de la mol6cule d'iode, Editions du C.N.R.S. (1978). [7] P. Luc, J. Mol. Spect., to be published. [8] T.C. English and J.C. Zorn, Methods of experimental physics, Vol. 3B, Chapter 6, ed. L. Marton (Ac. Press, N.Y., 1974). [9] R. Campargue, Thesis, Paris (1970). [10] M. Broyer, Thesis, Paris (1977).