New Dunham coefficients of the A1Σ+-State of NaH and NaD

Article abstract of DOI:10.1007/s004600050060

We determined new Dunham coefficients of the A¹Σ⁺-State of NaH and NaD from degenerate Four-Wave-Mixing (DFWM) spectra in the near UV and in the blue spectral region. In the case of NaH we combined these data with results of Rafi et al. and Orth et al.. The new set of coefficients describes the vibrational dependence of the rotational constants B and D and of the band origins from v′ = 0 up to 25. The spectral positions of the lines in our DFWM-spectra can be reproduced by this coefficients with an accuracy better than 0.3 cm^-1 for J-values ≤ 15 and 2 cm^-1 for J-values ≤ 25. Especially for high J-values this is an improvement up to 30 times in comparison to Dunham coefficients recommended before. A RKR-potential of the A¹Σ⁺-State was calculated with the new coefficients. The Dunham coefficients of NaD were obtained by scaling the NaH coefficients with the reduced masses of the molecules. A comparison of our results to molecular constants determined from the measured NaD-spectra shows good agreement. Springer-Verlag 1996.

Full text of DOI:10.1007/s004600050060

Z. Phys. D 38, 35—40 (1996)
ꢀ >
New Dunham coefficients of the A R -State of NaH and NaD
ꢀ
ꢀ
*
ꢀ
ꢀꢁ ꢂ
S. Lochbrunner , M. Motzkus , G. Pichler , K. L. Kompa , P. Hering
ꢀ
ꢂ
Max-Planck-Institut fur Quantenoptik, D-85748 Garching, Germany
Institut fur Lasermedizin, Universitat Dusseldorf, D-40225 Dusseldorf, Germany
¨
Received: 1 March 1996 / Final version: 28 May 1996
Abstract. We determined new Dunham coefficients of the
test the results of these studies and the methods used
therein.
ꢀ >
A R -State of NaH and NaD from degenerate Four-
Wave-Mixing (DFWM) spectra in the near UV and in the
blue spectral region. In the case of NaH we combined
these data with results of Rafi et al. and Orth et al.. The
new set of coefficients describes the vibrational depend-
ence of the rotational constants B and D and of the band
Since 1990 our group [14] has investigated the forma-
tion of NaH via collisions of excited sodium atoms
with molecular hydrogen in the gas phase by resonance
coherent anti-Stokes-Raman-Scattering (RECARS) and
DFWM. Although the spectroscopic features of NaH
seemed to be well known unexpected difficulties appeared
in assigning new spectral lines, which we identified later as
NaH-lines. Line positions calculated with Dunham coeffi-
cients recommended by Stwalley et al. [3] did not fit the
measured spectra. Especially for high rotational levels
the experimentally determined line positions differ from
ꢀ
origins from v "0 up to 25. The spectral positions of the
lines in our DFWM-spectra can be reproduced by this
\ꢀ
coefficients with an accuracy better than 0.3 cm
for
\ꢀ
J-values415 and 2 cm for J-values 425. Especially
for high J-values this is an improvement up to 30 times in
comparison to Dunham coefficients recommended before.
ꢀ >
\ꢀ
A RKR-potential of the A R -state was calculated with
the calculated ones up to 60 cm (see line P (15, 0) in
ꢂꢃ
ꢀ
ꢀꢀ
the new coefficients. The Dunham coefficients of NaD
were obtained by scaling the NaH coefficients with the
reduced masses of the molecules. A comparison of our
results to molecular constants determined from the meas-
ured NaD-spectra shows good agreement.
Fig. 1; the band is characterized by (v , v ). For this reason
the calculations led for many cases to a wrong ordering of
neighbouring lines. For example the R (12, 0)-line in the
spectrum was found at a shorter wavelength than the
(10, 0)-line in contradiction to the calculations (see
Fig. 1).
