Experimental investigation of krypton spectra

Ph~sica 96C (1979) 147 - 154 © North-Holland Publishing Company

EXPERIMENTAL INVESTIGATION OF KRYPTON SPECTRA P. BAESSLER, H.-U. OBBARIUS and E. SCHULZ-GULDE Institut f. Plasmaphysik der Universitat Hannover, Hannover, Federal Republic of Germany Received 10 August 1978

The spectra of a wall-stabilized arc operated at atmospheric pressure in krypton, or mixtures of krypton and helium, were investigated under the assumption of local thermodynamic equilibrium (LTE). The electron density (n e = 5 X 1015 1.9 × 1017 cm-3, corresponding to an LTE temperature T = 9000-13300 K) was determined with a maximum error of 4-6% from laser interferometric measurements of the plasma refractivities at 632,8 and 1152.3 nm. For the spectral range between 400 and 570 nm ~ factors (± 15%) for continuum radiation were obtained which decrease in the direction of larger electron densities. Application of correction factors given by Preston to the measured intensity of the Kr I 450.2 nm line resulted in a transition probability independent of the plasma state, Anm = 5.1 × 105 s-1, with a 7% standard deviation. Altogether transition probabilities for four Kr I lines (±20%) and six Kr II lines (+-30%),and the Stark broadening constant of the 450.2 nm line were obtained.

1. Introduction

which allowed a precise temperature determination under the assumption of local thermodynamic equilibrium (LTE). A wall-stabilized arc o f 4 mm canal diameter operated at full arc length of 8.45 cm in krypton, or mixtures of krypton and helium, was observed either end-on or side-on for spectroscopic investigation. The arc was run at atmospheric pressure at currents between 20 and 100 A. The spectra were recorded using a 1 m McPherson scanning monochromator with a C z e r n y - T u r n e r mounting. A carbon arc was used as the radiation standard [3].

In a recent paper [1] absolute transition probabilities for a number o f Kr I lines were reported which had been obtained from wall-stabilized arc measurements under the assumption of a S a h a - B o l t z m a n n relationship between the electron density and the population densities of the excited Kr I levels. The electron density was calculated from the measured emission coefficient for continuum radiation at 456.1 nm and published experimental ~ factors [2]. The electron temperature was determined from measurements of the Kr 1 811.3 nm center line intensity (at an optical depth of 3 - 5 ) in conjunction with Kirchhoff's law. The transition probabilities turned out to be decreasing in the direction o f larger electron densities. However, some o f the ~ factors used had been extrapolated, and for k T ~ 1 eV the temperature calculation from the Kirchhoff-Planck function at 811.3 nm is but o f moderate accuracy. Finally, in view of the "three-chamber-arc" setup employed in most of the experiments the intensity data might be affected by an interdiffusion of, e.g., k r y p t o n and neon admitted to adjacent arc sections. In the present investigation electron densities were obtained from laser interferometric measurements

2. Electron density determination Under the present experimental conditions the plasma refractivity is the sum of the atom, ion, and electron refractivities. The atom and ion refractivities are very nearly independent of the wavelength whereas the electron refractivity is proportional to the square of the wavelength [4]. The contribution to the refractivity due to the electrons in highly excited states was estimated not to exceed 2% [5]. The electron density determination was based on measurements of the plasma refractivities at the H e - N e laser wavelengths 632.8 and 1152.3 nm [5, 6]. 147

148

P. Baessleret al./Experimental investigation of krypton spectra

The interferometric setup consisted of two Michelson interferometers having common measurement and reference arms. The cascade arc was positioned in the measurement arm with the arc axis aligned along the laser beams. The beam waists were imaged into the middle of the arc canal by an appropriate optical system, thus minimizing the beam diameters at each end of the plasma column. The arc was shorted within about 1/is by means of a thyristor. For several hundred microseconds during the decay of the plasma the shifts of the interference fringes were detected by photodiodes. The sinusoidal interference signals were amplified and displayed on oscilloscope screens. Evaluation yielded the changes of refractivities from which the electron density of the stationary arc plasma before extinction was calculated. The error due to the uncertainties of the fringe shifts (1/50 fringe) and the plasma length is 4% and 2% for an electron density of 1016 and 1017 cm-3, respectively. Another 2% of uncertainty results from the influence of the electrons in highly excited states, correspondingly adding up to a maximum error of 6% or 4% of the electron density determination.

