- Email: [email protected]
Beam-foil spectroscopy for ions of lead and bismuth
206
Nuclear
BEAM-FOIL
SPECTROSCOPY
E.H. PINNINGTON, De~ari~ent
Instruments
and Methods
in Physics
FOR IONS OF LEAD AND BISMUTH
W. ANSBACHER,
J.A. KERNAHAN,
Research B31 (1988) 206-210 North-Holland, Amsterdam
*
Z.-Q. GE and A.S. INAMDAR
**
of Physics, Uniuersity of Alberta, Edmonton, Alberta, Canada T6G ZJi
The bean-foil technique is used to measure the lifetimes of levels in Pb III, Pb IV, Bi III and Bi IV. The problem of the energy loss incurred by heavy ions at the foil is discussed. Intensity decay curves including the region around the foil are analysed using VNET, a multiexponential fitting routine which includes the instrumental window function. These analyses are found to give results virtually identical with those obtained using normal curve-fitting of the data excluding the foil region in our case, where the window region only extends over one or two primary lifetimes. A comparison of the experimental and theoretical j-values trends for the resonance transitions of the ions belonging to the gold and mercury isoelectronic sequences shows that the model potential used by Migdalek and Baylis in 1985 to allow for valence-core correlation gives good agreement with observation for the mercury sequence, whereas their similar calculation in 1979 for the gold sequence appears to give f-values lower than those found by experiment for Tl III and Pb IV.
At the Third International Conference on Beam-Foil Spectroscopy held at Tucson in 1972, Andersen et al. [I] reported experimental f-values for the resonance transitions in ions belonging to the Cu I, Ag I and Au I (“one-electron”) and Zn I, Cd I and Hg I (“ two-electron”) isoelectronic sequences. A more detailed account of their measurements was published later in that year [2]. Since that time considerable progress has been made for the ions of the Cu I, Zn I, Ag I and Cd I isoelectronic sequences (see refs. [3-61 and refs. quoted therein). Of particular interest is the generally good agreement found between recent theoretical estimates of the f-values of the resonance transitions for those ions and the results of beam-foil measurements in which the ANDC method [7] is applied to correct for the effects of cascading. In contrast, relatively little attention has been given since 1972 to the ions of the Au I and Hg I isoelectronic sequences [S,9]. This is no doubt partly a result of the well-documented difficulties associated with lifetime measurements for very heavy ions at relatively low ion energies [9,10], not the least of which is the large and rather ill-defined energy loss sustained by the ions at the target foil. Migdalek and Bayiis [ll] have recently extended their relativistic calculations, in which they incorporate a model potential to represent valence-core correlation, to the case of resonance transition f-values for ions belonging to the HgI isoelectronic sequence.
* Work supported f~ancially by the Natural Sciences and Engineering Research Councii and the Province of Alberta. * * Permanent address: Abasahab Garware College, Pune, India. 0168-583X/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
Clearly a need exists at this time for reliable experimental data with which to compare this calculation. The installation in 1981 of a field-emission ion source in the University of Alberta’s 2 MV Van de Graaff [12] has enabled us to initiate a programme of beam-foil measurements for ions of lead and bismuth. Preliminary results from this programme are reported here.
2. Techniques for data acquisition and analysis Beams of Pb’ and Bi’ ions, having typical on-target currents of 0.5 pA, were obtained from a 2 MV Van de Graaff accelerator equipped with a liquid metal ion source that has been described previously [12]. For the Pb+ ions, a SO-50 lead-tin alloy was used in the source, while a 42-58 bismuth-tin alloy was employed for the Bii ions. It was also found possible to obtain a 0.2 PA beam of Pb” ions, but the corresponding Bi2+ beam was very weak, being less than 40 nA. This was unfortunate as the maximum energy that could be deflected by our analyzing magnet was around 0.9 MeV for singly-ionized bismuth ions and this energy proved to be too low for a useful study of the Bi V spectrum. It is planned to modify the experimental arrangement for a future, more detailed study of the Bi V beam-foil spectrum using a higher ion energy. Further details of our experimental techniques are available elsewhere in these Proceedings [13]. As was mentioned earlier, the loss in energy incurred at the target foil by ions as massive as bismuth and lead is not negligible, particularly for ion energies below 1 MeV. In addition to the high average energy loss, which theory suggests may be as high as 10% of the incident