The main reason for this is the following: Stwalley
ꢀꢄ
P
ꢂ
PACS: 33.15.Mt; 33.20.Kf; 42.65.Hw
et al. recommend molecular coefficients derived by com-
paring and analyzing data from the existing literature. The
ꢀ >
main source of information for the constants of the A R -
state are the measurements of Pankhurst [5]. However, he
derived the centrifugal distortion constant D for only
a few vibrational levels. The resulting Dunham coeffi-
1 Introduction
Since 1930 the spectrum of NaH was investigated by
several groups [2, 4—6]. Olsson [7] established for the first
time a correct numbering of the vibrational levels of the
cients ½ correctly describe the vibrational dependence
ꢀꢂ
ꢀ
of D only up to v "7 (see Fig. 2). Therefore Stwalley and
co-workers [2, 3] did not recommend specific values for
the related Dunham coefficients.
ꢀ >
first electronic excited state, the A R -state of NaH, and
Pankhurst [5] determined from his emission spectra a set
of Dunham coefficients [8] which was improved since
then several times [2, 9].
NaH is the subject of many theoretical studies because
of the interesting anomalous behaviour of the A R -state
For this reason the assignment of many NaH-lines
based on the comparison of spectral positions taken from
their spectra with calculated ones may be ambigious.
Therefore we measured overview spectra of NaH between
436 nm and 470 nm and between 370 nm and 405 nm to
cover the whole branches and to identify the lines step by
step proceeding from the band heads.
ꢀ >
and the simplicity of the molecule [10—13]. Spectroscopic
investigations of NaH with high accuracy are necessary to
We applied the Degenerate-Four-¼ave-Mixing
(DFWM) method, a non-linear optical technique, which
has attracted much attention recently [15 and references
therein]. DFWM is now widely used for kinetic studies
* Permanent address: Institute of Physics of the University,
HR-41000 Zagreb, Croatia

36
the involved states. It has been shown previously [23] that
this technique is also suitable to observe NaH.
Meanwhile Rafi et al. had measured the absorption
spectrum at shorter wavelengths and reported the band
ꢀ
origins and rotational constants for v "12 to 25 [1] while
ꢀ
our data covers the region v "2 to 15 and Orth et al. [2]
ꢀ
give experimental values for v "0 and 1. By using all this
data it was possible to fit a set of Dunham coefficients (see
Table 2) which describes the vibrational dependence of the
ꢀ >
ꢀ
molecular constants of the A R -state for v "0 to 25.
The comparison of NaH and NaD should give in-
formation about the influence of the mass of the nuclei on
potential surfaces and reaction kinetics. However, only
ꢀ >
very few spectroscopic data are available for the A R -
state of NaD. Therefore Stwalley et al. recommend to
scale the Dunham coefficients of NaH with the reduced
masses to get appropriate coefficients for NaD [3]. To
validate this procedure a set of NaD coefficients (see Table
4) was calculated from the new NaH coefficients and
compared with molecular constants obtained directly
from NaD spectra which were measured in the same
spectral regions as the NaH spectra.
Fig. 1. Small part of the DFWM-spectrum of NaH with the assign-
ment of some exemplary lines. The crosses indicate the line positions
calculated by Dunham coefficients recommended in [3]. The circles
with crosses show the calculated positions if the new set of coeffi-
ꢀ >
cients for the A R -state given in Table 2 is used. The improvement
of the accuracy is obvious especially for high J-values
2 Experiment
The Na#H collision system is prepared in a heat pipe
ꢂ
oven filled with sodium and 100 mbar of hydrogen
ꢀꢆ
\ꢃ
(n"1.2·10 cm ) and heated up to 600 K. A detailed
description of the heat pipe oven is given elsewhere [24].
ꢀꢇ
\ꢃ
The sodium atoms in the gas phase (n"6·10 cm ) are
ꢃꢈꢂ
excited in the 3p level by a flashlamp-pumped dye laser.
Via collisions between excited sodium atoms and hydro-
gen molecules sodium hydride is produced [14, 16]. The
concentration of NaH-molecules in vibrational levels up
ꢀꢀ
to v "3 is sufficient for our spectroscopic study.
