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Experimental transition probabilities for lines arising from 3s23p24p configuration of single ionized sulfur
Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
Experimental transition probabilities for lines arising from 3s3p4p configuration of single ionized sulfur J.A.M. Rojas, M. Ortiz, J. Campos* Ca& tedra de Fı& sica Ato& mica Experimental, Facultad de Ciencias Fı& sicas, Universidad Complutense de Madrid, Avda Complutense s/n, 28040 Madrid, Spain Received 9 September 1998
Abstract
Experimental transition probabilities for 103 lines with origin in the 3s3p4p configuration of S II have been determined. Relative values have been obtained from the measurement of emission-line intensities in a laser-produced plasma. The experiment was carried out with samples of zinc sulfide (ZnS) and antimony sulfide (Sb S ) in a pure argon controlled atmosphere in optically thin plasma conditions. The results were placed on an absolute scale by using line-strength sum rules and lifetime values. Comparison between previously published data and present experimental and calculated values has been made. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Experimental transition probabilities; Plasma electron density; Temperature; Self absorption
1. Introduction In spite of its interest in plasma physics and astrophysics, transition probability values of single ionized sulfur has been the subject of relatively few works. Experimental data were obtained by Miller et al. [1] and by Bridges and Wiese [2], which are to date the only extensive experimental studies for lines of S II. Theoretical calculations were performed by Aymar [3], and recently by Nahar [4]. A data compilation was made by Wiese and Martin [5]. The emission spectra were obtained in this experiment with a laser-produced plasma as the spectral source. We measured the emission intensities of lines arising from the same upper level to determine the relative transition probabilities and corresponding branching ratios. To place the
* Corresponding author. Tel.: 34 91 394 4546; fax: 34 91 394 5193; e-mail: [email protected] 0022-4073/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 9 8 ) 0 0 1 1 9 - 8
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J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
data on an absolute scale, calculated lifetime values have been used. These values were obtained in this work performing transition probability calculations in Intermediate Coupling (IC) by the least squares fitting (LSF) method with multiconfiguration interaction and using ab initio Hartree— Fock (HF) calculations made with Cowan’s computer code [6]. Plasma electron density, temperature and self-absorption of the S II transitions have been studied in order to find the best experimental conditions to carry out the measurements. The wavelengths of the measured transitions range from 1900 to 7000 A> . The tables of Kaufman and Martin [7], Wiese and Martin [5], Striganov and Sventitskii [8], Vujnovic and Wiese [9] and Pellerin et al. [10] have been used to identify the transitions. To provide level energies for our calculations, the tables of Martin et al. [11] have been employed.
2. Experimental set-up The experimental arrangement is similar to that described in previous works [12,13]. A Q-switch Nd : YAG laser generates 200 mJ pulses of 7 ns of duration at 20 Hz frequency and 10 640 A> wavelength. The laser light was focused with a 12.5 cm focal length lens onto samples of ZnS or Sb S that were placed in a chamber filled with 4 Torr of argon. As is known, the temperature, temporal evolution and electron densities of laser produced plasmas can be partially controlled by the use of suitable buffer gases. In addition the use of Ar provides us with several spectral lines of well known Stark parameters and transition probabilities, that will be useful to complete the determination of plasma electron densities and temperatures. We studied the variation of intensity and width of S II and Ar II lines vs the argon pressure at different delay times from the laser pulse. Measurements were carried out from vacuum (10\ Torr) to 700 Torr and at 0.3, 0.5, 0.7 and 0.9 ls delay times. Maximum line intensity was achieved at 4 Torr the and 0.3 ls from the laser pulse. Also, at this time and pressure the line widths were sufficiently narrow to carry out the present experiment. Laser irradiance was 5;10 W cm\. The light emission perpendicular to the laser light from the plasma was analyzed by a 1 m Czerny—Turner monochromator. The spectral range was 1900—7000 A> with 0.3 A> spectral resolution in first order. The relative spectral response of the experimental system has been determined by using calibrated deuterium and tungsten lamps with the same experimental conditions that were used in the measurements. The analysis of the spectra was made by fitting the observed line shapes to numerically generated Voigt profiles. The instrumental profile was known previously from the analysis of narrow spectral lines from hollowcathode lamps. The fitting of the observed profiles provides the total intensity accurately, as well as the broadening of spectral lines when necessary. A time-resolved optical multichannel analyzer (OMA III, EG & G) allows recording of the spectra at the selected delay time from the laser pulse and during a preset time length. The spectral range of every spectrum section was 100 A> (first order). Detection was made in synchronism with the electronic trigger of the laser Q-switch. For every period of data acquisition, background accumulation and subtraction were made. Measurements were made at 0.3, 0.5, 0.7 and 0.9 ls delay from the laser pulse and light was collected during 0.2 ls. The corresponding results were compared and averaged. No dependence of relative intensities with time or type of sample was found. The statistical uncertainty of line-intensity values was about 8%.
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
435
To test the laser-produced plasma values, branching ratios have been obtained, where possible, by using a sulfur hollow-cathode lamp as the spectral source. The gas used to fill the tube was Ne. The operating current was typically 10 mA. In this case the single photon counting method was employed using as a detector an EMI 9558 QB photomultiplier cooled with dry ice. The results of both methods were in agreement within statistical uncertainties.
