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Release studies of a thin foil tantalum target for the production of short-lived radioactive nuclei
Nuclear Physics A 701 (2002) 327c–333c www.elsevier.com/locate/npe
Release studies of a thin foil tantalum target for the production of short-lived radioactive nuclei J.R.J. Bennett a,∗ , U.C. Bergmann b , P.V. Drumm a , J. Lettry c , T. Nilsson c , R. Catherall c , O.C. Jonsson c , H.L. Ravn c , H. Simon c Members of the ISOLDE Collaboration a CLRC, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, UK b Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark c CERN, CH-1211 Geneva 23, Switzerland
Abstract Measurements have been made at ISOLDE, of the release curves and yields of radioactive beams of lithium, sodium and beryllium from a target constructed from 2 µm thick foils. The release curves have been analysed by fitting to a mathematical model to determine the coefficients of diffusion of the particles in the foils and effusion through the target and ionizer at several temperatures. Through a better understanding of the rate of transport of the particles, it is possible to design targets and ionizers with improved yields. This is most important for the rare, short-lived isotopes in which there is considerable interest for physics experiments. This target has demonstrated large increases in the yields of 11 Li and 12 Be, in agreement with the predictions of the model. 2002 Elsevier Science B.V. All rights reserved. PACS: 29.25.-t; 29.25.Rm; 66.30.-h Keywords: Radioactive ion beam source; Targets; Diffusion; Effusion
1. Introduction There is a need to increase the currents of some radioactive species produced by the bombardment of thick targets by high-energy proton beams in the ISOL method. In particular this applies to the rare short-lived isotopes. Raising the proton current increases * Corresponding author.
E-mail address: [email protected] (J.R.J. Bennett). 0375-9474/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 1 ) 0 1 6 0 6 - 2
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J.R.J. Bennett et al. / Nuclear Physics A 701 (2002) 327c–333c
the power dissipation in the target. The RIST tantalum foil disc target [1] was developed to dissipate over 25 kW, corresponding to 100 µA (mean) of 1 GeV protons. The RIST target geometry was tested [2] at ISOLDE [3] to compare the performance with conventional ISOLDE tantalum roll-foil targets. Target development at ISOLDE has continued in an attempt to improve the yield efficiency of the target. The initial target (Ta050) had 25 µm thick tantalum foils; the measured yields of the alkali metals and rare earths were good and the release fast [2]. The next targets (Ta075 and Ta126) were of similar design, but were constructed from 100 µm tantalum foils. The release was even faster, but the yields not quite as good. A mathematical model [4] of the release in the target and ionizer was developed in an attempt to understand the results and an approximate solution of the diffusion equation was found. This provides a powerful tool in predicting the yields for different target geometries once the release characteristics for a particular combination of radioactive element and target has been established. The reader is referred to another paper [5] in this conference for definitions of yield, the release curve, release parameters and the mathematical model. Using the model, it was clear that even if the target mass was much less than in the previous targets, a reduction in delay times can be more important for short-lived isotopes in giving substantially increased yields.
2. The 2 µm thick tantalum foil target, number Ta129 The validity of this idea has been tested with a new target (see Fig. 1) constructed from tantalum foils of only 2 µm thickness [6]. The target mass is only 10 g cm−2 , compared to the usual mass of ∼ 100 g cm−2. As in all the tests, the standard ISOLDE tungsten thermal ionizer was used. It would have been advantageous to reduce its delay time by altering the geometry [7], but this was not possible for practical reasons.
Fig. 1. Cross section of the tantalum target, Ta129.
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3. The measurements The target was tested during a week in April 1999 and again in September 1999. During the first test, the yield of 11 Li was measured by counting the delayed neutrons [7]. The release curves of 7 Li (stable) were measured using a sensitive current meter at several target temperatures [8]. Also, the release curve of 8 Li was measured by counting the beta decays using a tape drive system. In the second test the yield measurement of 11 Li was repeated and yields of 12 Be, 14 Be, 23 Na and 27 Na were measured. The release curves of 8 Li and 11 Be were taken using the tape drive. Laser ionization in the tungsten thermal ionizer was used for the beryllium beams. Unfortunately, the laser ionization system was so unstable during the measurements of 11 Be that it was not possible to obtain a reasonably smooth release curve. The 11 Li and beryllium beams were deposited onto a Kapton foil and neutron and beta decays were counted in 0.1 ms time bins [7]. This gives an integral of the release function, p(t), as a function of time, I (t) = e
−λt
t p(t) dt.
