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84 IZVESTIYA VUZ. FIZIKA CONDITIONS FOR APPEARANCE OF CONTINUUM IN ABSORPTION/SPECTRUM OF Hg* M VAPOR AT THE Hg LINE 2537. G. I. Zav'yalov, N. A, Prilezhaeva, and A. Yu. Zav'yalova Izvestiya VUZ. Fizika, Volo 10, No. 9, pp. 140-143, 1967 UDC 535.34:546.49. Much work has been devoted to investigation of the effect of ex- traneous gases on the shape of absorption lines. However, so far there have been no investigations in which the vapor pressure of the mercury itself and the pressure of the extraneous gas would change over a wide range. We have Undertaken this task in the present work. The investigation was carried ofit by the spectrographic abiorption method described in [1]. A concentration of mercury atoms was estab- lished in a sealed quartz tube by introduction of the required amount of distilled mercury. The CsHr4 molecule was used as the extraneous gas. For each mercury atom concentration N o the absorption spectrum was photographed at various tube temperatures between 180" and 350" C. The photographs obtained were submitted to photometry, and the results am presented in Table 1. The following conclusions can be made from the figures in Table 1: 1) At mercury atom concentrations of N O ~ 10la cm -s and C~Ht4 molecule concentrations of N ~ 10 ~ cm "~ the 2537 ~ mercury line is narrow, and ij'k; d u does not depend on the temperature. A similar result was obtained in [2, 6] for rig + At. Almost identical broadening characteristics of the Hg 2537 A line were observed at NO ~ 10 Is cm -~ andN~ 10 ~ cm -s. 2) Considerable line broadening was observed at concentrations No ~ 10 ~ cm "s and N ~ 10 t9 cm -s, and also at N ~ 1017 cm -~ and N ~ l0 ~ cm-n, and there was a marked relationship between the broad- ening and temperature. 3) At concentrations No ~ 1017 cm -3 and N ~ 1019 cm -s there was a large extension of the line (a continuum) and ~ k, d was clearly related to temperature. Comparison of o~ results with those given in Table 2 leads to the suggestion that the appearance of the continuum at the Hg 2537 2{ line is due not only to the concentration of extraneous gas molecules but also to the concentration of mercury atoms. From this it follows that the absorption centers are weakly bound Hg + M complexes. According to existing theories for the effects of pressure in a bi- nary approach [7, 8, 9], which explain the broadening of the spectral lines on the basis of the Frank-Condon principle, approach of the per- tttrbing molecule to the absorbing molecule at a distance t changes the angular absorption frequency by an amount A~ = 2~ . In this case only interaction with one nearest particle is considered at each moment of time. The average value for the change in angular fre- quency A-~ can be evaluated from the average distance between the interacting particles [9] by using the equation A~ = 2~C . Since a van der Waals interaction (n = 6) is found in the (Hg + M) sys- tems shown in Table 2, 1 A(o = 2~ C --- (1) T6 " Here r is the average distance between the Hg and M particles, and it can be evaluated if it is assumed that the energy of interaction between the two particles is less than kT [10, il]. Then the probability after 1 sec of finding one perturbing molecule of extraneous gas inside the ef- fective (optical) interaction sphere ~, with a mercury atom at the center, can be determined by using the Poisson distribution [10, 15]. This pro- bability will be determined by the following expression: W = k e-x. (2) Table i No -3 cm N -3 cm Hg + C~H14 System No ._N TO cm K ~k~ d~. 10- m cm- i -1 see 1014 3.7.1015 --m-- 9.4.1015 --n-- 2.4.1016 m 9.1O TM n 9.1016 4.10 TM M 3' 1018 6.10 TM 1019 4. lO,S 3.1019 4.1038 lOai 5, 1034' 2.103s 4.1035 3,1036 453 503 553 623 453 503 553 453 503 553 453 503 553 453 5O3 553 623 453 503 553 623 1.98 1.88 1.98 1.98 2.10 1.98 2.08 2.51 2.52 2.52 3.20 3.56 3.75 5.45 5,52 5.90 6.10 24.4 29.5 34.5 38.0

Conditions for appearance of continuum in absorption/spectrum of Hg+M vapor at the Hg line 2537 Å

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84 I Z V E S T I Y A V U Z . F I Z I K A

CONDITIONS FOR APPEARANCE OF CONTINUUM IN ABSORPTION/SPECTRUM OF Hg* M VAPOR AT THE Hg LINE 2537.