3. Results and discussion Tables 1 and 2 show transition probabilities for lines corresponding to the S II 3s3p4p configuration studied in this work. These values were obtained from the branching-ratio measurements and the theoretical lifetimes calculated in the present work. In Table 1 are also shown the values obtained by line-strength sum rules. There is agreement with the lifetime results. To take into account the contribution to the lifetimes of the transitions out of our spectral range, we used the calculated values. This correction amounts to 5% or less in general. The experimental errors given have been calculated adding quadratically the statistical uncertainties (8%) and the experimental error of the spectral response determination (6%) of the measuring system. The error of the calculated lifetimes was not included in the quoted uncertainties. The line intensity self-absorption was lower than 1% in worst cases. Total errors are about 10% for intense transitions, about 25% for the weak ones and an error of 50% is estimated for some partially blended lines. The calculated lifetimes in both approximations, dipole length and velocity, are presented in Table 3 in order to permit future rescaling when accurate experimental lifetimes were available. The differences between both approximations are about 2%.The values used to put the transition probabilities on the absolute scale were those calculated in length form. The experimental lifetimes of Maleki and Head [14] are also shown for comparison in Table 3. Their values are higher than the present calculations (between 15% for 4p S and 40% for 4p P). In Tables 1 and 2 we show for comparison the experimental values of Miller et al. [1]. Bridges and Wiese [2], the ab initio calculations of Aymar [3] employing the HF#IC method and the values of Nahar [4] using the close coupling approximation with the R-matrix method in LS coupling. Tables 1 and 2 also show multiconfiguration calculations made in this work. The wavefunctions have been obtained by least-squares fitting to the experimental energies tabulated by Martin et al. [11]. Typical differences between the calculated and the experimental energies are lower than 20 cm\. The radial parts of the orbitals were calculated with the relativistic Hartree—Fock Cowan’s [6] code in length and velocity forms. Typical differences between them were about 3%. The calculations show a strong configuration interaction of the S II configurations. For the transitions studied the strongest mixing occurs between 3p4p#3p5p (odd) and 3p3d#3p4d#3p4s#3p#3p5s (even) configurations. There is good agreement between our configuration mixing percentages and those given by Martin et al. [11]. There is also a general good agreement within experimental errors between our absolute transition probabilities and the values of Miller et al. [1], Bridges and Wiese [2] and Aymar [3]. The calculated transition probabilities of this work differ from the values of Aymar [3] by less than 10% for most cases. The values of Nahar [4] are about 25% lower than ours for many lines.
436
j (A> )
Transition levels Upper
Lower
Absolute transition probabilities (10 s\) Experiment (This work)
3p (P) 4p D 3p (P) 4p D
3p (P) 4p D
3p (P) 4p D
3p (P) 4p P
(P) 4s P (P) 4s P (P) 3d F (P) 4s P — (P) 4s P (P) 4s P (P) 3d F (P) 3d F (P) 4s P (P) 4s P (P) 3d F (P) 3d F (P) 3d F (P) 4s P (P) 3d F (P) 3d F (P) 3d D (P) 3d D 3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D
Theory (This work)
Ref. 1
Ref. 2
(This work)
Ref. 3
Ref. 4
7.64 1.15 4.12
7.3 1.1 5.8
6.03 1.15 3.34
4.42 4.17 0.25 0.79 3.32
4.2 4.0 0.22 1.2 4.6
3.09 3.78 0.33 0.69 2.70
5473.620 5556.007 5664.780
7.8$0.8 1.3$0.2 3.9$0.4
7.60 1.26 3.78
8.4 2.9 5.2
8.6
5428.667 5509.718 5645.672 5616.639 5659.985
4.4$0.5 4.3$0.5 0.40$0.1 0.72$0.07 3.4$0.3
4.32 4.19 0.39 0.70 3.07
5.5 4.2 1.9 1.8 4.4
5.0 4.6
5432.815 5564.976 5536.723 5578.889 5640.333
6.7$0.7 1.7$0.2 0.03$0.01 0.86$0.09 3.7$0.4
7.12 1.86 0.04 0.92 3.92
7.7 2.0 1.0 1.1 4.9
7.8 2.0
7.05 1.85 0.03 0.68 3.40
6.8 1.7 0.06 1.1 4.8
5.18 2.07 0.03 0.61 2.77
5453.828 5526.253 5606.151 6957.934 6981.398
9.0$0.9 0.35$0.05 3.8$0.4 0.05$0.02 0.3$0.1
8.96 0.35 3.75 0.05 0.32
10.1 0.9 3.8
10.00
8.96 0.39 3.72 0.06 0.37
8.5 0.6 5.4
7.33 0.37 3.08 0.05 0.28
1998.765 2006.367 4942.466 5009.564 5932.962 6123.383 6397.990 6413.706
2.0$0.5 0.4$0.1 1.9$0.5 8.6$2 0.11$0.03 0.16$0.04 1.4$0.4 1.0$0.3
2.28 0.43 2.11 9.60 0.12 0.18 1.46 1.08
3.5 10.7
4.8
4.3
4.0
1.41 0.30 1.53 9.56 0.03 0.04 1.42 1.33
1.5 9.4
2.15 0.42 1.50 7.19
1.9 1.7
1.12 1.11
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
Table 1 Transition probabilities for lines arising from D and P levels of 3s3p4p configuration of S II
3p (P) 4p P
1981.662 2003.540 4925.347 4991.974 5103.340 6369.342 6384.893 6397.359
2.0$0.5 (0.5 5.1$0.5 3.6$0.4 3.0$0.3 (0.1 0.3$0.1 0.9$0.4
2.56 (0.5 5.11 3.63 3.01 (0.1 0.31 0.92
1970.878 1985.025 4924.115 5032.447 5093.989 5996.161 6274.306 6286.351 6305.483 6521.428
1.3$0.2 0.5$0.1 2.1$0.2 8.9$0.9 0.04$0.02 0.16$0.05 0.07$0.03 0.4$0.1 1.9$0.2 (0.04
1.36 0.52 2.22 9.40 0.05 0.17 0.08 0.44 2.04 (0.05
1.66 0.33 5.19 3.42 2.62 0.02 0.89 1.58
4.0 3.8 3.4
4.0 8.4
Experimental transition probabilities determined by theoretical lifetimes. Experimental transition probabilities determined by line-strength sum rules. Experimental uncertainties are the same in both cases. Estimated accuracies for the most prominent visible lines quoted by the authors are 13—30%. Uncertainties quoted by the authors are 35%. Calculated with Cowan’s code in dipole length form.
