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Experimental study of Stark broadened N II lines from states of high orbital angular momentum
J. Quant. Spectrosc. Radiat. Transfer Vol. 36, No. 4, pp. 289-294, 1986 Printed in Great Britain
0022-4073/86 $3.00 + 0.00 Pergamon Journals Ltd
EXPERIMENTAL STUDY OF STARK BROADENED LINES FROM STATES OF HIGH ORBITAL ANGULAR
N II
MOMENTUM
T. L. PITTMAN and N. KONJEVI~* Atomic and Plasma Radiation Division, National Bureau of Standards, Gaithersburg, MD 20899, U.S.A.
(Received 7 October 1985) Abstract--In this paper, we report experimental electron impact widths for six spectral lines belonging to 3d-4f transitions of singly ionized nitrogen. Line profiles were measured in a low pressure pulsed arc. An electron density in the range 5.9-7.5 x 1022m -3 was determined from the Stark width of the He II 4686/~ line, while electron temperatures of 28,300-32,300 K were measured using relative intensities of O II impurity lines. Comparison with semiempirical theoretical results does not resolve which coupling scheme, LS or LK, is better to describe atomic states in Stark broadening calculations of certain N II lines.
INTRODUCTION
The Stark broadening of non-hydrogenic ion lines has been the subject of numerous theoretical (see for example Ref. [1]) and experimental studies (see for example Refs [1-3]). In a number of experiments, j-3'5 the most comprehensive set of theoretical data t : for singly-ionized atoms were checked and average agreement within + 20% was found. For the evaluation of these data, Jones et al. t'4 used a semi-classical theoretical approach, l which contained certain simplifications (e.g. one-electron model, LS-coupling) in the treatment of the atomic states of the radiator. Some of these simplifications become questionable in the case of complex spectra. In a recent paper, Hey and Blaha6 examined the Stark broadening of complex spectra in order to show how to use proper coupling for the radiator states. They used LK coupling, which is a form of intermediate coupling in which the inner 3d electron is coupled to 4felectron predominantly through the direct Coulomb interaction (13d+ 14f= L), and the spin-orbit interaction of the inner electron is next most important ( t + S3d = K). TO demonstrate the effect of the transformation from LS to LK coupling in the evaluation of the line widths, these authors used a semi-empirical approximation to calculate electron-impact line widths of isolated 3 d - 4 f transitions of N II, a well known case for the breakdown of the validity of LS coupling. The results of these calculations showed systematic differences (up to 20-25%) between data obtained assuming pure LS to that of LK coupling. To assess the importance of accurate description of radiator structure in Stark broadening theory, an experiment measuring the Stark widths of spectral lines belonging to 3d--4f transitions of N II was performed and the results are reported in this paper. The experimental results are compared with the theoretical calculations of Hey and Blaha. 6 EXPERIMENT
Measurements of N II line widths were made in a pulsed arc discharge, filled with two or four Torr of gas mixtures consisting of He and N2. The arc is described elsewhere; 7 however, a number of details will be given here. The arc was observed end on with a 10.7m normal incidence spectrometer with a 1200 I/m grating blazed at 3000/~ with a plate factor 0.78/~/mm. An intensified array detector was placed at the exit plane of the spectrometer. The detector had 1024 pixels with a spectral bandpass of 0.0195/~ per pixel. The measured instrumental half width using a 23/~m input slit width was 0.10/~. The resolution of our spectrometer-array detector system was limited primarily by pixel-to-pixel charge leakage. The image intensifier was gated for 10/~s during the first half cycle of the discharge current 60/~s after discharge initiation. The electron density remained *Permanent address: Institute of Physics, P.O. Box 57, 11001 Beograd, Yugoslavia. QS.R.T. 36/4--B
289
290
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4035.1
4043.5
I
I