E. H. Pinnington ef al. / Beam-foil spectroscopy for lead and bismuth energy for a 5 pgm/cm’ carbon foil in the present experiment [14], energy straggling and particle scattering can result in an uncertainty in the effective energy loss that is comparable in magnitude to the energy loss itself. The consequences for beam-foil lifetime measurements have been discussed previously by several authors [7,10,15]. Geissel et al. [16] have recently demonstrated clearly the relationship between the average energy loss and the scattering angle for Bi+ ions incident on carbon foils, albeit at a significantly higher ion energy than in the present work. The problem still remains to estimate the energy loss which is appropriate for those ions which are actually observed in a bean-foil lifetime measurement, since there is an obvious tendency to observe fewer of the ions that are scattered through larger angles (and hence have a larger energy loss in the forward direction) as observations are made farther downstream from the foil. In other words, the average velocity of the observed ions in the forward direction is a slowly increasing function of the distance from the foil. More importantly, scattering at the foil results in fewer ions remaining in the field of view for observations made farther away from the foil, and hence in an apparent shortening of the observed lifetime. In order to make a simple estimate of the magnitude of this effect in the present experiment, we have recorded a series of decay curves using foils of thicknesses 5, 10 and 15 pg/cm2 for the two Bi IV transitions at 873 and 1317 A for which the upper state lifetimes are 0.3 ns and 8 ns respectively. For both transitions a systematic apparent shortening of the primary lifetime was observed with increasing foil thickness, enabling us to estimate the effective energy loss for a 5 pg/cm2 carbon foil and an incident Bi+ ion energy of 900 keV as being around 100 keV for the decay curves recorded at 873 A’aand around 150 keV for those decays recorded at 1317 A, the larger value in the second case presumably reflecting the more important role played by scattering for longer-lived decays. Since this estimate is still only a first approximation, we have included an uncertainty of 5% in the beam velocity in estimating the overall uncertainty of the lifetimes and f-values discussed later in this report. Another problem associated with beam-foil measurements, particularly for short lifetimes, is the need to record data as close to the foil as possible. This becomes more important for more massive ions because of their lower velocity. One approach that has been discussed previously [17,18] is to measure the decay right up to the foil, or even slightly upstream of it, by modelling the instrumental window function in the data analysis routine. This is very useful when the window function extends over many data points, as is the case if the ion beam is relatively distant from the spectrometer entrance slit [17]. In our case, the ion beam is just 2.0 cm from the slit, resulting in a typical observation window
207
of 0.4 mm. Thus, normal data analysis techniques can begin 0.2 mm from the foil. The actual shape taken by the window function depends not only on the f-number and slitwidth of the monochromator, but also on the geometry of the foil surface, which is difficult to control at the 0.1 mm level. Consequently, it is not possible to specify the precise form of the window function, a problem that has been reported elsewhere [18]. In order to test the efficacy of such an analysis for data acquired in our laboratory, we have recorded decay curves beginning upstream of the foil. The separation of the data points for the region containing the foil was 0.05 mm. The window region typically extended over 0.4 mm, corresponding to a 0.2 mm slitwidth and an f/l00 optical system, although for very short lifetimes narrower slitwidths and optical apertures were used. These data were analysed using a new routine, VNET, which is basically the multiexponential fitting programme TROY [19], modified to include a window function that is essentially the standard trapezoid [17] but includes also a factor allowing for the shadow cast by the foil and frame on which it is mounted. In general, these analyses gave results that were not significantly different from those found using HOMER/ TROY for the data recorded outside the region containing the foil. This is not too surprising since the overall extent of the window region corresponded to one or two decay lengths, and it is known that, in such circumstances, the extent of the window region is not a serious impediment to the resolution of the primary lifetime [20]. On the other hand, using such an analysis does provide a means of accurately locating the foil position for each decay curve. This can be important when several decay curves are analysed simultaneously, as in an ANDC analysis. The window function could, in principle, be included directly in the ANDC analysis itself. For example, the window function could be included in our nonlinear routine, CANADA [21], as an effective additional cascade, giving the modified ANDC relation dZ -=~z(f)+~qzJ(t)+z’(O)W(-t), dt where Z and Z, are the observed intensities of the primary and Zth cascade at time t, respectively, and 7 is the primary lifetime. Z’(t) is the sum of the exponential terms describing the shape of the primary population decay curve, i.e. Z’(0) is generally not equal to Z(O), and W(t) is the function describing to window. Naturally, W( - t) is zero outside the region containing the foil and then the ANDC equation reduces to its usual form, [7], where Z’(0) and C, are the arbitrary fitting parameters. Although such a procedure is possible, our results using VNET suggest that not too much may actually to be gained, at least for situations like ours IV. MANY-ELECTRON