8.7
2.3
1.11 0.53 2.48 8.37 0.01 0.20 0.07 0.55 2.18 (0.01
5.1 3.3 2.7 0.02 1.2 2.0
1.19 1.07 3.79 1.16 3.68 0.11 0.72 1.12
2.4 8.1
1.89 0.79 2.73 5.97
0.10 0.75 2.7
0.05 0.42 1.87
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
3p (P) 4p P
3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d D 3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 3d F (P) 4s P (P) 3d D (P) 3d D (P) 3d D (P) 3d F
437
438
Table 2 Transition probabilities of lines arising from levels of 3s3p4p configuration of S II
Upper
Lower
Absolute transition probabilities (10 s\) Experiment (This work)
3p (P) 4p D
3p (P) 4p S
3p (P) 4p D
3s(P)3pP 3s(D)3pD (P) 4s P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d F 3s 3p P 3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d D (P) 3d F 3s 3p P 3s 3p P 3s 3p D (P) 3d P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d F (P) 3d F
1951.379 3052.500 4742.389 4804.120 5647.033 5819.272 6080.838 6092.122 6312.661
(0.04 0.07$0.03 0.09$0.04 (0.07 7.1$0.7 1.1$0.2 (0.02 (0.04 2.2$0.3
1936.731 1950.378 1958.239 4656.777 4716.267 4815.549 5927.277 5940.732 5951.522 6161.840
2.4$0.6 1.6$0.4 1.6$0.4 1.6$0.2 3.7$0.9 10$1 (0.04 0.05$0.03 0.08$0.04 (0.03
1930.819 1944.379 3004.983 3906.951 4681.294 4779.094 5639.972 5895.910 5912.788 6102.277 6286.956
(0.05 (0.04 (0.03 0.13$0.03 0.2$0.1 0.37$0.04 7.7$0.8 (0.02 (0.04 0.34$0.09 2.3$0.2
Theory Ref. 1
4.9 1.1
Ref. 2
1.2
2.6
1.9 3.6 10.8
0.6 6.3
3.4 9.4
(This work) 0.06 0.07 0.08 0.10 6.48 1.12 0.01 0.02 2.66
Ref. 3
5.7 0.9
5.31 0.97
3.0
1.98
2.84 2.74 1.68 0.99 3.14 9.53 0.01 0.05 0.09 0.02 0.01 0.02 0.01 0.22 0.07 0.33 7.54 0.01 0.01 0.17 2.56
Ref. 4
3.28 2.14 1.06 2.17 4.18 5.90
0.02
6.6
2.8
0.10 1.91
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
j (A> )
Transition levels
3p (P) 4p P
3p (D) 4p F
3p (D) 4p P
3p (D) 4p P
3p (S) 4p P
3613.030 3672.122 4917.212 5047.292
0.71$0.08 1.7$0.2 7.3$0.7 4.0$0.4
3595.977 3654.497 4885.648 5014.069
2.1$0.2 0.55$0.1 1.6$0.2 9.5$0.9
2357.751 3839.158 3918.183 3993.502 5320.732
0.40$0.2 0.5$0.3 0.03$0.01 0.95$0.1 8.6$0.9
2669.812 3272.229 3329.330 4552.406 2185.932 2187.264 2629.110 3257.868 3314.469 4193.493 4524.718 4524.947 2877.120 4362.564 4450.712 5011.608
0.54 1.57 7.49 4.05
6.6 3.6
0.83 1.59 5.85 2.71
1.4 9.8
1.90 0.34 1.95 9.48
1.7 8.4
2.11 0.40 1.49 6.90
0.8 10.1
0.19 0.05 0.04 0.92 9.33
0.07 1.9 9.2
0.04 1.12 8.00
8.4
11.6
0.86$0.5 2.0$0.5 1.5$0.7 14.8$2 0.48$0.1 3.4$0.9 0.28$0.07 0.31$0.08 2.7$0.7 0.61$0.2 2.4$1 9.1$2
0.10 1.63 1.04 12.86
9.7
0.48$0.1 (0.01 (0.04 9.0$0.9
Experimental transition probabilities determined by theoretical lifetimes. Estimated accuracies for the most prominent visible lines quoted by the authors are 13—30%. Uncertainties quoted by the authors are 35%. Calculated with Cowan’s code in dipole length form.