(1)
0
The integral method [9] of measuring release curves provides very good data in general, is quick and easy to use and makes use of all the information from each pulse. Using small time intervals is particularly valuable where the release curve is changing rapidly with time.
4. Results Table 1 shows the yield measurements. The yield of 11 Li was much larger than had been measured previously with the standard ISOLDE roll foil tantalum targets despite the small target mass. Also the yield of 12 Be was much larger than had been found previously with uranium carbide targets. However, the yield of 14 Be was not much improved over previous measurements. Table 1 Yields of short-lived isotopes of lithium, beryllium and sodium from target Ta129. The values in brackets indicate previous yields from uranium carbide (UC) and standard ISOLDE roll foil tantalum (Ta) targets Run date
Particle
April 1999 September 1999
11 Li 11 Li 12 Be 14 Be 23 Al 32 Al 33 Al
Yield particles (µC) 7000 (500 Ta) 3000–1000 50 000 (4000 UC) 7 (4 UC) not detected not detected 10
Particle 29 Na 30 Na 31 Na 32 Na
Yield particles (µC) 6400 (1200 Ta) 300 (230 Ta) – (12 Ta) 8
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Table 2 Calculated release parameters found by fitting the mathematical model to the measured data. The release times for 11 Li in the April run are scaled from 8 Li by the square root of their masses Particle Isotope τ ms 8 Li
No.
Target Release parameters Temperature d h D E τD (K) (µm) (cm) (cm2 s−1 ) (cm2 s−1 ) (s)
1218 Ta050 2258
12.5
10
1E-8
τE (s)
τs (s)
εt (%)
389
63
0.1
0.015
8
528 285 –
0.67 0.2 0.23
0.043 0.08 0.09
0.005 0.006 0.007
100 84 2
April 1999 run on Ta129 7 Li 8 Li 11 Li
∞ Ta129 2423 1218 Ta129 2423 13 Ta129 2423
1 1 1
7.5 7.5 7.5
0.6E-8 2E-8 –
September/October 1999 run on Ta129 8 Li 11 Li 12 Be 14 Be
1218 13 34 6.3
Ta129 Ta129 Ta129 Ta129
2423 2423 2448 2448
1 1 1 1
7.5 7.5 7.5 7.5
0.9E-8 – – –
2280 – – –
0.46 0.001 ∼ 0.5 ∼ 0001 ∼ 0.01 ∼ 0.08 ∼ 0.01 ∼ 0.08
0.006 83 0.005 6 0.015 0.186 0.013 0.015
Fig. 2. Integral release curve for 11 Li. The circles are the measured points and the line is the approximately calculated fit.
Table 2 shows the calculated release parameters found by fitting the mathematical model to the measured release and integral release curves, see Fig. 2. Also shown in Table 2 is some lithium data from Ta050. Unfortunately, the integral release curves for the very shortlived isotopes, 11 Li (see Fig. 2), 12 Be and 14 Be are so dominated by the decay, that the time constants for diffusion, τD , and effusion through the target, τE , are largely indeterminate. They are calculated to lie within limits of a factor of ∼ 0.01 to ∼ 100 of the values shown in Table 2. However, the value of the ionizer time constant, τs is well-defined. Beryllium
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would appear to have a higher diffusion coefficient than lithium but a lower effusion, presumably because it is more sticky, but all values must be taken with caution. The diffusion coefficients of isotopes of the same element should scale with the square root of their masses. The release parameters of 11 Li have been calculated on this basis from those of 8 Li.