STRUCTURE: EXPERIMENT
E.H. Pinnington
208 Table 1 Lifetimes Term
of some triplet levels of Pb III and Bi IV J
Lifetime [ns]
Ion
Measured
Coulomb approximation
1 2 3
Pb III
0.35 +0.03 0.49 * 0.05
0.33 0.36 0.42
1 2 3
Bi IV
0.23 + 0.03 0.18 + 0.03 0.25 + 0.03
0.17 0.18 0.23
6p23P
0 1 2
Bi IV
0.38 f 0.05 0.30 * 0.03 0.31*0.03
0.33 0.22 0.17
6s7s3S
1 1
Pb III Bi IV
0.47 f 0.05 0.25 f 0.03
0.74 0.31
6s6d3D
et al. / Beam-foil
the ion beam is relatively close to the spectrometer slit. Further study of this problem is in progress. Full details of our various data analysis routines are available elsewhere [6,13,19-211. where
3. Discussion of results In table 1 we present the values we obtain using multi exponential curve-fitting analyses for the lifetimes of some triplet levels in Pb III and Bi IV. As no theoretical values are available for comparison, we have included some estimates made using the Coulomb approximation. The agreement between observation and the Coulomb approximation values is rather good for the 6s6d levels in both ions, but this is not the case for the 6p2 levels of Bi IV, nor for the 6~7s 3S level in Pb III. (The 6s6p-6p2 transitions in Pb III are either blended or very weak in our spectra.) In table 2 we compare the results we obtain for the 6s6p ‘Pi and 3P1
spectroscopy for lead and bismuth
levels in both ions, using TROY, VNET and ANDC analyses, with previous experiment [2] and with the calculation by Migdalek and Baylis [ll]. The agreement between the calculated values and the present measurements is seen to be good. Moreover, the experimental values are essentially independent of the method of analysis, although the ANDC results should be the most reliable. The f-values we obtain from these lifetimes are shown in fig. 1, together with other experimental values and the Migdalek and Baylis calculations. The corepolarization correction applied by Migdalek and Baylis may be seen to bring the theoretical and experimental trends into good agreement for the ions of the HgI isoelectronic sequence. In fig. 2 we show the f-value trend for the 6s 2S1,2-6~ *P3,2 transition along the Au1 sequence, including the value we obtain from an ANDC analysis for the Pb IV member. In this case, the ANDC lifetime was about 20% shorter than that obtained from HOMER/ TROY. As was mentioned previously, we were unable to complete a similar study for the BiV member of this sequence because the required cascade transitions from 7s and 6d were too weak at the maximum beam energy available to us. Such a measurement is highly desirable, however, to substantiate the suggestion in fig. 2 that the core-polarization correction applied by Migdalek and Baylis [23] may be too large, i.e. an over-correction, in this case. It is also interesting to compare figs. 1 and 2 with the corresponding trends for the AgI and Cd1 sequences [4,6]. For the AgI sequence the core-polarization factor applied by Migdalek and Baylis in 1979 [23] appears once again to give somewhat too large a correction, while a later calculation for the Cd1 sequence [24] agrees rather better with experiment. Finally, we summarize in table 3 the preliminary values we have measured for the lifetimes of the low-lying levels of Bi III. This spectrum is homologous with those of Ar VI [13] and Ti X [25], where ANDC analyses using cascade transitions from the 3p3 and 3s3p3d levels have given lifetimes for the 3s23d and
Table 2 Lifetimes of the 6s6p (J = 1) levels of Pb III and Bi IV Level
Ion
‘9
Pb III Bi IV
3P1
Pb III Bi IV
Lifetime TROY
a) b, ‘) d, e,
[ns] a)
0.396 +O.OlO 0.244 + 0.057 18.4 8.00
kO.3 *0.07
VNET
=)
0.393 * 0.007 0.260 f 0.058 18.4 7.92
+0.3 e, kO.08
ANDC
a)
0.380 i 0.010 0.229 f 0.008 14.8 8.0
+0.6 +0.5
Quoted uncertainties are those given by the statistical analyses only. ANDC result but including the 5% estimated uncertainty in the ion velocity. Earlier beam-foil result [2]. RHF calculation including a model potential correction for core-polarization Decay data begins too far from the foil for a useful VNET analysis.
Final value b, 0.380 * 0.021 0.229 + 0.014 14.8 8.0
[ll].
*l.O +0.6
Other exp. ‘) 0.49 f 0.08 0.39 + 0.08 -
Theory 0.35 0.25 17 9.0
d,
E.H. Pinnington
et al. / Beam-foil
spectroscopy for lead and bismuth
209
2.5
2.0
____ ___-___ _----------__-1 __-__-__-Ii
/ 1.5
I______1 _____ _ _-____---_4 l f
(a)
1
0
f
I f
1.0
(b)
0:
-
01
Au1
I
I
1
TIII
BiIV
Pblll
Fig. 1. f-value trends for (a) the 6s’ ‘Sa-6s6p ‘Pr transition, (b) the 6s * ‘Sa-6s6p 3Pi transition, for ions of the Hg I isoelectronic sequence. The solid curves show the RHF calculation by Migdalek and Baylis [ll], and the dashed curves show their calculation including a model potential valence-core correlation correction. The experimental values are derived from lifetimes measured using the beam-foil method, the open circles being from the present work and the solid circles from refs. [2,9,22].
