Interaction potentials of CdXe from temperature dependent absorption spectra

Chemical Physics ELSEVIER

Chemical Physics 209 (1996) 53-60

Interaction potentials of Cd-Xe from temperature dependent absorption spectra M.S. Helmi a, T. Grycuk b, G.D. Roston a a Faculty of Science, Alexandria University, Alexandria, Egypt b Institute of Experimental Physics, Warsaw University, Warsaw, Poland Received 17 November 1995; in final form 27 February 1996

Abstract The absorption profile and the temperature dependence of the Cd line at 326.1 nm perturbed by Xe at a density of about 1 x 1019 atoms cm -3 have been carefully studied over a spectral range extending from 750 cm-1 in the blue wing to 1400 cm-l in the red wing using a high resolution double beam spectrometer. Interatomic potentials for Cd-Xe in the ground electronic state 10+ as well as the exited (30+ and 31) states have been deduced from the spectrum. The van der Waals coefficient differences AC° and AC~ are also obtained. The well depths for the ground ]0 + and the exited (30+ and 31) states are found to be 192 + 18, 988 + 41 and 152 + 15 cm -~ respectively. The position of the ground state potential well minimum is deduced using the combination rule of Kong and Chakrabarty. The obtained well depth with their allowable errors are in good agreement with the values obtained before for the Cd-Xe system from other experimental methods.

I. Introduction During the past several decades, there have been numerous investigations of van der Waals molecules [1,2]. In recent years, several articles were published dealing with the spectroscopy of group IIb metalsnoble gas van der Waals dimers [3-5]. We report here the absorption spectra of the 326.1 nm cadmium intercombination line (5 3P l ~-- 5 IS 0) broadened by xenon. The temperature dependence of the far wing profile was studied for the first time and interpreted in the framework of the quasi-static theory. As was first pointed out by [6], this allows interaction energies to be determined. The C d - X e interaction potentials have thus been determined for the ground X ~0 +

state and the exited (30+ and 31) states dissociating in Cd(5 3Pj)-Xe(IS0). The van der Waals coefficient differences AC6° and AC61 between the ground X 10+ state and both of the excited (30+ and 31) states, respectively, are obtained from the near red wing analysis using Kuhn's law.

2. Theoretical

2.1. Quasi-static theory of line broadening On the basis of quantum mechanical quasi-molecular approach [7] to the theory of collisional broadening, Szudy and Baylis [8] obtained the absorption

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54

M.S. Helmi et al./ ChemicalPhysics 209 (1996) 53-60

coefficient in the line wings produced as a consequence of two particle interactions with an extremum in AV at Re. When normalized to the perturbing (Np) and the radiating (N r) atoms density, this is

=

K~'(Av, T) = 47rC,,

Km( AV) -

L(Zc ) = (36~Zc)(- 1/2) [8] may be used. Then additionally, if I~1 >> ~ and Av :~ A, Eq. (1) reduces for a single point to the formula R~(Av) d [ R ( A v ) ] d(Av)

-

NpNr

= Cm

X exp( - Vgk(TR¢) ) .

136~Z=I'/2R2L(Z¢)

4,tr~ 2

2

[

(3)

R here corresponds to the internuclear separation and Av = v 0 - v is the frequency separation from the unperturbed line frequency v 0.

Re

2.2. Determination of the van der Waals coefficients where ~ = Av - A, Z c is the reduced frequency given by

X

dR

re

d R2

rc

g.'(av)

'

L(Z~) the universal line shape function defined and tabulated in Ref. [8], ~/and A are the line half width and its shift, respectively, due to the collisions, ix the reduced mass of the radiating and the perturbing atoms and C the constant which relates the absorption coefficient to the normalized emission intensity. It can be given by

C m = ( 'rr e 2 / m c ) ( gm/gj)feg, where e and m are the electron charge and mass, c is the light velocity, gj and g,, are the atomic and molecular statistical weights (gin -- 1 or 2 for m = 0 or 1) and f,g the oscillator strength for the atomic transition e ~ g. The summation in Eq. (1) is taken over all Condon points at separations R c which satisfy the relation

AVm( Rc) = Vm( Rc) - Vg(gc) = h~.