5. Discussion The run in September 1999 showed that the yields were considerably lower than those taken in April. It is believed that this is due to the deterioration of the target; subsequently, the target was cut open and the foils were found to have fused together and in parts melted. Consequently the effective foil thickness increases and the diffusion time increases. Conversely, the effusion time decreases since there is little release from within the foil structure but mainly from the outer surface. Measurements of the release curve of 8 Li in September (see Table 2) show this clearly; τD has more than doubled while τE has decreased by nearly 2 orders of magnitude compared to the corresponding measurements in April. The low yield of 11 Li (between 1000 and 3000 atoms per µC of protons) in September is explained by this and means that the effective target mass is reduced by a factor of 6–20. This can also explain the low yield of 8 Li (∼ 20 times lower than in April) in September, despite the unchanged release efficiency (see Table 2). Fig. 3 shows the calculated diffusion coefficients, D and E, on an Arrhenius plot. D increases with temperature as would be expected. E also increases, but at a much faster rate than the expected square root of the temperature (i.e., the particle velocity). It is assumed that the difference is due to the more rapid change in sojourn time. Hence, the temperature can be very important for sticky particles. Since the target temperature remains almost constant, τs is unchanged at ∼ 10 ms for lithium. The value calculated from the conductance is ∼ 1 ms. Again, this difference is assumed to be due to the lithium being sticky. At the end of the run in April 1999, the release of stable 7 Li was measured [10] for a single pulse of protons on the target at several temperatures. It will be seen from Fig. 3, that the values of D are lower and E higher than for the corresponding values of 8 Li. It is likely that the fusion of the foils was already taking place at this time. The measured yield of 11 Li from the RIST disc target, Ta126, with 100 µm thick tantalum foils, was 2500 particles per µC. Scaling this with the expected release parameters of Ta129, gives a prediction of the yield of 11 Li which is almost exactly in agreement with the measured value. This shows the power of the model in predicting the performance of targets when the basic release parameters are known. The apparently low yield of 14 Be is simply explained. The ratio of the release efficiencies (Table 2) for 12 Be and 14 Be is 0.070. The corresponding ratio of the cross sections, calculated using Silberberg and Tsao [11], is 0.0022. Multiplying the measured yield of 12 Be by these ratios gives the yield of 14 Be as 9 atoms per µC, in almost exact agreement with the measurement of 7 atoms per µC.
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Fig. 3. Arrhenius plots of D and E for lithium.
Acknowledgements Grateful thanks are given to everyone who helped in performing the experiments at ISOLDE, including the PS staff.
References [1] R.J. Bennett, C.J. Densham, P.V. Drumm, W.R. Evans, M. Holding, G.R. Murdoch, V. Panteleev, Nucl. Instrum. Methods B 126 (1997) 117. [2] P.V. Drumm, J.R.J. Bennett, C.J. Densham, W.R. Evans, M. Holding, G.R. Murdoch, A.H. Evenson, E. Kugler, J. Lettry, H. Ravn, O. Tengblad, P. Van Duppen, R. Catherall, O. Jonsson, J. Kay, D.D. Warner, M. Harder, C. Thwaites, J. Honsi, R. Page, J. Billowes, S.J. Freeman, I.S. Grant, S. Schwebel, G. Smith, C. Bishop, P.M. Walker, Nucl. Instrum. Methods B 126 (1997) 121. [3] E. Kugler, D. Fiander, B. Jonson, H. Haas, A. Prewloka, H.L. Ravn, D.J. Simon, K. Zimmer, Nucl. Instrum. Methods B 70 (1992) 41. [4] J.R.J. Bennett, in: K.W. Shepard (Ed.), Proceedings of the Eight International Conference on Heavy Ion Accelerator Technology, Argonne National Laboratory, Chicago, 5–9 October 1998, AIP Conference Proceedings, Vol. 473, AIP, New York, 1999, p. 490.