Table 3 Lifetimes
of some low lying levels of Bi III
Level
Lifetime
6s6p2 * Pi,1 ‘I’,/2
*Ds,z 4pl,2
6s25f
*F5,*
* F,,z 6s26d ‘D,,, 6s*ls ‘Q2 6s27p *P,,* *p3/2
(ns)
Measured
Coulomb approx.
0.23 f 0.05 0.17+0.03 0.33 f 0.05 9.6 f0.9 2.6 *0.5 3.1 io.5 1.0 io.3 0.40 * 0.04 6.6 *0.4 3.1 kO.6
0.15 0.41 0.49 _ 1.2 1.7 0.40 0.68 7.0 4.0
I
HgII
I
TlIIl
I
I
PblV
BiV
Fig. 2. f-value trend for the 6s *S,,,-6p *P3,* transition for ions of the Au1 isoelectronic sequence. The solid and dashed curves indicate the RHF and the RHF+ core polarization calculations in ref. 1231. The open circle is based on the present measurement and the solid circles are derived from lifetimes reported in refs. [2,8, 221.
3s3p2 resonance levels that are typically lo-15% shorter than are obtained using normal multiexponential curve fitting. Unfortunately, we are not able to perform the corresponding ANDC analyses for the 6s26d and 6s6p2 resonance levels in Bi III as the important cascade transitions are not yet assigned. We suspect that the lifetimes reported in table 3 may well be subject to similar systematic errors and we have taken account of this possibility in assigning the error limits shown there. In the absence of any other comparison data, we have again included some estimates obtained using the Coulomb approximation. The agreement between these values and observation is generally poor, except for the 6s27p 2P levels. It is hoped that this study will encourage further theoretical investigations for ions of the Tl I sequence.
4. Conclusion We have presented some new data for the lifetimes of the 6s6p levels of Pb 111 and Bi IV, and we have compared the f-values derived from them with other experimental results and with calculation for ions of the HgI isoelectronic sequence. The model potential method for including valence-core correlation in RHF calculaIV. MANY-ELECTRON
STRUCTURE:
EXPERIMENT
210
E. H. Pinnington
et al. / Beam -foil spectroscopy for lead and bismuth
tions that has been developed by Migdalek and Baylis [ll] gives generally good agreement with experiment for this sequence. A similar analysis for the resonance transition of ions of the Au I sequence, including some new data for Pb IV, shows somewhat poorer agreement between observation and the Migdalek and Baylis calculations [23]. We have also presented lifetime data for some triplet levels in Pb III and for some low-lying levels in Bi III. Theoretical estimates are needed for both these ions. We have also tested a new curve-fitting routine, VNET, that includes the instrumental window function and have suggested how the window function may be included directly in ANDC analyses. Finally, we have discussed the problem of the energy loss incurred by heavy ions at the foil, which is a significant source of uncertainty in the lifetime results presented here. It is hoped to construct a velocity analyzer, which would measure the post-foil velocity directly, for future experiments with heavy ions.
References
111T. Andersen, A.K. Nielsen and G. Sorensen, Nucl. Instr. and Meth. 110 (1973) 143. 121 T. Andersen, O.H. Madsen and G. Sorensen, Phys. Scripta 6 (1972) 122. [31 E.H. Pinnington, J.L. Bahr, D.J.G. Irwin and J.A. Kernahan, Nucl. Instr. and Meth. 202 (1982) 67. [41 E.H. Pinnington, Nucl. Instr. and Meth B9 (1985) 549. [51 E.H. Pinnington, W. Ansbacher, J.A. Kernahan and AS. Inamdar, J. Opt. Sot. Am. B2 (1985) 331. 161 E.H. Pinnington, J.A. Kemahan and W. Ansbacher, Can. J. Phys. 65 (1987) 7. [71 L.J. Curtis, H.G. Berry and J. Bromander, Phys. Scripta 2 (1970) 216. PI P. Eriksen and 0. Poulsen, J. Quant. Spectr. Radiat. Transf. 23 (1980) 599.
[9] 0.