0.18 2.66 0.10 0.32 2.31 0.60 1.87 11.23 0.62 0.005 0.01 9.50
2.0 1.3 12.3
0.4 2.8 2.1 11.5
0.10 1.36 0.65 9.11 0.36 3.27 0.13 0.34 1.63 0.57 0.93 8.34 0.50 0.03 0.27 7.61
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
3p (P) 4p P
3d P 3d P 4s P 4s P (P) 3d P (P) 3d P (P) 4s P (P) 4s P 3s 3p D (P) 3d D (P) 3d F (P) 3d F (D) 4s D (P) 3d P (P) 4s P (P) 4s P (D) 4s D 3s 3p D 3s 3p D (P) 3d P (P) 4s P (P) 4s P 3s 3p S (D) 4s D (D) 4s D (D) 4s D (P) 3d D (P) 3d D (S) 4s S (P) (P) (P) (P)
439
440
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443 Table 3 Calculated lifetimes for the levels of the S II 3s3p4p configuration Level
Calculated lifetime (ns) Length
3p (P) 4p S 3p (P) 4p D N (P) 4p D 3p (P) 4p D 3p (P) 4p D 3p (P) 4p P 3p (P) 4p P 3p2 (3P) 4p P 3p (P) 4p D 3p (P) 4p D 3p (P) 4p S 3p (P) 4p P 3p (P) 4p P 3p (D) 4p F 3p (D) 4p F 3p (D) 4p D 3p (D) 4p D 3p (D) 4p P 3p (D) 4p P 3p (S) 4p P 3p (S) 4p P
Ref. 14
Velocity
11.89
11.61
7.50 7.46 7.40 7.34
7.34 7.30 7.24 7.19
6.40 6.29 6.44
6.27 6.16 6.31
9.09 8.91 4.73
8.88 8.70 4.63
6.87 6.87
6.71 6.71
8.15 8.10
7.98 7.94
6.02 6.00
5.89 5.87
5.17 5.15
5.06 5.03
7.06 6.88
6.86 6.69
10.25
8.95
5.46
10.20
Calculated with Cowan’s code. The authors give the same value for the levels in braces.
Boltzmann plots for the studied transitions were made in order to obtain the corresponding plasma temperature. One example is shown in Fig. 1. We used for this plots the values of transition probabilities obtained in this work for intense lines of wavelength ranging from 5000 to 5500 A> (Tables 1 and 2). The temperature in our experimental conditions for the sample of ZnS and 0.3 ls delay time from laser pulse was 21 100$900 K (Table 4). This value agrees within the error limits with the temperature 21 500$1000 K obtained from the Boltzmann plot of Ar II lines 3509.8, 3514.4, 3535.3, 3928.6, 3968.4, 4013.9, 4042.9, 4726.9, 4735.9, 4764.9, recorded in the same spectra, using the transition probabilities compiled by Vujnovic and Wiese [9] and Pellerin et al. [10]. There is also agreement between these two values and the ones deduced from the Saha equation: 21 700$1500 K for S III/S II lines and 22 700$2000 K for Ar III/Ar II lines. For the determination of Saha temperatures the transition probabilities for S III and Ar III lines compiled by Wiese and Martin [5] were used.
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
441
Fig. 1. Boltzmann plot for the population of the levels belonging to the 3s3p4p configuration of S II (¹"21 100$900 K, N "(8.5$2);10 cm\). Table 4 Temperatures determined for the laser produced plasma at several times from laser pulse Time (ls)
¹ (K)
¹ (K)
¹ (K)
¹ (K)
0.3 0.5 0.7
21 100$900 19 800$900 17 900$1000
21 500$1000 20 000$1000 15 000$1500
21 800$1500 19 300$1500
22 700$2000
¹ (K)
15 700$1000
Temperature determined by Boltzmann plot of S II lines. Temperature determined by Boltzmann plot of Ar II lines. Temperature determined by Saha equation of S III/S II lines. Temperature determined by Saha equation of Ar III/Ar II lines. Temperature determined by Saha equation of Ar II/Ar I lines.
The electron density has been determined from well-known data for the Stark broadening parameters of the most intense lines of Ar II tabulated by Konjevic, Roberts and Wiese [15—17]. We have obtained a value of (8.5$2);10 cm\ for the electron density for this experiment at 0.3 ls delay time from the laser pulse for the plasma of Ar-ZnS (T"21 100$900 K). In Table 5
442
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
Table 5 Stark widths (FWHM) of S II lines at ¹"21 100 K and N "8.5;10 cm\ j (A> )
*j (A> )
j (As )
*j (As )
5027.221 5473.620 5428.667 5432.815 5453.828 5032.447
0.40 0.43 0.40 0.41 0.40 0.53
5647.033 4815.549 5639.972 5320.732 4552.406 5011.608
0.64 0.72 0.66 0.49 0.58 0.61
Table 6 Stark widths (FWHM) of Ar II lines used to estimate the plasma electron density at 0.3 ls delay time from the laser pulse and ¹"21 100 K. k (A> )
*k (A> )
4013.9 4726.9 4735.9 4764.9
0.21 0.36 0.29 0.36
are shown the line widths (FWHM) measured in our spectra by deconvolution of the real profile from the instrumental profile (known with 2% error) at this electron density and temperature for some intense lines of S II. In Table 6 are given the Stark widths of Ar II lines employed to estimate the electron density. This plasma electron density allows us to assume LTE for the population of the studied levels as can be deduced by using the criterion of Griem [18] for the lower limit of the electron density (N ) necessary for LTE:
N 59;10 C
k¹(K) *E(eV) cm\, 13.6 13.6
(1)
where *E is the energy difference between the states which are expected to be in LTE, and ¹ is the temperature of the plasma. In our case, *E "7.2 eV for S II and the lower limit given by Eq. (1) is 4.9;10 cm\. From the temperature and electron density it could be inferred that S II and Ar II are both in LTE and the plasma can be considered in LTE. The temperature and electron density obtained allows an estimate to be made for the selfabsorption of the present emitting plasma. For this purpose, the absorption coefficient of the most intense lines of S II in our spectral range can be calculated assuming LTE in order to estimate the S II density and level population. Total density of S II can be deduced from the corresponding electron density and the ratio of the different ions present in the plasma measured through their intensity ratio. In this way, for a plasma thickness of 1 mm, the line intensity absorption integrated along the line profile, was lower than 1.2% for the line 5453.828 S II. For the rest of the lines this absorption coefficient is lower.
Acknowledgements This work was performed with financial support from the Spanish DGICYT (Project PB95-369CO1-2).