The spectra of sodium hydride are recorded via degen-
erate Four-Wave-Mixing in a phase conjugated geometry
with two crossed polarized and counterpropagating pump
beams. A p-polarized probe beam crosses them at an angle
°
of about 2 . All beams have a waist of 2 mm, measured
with a beam profile analyzer. The energy of the pump
beams is 20 kJ per pulse while the probe beam is five times
weaker. The source of these beams is an excimer pumped
dye laser, which delivers laser pulses of 10 ns time dura-
tion. The signal beam, which arises due to the interaction
of the probe and pump beams with the sample, is s-
polarized and counterpropagating to the probe beam. It is
split off the probe beam by a polarizer and guided through
a computer controlled attenuator to a photomultiplier.
The attenuator is necessary to adapt the dynamic range of
the signal (1 : 10000) to the photomultiplier. The spectra
are obtained by tuning the wavelength of the DFWM-
laser in steps of 0.002 nm and recording the signal of the
photomultiplier via a boxcar amplifier by a personal com-
puter. For further details see [23] and [17].
Adequate wavelength calibration of the DFWM-laser
beam is achieved with the help of an optogalvanic cell
(OG505, LAS) filled with neon or argon. A small fraction
of the radiation is sent through this cell and induces
changes of the lamp discharge current. These changes
are measured at a resistor, processed by another boxcar
ꢀ >
Fig. 2. The centrifugal distortion constant D of the A R -state of
NaH is plotted versus the vibrational level vꢀ. The experimental
TY
values (diamonds) are obtained from the measured DFWM-spectra.
The dashed line depicts a calculation of D by Dunham coefficients
which R.C. Pankhurst got from his emission measurements [5].
These coefficients do not lead to reasonable values at high vꢀ-levels.
Therefore Stwalley et al. do not recommend them [3]. However, the
new Dunham coefficients ½ and ½ given in Table 2 describe the
ꢅꢂ
ꢀꢂ
dependence of D on vꢀ within the experimental uncertainty (see solid
line)
[16, 17], investigations of combustion processes [18], and
ultrashort time dynamics [19—21]. Some features of
DFWM are of considerable interest for molecular struc-
ture investigations. Besides its sensitivity it is the subDop-
pler line resolution together with the phase conjugate
nature of the signal [22] which make this technique very
attractive. Using pulsed dye lasers with narrow bandwidth
one obtains, even at high temperatures, narrow linewidths
governed by the natural or collision-induced lifetimes of

37
amplifier, and stored simultaneously with the DFWM-
signal in the computer. An optogalvanic calibration spec-
trum is recorded for each DFWM-spectrum. Linear extra-
polation between the wavelengths of the features of the
optogalvanic spectra, tabulated in [25], allows the deter-
mination of the absolute NaH-line positions with an
uncertainty of the order of the laser linewidth, which is
Table 1. Rotational constants of the AꢀR>-state and band origins
determined by DFWM-spectra of NaH. For the band (2, 1) there is
no value for D given because in this case too few lines were
TY
observed to get a reasonable fit
Band: (vꢀ, vꢀꢀ)
B /cm\ꢀ
TY
D · 10ꢇ/cm\ꢀ Band origin/cm\ꢀ
TY
(2, 1)
(3, 1)
(4, 1)
(5, 1)
(6, 1)
(5, 2)
(6, 2)
(7, 2)
(9, 3)
1.869$0.014
—
21812.4$0.4
22149.6$0.3
22493.2$0.4
22842.9$0.3
23197.1$0.3
21747.9$0.3
22101.8$0.3
22459.3$0.4
22120.9$0.3
25046.5$0.5
25407.2$0.3
25767.4$0.3
26126.7$0.3
26484.5$0.4
26839.4$0.3
27191.2$0.4
27539.7$0.4
1.913$0.012 2.25$0.28
1.924$0.012 1.97$0.26
1.937$0.012 1.97$0.26
1.940$0.012 1.95$0.26
1.942$0.013 2.16$0.32
1.939$0.012 1.95$0.27
1.946$0.017 2.11$0.47
1.915$0.013 1.90$0.38
1.928$0.011 1.93$0.18
1.908$0.011 1.69$0.16
1.897$0.010 1.75$0.10
1.878$0.010 1.69$0.10
1.856$0.010 1.64$0.10
1.834$0.010 1.65$0.10
1.814$0.010 1.77$0.10
1.784$0.011 1.74$0.10
\ꢀ
0.2 cm
.