The part of wings near to the line center is arising as a result of electronic transition between the states which are only slightly perturbed by the long-range van der Waals interactions of the form [A[V(R)] = AC6R-6]. In this case for Vg(R) << kT, Eq. (3) takes the form

(2)

Here, Vg and V,. are the adiabatic potentials of the ground and excited states, respectively. For real Condon points for which h~ is smaller than the extremum AVex(R¢), the line shape of Eq. (1) is then determined by L(Z~) with positive Z c. For large Z c corresponding to the relatively far-quasi-static wings of the line, an asymptotic form of L(Z c) given by

= -2- h Cm -

,/2( AC~)I/2Av -3/2

3 = A,.(Av) -3/2

(4)

If log K~'(Av) is plotted versus log Av, a straight line with a slope ( - 3 / 2 ) is produced. The AC~' constant may then be obtained from a measurement of the A,. coefficient. Generally for Cd-rare gases such a linear dependence on log Av is observed in two regions of the near red wing profile: The first is due to the transition 3 0 + ~ X 10+, so that 2arC 0 ao = "--'~---h- l/2( A C ° ) 1/2.

(5)

The second is due to the transition from the ground X 10+ state to both molecular excited (30+ and 31) states. In this region the absorption coefficient is given from Eq. (4) as

gn(AlJ) =

E Kin(AI)) m=0,1

2~rC 0 - - h - 1 / 2 ( I a C ° I 1/2 + 21AC 3 X (Av) -3/2

= Al(Av)-3/2.

11/2)

(6)

M.S. Helmi et a l . / Chemical Physics 209 (1996) 53-60

The AC ° and AC~ constants may then be obtained from the measurements of A 0 and A~ coefficients.

2.3. Determination of potentialsfrom line shape data A more general method of inversion for the relation between the intensity distribution and AVm(R) has been developed by Behmenburg [9] and Gallagher et al. [6]. In this method the condition that R(Av) is a single-valued function and no overlapping bands ought to be fulfilled. If the bands close to the line center on the red wing have the same van der Waals form of AV(R), then the analysis used there is valid when it is interpreted in the framework of the quasi-static theory. From the temperature dependence spectra K~(Av, T) and Eq. (3) it is possible to deduce both Vg(R) and AVm(R) and hence the excited state potentials from line shape data. The general procedure is to plot In Kn~(Av, T) versus 1/T for a fixed Av. The slope of this plot gives Vg(Av) and extrapolation to the infinite temperature gives Ky(Av, T~). If the latter is integrated to give R as a function of Av, Eq. (3) leads to f a y Knm (Av, Ava

T = ~ ) d(Av)

= 4~C m

R dR Ra

- 4~Cm [R3(Av) - Ra3(Ava)] 3

(7)

giving R(Av). This function gives with the deduced Vg(Av), the ground state potential Vg(R). As Arm(R) is determined from wings analysis, then using Eq. (2) we obtain AVm(R), and hence the excited state potentials Vm(R), (m = 0 or 1).

3. Experiment A high pressure XBO 150 xenon lamp was used as a background source for absorption. The spectral profiles were measured with a high resolution double-beam spectrophotometer described previously for the C d - C d interactions [10]. In this paper the additivity of the effects produced by C d - C d interactions and Cd-rare gas was assumed. For this purpose two

55

identical absorption cells, 5 cm long and 3 cm in diameter, made of quartz were placed in a special oven which can be heated to temperatures up to 1300 K. Kanthal tape 5 mm width, 0.3 mm thick was used as an electrical heating material. The sample cell was filled with a C d - X e mixture and the reference one was empty. The signals of the two beams were corrected for the spectral response of the experimental system. It seems that the origin of this apparatus effect lies in some asymmetry of channels of our apparatus. Other contributions affecting the spectrometer instrumental function were canceled in view of the double-beam method being used. Calculation of the absorption coefficient (including all corrections) and all further computations leading to interatomic potential data were made automatically. Two types of measurements were performed: in order to study the intensity distribution over the spectral range near to the line center, the absorption profiles were measured at various densities of the saturated cadmium vapour. On the other hand, the pure temperature effects were studied for the unsaturated cadmium vapour. In the former case great care was taken to maintain a homogeneous temperature over both cells and to make accurate measurements of this temperature. We have used cells having rather short side arms as Cd reservoirs, heated to the same temperature as the cell bodies. Both cells together with their side arms were wrapped in an aluminum film and placed inside a specially constructed brass container which was put into the oven. The use of these thermostatting metal parts and the length of the oven (about 12 times larger than the length of the cell) helped to achieve a fairly uniform temperature (within 0.1 K) over the cells. The accuracy of temperature determination was better than 1 K and its fluctuations were below 0.03 K during the time of measurements. The absorption measurements near to the line center are performed using a saturated cadmium vapour whose pressure P is controlled by the temperature T using the formula proposed by Bousquet [11]. The interaction potentials for the ground 10+ and the excited ( 3 0 + and 31) states are obtained from the absorption measurements of unsaturated Cd vapour. It was found experimentally that to obtain this state of cadmium the cell and the arm connected

56

M.S. Helmi et a l . / Cheraical Physics 209 (1996) 53-60 908070-

•.::

Cd-Xe

i'

ot 1204.15 K

4-

4.