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Fig. 1. Typical measured data, along with fitted Lorentzian profiles. In this example, three lines could be observed in a single shot. constant during this period of time. The signal from the array was digitized and transferred to a minicomputer for analysis. Complete line spectra could be analyzed on a single shot basis. For weak signals we were able to accumulate data for several shots in the computer to improve the signal-to-noise ratio. Our main concern during the measurements of the line widths was possible distortion of the line profiles caused by self-absorption. Therefore, in order to diminish the influence of self-absorption, nitrogen was admixed with helium to decrease its concentration in the plasma. We made observations of N I I line profiles with a 40% N2 in 60% He mixture. In subsequent experiments the concentration was further diluted. Since, in this case, we could not use the standard technique (see for example Ref. [2]) of comparing line intensities within multiplets (since there is only one line per multiplet) as a self-absorption check, we had to apply another, less sensitive technique, but in our case the only possible one. In each gas mixture, the electron density and electron temperature were also measured while experimental conditions (initial pressure of gas mixture and firing voltage of capacitor bank) were changed. The linear dependence of the N II line widths as a function of the independently measured electron density, irrespective of experimental conditions, was used as an indication that self-absorption is negligible to within 5%. This dependence is expected from the theory of Stark broadening (see for example Ref. [1]) and has been experimentally proven in a number of experiments (see for example Refs [1-3]). A Gaussian instrumental profile with a full half-width of 0.10/~ was measured due to the spectral resolution of our spectrometer~letector system. Therefore, it was necessary to deconvolute this instrumental profile from the experimental profiless to obtain the Stark profile. For the electron density measurements, we used the width of He II 4686 ~ line (calibrated with an H e - N e laser interferometer) 7 while the electron temperature was determined from the ratio of the 4369.3 and 4366~9 ~ O I I impurity line intensities. For the temperature measurements thermal equilibrium in an optically thin medium was assumed. Transition probabilities for the temperature measurements were taken from Ref. [9]. Figure 1 shows a typical measured profile. Also shown are the fitted Lorentzian profiles used to determine the full widths of the lines. R E S U L T S AND D I S C U S S I O N The experimentally determined electron impact widths, Wm, of N II lines are given in Table 1 together with the electron density and electron temperature. For comparison, other experimental results ~°-j3 along with the experimental conditions are also included (see also Ref. [2]). The results of the 4552.5 ,& line from Refs [13] and [14] have been converted from half half-width ( H W H M ) to full half-width ( F W H M ) and are included in Table 1. The result from Ref. [15] for the 4552.5
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T. (KI Fig. 2.(a)-(c) Measured and calculated full Stark half-width ( F W H M ) for the N II lines, normalized to N , = 1023 m -3, as a function of temperature. Curves: W s c = semiclassical results by Jones e t al.; ~'3 WDw = distorted wave calculations by Hey and Blaha; 6 WLSand WLK are semiempirical results by Hey and Blaha 6 obtained using LS or L K coupling, respectively, to describe radiator structure. Experimental results: P = Popovic e t al., t2 B = Berg e t al., L° J = Jalufka and Craig, It K = Konjevic e t al. t3" 14
Stark broadened N II lines
293
line is not included, because of the possible systematic error arising from the undetected inhomogeneities in their T-tube plasma. For comparison, the experimental line widths are also normalized to an electron density of l0 23 m -3. In the next two columns of Table 1, our experimental results are compared with theoretical data calculated by Hey and Blaha 6 using LS and LK coupling to describe the radiator structure. The results of this comparison are given in the form of the ratios of the experiment and the theory, Wm/WLsand Wm/WLK. We estimated errors for our experimental data in Table 1 as follows: electron density, + 10%; electron temperature, + 15%; line widths, + 10%. Comparison of our data with other experimental