3. Stark broadening In the present experiments the predominant broadening mechanism of Kr I lines is the quadratic Stark effect. In table I the experimental full half widths 2w of the Kr 1 450.2 nm line are listed together with the corresponding electron densities obtained from two-wavelength interferometry. From the data an experimental Stark broadening constant of win e = 0.139 nm/1017 cm -3 (+3%) was determined. Klein and Meiners [7] reported a value of win e = 0.159 nm/1017 cm -3 (+9%) obtained from shock tube experiments.

4. Kr II line transition probabilities The temperature T was calculated from the experimental electron density under the assumption of LTE by taking into account quasineutrality, Saha's equation, and Dalton's law. Transition probabilities Anm for Kr II lines were obtained from the corresponding measured total line

emission coefficients enrn and the equation,

enm = (hc/4rrknm)[(grnAnmne)/u +(T)] exp (-Em/kT),

(1) where gm and E m are the statistical weight and the energy of the upper level, respectively, and knm is the wavelength. The partition function for singly ionized krypton is denoted by u+(T). Finally, c, h, and k are the velocity of light, Planck's constant, and Boltzmann's constant, respectively. At electron densities 3.8 X 1016 cm -3 ~
3.08

ne [1016 cm -3]

465.9 520.8

429.3

5s 4P5/2-5 p 4P~/2 5s 4P3/2-5p 4P~/2

5s 4P3/2-5P 4D~/2

7.3

7.3 1.5

8.6 10.4

3.76

0.109

-

1.1

-

-

[8]

Uhlenbusch et al.

* Uncertainties are ± 10% on a relative scale, +-30% absolute.

463.4 473.9

5s' 2D3/2-5P' 2F0/2 5s 4 P s / 2 - 5 p 4p0/2

10.5

Present exper.*

length [rim]

457.7

Experiment

3.78

0.113

Wave-

5s' 2D5/2-5 p' 2F°/2

Transition

Table II Transition probabilities o f Kr II lines, 107 s-1

0.094

[nm]

2w

Table I Full half widths o f the Kr 1 450.2 n m line

4.68

7.80 22.2

8.63 10.40

10.70

Miller et al. [9]

5.69

0.160

11.8

76 28.8

66 -

69

Levchenko [10]

6.32

0.180 10.79

0.305

-

9.138 6.183 1.311 9.366

-

27.2 11.9 4.5

LS

9.273 1.486 4.893

12.29

-

-

mixed

Koozekanani and Trusty [12]

Theory

9.00

0.245

25.4

Podbiralina et al. [ 11 ]

8.64

0.250 18.66

0.525

10.12 1.73 10.97

12.44

11.73

14.15

Spector and Garpman [13]

12.65

0.355

4.1

5.5 3.68

7.3 3.34

Samoilov et al. [14]

Compilation

T~

r~

t~

150

P. Baessleret aL/Experimental investigation of krypton spectra

systematic relation to the other data of table II. On a relative scale the agreement of the remainder of the data with the present results is satisfactory. Koozekanani and Trusty [ 12] calculated transition probabilities with the assumptions of pure LS and mixed coupling. Spector and Garpman [13] carried out calculations using the effective operator formalism and intermediate coupling. In general, the absolute data of Spector and Garpman, and the data compiled by Samoilov et al. [14] are outside the present error limits.

5. Continuous emission For the rare gases the emission coefficient e x for continuum radiation at wavelength X is given by

ex =~(21r)}(3km3)-}e6c-2X-2T~e}n2~(X, T),

(2)

where m e is the mass of electron, and e is the elementary charge, Te being the electron temperature, i.e. the parameter governing the Maxwellian velocity distribution of the free electrons. In the above equation ~(X, T) is a dimensionless factor related to the atomic absorption coefficient. Recently Hofsaess [15] calculated photoionization cross sections and ~(k, T) factors, which latter are but weakly temperature dependent in the visible spectral range, by using the scaled Thomas-Fermi method. In the present investigation experimental ~ factors for krypton at X = 456.1 nm were obtained from eq. (2) by inserting the measured emission coefficients e x and the results of the electron and temperature determinations described above. In order to extend the electron density range under investigation down to 5 × 1015 cm -3 the krypton plasma was diluted with helium in some of the experiments. The minimum kryptor~ to helium concentration ratio was 2.5% at an arc temperature of 12300 K. The temperature of the Kr-He plasmas was determined from the measured total line emission coefficient of a Kr II line and the electron density by using eq. (1). For the parameters given the production of electrons due to the ionization of helium atoms is negligible under LTE conditions. Thus the emission coefficients for continuum radiation are not likely to be affected by spurious contributions due to the presence of helium. Because of the weak temperature

