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RADIATIVE LIFETIMES OF SOME ENERGY LEVELS IN Ne II
J. Quant. Spectrosc. Radiat. ¹ransfer Vol. 61, No. 3, pp. 405—416, 1999 1998 Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain
PII: S0022-4073(98)00026-0
0022—4073/98 $19.00#0.00
RADIATIVE LIFETIMES OF SOME ENERGY LEVELS IN Ne II P. VAN DER WESTHUIZEN-, K. VISSER and D. C. BEUKMAN Department of Physics, University of Stellenbosch, Private Bag X1, 7602 Matieland, South Africa (Received 4 September 1997)
Abstract—The article describes beam—foil measurements of a number of primary as well as cascading levels in Ne II. A detailed cascade—corrected energy level lifetime analysis of the 3p P° , 3p D° and 3p F° levels in Ne II was undertaken. 1998 Published by Elsevier Science Ltd. All rights reserved.
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We have employed the beam-foil spectroscopy (BFS) method to measure the radiative lifetimes of the 3p P° , 3p D° and 3p F° levels of Ne II (2s2p (D) electronic core) correcting for the effect of cascades with the ANDC (arbitrarily normalized decay curve) technique described by Curtis et al. In the analyses care had to be given to line blending and repopulation via cascading levels due to the indiscriminate excitation of levels and Doppler broadening. We calculated the lifetimes assuming LS coupling with the Coulomb approximation to facilitate the assignment of the measured lines. Our results are compared with values obtained through the delayed coincidence (DC) method, as well as the beam-foil,\ beam-gas and phase shift methods. The experimental results are also compared with intermediate coupling (IC) calculations\ and LS coupling calculations with the Coulomb approximation. This work was conducted to attempt to resolve discrepancies amongst existing experimental values and between experimental and theoretical values. 2 . E XP ERI M EN T AL PR OC ED UR E
The experiment was conducted using the HVEC model CN 5.5 MV single-ended Van de Graaff accelerator at the National Accelerator Centre at Faure. The accelerator produced stable beams with beam currents of approximately 4 lA which was passed through hydrocarbon cracked foils. The neon spectral lines were detected with a refocused scanning monochromator equipped with a 2400 lines mm\ grating blazed for 300 nm. A more complete discription of the experimental set up is given in Refs. 16 and 17. A typical spectrum scan is shown in Fig. 1. The tables of Persson and Striganov et al were used for line identification. The lifetime measurements were made with a 0.5 MeV beam since it produced the optimum Ne II line intensities. The recorded decay curves were analysed with the DISCRETE program using a multi-exponential curve-fitting technique. The CANDY program was used to carry out the ANDC analyses on the DISCRETE results. 3. PRIM ARY L EV ELS
3.1. The 3p P°( levels: Transitions from the 3p P°( levels to the 3s D( levels occur at 331.97, 334.55 and 334.58 nm. A Grotrian diagram of the relevant energy levels and observed transitions is shown in Fig. 2. The decay curves measured at 331.90 and 334.65 nm together with decay curves of the 4s D and 3d D cascade levels measured at 296.70 and 345.95 nm, respectively, are also shown in Fig. 2. - To whom all correspondence should be addressed. 405
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Fig. 1. The beam-foil spectrum of neon at 0.5 and 1.0 MeV.
It is a well known fact that in beam-foil work, insufficient spectral resolution, resulting in line blending can cause serious errors in lifetime determinations. Special care was therefore taken to assess the influence of possible blends. 3.1.1. The 3p P° level. The J"1/2 component, decaying via the 331.97 nm transition could be influenced by transitions from the 3d D level and to a lesser extent by the 332.37 nm transition from the 3p P° level. The theoretical lifetimes of these two levels are 2.4 and 5.5 ns, respectively, compared to the theoretical lifetime of 3.9 ns of the 3p P° level. To determine the lifetime of the J"1/2 component a decay curve was therefore obtained, not at the tabulated wavelength of 331.97 nm but to the shorter wavelength region at 331.90 nm in an attempt to minimize the possibility of a blend. The curve-fitting analysis yielded a three-component best fit with a primary value of 4.71 ns, a growing-in component of 0.78 ns and a third component of 34.2 ns. In an attempt to assess the influence of the possible blend due to the transition from the 3d D level (j"332.0196 nm) we also measured the decay at 332.10 nm. The primary decay constant obtained at this wavelength was very similar (4.70 ns) to the 4.71 ns obtained at 331.90 nm, whereas the two other components differ only slightly from the measurement at the shorter wavelength. In the analysis of the 3p ¸° (¸"1, 2, 3) levels, that will be published shortly, an in depth study ( was made of the 3d D levels because the decay constants were needed in the ANDC analysis as ( cascading can occur from these levels. From this study we conclude that the 3d D levels are indeed ( populated but the spectral analysis of the transitions from these levels is frequently blended by
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Fig. 2. Partial Grotrian diagram of the relevant energy levels in Ne II and measured transitions (wavelengths in nm) with the background-corrected decay curves of the 3p P° —3s D , 3p P° —3s D , 3d D —3p D° and 4s D —3p F° transitions. Transitions in brackets are tabulated wavelengths in nm.
transitions from other levels. Taking all possible blends into account we finally used the 3d D —3p P° transitions with a primary decay constant of 3.16 ns. From these arguments it is clear that the possibility of blending between transitions from the 3d D and 3p P° levels could not be ruled out completely. We nevertheless tried the decay constants, obtained at 331.90 nm, in the ANDC analysis and discuss these results in Sec. 7. 3.1.2. The 3p P° level. The 3p P° level decay to the 3s D and 3s D levels at 334.55 and 334.65 nm respectively. These two transitions are unresolved, but these blends do not create a problem as both transitions originate from the same J"3/2 fine structure level. The decay constants obtained at both measurements were very similar with a primary component of approximately 5.5 ns. The possibility of a blend with a transition from the 3p D° level (theoretical lifetime 5.2 ns) at 334.4395 nm was investigated by obtaining decay constants from the analysis of a measurement at 334.40 nm. Although our spectral analysis showed that the 3p D° levels are populated, we con( cluded, by comparing the decay constants obtained from the 334.40 and 334.65 nm measurements, that the 334.65 nm measurement was not affected by the 3p D° —3s P transition.