results in Table 1 shows agreement with Refs [12-14] for the 4041.3 and 4552.5 A lines. Discrepancies exceeding limits of estimated errors for 4552.5 and 4530.4/~ from Refs [10] and [11] are observed. Analysis of both experiments ~°.N and comparison with our results give no satisfactory explanation for this discrepancy. However, in further comparisons with the theoretical results, we give preference to our data for the 4530.4 A lines, in spite of a good mutual agreement of results for the 4530.4 A line in Refs [10] and [11]. We do this because all our investigated N I I lines are measured under the same experimental conditions (same electron density and temperature) which is certainly important for consistency in the comparisons. Comparison of our experimental results with the theoretical calculations by Hey and Blaha, 6 in Table 1, does not give a definitive answer to whether LS or LK coupling is better to describe atomic structure in these Stark broadening calculations. For the 4026.1 and 4530.4 A lines, the calculations with LK coupling agree better with the experimental results while for the 4552.5 and 4043.5 A lines, LS coupling seems to be more appropriate. Theoretical results for the 4041.1 and 4035.1 A lines are the same irrespective of the coupling approximation used. To illustrate these points Fig. 2(a)-(c) give three typical examples. In Fig. 2(a), besides the semiempirical theoretical results, 6 the results of the classical path m,4and the distorted-wave calculations6 are also presented. All three theoretical approaches give results which are sytematically larger than the experimental results by up to 50%. The authors in Ref. [6] offered an explanation for the overestimation of their semiempirical and distorted-wave results for the 4041.1/~ line. They suggested that this may be partly due to the difficulties associated with the calculation of exceedingly large cross section for the 2p4f-2p4d transition, even in the distorted-wave approximation. It should also be mentioned that contributions from ion perturbers are not likely to play a role in these discrepancies since they are usually negligible for non-hydrogenic charged radiators) Finally we conclude that the transformation from LS to LK coupling on the calculated Stark widths of nitrogen ion lines from states of high orbital angular momentum of 3d-4f transitions does not improve the overall agreement between the theory and experiment. To clear up this discrepancy, additional theoretical effort is needed. Acknowledgements--This work was partially supported by the U.S. Yugoslav Joint Board on Science and Technology Cooperation. The authors wish to thank J. D. Hey for the detailed tables of semiempirical results, which were only published for 20,000 K in Ref. [6]. We also wish to thank J. R. Roberts and D. E. Kelleher for the many discussions regarding this work and we appreciate the technical assistance of T. E. Sellner and M. Bassin.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
H. R. Griem. Spectral Line Broadening by Plasmas. Academic Press, New York (1974). N. Konjevi~ and W. L. Wiese, J. phys. chem. Ref. Data 5, 259 (1976). N. Konjevi6, M. S. Dimitrijevi6 and W. L. Wiese, J. phys. chem. Ref Data. In press. W. W. Jones, S. M. Bennett and H. R. Greta, Calculated electron impact broadening parameters for isolated spectral lines from the singly charged ions: lithium through calcium. Tech. Rep. No. 71-128, University of Maryland, College Park, Md (1971). W. W. Jones, Phys. Rev. A 7, 1826 (1973). J. D. Hey and M. Blaha, JQSRT 20, 557 (1978). T. Pittman and C. Feuder, in Spectral Line Shapes (Edited by K. Burnett and Walter de Gruyter), Vol. 2. Berlin 0983). J. T. Davies and J. M. Vaughan, Astrophys. J., 137, 1302 (1963). W. L. Wiese, M. W. Smith and B. M. Glennon, Atomic transition probabilities, Vol. I. NSRDS-NBS-4, U.S. Govt. Print. Office, Washington, D.C. (1966). H. E. Berg, W. Ervens and B. Fureh, Z. Phys. 206, 309 (1967).
294 11. 12. 13. 14. 15.
T . L . PITTMANand N. KONJEVld N. W. Jalufka and J. P. Craig, Phys. Rev A 1, 221 (1970). M. Popovi6, M. Platisa and N. Konjevi6, Astron. Astrophys. 41, 463 (1975). N. Konjevi6, V. Mitrovi6, Lj. Cirkovi~ and J. Labat, Fizika 2, 129 (1975). V. Mitrovi6, M.Sc. thesis, Belgrade (1971) unpublished. R. A. Day and H. R. Griem, Phys. Rev. 140, Al129 (1965).