3 Results
3.1 NaH
(8, 0)
(9, 0)
The measured DFWM-spectra of NaH show R- and P-
ꢀ >
ꢀ >
lines of bands of the A R PX R transition with upper
(10, 0)
(11, 0)
(12, 0)
(13, 0)
(14, 0)
(15, 0)
ꢀ
vibrational levels v "2 to 15 and rotational numbers up
to 25. As discussed for example by Herzberg [26] the
analysis was carried out by calculating the differences DF
between the wave numbers of the R- and P-lines belong-
ing to the same ground state level. DF (J) depends only on
ꢀ
T
the rotational constant B , the centrifugal distortion con-
ꢀ
T
stant D and higher order rotational terms of the vibronic
ꢀ
T
ꢀ
ꢀ >
level v of the A R -state:
ꢀ
ꢃ
DF (J)"4B (J# )!D ((2J#1) #3(2J#1))#h.o. .
ꢀ
ꢀ
ꢀ
T
T
T
ꢂ
(1)
We obtained the constants B and D, dependent on the
ꢀ
vibronic level v , by fitting this function with a least square
method to the experimental determined DF (J) values.
ꢀ
T
The constants are listed in Table 1.
Values of the B and D coefficients for the ground state
were obtained by applying the same procedure to R- and
P-lines which belong to the same excited state level. These
constants were found to be in excellent agreement with
published values [3] within the accuracy of the measure-
ments. For the determination of the band origins the
rotational part of the transition energies of the lines was
calculated from the obtained B and D values and subtrac-
ted from the transition energies. For each band the mean
value and the standard deviation of these results were
calculated for all observed lines of the band (see Table 1).
Together with published data from Orth et al. [2] and
Rafi et al. [1] (see Fig. 3) the newly derived values repres-
ent a complete set of experimental values for the rota-
tional constants and band origins of the excited state for
Fig. 3. The difference DG(vꢀ) between the vibrational energies of
ꢀ >
successive levels of the A R -state of NaH is plotted against the
vibrational level vꢀ. The experimental values are obtained from the
DFWM-spectra (this work, diamonds) and references [2, 1] (triangle,
circles). The size of these symbols corresponds to the experimental
uncertainty. The dashed line depicts the values calculated from the
Dunham coefficients given in [3]. For vꢀ-values '10 there is an
increasing discrepancy between the measurements and the calcu-
lations. Therefore new Dunham coefficients ½ were fitted (solid
ꢀ
v "0 up to 25. It was found that the Dunham coefficients
ꢀ
recommended in [3] reproduce the B - and DG(v )-values
ꢀ
Iꢅ
T
line) to the data points
ꢀ
ꢀ
ꢀ
[DG(v )" band origin (v #1)-band origin (v )] very well
ꢀ
ꢀ
up to v "10 but for higher v there are increasing discrep-
ancies (see Fig. 3).
to the data. They are listed in Table 2. The coefficients
correlate partly. Within the given errors (Table 2) different
sets can be found, which reproduce the data with the same
accuracy.