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The decay constants obtained from the curve-fitting procedure are given in Table 1. Transitions from the 3p P° states to the 3s P , 3s P and 2s2p S states occur at wavelengths ( ( ( that are outside the detection region of our spectrometer system and could therefore not be studied. 3.2. The 3p D° levels ( The decay constants associated with transitions from these levels were obtained from measurements at 323.05 nm (3p D° —3s D ) and 323.20 nm (3p D° —3s D ). The Grotrian diagram indicating the energy levels involved in these transitions as well as the measured decay curves are shown in Fig. 3. The decay curve obtained at 340.70 nm for the 3d F cascade level is also shown in Fig. 3. The results of the measurements are shown in Table 1. The spectrum analysis showed that these two transitions are not completely resolved and that the possible effect of the 3d G —3p F (322.48—322.96 nm) transitions should be assessed. The effect of ( ( these possible blends were investigated by obtaining decay constants from measurements at 322.50 and 322.90 nm. Both curves yielded a three component best fit with primary components of 3.94 and 4.94 ns, respectively. These results show a 25% increase in the primary component obtained from the measurement at the wavelength closer to the wavelength associated with the transition from the 3p D° levels. These two long decay times for the 3d G (in comparison to the theoretical lifetime of 2.7 ns ( suggested that the 3p D° —3s D measurements are not affected to a great extent and that DISCRETE results can be tried in an ANDC-analysis. Depopulation from the 3p D° states can also occur via transitions to the 3s P states (187.7679, ( ( 190.0189 nm) but are outside the detection region of our spectrometer system.
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Fig. 3. Partial Grotrian diagram of the relevant energy levels in Ne II and measured transitions (wavelengths in nm) with the background-corrected decay curves of the 3p D° —3s D , 3p D° —3s D and 3d F —3p D° transitions. Transitions in brackets are tabulated wavelengths in nm.
3.3. The 3p F° levels The decay constants associated with these upper levels were obtained from measurements at 356.85 nm (3p F° —3s D ) and 357.45 nm (3p F° —3s D ) and are shown in Table 1. The Grotrian diagram indicating the energy levels involved in these transitions as well as the possible cascading levels is shown in Fig. 4. The decay curves obtained at 356.85 and 357.45 nm as well as the decay curve of the 3d G cascade level obtained at 322.50 nm are also shown in Fig. 4. 3.3.1. The 3p F° level. Transitions from the 3d P , 5p D° and 3d F levels occur at 356.58, 356.76 and 357.12 nm, respectively, and the effect of these possible blends should be assessed. The theoretical lifetimes of both the 3d P (1.0 ns) and 3d F (1.7 ns) are considerably shorter than that of the 3p F° (6.4 ns) level and should (if they occur) only affect the measurement at small foil positions. To assess the influence of the 5p D° level we did a Coulomb approximation calculation and found the lifetime of this level to be :28.7 ns. It is clear that if this level is populated the decay curve will only be affected at large foil positions.
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Fig. 4. Partial Grotrian diagram of the relevant energy levels in Ne II and measured transitions (wavelengths in nm) with the background-corrected decay curves of the 3p F° —3s D , 3p F° —3s D and 3d G —3p F° transitions. Transitions in brackets are tabulated wavelengths in nm.
3.3.2. The 3p F° level. Transitions from this level to the J"5/2 and J"3/2 fine structure components of the 3s D term are tabulated at 357.42 and 357.46 nm and are unresolved. This is not a problem as these transitions originate from the same upper level and only the influence of the transitions from the 5p P° and 5p P° levels occurring at 357.20 and 357.24 nm should be assessed. Our Coulomb approximation calculations revealed the relatively long lifetimes of :27.5 and 29.0 ns for the 5p P° and 5p P° levels, respectively. If these levels are populated the decay curve will only be affected at large foil positions. 4. C AS CA DIN G L EVELS
It is evident from Table 2 that a total of six possible cascading levels had to be investigated. 4.1. The 3d S cascading level If populated this level will only influence one of the terms under investigation, i.e. the 3p P° ( levels. The 3d S level decay via transitions to the 3p P° and 3p P° levels at 336.22 and
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Table 2. Cascading levels that may contribute to primary levels
338.89 nm, respectively. The spectrum analysis showed that both transitions were probably unresolved and the decay measurements indeed confirmed the suspected blends. The decay constant obtained from the measurement at 336.22 nm, i.e. :6 ns, is probably due to the depopulation of the 3p D° level, whereas the 338.89 nm transition is blended with a number of transitions. The 3d S level with a very short lifetime of :0.19 ns was therefore not included in the analysis as a cascading level. 4.2. The 3d P cascading levels Transitions from the 3d P and 3d P levels to the 3p P° level occur at 341.10 and 341.30 nm, respectively. Measurements obtained at these wavelengths revealed decay constants of 3.92 and 3.71 ns, respectively. The spectrum analysis showed that these transitions were unresolved from transitions from the 3d F levels and it is possible that these decay constants should rather be ( associated with the 3d F levels, considering the fact that the theoretical lifetimes of these levels ( are 2.6 ns (3d F ) and 0.28 ns (3d P ), respectively. ( ( Very weak transitions also occur at 343.89 and 344.07 nm whereas the transitions to the 3p D° levels at 353.80P354.22 nm were blended with the 3d P —3p S° transition. The 3d P levels (with a very short lifetime of :0.28 ns) were therefore not used in the ANDC ( analysis. 4.3. The 3d D cascading levels The spectral analysis showed that transitions from the 3d D term are either of a low intensity or blended with transitions from other levels with the possible exception of the transitions to the 3p D° term occurring at 345.48—345.93 nm. The measurement at the shorter wavelength revealed a primary component of 3.33 ns and a second component of 18.1 ns. These values may be affected by the 3d P (q"0.31 ns) and 3d D (q"0.23 ns) levels. A measurement at the higher wavelength (j"345.95 nm) revealed very similar results of a primary and second component of 3.33 and 25.9 ns, respectively. The good agreement between the different measurements probably indicates that the mentioned blending is improbable. We used the decay constants obtained at 345.95 nm in the ANDC analysis, although the primary decay constant differ considerably from the theoretical lifetime of the 3d D level, i.e. 3.33 ns vs 0.55 ns. We want to emphasize the fact that the primary decay constant of 3.33 ns cannot be regarded as the lifetime of this level—a reliable lifetime can only be obtained after an ANDC analysis. 4.4. The 3d F cascading levels The decay constants of these levels were obtained from measurements at 309.30, 309.75 nm (3d F !3p F° ) and 340.70 nm (3d F —3p D° ). It is interesting to note that these transitions at these wavelengths were reclassified by Persson. Prior to the reclassification, a number of authors made measurements at these wavelengths and allocated these lifetimes to the different fine structure components of the 3d D term. A Grotrian diagram of the original classifications, prior to the reclassification of Persson, of the transitions investigated in this work, is shown in Fig. 5. The decay constants obtained from the measurements at 309.30 and 309.75 nm were very similar with a primary component of :4.2 ns, a growing-in component of :0.5 ns and a third component of
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Fig. 5. Grotrian diagram indicating the classification of the encircled measured transitions prior to the reclassification by Persson.