dependence of the emission coefficient any moderate deviation from LTE is expected to bear a negligible effect on the resulting ~ factors whose maximum uncertainties are about 15%. In fig. 1 the present experimental ~ factors as well as those obtained from shock tube experiments by Meiners and Weiss [2] are plotted versus the ratio n2/V~. The ~ factors decrease in the direction of larger n2/x/~values. In addition, the continuum radiation was investigated between 400 and 570 nm at wavelengths not appearing to be affected by line radiation. Side-on measurements were carried out with the arc operated in krypton, and a mixture of krypton and helium, in conjunction with an Abel inversion procedure [16]. Relative ~ factors were obtained which were scaled to the above absolute data at 456.1 nm. The results are presented in fig. 2. The experimental ~ factors determined for n e = 4.3 X 1016 cm -3, T = 10150 K and n e = 4.7 × 1016cm -3, T = 12450 K are in close agreement with one another, whereas those forn e = 1.4 X 1017 cm -3, T = 12200 K in general are significantly lower. As reported by Hofsaess [15] a comparison between experimental and theoretical data is only reasonable for wavelengths below 500 nm. For X ~< 480 nm the experimental factors are close to the curves based on the theoretical data. The ~ factor which is composed of the ~fb and ~ff factors given for free-bound [15] and free-free [17] transitions, respectively, is calculated from eq. (4a) of ref. 18. For krypton at the wavelengths and temperatures under investigation the ~ff factors are ranging from 1.14 to 1.19.

6. Kr I line transition probabilities Transition probabilities for a few selected Kr I lines of different excitation energies Em were determined from the corresponding measured total line emission coefficients enrn and the following relationship,

enm = (h 4 c/ 47rXnm) ~mAnmn2 /2u +( T) ] × (21rmekT) -3/2 exp [(X - Em - Ax)/kTI,

(3)

where use has been made of Saha's equation to relate the population densities of the excited krypton atoms to the electron density. The lowering AX of the ioniza-

P. Baessler et al./Experimental investigation of krypton spectra

ct

,---].

151

0 0

...-r II

o

u_

A

Z~

1 I

1029

I

I

1030

I

1031 2 RATIO N E /,,/T'.

I

1032

1033

-6 -1/2 CM K

Fig. 1. Continuum ~ factors at ?~ = 456.1 nm versus the ratio ne/~/T, z~measurements with pure krypton, o measurements with mixtures of krypton and helium. The error bars refer to the maximum uncertainties. - - - results obtained by Meiners and Weiss [2] from shock tube experiments.

~ 0 0 0 o

o

I-

z

2

I

L,C0

I

I

I

r:'0~., I~AVE LEi'~G TH

),. ,

I

600 NN

Fig. 2. Continuum I[ factors versus wavelength. Side-on measurements: z~pure krypton, n e = 1.4 X 1017 cm -3, T = 12200 K, o pure krypton, n e = 4.3 X 1016 cm -3, T = 10150 K, • k r y p t o n - h e l i u m mixture, n e = 4.7 X 1016 cm -3, T = 12450 K. Theory: Hofsaess [15, 17] - T = 1 0 0 0 0 K, - - T = 14000 K.

152

P. Baessler et al./Experimental investigation of krypton spectra

tion energy X of krypton atoms was taken into account by the equation [19] AX = e3(81r ne/kT)~,

(4)

Eq. (3) holds under the assumption of partial LTE, which is less rigid than that of LTE. Here T is the electron temperature. In fig. 3 the transition probabilities obtained from end-on measurements for the Kr 1 450.2 nm line are plotted versus the ratio n2/x/~. The error bars indicate the maximum errors of 20%. The data are fairly constant in the region of low electron densities. I f eq. (3) is divided by eq. (2) then the electron density virtually cancels out and a relationship is obtained which allows the determination of the ratio Anm/~. There is no evident dependence of the present Anm/~ data on the plasma state, see fig. 3. The mean value is 2.16 X 105 s -1. Transition probabilities for the Kr 1 450.2,758.7, 769.5, and 785.5 nm lines were also obtained from side-on measurements with mixtures of krypton and

helium, for the temperature and electron density range (9000 K, 1 X 1016 cm -3) ~< (T, ne.) ~< (12000 K, 3.5 X 1016 cm-3). The mean values and the relative standard deviations are listed in table III. For the red lines there is agreement with the results reported previously [ 1]. The value given in table I of ref. 1 for the 450.2 nm line is higher by 50%.