E o

60-

%

".,,,

~t E) 2-

o 50E, 40-

~- 3o-

1

slope ~

9~"Cd_Cd

~.~ 20E

v. 10=

v

" Cd-X,

O-10

-8oo-~oo

6

460 860 (~,,- ~,) (~m")

-2 0.25

12'oo

Fig. 1. Absorption profile of the Cd 326.1 nm line for the Cd-Xe system.

I

I

1.25 2.25 log (Z)o- ~') (cm')

Fig. 2. Red wing profiles for the Cd-Xe system and its comparison with the Cd-Cd system in logarithmic scale (10 -40 eroS). The Cd-Xe profile is divided by 20.

with it must be heated to a temperature equal to 1000 K. The contribution due to Cd-Cd interactions for both saturated and unsaturated vapour had then to be determined by independent measurements taken by the authors [10]. This contribution was reduced at the same Cd density to the Cd-Xe interactions only by using the relation: r n ( A v ) [Cd-Xe] = r n ( A v ) [ e x p ] - K . ( A v ) [CO-Cd](NcJNg~,).

4. Results and discussions 4.1. Red wing of the Cd 326.1 nm line Fig. 1 illustrates the absorption profile of the cadmium line at 326.1 nm for the Cd-Xe system over a spectral range extending from 750 c m - t in the blue wing to 1400 cm-~ in the red wing. The red wing profile of the Cd 326.1 nm line broadened by Xe, compared with the self-broadened line profile

obtained from Ref. [10], in logarithmic scale is illustrated in Fig. 2. In this figure one can see a single satellite at about 10 cm -~. In the vicinity of this band two linear regions with slope - 3 / 2 are observed for the Cd-Xe system. The first one close to the line center may be interpreted as the quasi-static line wing which is formed by transitions between the ~round state ~0+ and excited states 30+ as well as 1, while the second corresponds to the transition to the excited 30+ state only. By using Eq. (5) for the second region, A 0 was calculated and AC6° for the C d - X e system was obtained. The intersection of the first region with the ordinate axis, gives the value of the coefficient A~. As the values A t and AC° are obtained, then AC~ can be determined, (see Eq. (6)). The oscillator strength feg was taken as 1.6 × 10 - 3 (theoretical value) [12]. These values are illustrated in Table 1 with the van der Waals coefficients C° and C~ for the excited (30+ and 31) states when the van der Waals coefficient C~ for the ground state obtained theoretically by Ref. [13] was used. The obtained AC 6 values are reliable comparatively to

Table 1 The van der Waals coefficients for the Cd-Xe system in eV ~6

Mol~ule Cd-Xe

AcO 43 + 3

AC~ 86 + 4

C~ 147.3

C° 190 + 3

C~' 233 ± 4

M.S. Helmi et al. / Chemical Physics 209 (1996) 53-60

57

4.50 0.40

T =

Cd- Xe

4.25

1240 K

20

i

¢.00 -

0.30

I

30 "

~ 3.75

37

L3.50

~ 0.20

~,3.25 5O

,, 3.00

%

<1

0.10

""2.75

0.00 -200

"-'2.50 I . _= 70 2.25 0.80 0.85

!

I

- 150

- 1100

-50

0

(Vo- v). (cm-') Fig. 3. The blue wing for the C d - X e system (uncorrected from C d - C d interactions) and its comparison with the C d - C d system at the same concentration of cadmium.

the AC 6 values for the H g - X e system obtained by Ref. [ 14].

4.2. Blue wing of the Cd 326.1 nm line Fig. 3 shows the blue wing for both the C d - X e and the C d - C d systems at the same density of cadmium (3.62 × 10 Is c m - 3 ) . It is seen from this figure that the effect of the C d - X e interaction extends only to Av -- 100 c m - t from the line center. It

80-

0.60

~O00/T (K-')

-.

0.45

1.0C

is also seen that this wing has a distinct structure in the form of principle maxima called the blue satellite. the temperature dependence of the blue wing of the C d - X e system in the interval of temperature from 1000 to 1270 K for the unsaturated cadmium vapour is illustrated in Fig. 4. The densities of cadmium and xenon atoms in this state are, respectively, 3.62 × l0 ts and 1.325 X 1019 c m - 3 . The blue wing profile of the Cd-rare gas systems is mainly attributed to the electronic transition between the ground state 10+ and the excited (31) state [15].