:21.6 ns. These values were, due to the possibility of a number of blends, not used in the ANDC analysis. The measurement at 340.70 nm revealed a three component best fit with a growing-in, primary and third component of 0.58, 4.12 and 21.3 ns, respectively. These values were in good agreement with the curve-fitting results of the measurements at 309.30 and 309.75 nm. The decay constants represent the decay of the term, rather than the individual fine structure components as the transitions at 340.48 and 340.69 nm, originating from the J"5/2 and J"7/2 levels, respectively, are not resolved. The growing-in component could be due to cascading from higher lying levels but the data at small foil positions could be affected by the 3d P levels with a theoretical lifetime of :0.28 ns ( (transitions from these levels occur at 341.14 and 341.31 nm). The decay constants obtained at 340.70 nm were used in the ANDC analysis. Although the primary component of 4.12 ns is in fair agreement with previous measurements, i.e. 4.7 and 4.5 ns and 4.8 and 4.4 ns, this value does not necessarily represent the lifetime of this level—a reliable lifetime could only be obtained from an ANDC analysis. (As mentioned previously the measurements by these authors were at the same wavelength but the lifetime was allocated to the 3d D levels due to a wrong classification.) ( 4.5. The 3d G cascading levels The decay constants were obtained from measurements at 322.50 (3d G —3p F° ) and 322.90 nm (3d G —3p F° ). The 3d G —3p F° transitions occurring at 322.48—322.96 nm were ( ( unresolved and the decay constants obtained must be associated with the 3d G term rather than the different fine structure components. We used the result of the 322.50 nm measurement in further analysis, as the effects of the near lying (3p D —3s D ) transitions at 323.01—323.24 nm were evident ( ( in the results obtained from the 322.90 nm measurement. The 322.50 nm measurement yielded a three-component best fit with a primary component of 3.94 ns. This value is in good agreement with the BFS values of 3.69 and 3.72 ns obtained by Coetzer et al at 0.4 and 1.0 MeV. These results were also obtained by a curve-fitting method only. Blagoev et al used a delayed coincidence method and obtained a lifetime of 4.5 ns. Again we want to point
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out that our result of 3.94 ns is only a decay constant and no statement regarding the lifetime of these levels is made as the effect of cascading was not taken into account. 4.6. The 4s D cascading levels The 4s D-term can decay to the 3p F°, 3p P° and 3p D° terms. The 4s D —3p F° transitions occurring at 296.32 (J"3/2, 5/2) and 296.72 nm (J"5/2, 7/2) were ( ( unresolved and the decay constants obtained at 296.70 nm must therefore be associated with the 4s D term. It is interesting to note that Striganov et al assigned these wavelengths to transitions from the 3d F level (see Fig. 5). The measurement at 296.70 nm yielded a two-component best fit with a primary component of 4.22 ns. Blagoev et al used the delayed coincidence method and obtained lifetimes of 3.3 and 3.5 ns. We tried to confirm our measurement at 296.70 nm by obtaining decay constants at 314.10 (4s D —3p P° ), 316.40 (4s D —3p P° ) and 324.80 nm (4s D —3p D° ), but all these measurements were influenced by other transitions. 5 . THE A NDC A NALY SI S OF THE 3 p F° LEV EL S
The decay constants obtained at 357.45 nm were used as input data in die CANDY program together with the decay constants of the 3d D , 3d F , 3d G and 4s D levels respectively. All these individual fits show a missing cascade and all possible combinations of these levels were tried. The best fits in terms of the best criteria were obtained when the decay constants of the 4s D level were used in combination with either of the other three cascading levels. These fits yielded very similar results and the average of 6.78 ns is given in Table 3. Fink et al used the beam-foil method and obtained a lifetime of 6.2 ns from a measurement at 357.53 nm. The BFS value of Coetzer et al (7.32 ns) and the 7.3 ns obtained by Martin et al (delayed coincidence method) are very similar to our curve-fitting result of 7.5 ns. The effect of cascading however is important as can be seen from the :10% difference in the lifetime of this level when cascading is taken into account. In Table 3 we not only compare our result with these experimental values but also with various theoretical lifetimes.