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443
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Experimental transition probabilities for lines arising from 3s3p4p configuration of single ionized sulfur J.A.M. Rojas, M. Ortiz, J. Campos* Ca& tedra de Fı& sica Ato& mica Experimental, Facultad de Ciencias Fı& sicas, Universidad Complutense de Madrid, Avda Complutense s/n, 28040 Madrid, Spain Received 9 September 1998
Abstract
Experimental transition probabilities for 103 lines with origin in the 3s3p4p configuration of S II have been determined. Relative values have been obtained from the measurement of emission-line intensities in a laser-produced plasma. The experiment was carried out with samples of zinc sulfide (ZnS) and antimony sulfide (Sb S ) in a pure argon controlled atmosphere in optically thin plasma conditions. The results were placed on an absolute scale by using line-strength sum rules and lifetime values. Comparison between previously published data and present experimental and calculated values has been made. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Experimental transition probabilities; Plasma electron density; Temperature; Self absorption
1. Introduction In spite of its interest in plasma physics and astrophysics, transition probability values of single ionized sulfur has been the subject of relatively few works. Experimental data were obtained by Miller et al. [1] and by Bridges and Wiese [2], which are to date the only extensive experimental studies for lines of S II. Theoretical calculations were performed by Aymar [3], and recently by Nahar [4]. A data compilation was made by Wiese and Martin [5]. The emission spectra were obtained in this experiment with a laser-produced plasma as the spectral source. We measured the emission intensities of lines arising from the same upper level to determine the relative transition probabilities and corresponding branching ratios. To place the
* Corresponding author. Tel.: 34 91 394 4546; fax: 34 91 394 5193; e-mail: [email protected] 0022-4073/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 9 8 ) 0 0 1 1 9 - 8
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data on an absolute scale, calculated lifetime values have been used. These values were obtained in this work performing transition probability calculations in Intermediate Coupling (IC) by the least squares fitting (LSF) method with multiconfiguration interaction and using ab initio Hartree— Fock (HF) calculations made with Cowan’s computer code [6]. Plasma electron density, temperature and self-absorption of the S II transitions have been studied in order to find the best experimental conditions to carry out the measurements. The wavelengths of the measured transitions range from 1900 to 7000 A> . The tables of Kaufman and Martin [7], Wiese and Martin [5], Striganov and Sventitskii [8], Vujnovic and Wiese [9] and Pellerin et al. [10] have been used to identify the transitions. To provide level energies for our calculations, the tables of Martin et al. [11] have been employed.
2. Experimental set-up The experimental arrangement is similar to that described in previous works [12,13]. A Q-switch Nd : YAG laser generates 200 mJ pulses of 7 ns of duration at 20 Hz frequency and 10 640 A> wavelength. The laser light was focused with a 12.5 cm focal length lens onto samples of ZnS or Sb S that were placed in a chamber filled with 4 Torr of argon. As is known, the temperature, temporal evolution and electron densities of laser produced plasmas can be partially controlled by the use of suitable buffer gases. In addition the use of Ar provides us with several spectral lines of well known Stark parameters and transition probabilities, that will be useful to complete the determination of plasma electron densities and temperatures. We studied the variation of intensity and width of S II and Ar II lines vs the argon pressure at different delay times from the laser pulse. Measurements were carried out from vacuum (10\ Torr) to 700 Torr and at 0.3, 0.5, 0.7 and 0.9 ls delay times. Maximum line intensity was achieved at 4 Torr the and 0.3 ls from the laser pulse. Also, at this time and pressure the line widths were sufficiently narrow to carry out the present experiment. Laser irradiance was 5;10 W cm\. The light emission perpendicular to the laser light from the plasma was analyzed by a 1 m Czerny—Turner monochromator. The spectral range was 1900—7000 A> with 0.3 A> spectral resolution in first order. The relative spectral response of the experimental system has been determined by using calibrated deuterium and tungsten lamps with the same experimental conditions that were used in the measurements. The analysis of the spectra was made by fitting the observed line shapes to numerically generated Voigt profiles. The instrumental profile was known previously from the analysis of narrow spectral lines from hollowcathode lamps. The fitting of the observed profiles provides the total intensity accurately, as well as the broadening of spectral lines when necessary. A time-resolved optical multichannel analyzer (OMA III, EG & G) allows recording of the spectra at the selected delay time from the laser pulse and during a preset time length. The spectral range of every spectrum section was 100 A> (first order). Detection was made in synchronism with the electronic trigger of the laser Q-switch. For every period of data acquisition, background accumulation and subtraction were made. Measurements were made at 0.3, 0.5, 0.7 and 0.9 ls delay from the laser pulse and light was collected during 0.2 ls. The corresponding results were compared and averaged. No dependence of relative intensities with time or type of sample was found. The statistical uncertainty of line-intensity values was about 8%.
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
435
To test the laser-produced plasma values, branching ratios have been obtained, where possible, by using a sulfur hollow-cathode lamp as the spectral source. The gas used to fill the tube was Ne. The operating current was typically 10 mA. In this case the single photon counting method was employed using as a detector an EMI 9558 QB photomultiplier cooled with dry ice. The results of both methods were in agreement within statistical uncertainties.