0022-4073/86 $3.00 + 0.00 Pergamon Journals Ltd
EXPERIMENTAL STUDY OF STARK BROADENED LINES FROM STATES OF HIGH ORBITAL ANGULAR
N II
MOMENTUM
T. L. PITTMAN and N. KONJEVI~* Atomic and Plasma Radiation Division, National Bureau of Standards, Gaithersburg, MD 20899, U.S.A.
(Received 7 October 1985) Abstract--In this paper, we report experimental electron impact widths for six spectral lines belonging to 3d-4f transitions of singly ionized nitrogen. Line profiles were measured in a low pressure pulsed arc. An electron density in the range 5.9-7.5 x 1022m -3 was determined from the Stark width of the He II 4686/~ line, while electron temperatures of 28,300-32,300 K were measured using relative intensities of O II impurity lines. Comparison with semiempirical theoretical results does not resolve which coupling scheme, LS or LK, is better to describe atomic states in Stark broadening calculations of certain N II lines.
INTRODUCTION
The Stark broadening of non-hydrogenic ion lines has been the subject of numerous theoretical (see for example Ref. [1]) and experimental studies (see for example Refs [1-3]). In a number of experiments, j-3'5 the most comprehensive set of theoretical data t : for singly-ionized atoms were checked and average agreement within + 20% was found. For the evaluation of these data, Jones et al. t'4 used a semi-classical theoretical approach, l which contained certain simplifications (e.g. one-electron model, LS-coupling) in the treatment of the atomic states of the radiator. Some of these simplifications become questionable in the case of complex spectra. In a recent paper, Hey and Blaha6 examined the Stark broadening of complex spectra in order to show how to use proper coupling for the radiator states. They used LK coupling, which is a form of intermediate coupling in which the inner 3d electron is coupled to 4felectron predominantly through the direct Coulomb interaction (13d+ 14f= L), and the spin-orbit interaction of the inner electron is next most important ( t + S3d = K). TO demonstrate the effect of the transformation from LS to LK coupling in the evaluation of the line widths, these authors used a semi-empirical approximation to calculate electron-impact line widths of isolated 3 d - 4 f transitions of N II, a well known case for the breakdown of the validity of LS coupling. The results of these calculations showed systematic differences (up to 20-25%) between data obtained assuming pure LS to that of LK coupling. To assess the importance of accurate description of radiator structure in Stark broadening theory, an experiment measuring the Stark widths of spectral lines belonging to 3d--4f transitions of N II was performed and the results are reported in this paper. The experimental results are compared with the theoretical calculations of Hey and Blaha. 6 EXPERIMENT
Measurements of N II line widths were made in a pulsed arc discharge, filled with two or four Torr of gas mixtures consisting of He and N2. The arc is described elsewhere; 7 however, a number of details will be given here. The arc was observed end on with a 10.7m normal incidence spectrometer with a 1200 I/m grating blazed at 3000/~ with a plate factor 0.78/~/mm. An intensified array detector was placed at the exit plane of the spectrometer. The detector had 1024 pixels with a spectral bandpass of 0.0195/~ per pixel. The measured instrumental half width using a 23/~m input slit width was 0.10/~. The resolution of our spectrometer-array detector system was limited primarily by pixel-to-pixel charge leakage. The image intensifier was gated for 10/~s during the first half cycle of the discharge current 60/~s after discharge initiation. The electron density remained *Permanent address: Institute of Physics, P.O. Box 57, 11001 Beograd, Yugoslavia. QS.R.T. 36/4--B
289
290
T.L. thTTMANand N. KONJEVt6 4041.1
4035.1
4043.5
I
I
4035.0
4040.1
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4045.0
4050.1