Poulsen, T. Andersen, S.M. Bentzen and I. Koleva, Nucl. Instr. and Meth. 202 (1982) 139. [lo] T. Andersen, O.H. Madsen and G. Sorensen, Phys. Scripta 6 (1972) 125. [ll] J. Migdalek and W.E. BayIis, J. Phys. B18 (1985) 1533. [12] W. Ansbacher, E.H. Pinnington, J.L. Bahr and J.A. Kernahan, Can. J. Phys. 63 (1985) 1330. [13] E.H. Pinnington, Z.-Q. Ge and W. Ansbacher, these Proceedings, (SASHIA ‘87) Nucl. Instr. and Meth. B31 (1988) 191. [14] J.P. Biersack, E. Ernst, A. Monge and S. Roth, Hahn-Meitner Institute, Report HMI-B 175, Berlin, Germany (1975). [15] G.W. Carriveau, G. Beauchemin, E.J. Knystautas, E.H. Pinnington and R. Drouin, Phys. Lett. 46A (1973) 291. [16] H. Geissel, W.N. Lennard, H.R. Andrews, D.P. Jackson, I.V. Mitchell, D. Philips and D. Ward, Nucl. Instr. and Meth. B12 (1985) 38. [17] E. TrPbert, H. Winter, P.H. Heckmann and H.V. Buttlar, Nucl. Instr. and Meth. 135 (1976) 353. [18] Y. Baudinet-Robinet, H.P. Gamir, P.D. Dumont and A.E. Livingston, Phys. Scripta 14 (1976) 224. [19] E.H. Pinnington, R.N. GosseIin, J.A. Q’NeiII, J.A. Kemahan, K.E. Donnelly and R.L. Brooks, Phys. Scripta 20 (1979) 151. [20] J.A. G’Neill, E.H. Pinnington, K.E. DonneIIy and R.L. Brooks, Phys. Scripta 20 (1979) 60. [21] W. Ansbacher, E.H. Pinnington, J.A. Kemahan and R.N. Gosselin, Can J. Phys. 64 (1986) 1365. [22] T. Andersen and G. Sorensen, J. Quant. Spectr. Radiat. Transf. 13 (1973) 369. [23] J. Migdalek and W.E. Bayhs, J. Quant. Spectr. Radiat. Transf. 22 (1979) 113. [24] J. Migdalek and W.E. Baylis, J. Phys. B19 (1986) 1. [25] E.H. Pinmngton, W. Ansbacher, E. Trabert, P.H. Heckmann, H.M. Hellmann and G. Mijller, Z. Phys. D6 (1987) 241.
Nuclear
BEAM-FOIL
SPECTROSCOPY
E.H. PINNINGTON, De~ari~ent
Instruments
and Methods
in Physics
FOR IONS OF LEAD AND BISMUTH
W. ANSBACHER,
J.A. KERNAHAN,
Research B31 (1988) 206-210 North-Holland, Amsterdam
*
Z.-Q. GE and A.S. INAMDAR
**
of Physics, Uniuersity of Alberta, Edmonton, Alberta, Canada T6G ZJi
The bean-foil technique is used to measure the lifetimes of levels in Pb III, Pb IV, Bi III and Bi IV. The problem of the energy loss incurred by heavy ions at the foil is discussed. Intensity decay curves including the region around the foil are analysed using VNET, a multiexponential fitting routine which includes the instrumental window function. These analyses are found to give results virtually identical with those obtained using normal curve-fitting of the data excluding the foil region in our case, where the window region only extends over one or two primary lifetimes. A comparison of the experimental and theoretical j-values trends for the resonance transitions of the ions belonging to the gold and mercury isoelectronic sequences shows that the model potential used by Migdalek and Baylis in 1985 to allow for valence-core correlation gives good agreement with observation for the mercury sequence, whereas their similar calculation in 1979 for the gold sequence appears to give f-values lower than those found by experiment for Tl III and Pb IV.
At the Third International Conference on Beam-Foil Spectroscopy held at Tucson in 1972, Andersen et al. [I] reported experimental f-values for the resonance transitions in ions belonging to the Cu I, Ag I and Au I (“one-electron”) and Zn I, Cd I and Hg I (“ two-electron”) isoelectronic sequences. A more detailed account of their measurements was published later in that year [2]. Since that time considerable progress has been made for the ions of the Cu I, Zn I, Ag I and Cd I isoelectronic sequences (see refs. [3-61 and refs. quoted therein). Of particular interest is the generally good agreement found between recent theoretical estimates of the f-values of the resonance transitions for those ions and the results of beam-foil measurements in which the ANDC method [7] is applied to correct for the effects of cascading. In contrast, relatively little attention has been given since 1972 to the ions of the Au I and Hg I isoelectronic sequences [S,9]. This is no doubt partly a result of the well-documented difficulties associated with lifetime measurements for very heavy ions at relatively low ion energies [9,10], not the least of which is the large and rather ill-defined energy loss sustained by the ions at the target foil. Migdalek and Bayiis [ll] have recently extended their relativistic calculations, in which they incorporate a model potential to represent valence-core correlation, to the case of resonance transition f-values for ions belonging to the HgI isoelectronic sequence.
* Work supported f~ancially by the Natural Sciences and Engineering Research Councii and the Province of Alberta. * * Permanent address: Abasahab Garware College, Pune, India. 0168-583X/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
Clearly a need exists at this time for reliable experimental data with which to compare this calculation. The installation in 1981 of a field-emission ion source in the University of Alberta’s 2 MV Van de Graaff [12] has enabled us to initiate a programme of beam-foil measurements for ions of lead and bismuth. Preliminary results from this programme are reported here.