3. Results and discussion Tables 1 and 2 show transition probabilities for lines corresponding to the S II 3s3p4p configuration studied in this work. These values were obtained from the branching-ratio measurements and the theoretical lifetimes calculated in the present work. In Table 1 are also shown the values obtained by line-strength sum rules. There is agreement with the lifetime results. To take into account the contribution to the lifetimes of the transitions out of our spectral range, we used the calculated values. This correction amounts to 5% or less in general. The experimental errors given have been calculated adding quadratically the statistical uncertainties (8%) and the experimental error of the spectral response determination (6%) of the measuring system. The error of the calculated lifetimes was not included in the quoted uncertainties. The line intensity self-absorption was lower than 1% in worst cases. Total errors are about 10% for intense transitions, about 25% for the weak ones and an error of 50% is estimated for some partially blended lines. The calculated lifetimes in both approximations, dipole length and velocity, are presented in Table 3 in order to permit future rescaling when accurate experimental lifetimes were available. The differences between both approximations are about 2%.The values used to put the transition probabilities on the absolute scale were those calculated in length form. The experimental lifetimes of Maleki and Head [14] are also shown for comparison in Table 3. Their values are higher than the present calculations (between 15% for 4p S and 40% for 4p P). In Tables 1 and 2 we show for comparison the experimental values of Miller et al. [1]. Bridges and Wiese [2], the ab initio calculations of Aymar [3] employing the HF#IC method and the values of Nahar [4] using the close coupling approximation with the R-matrix method in LS coupling. Tables 1 and 2 also show multiconfiguration calculations made in this work. The wavefunctions have been obtained by least-squares fitting to the experimental energies tabulated by Martin et al. [11]. Typical differences between the calculated and the experimental energies are lower than 20 cm\. The radial parts of the orbitals were calculated with the relativistic Hartree—Fock Cowan’s [6] code in length and velocity forms. Typical differences between them were about 3%. The calculations show a strong configuration interaction of the S II configurations. For the transitions studied the strongest mixing occurs between 3p4p#3p5p (odd) and 3p3d#3p4d#3p4s#3p#3p5s (even) configurations. There is good agreement between our configuration mixing percentages and those given by Martin et al. [11]. There is also a general good agreement within experimental errors between our absolute transition probabilities and the values of Miller et al. [1], Bridges and Wiese [2] and Aymar [3]. The calculated transition probabilities of this work differ from the values of Aymar [3] by less than 10% for most cases. The values of Nahar [4] are about 25% lower than ours for many lines.
436
j (A> )
Transition levels Upper
Lower
Absolute transition probabilities (10 s\) Experiment (This work)
3p (P) 4p D 3p (P) 4p D
3p (P) 4p D
3p (P) 4p D
3p (P) 4p P
(P) 4s P (P) 4s P (P) 3d F (P) 4s P — (P) 4s P (P) 4s P (P) 3d F (P) 3d F (P) 4s P (P) 4s P (P) 3d F (P) 3d F (P) 3d F (P) 4s P (P) 3d F (P) 3d F (P) 3d D (P) 3d D 3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D
Theory (This work)
Ref. 1
Ref. 2
(This work)
Ref. 3
Ref. 4
7.64 1.15 4.12
7.3 1.1 5.8
6.03 1.15 3.34
4.42 4.17 0.25 0.79 3.32
4.2 4.0 0.22 1.2 4.6
3.09 3.78 0.33 0.69 2.70
5473.620 5556.007 5664.780
7.8$0.8 1.3$0.2 3.9$0.4
7.60 1.26 3.78
8.4 2.9 5.2
8.6
5428.667 5509.718 5645.672 5616.639 5659.985
4.4$0.5 4.3$0.5 0.40$0.1 0.72$0.07 3.4$0.3
4.32 4.19 0.39 0.70 3.07
5.5 4.2 1.9 1.8 4.4
5.0 4.6
5432.815 5564.976 5536.723 5578.889 5640.333
6.7$0.7 1.7$0.2 0.03$0.01 0.86$0.09 3.7$0.4
7.12 1.86 0.04 0.92 3.92
7.7 2.0 1.0 1.1 4.9
7.8 2.0
7.05 1.85 0.03 0.68 3.40
6.8 1.7 0.06 1.1 4.8
5.18 2.07 0.03 0.61 2.77
5453.828 5526.253 5606.151 6957.934 6981.398
9.0$0.9 0.35$0.05 3.8$0.4 0.05$0.02 0.3$0.1
8.96 0.35 3.75 0.05 0.32
10.1 0.9 3.8
10.00
8.96 0.39 3.72 0.06 0.37
8.5 0.6 5.4
7.33 0.37 3.08 0.05 0.28
1998.765 2006.367 4942.466 5009.564 5932.962 6123.383 6397.990 6413.706
2.0$0.5 0.4$0.1 1.9$0.5 8.6$2 0.11$0.03 0.16$0.04 1.4$0.4 1.0$0.3
2.28 0.43 2.11 9.60 0.12 0.18 1.46 1.08
3.5 10.7
4.8
4.3
4.0
1.41 0.30 1.53 9.56 0.03 0.04 1.42 1.33
1.5 9.4
2.15 0.42 1.50 7.19
1.9 1.7
1.12 1.11
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
Table 1 Transition probabilities for lines arising from D and P levels of 3s3p4p configuration of S II
3p (P) 4p P
1981.662 2003.540 4925.347 4991.974 5103.340 6369.342 6384.893 6397.359
2.0$0.5 (0.5 5.1$0.5 3.6$0.4 3.0$0.3 (0.1 0.3$0.1 0.9$0.4
2.56 (0.5 5.11 3.63 3.01 (0.1 0.31 0.92
1970.878 1985.025 4924.115 5032.447 5093.989 5996.161 6274.306 6286.351 6305.483 6521.428
1.3$0.2 0.5$0.1 2.1$0.2 8.9$0.9 0.04$0.02 0.16$0.05 0.07$0.03 0.4$0.1 1.9$0.2 (0.04
1.36 0.52 2.22 9.40 0.05 0.17 0.08 0.44 2.04 (0.05
1.66 0.33 5.19 3.42 2.62 0.02 0.89 1.58
4.0 3.8 3.4
4.0 8.4
Experimental transition probabilities determined by theoretical lifetimes. Experimental transition probabilities determined by line-strength sum rules. Experimental uncertainties are the same in both cases. Estimated accuracies for the most prominent visible lines quoted by the authors are 13—30%. Uncertainties quoted by the authors are 35%. Calculated with Cowan’s code in dipole length form.