A new set of Dunham coefficients ½ was obtained by
IJ
fitting the functions
ꢃ
ꢀ
ꢀ
ꢀ
I
ꢀ
I
DG(v )" + ½ ((v # ) !(v # ) ),
(2)
(3)
Iꢅ
ꢂ
ꢂ
Good agreement between (2) and the experimental
Iꢉꢀ
ꢀ
values of DG(v ) is achieved only if the coefficients ½ rec-
ꢀ
ꢂ
ꢀ
I
B " + ½ (v # )
Iꢅ
ꢀ
T
Iꢀ
ommended in [3] with 24k46 are modified and an
Iꢉꢅ
additional coefficient ½ is introduced (see Fig. 3). To
ꢊꢅ
and
adapt (3) to the data for the rotational constant B it was
ꢀ
T
necessary to modify the coefficients ½ given in [3] with
Iꢀ
ꢀ
ꢀ
I
D "! + ½ (v # )
(4)
ꢀ
T
Iꢂ
ꢂ
k52. The values for the coefficients ½ and ½ , which
ꢅꢂ
ꢀꢂ
Iꢉꢅ

38
Table 2. Dunham coefficients of the
AꢀR>-state of NaH. Values without
errors are the same as in [3] and did not
have to be changed. Since the
coefficients are partly correlated
a variation within the given errors
conserves the accuracy of calculated
transition energies only if several
coefficients are changed simultaneously
½ /cm\ꢀ
l"0
l"1
l"2
IJ
k"0
k"1
k"2
k"3
k"4
k"5
k"6
k"7
0.86
317.56
1.7121
0.09152
(!12.09$0.01)·10\ꢃ
(6.50$0.02)·10\ꢇ
(!1.80$0.05)·10\ꢋ
(1.9$0.1)·10\ꢊ
(!2.30$0.10)·10\ꢇ
(4.9$0.4)·10\ꢄ
2.701$0.001
(27.31$0.01)·10\ꢂ
(!43.29$0.01)·10\ꢃ
(21.59$0.05)·10\ꢇ
(!5.25$0.05)·10\ꢋ
(5.3$0.3)·10\ꢊ
ꢀ
describe the v -dependence of the centrifugal distortion
constant D , were derived by fitting (4) to the experi-
ꢀ
T
\ꢇ \ꢀ
does not coincide with the prediction
mental results (see Fig. 2). The value !2.30 · 10 cm
of
½
ꢅꢂ
\ꢇ
\ꢀ
!1.99 · 10 cm from the Kratzer relation (5) [26].
ꢃ
ꢂ
½ "! 4 · ½ /½
(5)
ꢅꢂ ꢅꢀ ꢀꢅ
But this formula is strictly valid only for a harmonic or
ꢀ >
a Morse potential. The bottom of the A R -potential is
more shallow than in the case of these potentials (see
Fig. 4) and the retractility nearby the equilibrium distance
is weaker than indicated by ½ leading to a larger centri-
ꢀꢅ
fugal distortion. This anomalous behavior of the potential
ꢀ
results also in increasing vibrational spacings DG(v ) with
ꢀ
increasing vibrational quantum number up to v "9 (see
Fig. 3) whereas a harmonic potential shows equidistant
and a Morse potential decreasing spacings.
Mostly because ½ and ½ are missing in the set of
ꢀ >
Fig. 4. The RKR potential energy curve of the A R -state of NaH.
G is the vibrational energy inclusive the Dunham correction and
ꢅꢂ
ꢀꢂ
coefficients recommended up to now the spectral line
positions are reproduced with a much higher accuracy, in
particular for high J-values, if they are calculated with the
new coefficients instead the previously recommended ones
(see Fig. 1). Apart from the Dunham coefficients of the
equals +
½
(vꢀ#1/2)I
Iꢅ
Iꢉꢅ
Table 3. Turning points of the RKR potential energy curve of the
AꢀR>-state of NaH. G(vꢀ) is the vibrational energy inclusive the
ꢀ >
A R -state the coefficients of the ground state inclusive
Dunham correction and equals +
½
(vꢀ#1/2)I
Iꢅ
the centrifugal distortion [3, 27] and an electronic energy
Iꢉꢅ
\ꢀ
of 22713.0 cm
energies.