Cd-Xe 1 ,"Jr 1011.65 K 2 ot 1204.15 K

-25-

J

/7/

=E 50 o

p

Fig. 5. Reduced absorption coefficient (10 -40 cm 5) in the logarithmic scale against IO00/T at different values of Av.

7060-

I

60

-7'5-

/

40-

Cd-Xe

-50-

~"~- 100-

~" 30"

~

"-"-125-

:¢//

20-

¢,

-150-

,--X / 3

10-

-175-

~:° 0-10 -120

-200"

-i'oo

-~o

-~o

-~o

-~,o

(I/o- 7)) (cm-') Fig. 4. The temperature dependence of the blue wing of the Cd 326.1 nm line for the pure Cd-Xe system.

-225

-so

-~o

-~o -~o -~o (Vo- v) (cm-~)

-~o

Fig. 6. The ground state potential as a function of Av.

M.S. Helmi et a l . / Chemical Physics 209 (1996) 53-60

58

500

100- L

Cd-Xe

\

50O-

0-

Vg

C

-50-

-500-

g,-loo-150-

Cd-Xe

>'-1000-

-200-

Vg

-250

-1500

s.7s 4.60 4.~s 4.1o 4.-~s s.6o 515 s.so

~.5

R (A*)

4.b

4.'s

s.~

c

i

~,.s

R (A*)

ob

o.'s

7.0

Fig. 7. The difference potential AV l and the experimental ground state potential Vg ( * ) . Morse potential ( - ) is fitted to the experimental data (" ).

Fig. 8. The difference potential AVo and the ground state potential Vg.

4.3. Interaction potential for the states X 10 + and ~1

versus IO00/T. The slopes of these lines give the ground state potential Vg(Av). This is shown in Fig. 6. The well depth of this state is thus determined. After fitting the experimental results by the leastsquares method, the well depth was estimated to be equal to 192 ___18 cm - l . To obtain the ground state potential Vg(R) the relation Av(R) must be obtained, as was established in the theoretical part (Section 2.3). This relation can be obtained if there is at least a point in the ground state potential at which Av(R) is known. As there are no published data concerning the potentials for the Cd-Xe system, the intercombination rules of Ref. [16] for the determination of the well depth and the position of the ground state potential was used. In these rules we used our parameters for the Cd-Cd interaction [10] (¢Cd = 390 c m - 1 , R,,cd = 3.3 .~ and etcd = 8). The parameters

For the blue wing a temperature dependence was observed. This is shown in Fig. 4. As this dependence lies in the same region of the classical blue satellite, then according to the UFC theory developed by Ref. [8] the profile can be interpreted due to the quasi-static theory (Eq. (3)) if it is multiplied by ( T ) 1/6 [8,11] or (T/Tmin) 1/6 when the profile is normalized to the temperature Tmin. Tmin here is the minimum temperature taken for obtaining the temperature dependence of the profile. It is clear from Fig. 4 that the maximum temperature dependence lies at about Av = 37 cm -1. This gives the position of the well depth for the ground state potential. Fig. 5 shows the linear dependence between the normalized absorption coefficient (cm 5) in logarithmic scale

Table 2 Comparison of our data for C d - X e potential parameters with others (R m in ,~ and ~ in c m - ' ) X 10+ R m

30+ E

4.28 4.28 3.73 -

-

~

192 + 18 230.4 370 185 -

31

Ref.

R m

E

Rra

E

3.93 . .

988 -I- 41 . . . . 1086 + 60

4.41

152 + 15

-

-

.

. . .

-

. . .

this work intercomb, rules [ 16] [18] [191 [41

59

M.S. Helmi et a l . / Chemical Physics 209 (1996) 53-60

for Xe-Xe interaction (exe = 184.2 cm-~, Rmxe = 4.38 ,~. and the fitting parameter etxe = 15) was taken from Ref. [17]. By using these rules the well depth of the ground state potential ~ and its position R,, for the Cd-Xe system were found to be equal to 230.4 c m - t and 4.28 ,~, respectively. As this R,, point is determined, the relation Av(R) can be obtained as explained in Section 2.3 by the extrapolation of the absorption spectrum to an infinite temperature. This is shown in Fig. 4. As the relation Av(R) is obtained then, the ground state potential Vg(R) for the Cd-Xe system can be obtained for values of R extending from 3.8 to 4.7 ,~. Apt(R) here represents the difference potential between the two states X tO+ and 31. From this the excited state 31 potential can be obtained as

V1(31) = V~( R) + AV,( R). Fig. 7 shows the potential difference AVt(R)= V(31 ) - V( i 0 + ), and the ground state potential in the o interval of nuclear separation from R = 3.8 to 4.7 A. The ground state potential was fitted to Morse potential with parameters ~ = 192.2 cm - t , R,, = 4.28 .~ and 13 = 1.75. The potential for the excited state V~(R) is illustrated in Fig. 9.