8.7
2.3
1.11 0.53 2.48 8.37 0.01 0.20 0.07 0.55 2.18 (0.01
5.1 3.3 2.7 0.02 1.2 2.0
1.19 1.07 3.79 1.16 3.68 0.11 0.72 1.12
2.4 8.1
1.89 0.79 2.73 5.97
0.10 0.75 2.7
0.05 0.42 1.87
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
3p (P) 4p P
3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d D 3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 3d F (P) 4s P (P) 3d D (P) 3d D (P) 3d D (P) 3d F
437
438
Table 2 Transition probabilities of lines arising from levels of 3s3p4p configuration of S II
Upper
Lower
Absolute transition probabilities (10 s\) Experiment (This work)
3p (P) 4p D
3p (P) 4p S
3p (P) 4p D
3s(P)3pP 3s(D)3pD (P) 4s P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d F 3s 3p P 3s 3p P 3s 3p P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d D (P) 3d F 3s 3p P 3s 3p P 3s 3p D (P) 3d P (P) 4s P (P) 4s P (P) 4s P (P) 3d D (P) 3d D (P) 3d F (P) 3d F
1951.379 3052.500 4742.389 4804.120 5647.033 5819.272 6080.838 6092.122 6312.661
(0.04 0.07$0.03 0.09$0.04 (0.07 7.1$0.7 1.1$0.2 (0.02 (0.04 2.2$0.3
1936.731 1950.378 1958.239 4656.777 4716.267 4815.549 5927.277 5940.732 5951.522 6161.840
2.4$0.6 1.6$0.4 1.6$0.4 1.6$0.2 3.7$0.9 10$1 (0.04 0.05$0.03 0.08$0.04 (0.03
1930.819 1944.379 3004.983 3906.951 4681.294 4779.094 5639.972 5895.910 5912.788 6102.277 6286.956
(0.05 (0.04 (0.03 0.13$0.03 0.2$0.1 0.37$0.04 7.7$0.8 (0.02 (0.04 0.34$0.09 2.3$0.2
Theory Ref. 1
4.9 1.1
Ref. 2
1.2
2.6
1.9 3.6 10.8
0.6 6.3
3.4 9.4
(This work) 0.06 0.07 0.08 0.10 6.48 1.12 0.01 0.02 2.66
Ref. 3
5.7 0.9
5.31 0.97
3.0
1.98
2.84 2.74 1.68 0.99 3.14 9.53 0.01 0.05 0.09 0.02 0.01 0.02 0.01 0.22 0.07 0.33 7.54 0.01 0.01 0.17 2.56
Ref. 4
3.28 2.14 1.06 2.17 4.18 5.90
0.02
6.6
2.8
0.10 1.91
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
j (A> )
Transition levels
3p (P) 4p P
3p (D) 4p F
3p (D) 4p P
3p (D) 4p P
3p (S) 4p P
3613.030 3672.122 4917.212 5047.292
0.71$0.08 1.7$0.2 7.3$0.7 4.0$0.4
3595.977 3654.497 4885.648 5014.069
2.1$0.2 0.55$0.1 1.6$0.2 9.5$0.9
2357.751 3839.158 3918.183 3993.502 5320.732
0.40$0.2 0.5$0.3 0.03$0.01 0.95$0.1 8.6$0.9
2669.812 3272.229 3329.330 4552.406 2185.932 2187.264 2629.110 3257.868 3314.469 4193.493 4524.718 4524.947 2877.120 4362.564 4450.712 5011.608
0.54 1.57 7.49 4.05
6.6 3.6
0.83 1.59 5.85 2.71
1.4 9.8
1.90 0.34 1.95 9.48
1.7 8.4
2.11 0.40 1.49 6.90
0.8 10.1
0.19 0.05 0.04 0.92 9.33
0.07 1.9 9.2
0.04 1.12 8.00
8.4
11.6
0.86$0.5 2.0$0.5 1.5$0.7 14.8$2 0.48$0.1 3.4$0.9 0.28$0.07 0.31$0.08 2.7$0.7 0.61$0.2 2.4$1 9.1$2
0.10 1.63 1.04 12.86
9.7
0.48$0.1 (0.01 (0.04 9.0$0.9
Experimental transition probabilities determined by theoretical lifetimes. Estimated accuracies for the most prominent visible lines quoted by the authors are 13—30%. Uncertainties quoted by the authors are 35%. Calculated with Cowan’s code in dipole length form.