7. Discussion The present ratio of transition probabilities for the Kr 1 450.2 nm ( 5 s - 6 p ) and the Kr 1 758.7 nm ( 5 s 5p) lines, A450.2/A758.7 = 0.011, is significantly lower than the corresponding value of 0.018 calculated from the data given in table I of ref. 1. In order to clear the discrepancy the earlier data were checked again. It turned out that the ratio in question as derived from extensive measurements with mixtures of krypton and argon or neon at relatively low electron densities is in agreement with the present result. However, in

FRACTION OF TRUE lINE INTENSITY i

&

6

--

5

)

4

:I

A A AA Z~

<

•

T

3

• ~

0,69

I i

• ¢

' T'

o

~

0,80

J

O

J ~

0,94

i

•

2

"" •

"'-

"

v•

i I

1029

I

1030

I

1031

J

I

1032

1033

2 -6 -1/2 RATIO NE /J-T~, CM K

Fig. 3. Experimental transition probability Anm for the Kr 1 450.2 nm line, and ratio of Anm to continuum ~ factor at X = 456.1 nm, versus the ratio n2]x/-T. A An m measurements with pure krypton; o Anm measurements with mixtures of krypton and helium; • ratio Anm/~. The error bars refer to the maximum uncertainties. • Anm divided by the "measured fraction of the true intensity" as calculated by Preston [25].

P. Baessler et al./Experimen tal investigation of krypton spectra

Table III Transition probabilities of Kr I lines, 106 s-1 Transition

Wavelength

Present investigation*

Ref. 1

Paschen numbers

h [nm]

Ant n

Anm

1 s 3 - 2 P3

785.5

22.1

758.7 769.5 450.2

46.1 5.7 0.50

1 s4-2 Ps 1 S s - 2 P7 1 s4-3 PS

standard deviation 3%

3% 5% 10%

19.5

42.8 4.70 0.764

* Absolute uncertainties +-20%.

the final compilation of the table that ratio had been confused with the one obtained from the absolute transition probabilities read from fig. 2 of ref. 1. In view of the present measurements some of the data in the figure may be affected by systematic errors for the following reasons: (i) The 758.7 nm line is sensitive to krypton concentration, and because of its close proximity to the strong 760.1 nm line the intensity measurement is difficult. Moreover, the 758.7 nm line intensities had been measured at a krypton plasma length of 1.2 cm, and those of the 450.2 nm line at plasma lengths greater than 1.2 cm. Pure neon had been admitted to the remainder of the column including the electrode regions. In contrast to arc measurements with argon and sulfur hexafiuoride [20] recent arc experiments [21] carried out with argon and neon being fed into adjacent arc sections of various lengths indicated that the mixing zones of the different gases are not limited to regions of ~1 mm between the cascade plates but may be much longer, depending on the gas flow rates and the flow patterns. Thus, for the krypton region under investigation in [1 ] neither the length nor the degree of inhomogeneity might have been known reliably. (ii) Consequently, those uncertainties of the plasma lengths of interest had affected the determination of the Kirchhoff-Planck function B x at 811.3 nm and the subsequent temperature calculation. (iii) Use of extrapolated ~ factors resulted in electron densities which were too small, and thus led to absolute Kr I line transition probabilities too large, for the low electron density range. Since the Kr I 450.2 nm line had been used as the reference line in the determination of relative transition probabilities for the Kr I 5s-6p lines the corresponding data listed

153

in table I of ref. 1 should be multiplied by a factor of 0.62. An attempt had been made in [1] to modify the statistical weights gm as suggested by Gtindel [22, 23] in order to give an explanation of the tendency of the transition probabilities of Kr I lines to decrease towards larger electron densities. The results, however, were inconclusive. Recently Preston [24] investigated the influence of spectral line blending, line wing loss, and self-absorption on the experimental determination of the integrated intensity of various Ar I lines emitted by a homogeneous LTE plasma, based on a computer model of the spectrum. The model was also applied to parts of the spectrum of krypton [25], and correction factors, i.e. the measured fractions of the true intensities, were determined for the Kr 1 450.2 nm line as a function of electron density, for an LTE krypton plasma at atmospheric pressure. Preston took into account six Kr I 5s-6p lines in the neighborhood of the 450.2 nm line by using the relative transition probabilities given in [9] normalized to Anm = 106 s -1 for the 450.2 nm line. Stark broadening parameters were taken from ref. 7, continuum ~ factors from ref. 15. Application of the correction factors to the experimental line intensities resulted in transition probabilities independent of the plasma state. The corrected values are represented by the solid data points in fig. 3. The mean value of the transition probability for the Kr I 450.2 nm line isAnm =5.1× 105s l w i t h a 7 % standard deviation. By the way, identical correction factors P(Xm) can be obtained from Gtindel's relationship [22]