2. Techniques for data acquisition and analysis Beams of Pb’ and Bi’ ions, having typical on-target currents of 0.5 pA, were obtained from a 2 MV Van de Graaff accelerator equipped with a liquid metal ion source that has been described previously [12]. For the Pb+ ions, a SO-50 lead-tin alloy was used in the source, while a 42-58 bismuth-tin alloy was employed for the Bii ions. It was also found possible to obtain a 0.2 PA beam of Pb” ions, but the corresponding Bi2+ beam was very weak, being less than 40 nA. This was unfortunate as the maximum energy that could be deflected by our analyzing magnet was around 0.9 MeV for singly-ionized bismuth ions and this energy proved to be too low for a useful study of the Bi V spectrum. It is planned to modify the experimental arrangement for a future, more detailed study of the Bi V beam-foil spectrum using a higher ion energy. Further details of our experimental techniques are available elsewhere in these Proceedings [13]. As was mentioned earlier, the loss in energy incurred at the target foil by ions as massive as bismuth and lead is not negligible, particularly for ion energies below 1 MeV. In addition to the high average energy loss, which theory suggests may be as high as 10% of the incident
E. H. Pinnington ef al. / Beam-foil spectroscopy for lead and bismuth energy for a 5 pgm/cm’ carbon foil in the present experiment [14], energy straggling and particle scattering can result in an uncertainty in the effective energy loss that is comparable in magnitude to the energy loss itself. The consequences for beam-foil lifetime measurements have been discussed previously by several authors [7,10,15]. Geissel et al. [16] have recently demonstrated clearly the relationship between the average energy loss and the scattering angle for Bi+ ions incident on carbon foils, albeit at a significantly higher ion energy than in the present work. The problem still remains to estimate the energy loss which is appropriate for those ions which are actually observed in a bean-foil lifetime measurement, since there is an obvious tendency to observe fewer of the ions that are scattered through larger angles (and hence have a larger energy loss in the forward direction) as observations are made farther downstream from the foil. In other words, the average velocity of the observed ions in the forward direction is a slowly increasing function of the distance from the foil. More importantly, scattering at the foil results in fewer ions remaining in the field of view for observations made farther away from the foil, and hence in an apparent shortening of the observed lifetime. In order to make a simple estimate of the magnitude of this effect in the present experiment, we have recorded a series of decay curves using foils of thicknesses 5, 10 and 15 pg/cm2 for the two Bi IV transitions at 873 and 1317 A for which the upper state lifetimes are 0.3 ns and 8 ns respectively. For both transitions a systematic apparent shortening of the primary lifetime was observed with increasing foil thickness, enabling us to estimate the effective energy loss for a 5 pg/cm2 carbon foil and an incident Bi+ ion energy of 900 keV as being around 100 keV for the decay curves recorded at 873 A’aand around 150 keV for those decays recorded at 1317 A, the larger value in the second case presumably reflecting the more important role played by scattering for longer-lived decays. Since this estimate is still only a first approximation, we have included an uncertainty of 5% in the beam velocity in estimating the overall uncertainty of the lifetimes and f-values discussed later in this report. Another problem associated with beam-foil measurements, particularly for short lifetimes, is the need to record data as close to the foil as possible. This becomes more important for more massive ions because of their lower velocity. One approach that has been discussed previously [17,18] is to measure the decay right up to the foil, or even slightly upstream of it, by modelling the instrumental window function in the data analysis routine. This is very useful when the window function extends over many data points, as is the case if the ion beam is relatively distant from the spectrometer entrance slit [17]. In our case, the ion beam is just 2.0 cm from the slit, resulting in a typical observation window
207
of 0.4 mm. Thus, normal data analysis techniques can begin 0.2 mm from the foil. The actual shape taken by the window function depends not only on the f-number and slitwidth of the monochromator, but also on the geometry of the foil surface, which is difficult to control at the 0.1 mm level. Consequently, it is not possible to specify the precise form of the window function, a problem that has been reported elsewhere [18]. In order to test the efficacy of such an analysis for data acquired in our laboratory, we have recorded decay curves beginning upstream of the foil. The separation of the data points for the region containing the foil was 0.05 mm. The window region typically extended over 0.4 mm, corresponding to a 0.2 mm slitwidth and an f/l00 optical system, although for very short lifetimes narrower slitwidths and optical apertures were used. These data were analysed using a new routine, VNET, which is basically the multiexponential fitting programme TROY [19], modified to include a window function that is essentially the standard trapezoid [17] but includes also a factor allowing for the shadow cast by the foil and frame on which it is mounted. In general, these analyses gave results that were not significantly