Table 3. Results of ANDC analyses on the 3p F° electronic states in Ne II
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The decay constants obtained at 356.85 nm were used to determine the cascade corrected lifetime of the 3p F° level. These data were first used together with the individual decay constants of the 3d D, 3d F, 3d G and 4s D terms, but in all cases there were indications of a missing cascade. All the possible combinations of these cascading levels were tried. The best results were again obtained when the 4s D term was used in conjunction with either one of the other three cascading levels (as was the case for the J"5/2 level). The fits were very similar and the average of these results is given in Table 3. The BFS-technique were used by Fink et al, Brand et al and Denis et al to obtain a lifetime of 6.2, 8.3 and 8.8 ns, respectively. Other techniques were used by Martin et al (7.4 ns), Head et al (8.96, 8.5 ns) and Hesser (8.8 ns) to obtain lifetimes for the 3p F level. All these results, with the exception of the 6.2 ns obtained by Fink et al are 20—30% longer than the cascade corrected lifetime obtained in this work. In Table 3 we also compare our result with various theoretical lifetimes. The lifetime obtained in this work is slightly longer than the intermediate coupling calculations of Loginov et al (6.2 ns), Hodges et al (6.4 ns) and Koozekanani et al (4.2 ns). Loginov et al and Koozekanani et al used the Hartree—Fock function in their calculations whereas Hartree— Fock—Slater functions were used by Hodges et al. Our results are slightly shorter than the lifetime of 7.2 ns obtained by Luyken. 6. TH E A ND C AN AL YS I S OF TH E 3 p D ° L EVELS
The decay constants (J"3/2 level) obtained at 323.20 nm were used in the ANDC analysis, together with the decay constants of all the possible cascading terms, i.e. 3d D, 3d F and 4s D. The analysis using the 3d D and 4s D levels, individually yielded lifetimes of 5.08 and 5.33 ns, ( ( respectively. The decay constants of these two cascading levels were used simultaneously as input data as the individual analysis showed the possibility of a missing cascade. The final result is given in Table 4. The same procedure was followed in the determination of the cascade corrected lifetime of the J"5/2 level. The analysis again showed that the 3d D and 4s D terms are probably the major cascading terms. The individual analysis using the 3d D and 4s D levels yielded lifetimes of 4.89 ( ( and 5.14 ns, respectively, a value of 4.66 ns was obtained when both levels were used simultaneously as cascading levels. Our results, for both the J"3/2 and J"5/2 levels differ considerably from other experimental values \ as can be seen in Table 4.
Table 4. Results of ANDC analyses on the 3p D° electronic states in Ne II
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If we compare our results with the calculations of Hodges et al and Koozekanani et al the situation is far more satisfactory. The 4.4 (J"3/2) and 4.5 ns (J"5/2) obtained by Loginov et al is slightly lower, whereas the 5.3 ns (J"3/2, 5/2) obtained by Luyken is higher than our experimental result. 7 . THE A NDC A NALY SI S OF THE 3 p P° LEV EL S
The decay constants of the 3p P° level, obtained at 334.65 nm together with the decay constant of the 3d D and 4s D cascading levels yielded lifetimes of 4.71 and 4.92 ns, respectively. These ( ( individual analysis both showed a missing cascade and the best fit in terms of the best criteria were obtained when both cascading levels were used simultaneously in the analysis. The cascade corrected lifetime of 4.20 ns, which is :23% shorter than our curve-fitting result, is compared with other experimental and theoretical lifetimes in Table 5. Our result is slightly longer than both the BFS result of Brand et al and the phase-shift method result of Hesser. Our experimental lifetime is also in good agreement with the calculations of Luyken, Hodges et al and Koozekanani et al, whereas the 3.8 ns obtained by Loginov et al is slightly shorter. In our discussion of the decay of the 3p P° primary level, we mentioned that the decay constants obtained could be influenced by transitions from the 3d D and 3p P° levels. We tried to minimize these effects as discussed in Section 3.1.1. In an attempt to determine the lifetime of this level, in spite of possible interferences, we again used both cascading levels (4s D and 3d D ) in the ANDC analysis. The result is given in Table 5, and ( ( although a reasonable fit in terms of the test criteria was obtained we increased the error estimate in recognition of the fact that, in spite of our precaution, the possibility exists that blending may influence this result. In spite of the fact that the ANDC correction reduced the curve-fitting result by as much as 20%, our lifetime with the J"1/2 level of 3.74 ns is considerably longer than the 2.8 ns of Fink et al but in better agreement with the 3.5 ns of Savage et al. Our experimental lifetime is in good agreement with the calculations of Loginov et al (3.7 ns), Hodges et al (3.9 ns) and Koozekanani et al (3.9 ns). 8 . C ON CL US I O N
We have obtained radiative lifetimes for the different fine structure levels of 3p P°, 3p D° and ( ( 3p F° levels in Ne II. Cascading was compensated for by the ANDC technique and, as can be seen ( in Tables 3—5, better agreement between theory and experiment is obtained. In our analysis we used
Table 5. Results of ANDC analyses on the 3p P° electronic states in Ne II
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the reclassified energy level classification of Persson, which was specifically important for obtaining the correct decay constants for the 3d F cascading level. R EFE RE NC ES
Curtis, L., Berry, H. G. and Bromander, J., Phys. ¸ett., 1971, 34A, 169. Blagoev, K. and Stankova, K., JQSR¹, 1986, 35, 483. Martin, P. and Campos, J., JQSR¹, 1983, 30, 131. Coetzer, F. J., Kotze, P. B. and Van der Westhuizen, P., Nucl. Instr. Methods, 1982, 202, 19. Fink, U., Bashkin, S. and Bickel, W. S., JQSR¹, 1970, 10, 1241. Brand, J. H., Cocke, C. L., Curnutte, B. and Swenson, C., Nucl. Instr. Methods, 1970, 90, 63. Denis, A., Ceyze´riat, P. and Dufay, M., J. Opt. Soc. Amer., 1970, 60, 1186. Lawrence, T. N. and Head, C. E., Phys. Rev., 1973, A8, 1644. Head, C. E. and Head, M. E. M., Phys. Rev., 1970, A2, 2244. Hesser, J. E., Phys. Rev., 1968, A174, 68. Savage, B. D. and Lawrence, G. M., Astrophys. J., 1966, 146, 940. Loginov, A. V. and Gruzdev, P. F., Opt. Spectroscopy, 1978, 44, 123. Luyken, B. F. J., Physica, 1971, 51, 445. Hodges, D., Marantz, H. and Tang, C. L., Opt. Soci. Amer., 1970, 60, 192. Koozekanani, H. and Trusty, G. L., J. Opt. Soc. Amer., 1969, 59, 1281. Coetzer, F. J. and Van der Westhuizen, P., Z. Physik, 1979, A292, 369. Coetzer, F. J., Kotze, T. C. and Van der Westhuizen, P., JQSR¹, 1987, 38, 253. Persson, W., Physica Scripta, 1971, 3, 133. Striganov, A. R. and Sventitskii, N. S., ¹ables of Spectral lines of Neutral and Ionized Atoms. Plenum Press, New York, 1968, p. 199. 20. Provencher, S. W., Chem. Phys., 1976, 64, 2772. 21. Engstro¨m, L., Nucl. Instr. & Methods, 1982, 202, 369.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
PII: S0022-4073(98)00026-0
0022—4073/98 $19.00#0.00
RADIATIVE LIFETIMES OF SOME ENERGY LEVELS IN Ne II P. VAN DER WESTHUIZEN-, K. VISSER and D. C. BEUKMAN Department of Physics, University of Stellenbosch, Private Bag X1, 7602 Matieland, South Africa (Received 4 September 1997)
Abstract—The article describes beam—foil measurements of a number of primary as well as cascading levels in Ne II. A detailed cascade—corrected energy level lifetime analysis of the 3p P° , 3p D° and 3p F° levels in Ne II was undertaken. 1998 Published by Elsevier Science Ltd. All rights reserved.