[3] were used to obtain the transition
vꢀ
G(vꢀ)/cm\ꢀ
R /A
R /A
\
>
0
1
2
3
4
5
6
7
8
160.34
483.99
814.41
2.8529
2.6065
2.4478
2.3293
2.2358
2.1596
2.0959
2.0416
1.9947
1.9535
1.9168
1.8840
1.8542
1.8270
1.8021
1.7792
1.7580
1.7386
1.7209
1.7047
1.6902
1.6775
1.6666
1.6577
1.6511
1.6472
3.5154
3.7425
3.9011
4.0343
4.1541
4.2659
4.3727
4.4765
4.5784
4.6793
4.7798
4.8805
4.9815
5.0831
5.1855
5.2890
5.3935
5.4992
5.6062
5.7144
5.8239
5.9345
6.0458
6.1572
6.2677
6.3758
By means of the new coefficients a Rydberg-Klein-
ꢀ >
Rees (RKR) potential for the A R -state was calculated
ꢀ
up to v "25 using an algorithm reported by Telling-
1151.66
1495.28
1844.46
2198.19
2555.33
2914.70
3275.16
3635.63
3995.13
4352.78
4707.83
5059.65
5407.70
5751.56
6090.89
6425.45
6755.10
7079.78
7399.59
7714.79
8025.85
8333.54
8639.05
huisen [28]. The result is depicted in Fig. 4 and the RKR
turning points are listed in Table 3. The potential is in
good agreement with the one published by Orth et al. [2].
However, it includes five additional vibrational levels.
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
3.2 NaD
The spectra of NaD were recorded in the region between
371—405 nm and 430—468 nm and were analyzed in the
same way as the NaH-spectra in order to get the band
origins and rotational constants for the vibrational levels
ꢀ
ꢀ >
v "4 to 17 of the A R -state. The results are given in
Table 4.
ꢀ
The constants of the levels v "4, 5 and 6 were, to our
knowledge for the first time, directly derived from NaD-
ꢀ
spectra. For v 57 the obtained values are in good agree-
ment with data of Olsson [7] (see Fig. 5).
As discussed by several authors [e.g. 8, 26, 29] the
Dunham coefficients of two isotopic molecules A, B with

39
Table 4. Rotational constants of the AꢀR>-state of NaD and band
origins determined by DFWM-spectra of NaD. For some bands
there are no values for D given because in these cases too few lines
TY
were observed to get a reasonable fit
Band: (vꢀ, vꢀꢀ)
B /cm\ꢀ
TY
D ·10ꢇ/cm\ꢀ Band origin/cm\ꢀ
TY
(10, 0)
(11, 0)
(12, 0)
(13, 0)
(14, 0)
(15, 0)
(16, 0)
(17, 0)
(5, 1)
(6, 1)
(7, 1)
(8, 1)
(4, 2)
1.010$0.011
—
24877.0$0.4
25136.4$0.4
25396.5$0.4
25656.7$0.4
25916.8$0.4
26176.3$0.4
26435.3$0.4
26693.2$0.5
22778.1$0.4
23028.2$0.3
23280.6$0.3
23536.5$0.4
21725.7$0.3
21972.1$0.3
22221.9$0.3
22474.6$0.3
22729.5$0.3
22986.7$0.3
23244.9$0.4
23504.2$0.4
21688.1$0.3
21943.2$0.3
22978.1$0.4
21691.6$0.3
21951.2$0.3
1.007$0.010 0.51$0.15
1.004$0.010 0.52$0.13
0.997$0.010 0.49$0.13
0.991$0.010 0.48$0.13
0.983$0.010 0.47$0.13
0.977$0.010 0.47$0.13
0.969$0.010 0.47$0.13
1.006$0.008 0.68$0.14
1.003$0.006 0.50$0.06
1.009$0.005 0.52$0.04
1.004$0.013 0.41$0.10
0.993$0.009
—
(5, 2)
(6, 2)
(7, 2)
(8, 2)
1.002$0.007 0.58$0.11
1.008$0.007 0.59$0.06
1.011$0.005 0.54$0.04
1.012$0.005 0.52$0.04
1.014$0.005 0.55$0.04
1.009$0.006 0.51$0.06
Fig. 5. Experimental values for the rotational constant B of the
TY
ꢀ >
A R -state of NaD obtained from DFWM-spectra (this work, dia-
monds) and from [7] (circles) are compared to values which were
calculated by scaling the new Dunham coefficients of NaH with the
reduced masses (solid line)
(9, 2)
(10, 2)
(11, 2)
(7, 3)
0.994$0.023
—
1.013$0.008 0.66$0.19