different from those found using HOMER/ TROY for the data recorded outside the region containing the foil. This is not too surprising since the overall extent of the window region corresponded to one or two decay lengths, and it is known that, in such circumstances, the extent of the window region is not a serious impediment to the resolution of the primary lifetime [20]. On the other hand, using such an analysis does provide a means of accurately locating the foil position for each decay curve. This can be important when several decay curves are analysed simultaneously, as in an ANDC analysis. The window function could, in principle, be included directly in the ANDC analysis itself. For example, the window function could be included in our nonlinear routine, CANADA [21], as an effective additional cascade, giving the modified ANDC relation dZ -=~z(f)+~qzJ(t)+z’(O)W(-t), dt where Z and Z, are the observed intensities of the primary and Zth cascade at time t, respectively, and 7 is the primary lifetime. Z’(t) is the sum of the exponential terms describing the shape of the primary population decay curve, i.e. Z’(0) is generally not equal to Z(O), and W(t) is the function describing to window. Naturally, W( - t) is zero outside the region containing the foil and then the ANDC equation reduces to its usual form, [7], where Z’(0) and C, are the arbitrary fitting parameters. Although such a procedure is possible, our results using VNET suggest that not too much may actually to be gained, at least for situations like ours IV. MANY-ELECTRON
STRUCTURE: EXPERIMENT
E.H. Pinnington
208 Table 1 Lifetimes Term
of some triplet levels of Pb III and Bi IV J
Lifetime [ns]
Ion
Measured
Coulomb approximation
1 2 3
Pb III
0.35 +0.03 0.49 * 0.05
0.33 0.36 0.42
1 2 3
Bi IV
0.23 + 0.03 0.18 + 0.03 0.25 + 0.03
0.17 0.18 0.23
6p23P
0 1 2
Bi IV
0.38 f 0.05 0.30 * 0.03 0.31*0.03
0.33 0.22 0.17
6s7s3S
1 1
Pb III Bi IV
0.47 f 0.05 0.25 f 0.03
0.74 0.31
6s6d3D
et al. / Beam-foil
the ion beam is relatively close to the spectrometer slit. Further study of this problem is in progress. Full details of our various data analysis routines are available elsewhere [6,13,19-211. where
3. Discussion of results In table 1 we present the values we obtain using multi exponential curve-fitting analyses for the lifetimes of some triplet levels in Pb III and Bi IV. As no theoretical values are available for comparison, we have included some estimates made using the Coulomb approximation. The agreement between observation and the Coulomb approximation values is rather good for the 6s6d levels in both ions, but this is not the case for the 6p2 levels of Bi IV, nor for the 6~7s 3S level in Pb III. (The 6s6p-6p2 transitions in Pb III are either blended or very weak in our spectra.) In table 2 we compare the results we obtain for the 6s6p ‘Pi and 3P1
spectroscopy for lead and bismuth
levels in both ions, using TROY, VNET and ANDC analyses, with previous experiment [2] and with the calculation by Migdalek and Baylis [ll]. The agreement between the calculated values and the present measurements is seen to be good. Moreover, the experimental values are essentially independent of the method of analysis, although the ANDC results should be the most reliable. The f-values we obtain from these lifetimes are shown in fig. 1, together with other experimental values and the Migdalek and Baylis calculations. The corepolarization correction applied by Migdalek and Baylis may be seen to bring the theoretical and experimental trends into good agreement for the ions of the HgI isoelectronic sequence. In fig. 2 we show the f-value trend for the 6s 2S1,2-6~ *P3,2 transition along the Au1 sequence, including the value we obtain from an ANDC analysis for the Pb IV member. In this case, the ANDC lifetime was about 20% shorter than that obtained from HOMER/ TROY. As was mentioned previously, we were unable to complete a similar study for the BiV member of this sequence because the required cascade transitions from 7s and 6d were too weak at the maximum beam energy available to us. Such a measurement is highly desirable, however, to substantiate the suggestion in fig. 2 that the core-polarization correction applied by Migdalek and Baylis [23] may be too large, i.e. an over-correction, in this case. It is also interesting to compare figs. 1 and 2 with the corresponding trends for the AgI and Cd1 sequences [4,6]. For the AgI sequence the core-polarization factor applied by Migdalek and Baylis in 1979 [23] appears once again to give somewhat too large a correction, while a later calculation for the Cd1 sequence [24] agrees rather better with experiment. Finally, we summarize in table 3 the preliminary values we have measured for the lifetimes of the low-lying levels of Bi III. This spectrum is homologous with those of Ar VI [13] and Ti X [25], where ANDC analyses using cascade transitions from the 3p3 and 3s3p3d levels have given lifetimes for the 3s23d and
Table 2 Lifetimes of the 6s6p (J = 1) levels of Pb III and Bi IV Level
Ion
‘9
Pb III Bi IV
3P1
Pb III Bi IV
Lifetime TROY
a) b, ‘) d, e,
[ns] a)
0.396 +O.OlO 0.244 + 0.057 18.4 8.00
kO.3 *0.07
VNET
=)
0.393 * 0.007 0.260 f 0.058 18.4 7.92
+0.3 e, kO.08
ANDC
a)
0.380 i 0.010 0.229 f 0.008 14.8 8.0
+0.6 +0.5
Quoted uncertainties are those given by the statistical analyses only. ANDC result but including the 5% estimated uncertainty in the ion velocity. Earlier beam-foil result [2]. RHF calculation including a model potential correction for core-polarization Decay data begins too far from the foil for a useful VNET analysis.