1 . I NTROD UC TIO N
We have employed the beam-foil spectroscopy (BFS) method to measure the radiative lifetimes of the 3p P° , 3p D° and 3p F° levels of Ne II (2s2p (D) electronic core) correcting for the effect of cascades with the ANDC (arbitrarily normalized decay curve) technique described by Curtis et al. In the analyses care had to be given to line blending and repopulation via cascading levels due to the indiscriminate excitation of levels and Doppler broadening. We calculated the lifetimes assuming LS coupling with the Coulomb approximation to facilitate the assignment of the measured lines. Our results are compared with values obtained through the delayed coincidence (DC) method, as well as the beam-foil,\ beam-gas and phase shift methods. The experimental results are also compared with intermediate coupling (IC) calculations\ and LS coupling calculations with the Coulomb approximation. This work was conducted to attempt to resolve discrepancies amongst existing experimental values and between experimental and theoretical values. 2 . E XP ERI M EN T AL PR OC ED UR E
The experiment was conducted using the HVEC model CN 5.5 MV single-ended Van de Graaff accelerator at the National Accelerator Centre at Faure. The accelerator produced stable beams with beam currents of approximately 4 lA which was passed through hydrocarbon cracked foils. The neon spectral lines were detected with a refocused scanning monochromator equipped with a 2400 lines mm\ grating blazed for 300 nm. A more complete discription of the experimental set up is given in Refs. 16 and 17. A typical spectrum scan is shown in Fig. 1. The tables of Persson and Striganov et al were used for line identification. The lifetime measurements were made with a 0.5 MeV beam since it produced the optimum Ne II line intensities. The recorded decay curves were analysed with the DISCRETE program using a multi-exponential curve-fitting technique. The CANDY program was used to carry out the ANDC analyses on the DISCRETE results. 3. PRIM ARY L EV ELS
3.1. The 3p P°( levels: Transitions from the 3p P°( levels to the 3s D( levels occur at 331.97, 334.55 and 334.58 nm. A Grotrian diagram of the relevant energy levels and observed transitions is shown in Fig. 2. The decay curves measured at 331.90 and 334.65 nm together with decay curves of the 4s D and 3d D cascade levels measured at 296.70 and 345.95 nm, respectively, are also shown in Fig. 2. - To whom all correspondence should be addressed. 405
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Fig. 1. The beam-foil spectrum of neon at 0.5 and 1.0 MeV.
It is a well known fact that in beam-foil work, insufficient spectral resolution, resulting in line blending can cause serious errors in lifetime determinations. Special care was therefore taken to assess the influence of possible blends. 3.1.1. The 3p P° level. The J"1/2 component, decaying via the 331.97 nm transition could be influenced by transitions from the 3d D level and to a lesser extent by the 332.37 nm transition from the 3p P° level. The theoretical lifetimes of these two levels are 2.4 and 5.5 ns, respectively, compared to the theoretical lifetime of 3.9 ns of the 3p P° level. To determine the lifetime of the J"1/2 component a decay curve was therefore obtained, not at the tabulated wavelength of 331.97 nm but to the shorter wavelength region at 331.90 nm in an attempt to minimize the possibility of a blend. The curve-fitting analysis yielded a three-component best fit with a primary value of 4.71 ns, a growing-in component of 0.78 ns and a third component of 34.2 ns. In an attempt to assess the influence of the possible blend due to the transition from the 3d D level (j"332.0196 nm) we also measured the decay at 332.10 nm. The primary decay constant obtained at this wavelength was very similar (4.70 ns) to the 4.71 ns obtained at 331.90 nm, whereas the two other components differ only slightly from the measurement at the shorter wavelength. In the analysis of the 3p ¸° (¸"1, 2, 3) levels, that will be published shortly, an in depth study ( was made of the 3d D levels because the decay constants were needed in the ANDC analysis as ( cascading can occur from these levels. From this study we conclude that the 3d D levels are indeed ( populated but the spectral analysis of the transitions from these levels is frequently blended by
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Fig. 2. Partial Grotrian diagram of the relevant energy levels in Ne II and measured transitions (wavelengths in nm) with the background-corrected decay curves of the 3p P° —3s D , 3p P° —3s D , 3d D —3p D° and 4s D —3p F° transitions. Transitions in brackets are tabulated wavelengths in nm.
transitions from other levels. Taking all possible blends into account we finally used the 3d D —3p P° transitions with a primary decay constant of 3.16 ns. From these arguments it is clear that the possibility of blending between transitions from the 3d D and 3p P° levels could not be ruled out completely. We nevertheless tried the decay constants, obtained at 331.90 nm, in the ANDC analysis and discuss these results in Sec. 7. 3.1.2. The 3p P° level. The 3p P° level decay to the 3s D and 3s D levels at 334.55 and 334.65 nm respectively. These two transitions are unresolved, but these blends do not create a problem as both transitions originate from the same J"3/2 fine structure level. The decay constants obtained at both measurements were very similar with a primary component of approximately 5.5 ns. The possibility of a blend with a transition from the 3p D° level (theoretical lifetime 5.2 ns) at 334.4395 nm was investigated by obtaining decay constants from the analysis of a measurement at 334.40 nm. Although our spectral analysis showed that the 3p D° levels are populated, we con( cluded, by comparing the decay constants obtained from the 334.40 and 334.65 nm measurements, that the 334.65 nm measurement was not affected by the 3p D° —3s P transition.