G. I. Zav'yalov, N . A, Prilezhaeva, and A. Yu. Zav'yalova

Izvestiya VUZ. Fizika, Volo 10, No. 9, pp. 140-143, 1967

UDC 535.34:546.49.

Much work has been devoted to investigation of the effect of ex- traneous gases on the shape of absorption lines. However, so far there have been no investigations in which the vapor pressure of the mercury itself and the pressure of the extraneous gas would change over a wide range. We have Undertaken this task in the present work.

The investigation was carried ofit by the spectrographic abiorption method described in [1]. A concentration of mercury atoms was estab- lished in a sealed quartz tube by introduction of the required amount of distilled mercury. The CsHr4 molecule was used as the extraneous gas. For each mercury a tom concentration N o the absorption spectrum was photographed at various tube temperatures between 180" and 350" C. The photographs obtained were submitted to photometry, and the results am presented in Table 1.

The following conclusions can be made from the figures in Table 1: 1) At mercury atom concentrations of N O ~ 10 la cm -s and C~Ht4

molecule concentrations of N ~ 10 ~ cm "~ the 2537 ~ mercury line

is narrow, and i j ' k ; d u does not depend on the temperature. A similar

result was obtained in [2, 6] for rig + At. Almost identical broadening characteristics of the Hg 2537 A line were observed at N O ~ 10 Is cm -~ a n d N ~ 10 ~ cm -s.

2) Considerable line broadening was observed at concentrations No ~ 10 ~ cm "s and N ~ 10 t9 cm -s, and also at N ~ 1017 cm -~ and

N ~ l0 ~ cm-n, and there was a marked relationship between the broad- ening and temperature.

3) At concentrations N o ~ 1017 cm -3 and N ~ 1019 cm -s there was

a large extension of the line (a continuum) and ~ k, d w a s clearly

related to temperature.

Comparison of o ~ results with those given in Table 2 leads to the suggestion that the appearance of the continuum at the Hg 2537 2{ line is due not only to the concentration of extraneous gas molecules but also to the concentration of mercury atoms. From this it follows that the absorption centers are weakly bound Hg + M complexes.

According to existing theories for the effects of pressure in a bi- nary approach [7, 8, 9], which explain the broadening of the spectral lines on the basis of the Frank-Condon principle, approach of the per- tttrbing molecule to the absorbing molecule at a distance t changes

the angular absorption frequency by an amount A~ = 2~ . In this

case only interaction with one nearest particle is considered at each moment of time. The average value for the change in angular fre- quency A-~ can be evaluated from the average distance between the

interacting particles [9] by using the equation A~ = 2~C .

Since a van der Waals interaction (n = 6) is found in the (Hg + M) sys- tems shown in Table 2,

1 A(o = 2~ C --- (1)

T6 "

Here r is the average distance between the Hg and M particles, and it

can be evaluated if it is assumed that the energy of interaction between the two particles is less than kT [10, i l ] . Then the probability after 1 sec of finding one perturbing molecule of extraneous gas inside the ef- fective (optical) interaction sphere ~, with a mercury atom at the center, can be determined by using the Poisson distribution [10, 15]. This pro- bability will be determined by the following expression:

W = k e -x. (2)

Table i

No - 3

c m

N - 3

c m

Hg + C~H14 System

No ._N T O cm K

~k~ d~. 10- m cm- i - 1

s e e

1014

3.7.1015

- - m - -

9.4.1015

- - n - -

2.4.1016

m

9.1O TM

n

9.1016

4.10 TM

M

3 ' 1018

6.10 TM

1019

4. lO,S

3.1019

4.1038

lOai

5 , 1034'