0.18 2.66 0.10 0.32 2.31 0.60 1.87 11.23 0.62 0.005 0.01 9.50
2.0 1.3 12.3
0.4 2.8 2.1 11.5
0.10 1.36 0.65 9.11 0.36 3.27 0.13 0.34 1.63 0.57 0.93 8.34 0.50 0.03 0.27 7.61
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
3p (P) 4p P
3d P 3d P 4s P 4s P (P) 3d P (P) 3d P (P) 4s P (P) 4s P 3s 3p D (P) 3d D (P) 3d F (P) 3d F (D) 4s D (P) 3d P (P) 4s P (P) 4s P (D) 4s D 3s 3p D 3s 3p D (P) 3d P (P) 4s P (P) 4s P 3s 3p S (D) 4s D (D) 4s D (D) 4s D (P) 3d D (P) 3d D (S) 4s S (P) (P) (P) (P)
439
440
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443 Table 3 Calculated lifetimes for the levels of the S II 3s3p4p configuration Level
Calculated lifetime (ns) Length
3p (P) 4p S 3p (P) 4p D N (P) 4p D 3p (P) 4p D 3p (P) 4p D 3p (P) 4p P 3p (P) 4p P 3p2 (3P) 4p P 3p (P) 4p D 3p (P) 4p D 3p (P) 4p S 3p (P) 4p P 3p (P) 4p P 3p (D) 4p F 3p (D) 4p F 3p (D) 4p D 3p (D) 4p D 3p (D) 4p P 3p (D) 4p P 3p (S) 4p P 3p (S) 4p P
Ref. 14
Velocity
11.89
11.61
7.50 7.46 7.40 7.34
7.34 7.30 7.24 7.19
6.40 6.29 6.44
6.27 6.16 6.31
9.09 8.91 4.73
8.88 8.70 4.63
6.87 6.87
6.71 6.71
8.15 8.10
7.98 7.94
6.02 6.00
5.89 5.87
5.17 5.15
5.06 5.03
7.06 6.88
6.86 6.69
10.25
8.95
5.46
10.20
Calculated with Cowan’s code. The authors give the same value for the levels in braces.
Boltzmann plots for the studied transitions were made in order to obtain the corresponding plasma temperature. One example is shown in Fig. 1. We used for this plots the values of transition probabilities obtained in this work for intense lines of wavelength ranging from 5000 to 5500 A> (Tables 1 and 2). The temperature in our experimental conditions for the sample of ZnS and 0.3 ls delay time from laser pulse was 21 100$900 K (Table 4). This value agrees within the error limits with the temperature 21 500$1000 K obtained from the Boltzmann plot of Ar II lines 3509.8, 3514.4, 3535.3, 3928.6, 3968.4, 4013.9, 4042.9, 4726.9, 4735.9, 4764.9, recorded in the same spectra, using the transition probabilities compiled by Vujnovic and Wiese [9] and Pellerin et al. [10]. There is also agreement between these two values and the ones deduced from the Saha equation: 21 700$1500 K for S III/S II lines and 22 700$2000 K for Ar III/Ar II lines. For the determination of Saha temperatures the transition probabilities for S III and Ar III lines compiled by Wiese and Martin [5] were used.
J.A.M. Rojas et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 433—443
441
Fig. 1. Boltzmann plot for the population of the levels belonging to the 3s3p4p configuration of S II (¹"21 100$900 K, N "(8.5$2);10 cm\). Table 4 Temperatures determined for the laser produced plasma at several times from laser pulse Time (ls)
¹ (K)
¹ (K)
¹ (K)
¹ (K)
0.3 0.5 0.7
21 100$900 19 800$900 17 900$1000
21 500$1000 20 000$1000 15 000$1500
21 800$1500 19 300$1500
22 700$2000
¹ (K)
15 700$1000
Temperature determined by Boltzmann plot of S II lines. Temperature determined by Boltzmann plot of Ar II lines. Temperature determined by Saha equation of S III/S II lines. Temperature determined by Saha equation of Ar III/Ar II lines. Temperature determined by Saha equation of Ar II/Ar I lines.
The electron density has been determined from well-known data for the Stark broadening parameters of the most intense lines of Ar II tabulated by Konjevic, Roberts and Wiese [15—17]. We have obtained a value of (8.5$2);10 cm\ for the electron density for this experiment at 0.3 ls delay time from the laser pulse for the plasma of Ar-ZnS (T"21 100$900 K). In Table 5
442
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Table 5 Stark widths (FWHM) of S II lines at ¹"21 100 K and N "8.5;10 cm\ j (A> )
*j (A> )
j (As )
*j (As )
5027.221 5473.620 5428.667 5432.815 5453.828 5032.447
0.40 0.43 0.40 0.41 0.40 0.53
5647.033 4815.549 5639.972 5320.732 4552.406 5011.608
0.64 0.72 0.66 0.49 0.58 0.61
Table 6 Stark widths (FWHM) of Ar II lines used to estimate the plasma electron density at 0.3 ls delay time from the laser pulse and ¹"21 100 K. k (A> )
*k (A> )
4013.9 4726.9 4735.9 4764.9
0.21 0.36 0.29 0.36
are shown the line widths (FWHM) measured in our spectra by deconvolution of the real profile from the instrumental profile (known with 2% error) at this electron density and temperature for some intense lines of S II. In Table 6 are given the Stark widths of Ar II lines employed to estimate the electron density. This plasma electron density allows us to assume LTE for the population of the studied levels as can be deduced by using the criterion of Griem [18] for the lower limit of the electron density (N ) necessary for LTE:
N 59;10 C
k¹(K) *E(eV) cm\, 13.6 13.6
(1)
where *E is the energy difference between the states which are expected to be in LTE, and ¹ is the temperature of the plasma. In our case, *E "7.2 eV for S II and the lower limit given by Eq. (1) is 4.9;10 cm\. From the temperature and electron density it could be inferred that S II and Ar II are both in LTE and the plasma can be considered in LTE. The temperature and electron density obtained allows an estimate to be made for the selfabsorption of the present emitting plasma. For this purpose, the absorption coefficient of the most intense lines of S II in our spectral range can be calculated assuming LTE in order to estimate the S II density and level population. Total density of S II can be deduced from the corresponding electron density and the ratio of the different ions present in the plasma measured through their intensity ratio. In this way, for a plasma thickness of 1 mm, the line intensity absorption integrated along the line profile, was lower than 1.2% for the line 5453.828 S II. For the rest of the lines this absorption coefficient is lower.
Acknowledgements This work was performed with financial support from the Spanish DGICYT (Project PB95-369CO1-2).
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443
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