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The decay constants obtained from the curve-fitting procedure are given in Table 1. Transitions from the 3p P° states to the 3s P , 3s P and 2s2p S states occur at wavelengths ( ( ( that are outside the detection region of our spectrometer system and could therefore not be studied. 3.2. The 3p D° levels ( The decay constants associated with transitions from these levels were obtained from measurements at 323.05 nm (3p D° —3s D ) and 323.20 nm (3p D° —3s D ). The Grotrian diagram indicating the energy levels involved in these transitions as well as the measured decay curves are shown in Fig. 3. The decay curve obtained at 340.70 nm for the 3d F cascade level is also shown in Fig. 3. The results of the measurements are shown in Table 1. The spectrum analysis showed that these two transitions are not completely resolved and that the possible effect of the 3d G —3p F (322.48—322.96 nm) transitions should be assessed. The effect of ( ( these possible blends were investigated by obtaining decay constants from measurements at 322.50 and 322.90 nm. Both curves yielded a three component best fit with primary components of 3.94 and 4.94 ns, respectively. These results show a 25% increase in the primary component obtained from the measurement at the wavelength closer to the wavelength associated with the transition from the 3p D° levels. These two long decay times for the 3d G (in comparison to the theoretical lifetime of 2.7 ns ( suggested that the 3p D° —3s D measurements are not affected to a great extent and that DISCRETE results can be tried in an ANDC-analysis. Depopulation from the 3p D° states can also occur via transitions to the 3s P states (187.7679, ( ( 190.0189 nm) but are outside the detection region of our spectrometer system.
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Fig. 3. Partial Grotrian diagram of the relevant energy levels in Ne II and measured transitions (wavelengths in nm) with the background-corrected decay curves of the 3p D° —3s D , 3p D° —3s D and 3d F —3p D° transitions. Transitions in brackets are tabulated wavelengths in nm.
3.3. The 3p F° levels The decay constants associated with these upper levels were obtained from measurements at 356.85 nm (3p F° —3s D ) and 357.45 nm (3p F° —3s D ) and are shown in Table 1. The Grotrian diagram indicating the energy levels involved in these transitions as well as the possible cascading levels is shown in Fig. 4. The decay curves obtained at 356.85 and 357.45 nm as well as the decay curve of the 3d G cascade level obtained at 322.50 nm are also shown in Fig. 4. 3.3.1. The 3p F° level. Transitions from the 3d P , 5p D° and 3d F levels occur at 356.58, 356.76 and 357.12 nm, respectively, and the effect of these possible blends should be assessed. The theoretical lifetimes of both the 3d P (1.0 ns) and 3d F (1.7 ns) are considerably shorter than that of the 3p F° (6.4 ns) level and should (if they occur) only affect the measurement at small foil positions. To assess the influence of the 5p D° level we did a Coulomb approximation calculation and found the lifetime of this level to be :28.7 ns. It is clear that if this level is populated the decay curve will only be affected at large foil positions.
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Fig. 4. Partial Grotrian diagram of the relevant energy levels in Ne II and measured transitions (wavelengths in nm) with the background-corrected decay curves of the 3p F° —3s D , 3p F° —3s D and 3d G —3p F° transitions. Transitions in brackets are tabulated wavelengths in nm.
3.3.2. The 3p F° level. Transitions from this level to the J"5/2 and J"3/2 fine structure components of the 3s D term are tabulated at 357.42 and 357.46 nm and are unresolved. This is not a problem as these transitions originate from the same upper level and only the influence of the transitions from the 5p P° and 5p P° levels occurring at 357.20 and 357.24 nm should be assessed. Our Coulomb approximation calculations revealed the relatively long lifetimes of :27.5 and 29.0 ns for the 5p P° and 5p P° levels, respectively. If these levels are populated the decay curve will only be affected at large foil positions. 4. C AS CA DIN G L EVELS
It is evident from Table 2 that a total of six possible cascading levels had to be investigated. 4.1. The 3d S cascading level If populated this level will only influence one of the terms under investigation, i.e. the 3p P° ( levels. The 3d S level decay via transitions to the 3p P° and 3p P° levels at 336.22 and
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Table 2. Cascading levels that may contribute to primary levels
338.89 nm, respectively. The spectrum analysis showed that both transitions were probably unresolved and the decay measurements indeed confirmed the suspected blends. The decay constant obtained from the measurement at 336.22 nm, i.e. :6 ns, is probably due to the depopulation of the 3p D° level, whereas the 338.89 nm transition is blended with a number of transitions. The 3d S level with a very short lifetime of :0.19 ns was therefore not included in the analysis as a cascading level. 4.2. The 3d P cascading levels Transitions from the 3d P and 3d P levels to the 3p P° level occur at 341.10 and 341.30 nm, respectively. Measurements obtained at these wavelengths revealed decay constants of 3.92 and 3.71 ns, respectively. The spectrum analysis showed that these transitions were unresolved from transitions from the 3d F levels and it is possible that these decay constants should rather be ( associated with the 3d F levels, considering the fact that the theoretical lifetimes of these levels ( are 2.6 ns (3d F ) and 0.28 ns (3d P ), respectively. ( ( Very weak transitions also occur at 343.89 and 344.07 nm whereas the transitions to the 3p D° levels at 353.80P354.22 nm were blended with the 3d P —3p S° transition. The 3d P levels (with a very short lifetime of :0.28 ns) were therefore not used in the ANDC ( analysis. 4.3. The 3d D cascading levels The spectral analysis showed that transitions from the 3d D term are either of a low intensity or blended with transitions from other levels with the possible exception of the transitions to the 3p D° term occurring at 345.48—345.93 nm. The measurement at the shorter wavelength revealed a primary component of 3.33 ns and a second component of 18.1 ns. These values may be affected by the 3d P (q"0.31 ns) and 3d D (q"0.23 ns) levels. A measurement at the higher wavelength (j"345.95 nm) revealed very similar results of a primary and second component of 3.33 and 25.9 ns, respectively. The good agreement between the different measurements probably indicates that the mentioned blending is improbable. We used the decay constants obtained at 345.95 nm in the ANDC analysis, although the primary decay constant differ considerably from the theoretical lifetime of the 3d D level, i.e. 3.33 ns vs 0.55 ns. We want to emphasize the fact that the primary decay constant of 3.33 ns cannot be regarded as the lifetime of this level—a reliable lifetime can only be obtained after an ANDC analysis. 4.4. The 3d F cascading levels The decay constants of these levels were obtained from measurements at 309.30, 309.75 nm (3d F !3p F° ) and 340.70 nm (3d F —3p D° ). It is interesting to note that these transitions at these wavelengths were reclassified by Persson. Prior to the reclassification, a number of authors made measurements at these wavelengths and allocated these lifetimes to the different fine structure components of the 3d D term. A Grotrian diagram of the original classifications, prior to the reclassification of Persson, of the transitions investigated in this work, is shown in Fig. 5. The decay constants obtained from the measurements at 309.30 and 309.75 nm were very similar with a primary component of :4.2 ns, a growing-in component of :0.5 ns and a third component of
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Fig. 5. Grotrian diagram indicating the classification of the encircled measured transitions prior to the reclassification by Persson.