4.4. Interaction potential for the state 30 + The potential Vo(R) for the s t a t e (30+) Can be obtained from the temperature dependence of the red 250

O-

~v,

-250-

c

E -500-

.5

" -750~r

wing profile. As the temperature dependence of this wing is very weak, then the ground state potential Vg(R) cannot be determined. Nevertheless in this case the excited state potential Vo(R) can be obtained with sufficient accuracy, if Vg(R) is known from other data. At any temperature T the relation Avo(R) can be obtained from the integration:

faaVKn(±V,T) d(ap) Va

41TCojRR 2 [ exp R~

kT

dR.

(8)

By using the ground state potential obtained in this work from the blue wing data, and the red wing profile data, it was possible to obtain the potential difference AVo(R) if the starting point Ra(A1Ja) in the integration (8) is established. This point was obtained due to the fact that Khun's law is observed in the near red wing at 25 < Av < 100 cm- ~ and the van der Waals potential difference AVa = AC6Ra 6 can be applied. As AC ° is known, then R, corresponding to Ava = 25 cm-~ is 4.9 ,~. Fig. 8 shows the determined AVo(R) for R between 3.5 and 4.9 ,~ and the ground state potential Vg(R). As AVo(R) is obtained and Vg(R) is known, then Vo(R) for the excited state 30+ is determined. This is shown in Fig. 9. The well depth for the ground (X 10+) and the two excited (31 and 30+) states potentials with their positions R m are illustrated in Table 2. It is seen from this table that the well depth of the ground state potential obtained in this work is in reasonable agreement with that obtained from the combination rule [16] and [19], but it is very far from Szuchaj's result [18]. The well depth obtained in this work for the excimer state 30+ agrees well with the corresponding value obtained by Kvaran et al. [4] from the laser induced fluorescence of the jet-cooled Cd-Xe complex.

Cd-Xe

- 1000-

Acknowledgement -

1250

35 4b 4's ~'0 ~'~ 6~ 6~ R (A*)

Fig. 9. The ground Vg(X 10+ ), the excited Vl(31) and Vo(30 + ) potentials relative to the atomic energies for the Cd-Xe system.

This work is supported by the Polish Committee for scientific research within the project 2 0261 91 01.

60

M.S. Helmi et aL / Chemical Physics 209 (1996) 53-60

References [1] C. Miller and L. Andrews, J. Chem. Phys. 69 (1978) 3034. [2] C. Miller and L. Andrews, Appl. Specify. Rev. 16 (1980) 1. [3] A. Kowalski, Czaj~owski and W.H. Breekenridge, J. Chem. Phys. Letters 121 (1985) 217. [4] A Kvaran, D.J. Funk, A. Kowalsk~ and W.H. Breckenridge, J. Chem. Phys. 89 (1988) 6069. [5] D.J. Funk, A Kvaran and W.H. Breckenridge, J. Chem. Phys. 90 (1989) 2915. [6] A. Gailagher, Atomic physics, Vol. 4 (Plenum, New York, 1975). [7] A. Jablonski, Phys. Rev. 68 (1973) 78. [8] J. Szudy and W. Baylis, J. Quantum Spectrom. Radial Transfer 15 (1975) 641. [9] W. Behmenburg, Z. Naturforsch. 27a (1972) 31.

[10] M.S. Heimi, T. Grycuk and G.D. Roston, SACTAB (1996), to be published. [11] C. Bousquet, J. Phys. B 19 (1986) 3859. [12] J. Migdalek and W.E. Baylis, J. Phys. B 19 (1986) 1. [13] J. Sienkiewicz, PhD Thesis, University Gdansk, Poland (1983). [14] T. Grycuk and M. Findeisen, J. Phys. B 16 (1983) 975. [15] L.K. Lain, A. Gallagher and R. Drullinger, J. Chem. Phys. 68 (1989) 4411. [16] C.L. Kong and M.R. Chakrabarty, J. Phys. Chem. 77 (1973) 2668. [17] J.A. Barker, M.L. Klein and M.V. Bobetic, IBM J. Res. Dev. 20 (1976) 222. [18] E. Czuchaj and J. Sienkiewicz, J. Phys. B 17 (1984) 2251. [19] J.D. Funk and W.H. Breckenridge, J. Chem. Phys. 90 (1989) 2927.