Table 5. Dunham coefficients of the AꢀR>-state of NaD calculated
(8, 3)
1.013$0.008 0.54$0.14
by means of the reduced mass-method from the coefficients of NaH
(12, 3)
(10, 4)
(11, 4)
1.006$0.012
1.015$0.011
1.004$0.010
—
—
—
½ /cm\ꢀ
l"0
0.86
229.30
1.408
10.28 · 10\ꢂ
!11.78 · 10\ꢃ
4.238 · 10\ꢇ
!7.44 · 10\ꢄ
5.4 · 10\ꢆ
l"1
0.8926
0.03445
!3.286 · 10\ꢃ
1.28 · 10\ꢇ
l"2
IJ
k"0
k"1
k"2
k"3
k"4
k"5
k"6
k"7
!6.3 · 10\ꢋ
9.6 · 10\ꢊ
identical potential functions scale to a very good approxi-
mation with the reduced masses k of the molecules:
!2.55 · 10\ꢄ
1.9 · 10\ꢆ
"A
T
k
kꢀBIꢈꢂ>J
½
½
(6)
IJ
IJꢀ
ꢀ
B , D and DG(v )-values were calculated via Dunham
ꢀ
ꢀ
T
coefficients which were obtained by this formula from the
NaH-lines, although one studies only a small part of the
spectrum which does not contain any band head.
The results presented above show also that DFWM is
a suitable method to investigate the structure of molecules
particularly if it is combined with an optogalvanic calib-
ration.
ꢀ >
new determined NaH-coefficient of the A R -state. Then
they were compared with the data derived from the
spectra (see Fig. 5). The agreement is within the experi-
\ꢀ
\ꢄ \ꢀ
mental accuracy of 0.007 cm for B and 6 · 10 cm
ꢀ
T
for D .
ꢀ
T
A determination of Dunham coefficients from experi-
mental data which are available only for a limited number
The DFWM-signal varies with the dephasing time
¹ depending on the intensity of the laser beams [30]. In
ꢂ
ꢀ
of vibrational levels (v "4 to 17) of NaD would lead to
our experiment ¹ is given by the coherence-time of the
ꢂ
very inaccurate molecular constants for vibrational levels
outside of the observed region. Thus the scaling of the
NaH-coefficients leads to the more suitable set of Dun-
laser which is 0.3 ns (corresponding to a bandwidth of
\ꢀ
0.01 cm for one mode) and independent on the lifetime
of any involved level as long as this lifetime is larger than
the laser-coherence-time. The signal of LIF or of emission
spectroscopy might be suppressed by quenching or react-
ive processes, which may depopulate the irradiating levels.
Therefore in some cases a transient species can still be
investigated by DFWM while other techniques may fail
due to an inadequate signal level. In addition the DFWM-
signal arises as a laser like beam. This is a great advantage
if the sample has reactive components-like in our case of
sodium- which would destroy collecting optics if they are
in contact with the sample.
ꢀ >
ham coefficients of the A R -state of NaD. This set is
given in Table 5.
4 Discussion and conclusions
A comparison between the measured NaH-spectra and
line positions calculated with the new Dunham-coeffi-
cients shows an agreement better than 0.3 cm
\ꢀ
for
J-values below 15. For higher angular momenta up to
\ꢀ
J"25 the differences are still less than 2 cm (see Fig. 1).
Thus these coefficients lead to a reliable identification of
By using a laser with a smaller linewidth it is possible
to measure the spectral DFWM-profiles of the observed

40
transitions. With the help of the existing knowledge about
DFWM [31] the analysis of these profiles should yield
information on interaction potentials and on the live
times as well as on the coherence times of the states
involved.