:21.6 ns. These values were, due to the possibility of a number of blends, not used in the ANDC analysis. The measurement at 340.70 nm revealed a three component best fit with a growing-in, primary and third component of 0.58, 4.12 and 21.3 ns, respectively. These values were in good agreement with the curve-fitting results of the measurements at 309.30 and 309.75 nm. The decay constants represent the decay of the term, rather than the individual fine structure components as the transitions at 340.48 and 340.69 nm, originating from the J"5/2 and J"7/2 levels, respectively, are not resolved. The growing-in component could be due to cascading from higher lying levels but the data at small foil positions could be affected by the 3d P levels with a theoretical lifetime of :0.28 ns ( (transitions from these levels occur at 341.14 and 341.31 nm). The decay constants obtained at 340.70 nm were used in the ANDC analysis. Although the primary component of 4.12 ns is in fair agreement with previous measurements, i.e. 4.7 and 4.5 ns and 4.8 and 4.4 ns, this value does not necessarily represent the lifetime of this level—a reliable lifetime could only be obtained from an ANDC analysis. (As mentioned previously the measurements by these authors were at the same wavelength but the lifetime was allocated to the 3d D levels due to a wrong classification.) ( 4.5. The 3d G cascading levels The decay constants were obtained from measurements at 322.50 (3d G —3p F° ) and 322.90 nm (3d G —3p F° ). The 3d G —3p F° transitions occurring at 322.48—322.96 nm were ( ( unresolved and the decay constants obtained must be associated with the 3d G term rather than the different fine structure components. We used the result of the 322.50 nm measurement in further analysis, as the effects of the near lying (3p D —3s D ) transitions at 323.01—323.24 nm were evident ( ( in the results obtained from the 322.90 nm measurement. The 322.50 nm measurement yielded a three-component best fit with a primary component of 3.94 ns. This value is in good agreement with the BFS values of 3.69 and 3.72 ns obtained by Coetzer et al at 0.4 and 1.0 MeV. These results were also obtained by a curve-fitting method only. Blagoev et al used a delayed coincidence method and obtained a lifetime of 4.5 ns. Again we want to point
Radiative lifetimes in Ne II
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out that our result of 3.94 ns is only a decay constant and no statement regarding the lifetime of these levels is made as the effect of cascading was not taken into account. 4.6. The 4s D cascading levels The 4s D-term can decay to the 3p F°, 3p P° and 3p D° terms. The 4s D —3p F° transitions occurring at 296.32 (J"3/2, 5/2) and 296.72 nm (J"5/2, 7/2) were ( ( unresolved and the decay constants obtained at 296.70 nm must therefore be associated with the 4s D term. It is interesting to note that Striganov et al assigned these wavelengths to transitions from the 3d F level (see Fig. 5). The measurement at 296.70 nm yielded a two-component best fit with a primary component of 4.22 ns. Blagoev et al used the delayed coincidence method and obtained lifetimes of 3.3 and 3.5 ns. We tried to confirm our measurement at 296.70 nm by obtaining decay constants at 314.10 (4s D —3p P° ), 316.40 (4s D —3p P° ) and 324.80 nm (4s D —3p D° ), but all these measurements were influenced by other transitions. 5 . THE A NDC A NALY SI S OF THE 3 p F° LEV EL S
The decay constants obtained at 357.45 nm were used as input data in die CANDY program together with the decay constants of the 3d D , 3d F , 3d G and 4s D levels respectively. All these individual fits show a missing cascade and all possible combinations of these levels were tried. The best fits in terms of the best criteria were obtained when the decay constants of the 4s D level were used in combination with either of the other three cascading levels. These fits yielded very similar results and the average of 6.78 ns is given in Table 3. Fink et al used the beam-foil method and obtained a lifetime of 6.2 ns from a measurement at 357.53 nm. The BFS value of Coetzer et al (7.32 ns) and the 7.3 ns obtained by Martin et al (delayed coincidence method) are very similar to our curve-fitting result of 7.5 ns. The effect of cascading however is important as can be seen from the :10% difference in the lifetime of this level when cascading is taken into account. In Table 3 we not only compare our result with these experimental values but also with various theoretical lifetimes.