2.103s

4.1035

3,1036

453

5 0 3

553

623

453

503

553

453

503

553

453

503

553

453

5O3

553

623

453

503

553

623

1.98 1.88 1.98 1.98 2.10

1.98

2.08

2.51

2.52

2.52

3.20

3.56

3.75

5.45 5,52

5.90

6.10

24.4

29.5

34.5

38.0

SOVIET PHYSICS JOURNAL 85

Table 2

System

Hg+C~HI~ Hg+Ar

Hg+Ar

Hg+Kr

Hg+Xe

Hg+Ar

Hg+He

Hg+COz

H g + C~H ~4

Hg+Ar

.Hg-bAr

Hgq-C~U1~

Hgq-N~

Hg+CO

Hgq-Ne

Hgq-Ar

Refer-

e n c e

[1]

[21 [6]

[61

[6I

[51

[41

[31

[ l l

[121

in]

[11

[131

[141

[121

[121

No, cm -3

10 TM

4.101~

4. I0 TM

2.1O TM

4.10 u

6.10 I~ 9.101. 4.1013

9.10 I~

4.10 TM

5.1016

9.1016

7.1O Is

8.10 I~ 2.10 is

9.1015

N O �9 N, cm -s

4 - 1 O a~ 4 1O 33 4.10 a3

2.103a

4. 1033

8- I03a 10 s4

2- 10 a4

3.10 a5

9.10 a5

i036 2. l0 a6

1036

10 a6

2.1O a7

6. I0 a7

Extension of

contour, e m ' l

N20

~20

~25

~30

N3O

~400

~600

N500

~950

~7OO

N1200

N2OO0

Dependence of [line broadening bn temperature

Independent

Slight dependence Slight dependence

Marked dependence

Dependent

Dependent Dependent

Here X = 4 r.ra N, and N is the concentration of extraneous gas tool- 3

ecules. By means of Eq. (2) we find the average number of these spheres

(pairs of particles) in 1 cm s after 1 sec:

N* ~.~ No N 4 ,~a e -x. (3)

Since it can be assumed that k < 1 for all the Hg + M systems we ex- amined, Eq. (3) takes the following form:

4 - N*'~ No N-~ ~ra. (4)

On the other hand we have

1 N* N -----=-_ . (S)

4/3 7~F 3.

From Eqs. (1), (4), and (5) we find that

- - 1 . . . . No.N, (6)

r6

i. e . , the value of ~ , which characterizes the extension of the line (the continuum), is proportional to the product NoN. The results of our work and of the work presented in Table 2 lead to the conclusion that the formation of a continuum depends on the product NoN. With the Hg 2fi37 A line a broad continuum arises when NoN ~ 10 m (Table 2). Here the statistical effect makes a considerable constribution to the Line broadening.

A. S. Volk took part in the experimental work.

REFERENCES

1. A. Yu. Zav'yalova, G. I. Zav'yalov, and N. A. Prilezhaeva, Izv. VUZ. Fizika, no. 6, 1964.

2. T. Skalinski, Bull. Acad. Polon. Sci., 8, 119, 1960. 3. C. Ftichtbauer and G. Joos, Phys. Zeit . , 28. 73, 1922. 4. H. Horodniczy and A. Jablonski, Nature, 142, 1122, 1938. 5. H. Horodniczy and A. Jablonski, Nature, 144, 594, 1939, 6. T. Grytsuk, M. Kubyak, and I. Prokhorov, Bull. Acad, Polon.

Sci., 12, 517, 1964.

7. A. Unzold, Modern Problems in Astrophysics [Russian transla- tion], IL, 1951.

8. I. I. Sobel'man, Introduction to Atomic Spectra Theory [in Russian], Moscow, 1963.

9. S. E. Frish, Optical Spectra of Atoms [in Russian], Moscow,

1963. i0. A. /ablonski, Acta Physica. Polon., 27, 49, 1965.

Ii. H. Kuhn, Proc. Roy. Soc., A 168, 212, 1937. 12. A. Michels, H. de. Kluever, and Castla, C. r. Acad., Sci.,

77, 221, 1989. 13. Yu. A. Kuslmikov, Izv. AN SSSR, 18, 252, 1954.

14. V. N. Ivanov, Opt. i Spektr., 7, 813; 1959. 15. E. S. Venttsel, Probability Theory [in Russian], Moscow, 1962.

12 January 1967 Kuznetsov Siberian Physicotechnical Institute