P(Xm)=exp{ -

f3[( FX Xi0)3 +(Xe0tT] , t ~

~m

J}

(5)

if the empirical factor F = 1.1 is used. In the above equation Xm is the difference between the ionization energy X and the excitation energy E m . The constant f related to the quantum defect of the s state is 1.876 for the Kr 1 450.2 nm line. The quantities X-'o = (36n e6ne) 1/3 and Xeo = (21r3/2e6ne(kT)l/'~) 2/7 refer to the perturbation of the bound electronic state due to ion and electron collisions, respectively. It is not clear whether the coincidence of the data given by Preston with those calculated from eq. (5) is an acci-

154

P. Baessleret al./Experimental investigation of krypton spectra

dental one. Unfortunately the 5 s - 5 p lines tend to overlap and/or will be affected by self-absorption at larger electron densities, thus making it difficult to measure accurate line intensities required for further comparisons of the two methods.

D. Hofsaess for providing his tables of free-bound and free-free continuum factors. The technical assistance of L. Borth, G. Dietrich, D. Henkel, and K. Witkop is gratefully acknowledged.

References 8. Conclusiohs The significance of the present experiments is the combination of two-wavelength interferometry for precise electron density determination with plasmaspectroscopic measurements. As a result, transition probabilities for Kr I and Kr II lines were derived having maximum uncertainties of 20% and 30%, respectively. The relative Kr I transition probabilities obtained in a previous investigation [ 1 ] were corroborated for a number o f 5 s - 5 p lines whereas the data for the 5s--6p transitions should be multiplied by a factor of 0.62. An apparent dependence on the plasma state of the absolute transition probabilities Anm of Kr I lines noticed here vanishes by application of correction factors calculated by Preston [25]. However, the ~ factors for continuum radiation decrease towards larger electron densities, though to a lesser degree than discovered in shock tube experiments [2]. The experimental observation - prior to the application of correction factors to the Kr 1 line intensities that the ratio Anm/~ is independent of the plasma state might be again of interest once the ~ factors will have been corrected or modified by reason of physics.

Acknowledgments We would like to thank W. B~Stticher and M. Kock for helpful discussions and suggestions. We would also like to express our appreciation to R. C. Preston for applying his program to the spectrum of krypton and for permission to use his data. Thanks are also due to

[1] W. E. Ernst and E. Schulz-Gulde, Physica 93C (1978) 136. [2] D. Meiners and C. O. Weiss, J. Quant. Spectrosc. Radiat. Transfer 16 (1976) 273. [3] H. Magdeburg and U. Schley, Z. Angew. Phys. 20 (1966) 465. [4] H. R. Griem, Plasma Spectroscopy, New York (1964) 299. [5] P. Baessler, Dissertation, TU Hannover (1978). [6] M. Briinger and M. Kock, Z. Naturforsch. 30a (1975) 1560. [7] P. Klein and D. Meiners, J. Quant. Spectrosc. Radiat. Transfer 17 (1977) 197. [8] J. Uhlenbusch, E. Fischer and J. Hackmann, Z. Phys. 239 (1970) 120. [9] M. H. Miller, R. A. Roig and R. D. Bengtson, J. Opt. Soc. Amer. 62 (1972) 1027. [10] M. A. Levchenko, Soy. Phys. J. 14 (1971) 1445. [ 11 ] V. P. Podbiralina, Yu. M. Smirnov and N. V. Stegnova, Opt. Spectrosc. 34 (1973) 467. [12] S. H. Koozekanani and G. L. Trusty, J. Opt. Soc. Amer. 59 (1969) 1281. [13] N. Spector and S. Garpman, J. Opt. Soc. Amer. 67 (1977) 155. [14] V. P. Samoilov, Yu. M. Smirnov and G. S. Starikova, J. Appl. Spectrosc. (USSR) 38 (1975) 1117. [15] D. Hofsaess, J. Quant. Spectrosc. Radiat. Transfer 19 (1978) 339. [16] M. Kock and J. Richter, Ann. Phys. (7) 24 (1969) 30. [ 17 ] D. Hofsaess, private communication. [18] E. Schulz-Gulde, Z. Phys. 230 (1970) 449. [19] H. R. Griem, Phys. Rev. 128 (1962) 997. [20] G. Baruschka and E. Schulz-Gulde, Astron. Astrophys. 44 (1975) 335. [21] W. D. Bargmann, Diplomarbeit, TU Hannover (1977). [22] H. GiJndel, Beitr. Plasmaphys. 10 (1970) 455. [23] H. Giindel, Beitr. Plasmaphys. 11 (1971) 1. [24] R. C. Preston, J. Phys. B10 (1977) 2381. [25] R. C. Preston, private communication.