13. Lewis, E.L., McNamara, L.F., Michels, H.H.: Phys. Rev. A 3,
1939 (1971)
14. Correia, R.R.B., Cunha, S.L., De Vivie Riedle, R., Pichler, G.,
Kompa, K.L., Hering, P.: Chem. Phys. Lett. 186, 531 (1991)
15. Fisher, R.A.: Optical phase conjugation. New York: Academic
Press 1983
16. Motzkus, M., Pichler, G., Kompa, K.L., Hering, P.: to be pub-
lished
We like to thank A. Klamminger for his experimental data of the
NaH-spectrum in the blue spectral region, L. Lehr and H. Bauer for
their helpful support with the experiments and R. de Vivie-Riedle
and S. Rutz for using their RKR-programm.
17. Klamminger, A., Motzkus, M., Lochbrunner, S., Pichler, G.,
Kompa, K.L., Hering, P.: Appl. Phys. B 61, 311 (1995)
18. Farrow, R.L., Rakestraw, D.J.: Science 257, 1894 (1992)
19. Hofer, T., Kruck, P., Kaiser, W.: Chem. Phys. Lett. 224, 411
(1994)
20. Bardeen, C.J., Shank, C.V.: Chem. Phys. Lett. 226, 310 (1994)
21. Lohner, A., Rick, K., Leisching, P., Leitenstorfer, A., Elsaesser,
T., Kuhn, T., Rossi, F., Stolz, W.: Phys. Rev. Lett. 71, 77 (1993)
22. Abrams, R.L., Lam, J.F., Lind, R.C., Steel, D.G., Liao, P.F.: In:
Fisher, R.A. (ed) NewYork: Academic Press 1983, pp 211—284
23. Motzkus, M., Pichler, G., Dillmann, M., Kompa, K.L., Hering,
P.: Appl. Phys. B 57, 261 (1993)
References
1. Rafi, M., Ali, N., Ahmed, K., Khan, I.A., Baig, M.A., Iqbal Zafar:
J. Phys. B 26, L129 (1993)
2. Orth, F.B., Stwalley, W.C., Yang, S.C., Hsieh, Y.K.: J. Mol.
Spectrosc. 79, 314 (1980)
3. Stwalley, W.C., Zemke, W.T., Yang, S.C.: J. Phys. Chem. Ref.
Data 20, 153 (1991)
24. Hering, P., Cunha, S.L., Kompa, K.L.: J. Phys. Chem. 91, 5459
(1987)
4. Hori, T.: Z. Phys. 62, 352 (1930)
25. Harrison, G.R.: Wavelength tables, edn. 1969. Cambridge,
Massachusetts, London: M.I.T. Press 1969
26. Herzberg, G.: Spectra of diatomic molecules, 2nd edn. New
York: Van Nostrand Reinhold 1950
5. Pankhurst, R.C.: Proc. Phys. Soc. London A 62, 191 (1949)
6. Giroud, M., Nedelec, O.: J. Chem. Phys. 73, 4151 (1980)
7. Olsson, E.: Z. Phys. 93, 206 (1935)
8. Dunham, J.L.: Phys. Rev. 41, 713 (1932)
9. Pardo, A., Camacho, J.J., Poyato, J.M.L., Martin, E.: Chem.
Phys. 121, 41 (1988)
10. Cade, P.E., Huo, W.M.: J. Chem. Phys. 47, 649 (1967)
11. Wilson, S. Silver, D.M.: J. Chem. Phys. 66, 5400 (1977)
12. Sachs, E.S., Hinze, J., Sabelli, N.H.: J. Chem. Phys. 62, 3377
(1975)
27. Maki, A.G., Olson, W.B.: J. Chem. Phys. 90, 12 (1989)
28. Tellinghuisen, J.: Comput. Phys. Commun. 6, 221 (1974)
29. Stwalley, W.C.: J. Chem. Phys. 63, 3062 (1975)
30. Farrow, R.L., Rakestraw, D.J., Dreier, T.: J. Opt. Soc. Am. B 9,
1770 (1992)
31. Williams, S., Zare, R.N., Rahn, L.A.: J. Chem. Phys. 101, 1072
(1994)
.