Final value b, 0.380 * 0.021 0.229 + 0.014 14.8 8.0
[ll].
*l.O +0.6
Other exp. ‘) 0.49 f 0.08 0.39 + 0.08 -
Theory 0.35 0.25 17 9.0
d,
E.H. Pinnington
et al. / Beam-foil
spectroscopy for lead and bismuth
209
2.5
2.0
____ ___-___ _----------__-1 __-__-__-Ii
/ 1.5
I______1 _____ _ _-____---_4 l f
(a)
1
0
f
I f
1.0
(b)
0:
-
01
Au1
I
I
1
TIII
BiIV
Pblll
Fig. 1. f-value trends for (a) the 6s’ ‘Sa-6s6p ‘Pr transition, (b) the 6s * ‘Sa-6s6p 3Pi transition, for ions of the Hg I isoelectronic sequence. The solid curves show the RHF calculation by Migdalek and Baylis [ll], and the dashed curves show their calculation including a model potential valence-core correlation correction. The experimental values are derived from lifetimes measured using the beam-foil method, the open circles being from the present work and the solid circles from refs. [2,9,22].
Table 3 Lifetimes
of some low lying levels of Bi III
Level
Lifetime
6s6p2 * Pi,1 ‘I’,/2
*Ds,z 4pl,2
6s25f
*F5,*
* F,,z 6s26d ‘D,,, 6s*ls ‘Q2 6s27p *P,,* *p3/2
(ns)
Measured
Coulomb approx.
0.23 f 0.05 0.17+0.03 0.33 f 0.05 9.6 f0.9 2.6 *0.5 3.1 io.5 1.0 io.3 0.40 * 0.04 6.6 *0.4 3.1 kO.6
0.15 0.41 0.49 _ 1.2 1.7 0.40 0.68 7.0 4.0
I
HgII
I
TlIIl
I
I
PblV
BiV
Fig. 2. f-value trend for the 6s *S,,,-6p *P3,* transition for ions of the Au1 isoelectronic sequence. The solid and dashed curves indicate the RHF and the RHF+ core polarization calculations in ref. 1231. The open circle is based on the present measurement and the solid circles are derived from lifetimes reported in refs. [2,8, 221.
3s3p2 resonance levels that are typically lo-15% shorter than are obtained using normal multiexponential curve fitting. Unfortunately, we are not able to perform the corresponding ANDC analyses for the 6s26d and 6s6p2 resonance levels in Bi III as the important cascade transitions are not yet assigned. We suspect that the lifetimes reported in table 3 may well be subject to similar systematic errors and we have taken account of this possibility in assigning the error limits shown there. In the absence of any other comparison data, we have again included some estimates obtained using the Coulomb approximation. The agreement between these values and observation is generally poor, except for the 6s27p 2P levels. It is hoped that this study will encourage further theoretical investigations for ions of the Tl I sequence.
4. Conclusion We have presented some new data for the lifetimes of the 6s6p levels of Pb 111 and Bi IV, and we have compared the f-values derived from them with other experimental results and with calculation for ions of the HgI isoelectronic sequence. The model potential method for including valence-core correlation in RHF calculaIV. MANY-ELECTRON
STRUCTURE:
EXPERIMENT
210
E. H. Pinnington
et al. / Beam -foil spectroscopy for lead and bismuth
tions that has been developed by Migdalek and Baylis [ll] gives generally good agreement with experiment for this sequence. A similar analysis for the resonance transition of ions of the Au I sequence, including some new data for Pb IV, shows somewhat poorer agreement between observation and the Migdalek and Baylis calculations [23]. We have also presented lifetime data for some triplet levels in Pb III and for some low-lying levels in Bi III. Theoretical estimates are needed for both these ions. We have also tested a new curve-fitting routine, VNET, that includes the instrumental window function and have suggested how the window function may be included directly in ANDC analyses. Finally, we have discussed the problem of the energy loss incurred by heavy ions at the foil, which is a significant source of uncertainty in the lifetime results presented here. It is hoped to construct a velocity analyzer, which would measure the post-foil velocity directly, for future experiments with heavy ions.
References
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