Table 3. Results of ANDC analyses on the 3p F° electronic states in Ne II
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The decay constants obtained at 356.85 nm were used to determine the cascade corrected lifetime of the 3p F° level. These data were first used together with the individual decay constants of the 3d D, 3d F, 3d G and 4s D terms, but in all cases there were indications of a missing cascade. All the possible combinations of these cascading levels were tried. The best results were again obtained when the 4s D term was used in conjunction with either one of the other three cascading levels (as was the case for the J"5/2 level). The fits were very similar and the average of these results is given in Table 3. The BFS-technique were used by Fink et al, Brand et al and Denis et al to obtain a lifetime of 6.2, 8.3 and 8.8 ns, respectively. Other techniques were used by Martin et al (7.4 ns), Head et al (8.96, 8.5 ns) and Hesser (8.8 ns) to obtain lifetimes for the 3p F level. All these results, with the exception of the 6.2 ns obtained by Fink et al are 20—30% longer than the cascade corrected lifetime obtained in this work. In Table 3 we also compare our result with various theoretical lifetimes. The lifetime obtained in this work is slightly longer than the intermediate coupling calculations of Loginov et al (6.2 ns), Hodges et al (6.4 ns) and Koozekanani et al (4.2 ns). Loginov et al and Koozekanani et al used the Hartree—Fock function in their calculations whereas Hartree— Fock—Slater functions were used by Hodges et al. Our results are slightly shorter than the lifetime of 7.2 ns obtained by Luyken. 6. TH E A ND C AN AL YS I S OF TH E 3 p D ° L EVELS
The decay constants (J"3/2 level) obtained at 323.20 nm were used in the ANDC analysis, together with the decay constants of all the possible cascading terms, i.e. 3d D, 3d F and 4s D. The analysis using the 3d D and 4s D levels, individually yielded lifetimes of 5.08 and 5.33 ns, ( ( respectively. The decay constants of these two cascading levels were used simultaneously as input data as the individual analysis showed the possibility of a missing cascade. The final result is given in Table 4. The same procedure was followed in the determination of the cascade corrected lifetime of the J"5/2 level. The analysis again showed that the 3d D and 4s D terms are probably the major cascading terms. The individual analysis using the 3d D and 4s D levels yielded lifetimes of 4.89 ( ( and 5.14 ns, respectively, a value of 4.66 ns was obtained when both levels were used simultaneously as cascading levels. Our results, for both the J"3/2 and J"5/2 levels differ considerably from other experimental values \ as can be seen in Table 4.
Table 4. Results of ANDC analyses on the 3p D° electronic states in Ne II
Radiative lifetimes in Ne II
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If we compare our results with the calculations of Hodges et al and Koozekanani et al the situation is far more satisfactory. The 4.4 (J"3/2) and 4.5 ns (J"5/2) obtained by Loginov et al is slightly lower, whereas the 5.3 ns (J"3/2, 5/2) obtained by Luyken is higher than our experimental result. 7 . THE A NDC A NALY SI S OF THE 3 p P° LEV EL S
The decay constants of the 3p P° level, obtained at 334.65 nm together with the decay constant of the 3d D and 4s D cascading levels yielded lifetimes of 4.71 and 4.92 ns, respectively. These ( ( individual analysis both showed a missing cascade and the best fit in terms of the best criteria were obtained when both cascading levels were used simultaneously in the analysis. The cascade corrected lifetime of 4.20 ns, which is :23% shorter than our curve-fitting result, is compared with other experimental and theoretical lifetimes in Table 5. Our result is slightly longer than both the BFS result of Brand et al and the phase-shift method result of Hesser. Our experimental lifetime is also in good agreement with the calculations of Luyken, Hodges et al and Koozekanani et al, whereas the 3.8 ns obtained by Loginov et al is slightly shorter. In our discussion of the decay of the 3p P° primary level, we mentioned that the decay constants obtained could be influenced by transitions from the 3d D and 3p P° levels. We tried to minimize these effects as discussed in Section 3.1.1. In an attempt to determine the lifetime of this level, in spite of possible interferences, we again used both cascading levels (4s D and 3d D ) in the ANDC analysis. The result is given in Table 5, and ( ( although a reasonable fit in terms of the test criteria was obtained we increased the error estimate in recognition of the fact that, in spite of our precaution, the possibility exists that blending may influence this result. In spite of the fact that the ANDC correction reduced the curve-fitting result by as much as 20%, our lifetime with the J"1/2 level of 3.74 ns is considerably longer than the 2.8 ns of Fink et al but in better agreement with the 3.5 ns of Savage et al. Our experimental lifetime is in good agreement with the calculations of Loginov et al (3.7 ns), Hodges et al (3.9 ns) and Koozekanani et al (3.9 ns). 8 . C ON CL US I O N
We have obtained radiative lifetimes for the different fine structure levels of 3p P°, 3p D° and ( ( 3p F° levels in Ne II. Cascading was compensated for by the ANDC technique and, as can be seen ( in Tables 3—5, better agreement between theory and experiment is obtained. In our analysis we used
Table 5. Results of ANDC analyses on the 3p P° electronic states in Ne II
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the reclassified energy level classification of Persson, which was specifically important for obtaining the correct decay constants for the 3d F cascading level. R EFE RE NC ES
Curtis, L., Berry, H. G. and Bromander, J., Phys. ¸ett., 1971, 34A, 169. Blagoev, K. and Stankova, K., JQSR¹, 1986, 35, 483. Martin, P. and Campos, J., JQSR¹, 1983, 30, 131. Coetzer, F. J., Kotze, P. B. and Van der Westhuizen, P., Nucl. Instr. Methods, 1982, 202, 19. Fink, U., Bashkin, S. and Bickel, W. S., JQSR¹, 1970, 10, 1241. Brand, J. H., Cocke, C. L., Curnutte, B. and Swenson, C., Nucl. Instr. Methods, 1970, 90, 63. Denis, A., Ceyze´riat, P. and Dufay, M., J. Opt. Soc. Amer., 1970, 60, 1186. Lawrence, T. N. and Head, C. E., Phys. Rev., 1973, A8, 1644. Head, C. E. and Head, M. E. M., Phys. Rev., 1970, A2, 2244. Hesser, J. E., Phys. Rev., 1968, A174, 68. Savage, B. D. and Lawrence, G. M., Astrophys. J., 1966, 146, 940. Loginov, A. V. and Gruzdev, P. F., Opt. Spectroscopy, 1978, 44, 123. Luyken, B. F. J., Physica, 1971, 51, 445. Hodges, D., Marantz, H. and Tang, C. L., Opt. Soci. Amer., 1970, 60, 192. Koozekanani, H. and Trusty, G. L., J. Opt. Soc. Amer., 1969, 59, 1281. Coetzer, F. J. and Van der Westhuizen, P., Z. Physik, 1979, A292, 369. Coetzer, F. J., Kotze, T. C. and Van der Westhuizen, P., JQSR¹, 1987, 38, 253. Persson, W., Physica Scripta, 1971, 3, 133. Striganov, A. R. and Sventitskii, N. S., ¹ables of Spectral lines of Neutral and Ionized Atoms. Plenum Press, New York, 1968, p. 199. 20. Provencher, S. W., Chem. Phys., 1976, 64, 2772. 21. Engstro¨m, L., Nucl. Instr. & Methods, 1982, 202, 369.
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