Fig. 1. Typical measured data, along with fitted Lorentzian profiles. In this example, three lines could be observed in a single shot. constant during this period of time. The signal from the array was digitized and transferred to a minicomputer for analysis. Complete line spectra could be analyzed on a single shot basis. For weak signals we were able to accumulate data for several shots in the computer to improve the signal-to-noise ratio. Our main concern during the measurements of the line widths was possible distortion of the line profiles caused by self-absorption. Therefore, in order to diminish the influence of self-absorption, nitrogen was admixed with helium to decrease its concentration in the plasma. We made observations of N I I line profiles with a 40% N2 in 60% He mixture. In subsequent experiments the concentration was further diluted. Since, in this case, we could not use the standard technique (see for example Ref. [2]) of comparing line intensities within multiplets (since there is only one line per multiplet) as a self-absorption check, we had to apply another, less sensitive technique, but in our case the only possible one. In each gas mixture, the electron density and electron temperature were also measured while experimental conditions (initial pressure of gas mixture and firing voltage of capacitor bank) were changed. The linear dependence of the N II line widths as a function of the independently measured electron density, irrespective of experimental conditions, was used as an indication that self-absorption is negligible to within 5%. This dependence is expected from the theory of Stark broadening (see for example Ref. [1]) and has been experimentally proven in a number of experiments (see for example Refs [1-3]). A Gaussian instrumental profile with a full half-width of 0.10/~ was measured due to the spectral resolution of our spectrometer~letector system. Therefore, it was necessary to deconvolute this instrumental profile from the experimental profiless to obtain the Stark profile. For the electron density measurements, we used the width of He II 4686 ~ line (calibrated with an H e - N e laser interferometer) 7 while the electron temperature was determined from the ratio of the 4369.3 and 4366~9 ~ O I I impurity line intensities. For the temperature measurements thermal equilibrium in an optically thin medium was assumed. Transition probabilities for the temperature measurements were taken from Ref. [9]. Figure 1 shows a typical measured profile. Also shown are the fitted Lorentzian profiles used to determine the full widths of the lines. R E S U L T S AND D I S C U S S I O N The experimentally determined electron impact widths, Wm, of N II lines are given in Table 1 together with the electron density and electron temperature. For comparison, other experimental results ~°-j3 along with the experimental conditions are also included (see also Ref. [2]). The results of the 4552.5 ,& line from Refs [13] and [14] have been converted from half half-width ( H W H M ) to full half-width ( F W H M ) and are included in Table 1. The result from Ref. [15] for the 4552.5
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T. (KI Fig. 2.(a)-(c) Measured and calculated full Stark half-width ( F W H M ) for the N II lines, normalized to N , = 1023 m -3, as a function of temperature. Curves: W s c = semiclassical results by Jones e t al.; ~'3 WDw = distorted wave calculations by Hey and Blaha; 6 WLSand WLK are semiempirical results by Hey and Blaha 6 obtained using LS or L K coupling, respectively, to describe radiator structure. Experimental results: P = Popovic e t al., t2 B = Berg e t al., L° J = Jalufka and Craig, It K = Konjevic e t al. t3" 14
Stark broadened N II lines
293
line is not included, because of the possible systematic error arising from the undetected inhomogeneities in their T-tube plasma. For comparison, the experimental line widths are also normalized to an electron density of l0 23 m -3. In the next two columns of Table 1, our experimental results are compared with theoretical data calculated by Hey and Blaha 6 using LS and LK coupling to describe the radiator structure. The results of this comparison are given in the form of the ratios of the experiment and the theory, Wm/WLsand Wm/WLK. We estimated errors for our experimental data in Table 1 as follows: electron density, + 10%; electron temperature, + 15%; line widths, + 10%. Comparison of our data with other experimental results in Table 1 shows agreement with Refs [12-14] for the 4041.3 and 4552.5 A lines. Discrepancies exceeding limits of estimated errors for 4552.5 and 4530.4/~ from Refs [10] and [11] are observed. Analysis of both experiments ~°.N and comparison with our results give no satisfactory explanation for this discrepancy. However, in further comparisons with the theoretical results, we give preference to our data for the 4530.4 A lines, in spite of a good mutual agreement of results for the 4530.4 A line in Refs [10] and [11]. We do this because all our investigated N I I lines are measured under the same experimental conditions (same electron density and temperature) which is certainly important for consistency in the comparisons. Comparison of our experimental results with the theoretical calculations by Hey and Blaha, 6 in Table 1, does not give a definitive answer to whether LS or LK coupling is better to describe atomic structure in these Stark broadening calculations. For the 4026.1 and 4530.4 A lines, the calculations with LK coupling agree better with the experimental results while for the 4552.5 and 4043.5 A lines, LS coupling seems to be more appropriate. Theoretical results for the 4041.1 and 4035.1 A lines are the same irrespective of the coupling approximation used. To illustrate these points Fig. 2(a)-(c) give three typical examples. In Fig. 2(a), besides the semiempirical theoretical results, 6 the results of the classical path m,4and the distorted-wave calculations6 are also presented. All three theoretical approaches give results which are sytematically larger than the experimental results by up to 50%. The authors in Ref. [6] offered an explanation for the overestimation of their semiempirical and distorted-wave results for the 4041.1/~ line. They suggested that this may be partly due to the difficulties associated with the calculation of exceedingly large cross section for the 2p4f-2p4d transition, even in the distorted-wave approximation. It should also be mentioned that contributions from ion perturbers are not likely to play a role in these discrepancies since they are usually negligible for non-hydrogenic charged radiators) Finally we conclude that the transformation from LS to LK coupling on the calculated Stark widths of nitrogen ion lines from states of high orbital angular momentum of 3d-4f transitions does not improve the overall agreement between the theory and experiment. To clear up this discrepancy, additional theoretical effort is needed. Acknowledgements--This work was partially supported by the U.S. Yugoslav Joint Board on Science and Technology Cooperation. The authors wish to thank J. D. Hey for the detailed tables of semiempirical results, which were only published for 20,000 K in Ref. [6]. We also wish to thank J. R. Roberts and D. E. Kelleher for the many discussions regarding this work and we appreciate the technical assistance of T. E. Sellner and M. Bassin.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
H. R. Griem. Spectral Line Broadening by Plasmas. Academic Press, New York (1974). N. Konjevi~ and W. L. Wiese, J. phys. chem. Ref. Data 5, 259 (1976). N. Konjevi6, M. S. Dimitrijevi6 and W. L. Wiese, J. phys. chem. Ref Data. In press. W. W. Jones, S. M. Bennett and H. R. Greta, Calculated electron impact broadening parameters for isolated spectral lines from the singly charged ions: lithium through calcium. Tech. Rep. No. 71-128, University of Maryland, College Park, Md (1971). W. W. Jones, Phys. Rev. A 7, 1826 (1973). J. D. Hey and M. Blaha, JQSRT 20, 557 (1978). T. Pittman and C. Feuder, in Spectral Line Shapes (Edited by K. Burnett and Walter de Gruyter), Vol. 2. Berlin 0983). J. T. Davies and J. M. Vaughan, Astrophys. J., 137, 1302 (1963). W. L. Wiese, M. W. Smith and B. M. Glennon, Atomic transition probabilities, Vol. I. NSRDS-NBS-4, U.S. Govt. Print. Office, Washington, D.C. (1966). H. E. Berg, W. Ervens and B. Fureh, Z. Phys. 206, 309 (1967).
294 11. 12. 13. 14. 15.
T . L . PITTMANand N. KONJEVld N. W. Jalufka and J. P. Craig, Phys. Rev A 1, 221 (1970). M. Popovi6, M. Platisa and N. Konjevi6, Astron. Astrophys. 41, 463 (1975). N. Konjevi6, V. Mitrovi6, Lj. Cirkovi~ and J. Labat, Fizika 2, 129 (1975). V. Mitrovi6, M.Sc. thesis, Belgrade (1971) unpublished. R. A. Day and H. R. Griem, Phys. Rev. 140, Al129 (1965).