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[5] J.R.J. Bennett, Nucl. Phys. A 701 (2002), proceedings of this conference. [6] J.R.J. Bennett, P.V. Drumm, R. Catherall, O.C. Jonsson, J. Lettry, T. Nilsson, H.L. Ravn, H. Simon and Members of the ISOLDE Collaboration, Nucl. Instrum. Methods B 155 (1999) 515. [7] U.C. Bergman, L. Axelsson, M.J.G. Borge, V.N. Fedoseyev, C. Forssén, H.O.U. Fynbo, S. Grévy, P. Hornshøj, Y. Jading, B. Jonson, U. Köster, K. Markenroth, F.M. Marqués, V.I. Mishin, I. Mukha, T. Nilsson, G. Nyman, A. Oberstedt, H.L. Ravn, K. Riisager, G. Schrieder, V. Sebastian, H. Simon, O. Tengblad, F. Wenander, K. Wilhelmsen Rolander, Nucl. Phys. A 658 (1999) 129. [8] J. Lettry, private communication. [9] Proceedings of European Particle Accelerator Conference, 22–26 June 1998, IOP, Bristol, 1998, p. 2383. [10] J. Lettry, private communication. [11] R. Silberberg, C.H. Tsao, Cross Sections of Proton–Nucleus Interactions at High Energies, Naval Research Laboratory, NRL report 7593, 1973.
Release studies of a thin foil tantalum target for the production of short-lived radioactive nuclei J.R.J. Bennett a,∗ , U.C. Bergmann b , P.V. Drumm a , J. Lettry c , T. Nilsson c , R. Catherall c , O.C. Jonsson c , H.L. Ravn c , H. Simon c Members of the ISOLDE Collaboration a CLRC, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, UK b Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark c CERN, CH-1211 Geneva 23, Switzerland
Abstract Measurements have been made at ISOLDE, of the release curves and yields of radioactive beams of lithium, sodium and beryllium from a target constructed from 2 µm thick foils. The release curves have been analysed by fitting to a mathematical model to determine the coefficients of diffusion of the particles in the foils and effusion through the target and ionizer at several temperatures. Through a better understanding of the rate of transport of the particles, it is possible to design targets and ionizers with improved yields. This is most important for the rare, short-lived isotopes in which there is considerable interest for physics experiments. This target has demonstrated large increases in the yields of 11 Li and 12 Be, in agreement with the predictions of the model. 2002 Elsevier Science B.V. All rights reserved. PACS: 29.25.-t; 29.25.Rm; 66.30.-h Keywords: Radioactive ion beam source; Targets; Diffusion; Effusion
1. Introduction There is a need to increase the currents of some radioactive species produced by the bombardment of thick targets by high-energy proton beams in the ISOL method. In particular this applies to the rare short-lived isotopes. Raising the proton current increases * Corresponding author.
E-mail address: [email protected] (J.R.J. Bennett). 0375-9474/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 1 ) 0 1 6 0 6 - 2
328c
J.R.J. Bennett et al. / Nuclear Physics A 701 (2002) 327c–333c
the power dissipation in the target. The RIST tantalum foil disc target [1] was developed to dissipate over 25 kW, corresponding to 100 µA (mean) of 1 GeV protons. The RIST target geometry was tested [2] at ISOLDE [3] to compare the performance with conventional ISOLDE tantalum roll-foil targets. Target development at ISOLDE has continued in an attempt to improve the yield efficiency of the target. The initial target (Ta050) had 25 µm thick tantalum foils; the measured yields of the alkali metals and rare earths were good and the release fast [2]. The next targets (Ta075 and Ta126) were of similar design, but were constructed from 100 µm tantalum foils. The release was even faster, but the yields not quite as good. A mathematical model [4] of the release in the target and ionizer was developed in an attempt to understand the results and an approximate solution of the diffusion equation was found. This provides a powerful tool in predicting the yields for different target geometries once the release characteristics for a particular combination of radioactive element and target has been established. The reader is referred to another paper [5] in this conference for definitions of yield, the release curve, release parameters and the mathematical model. Using the model, it was clear that even if the target mass was much less than in the previous targets, a reduction in delay times can be more important for short-lived isotopes in giving substantially increased yields.
2. The 2 µm thick tantalum foil target, number Ta129 The validity of this idea has been tested with a new target (see Fig. 1) constructed from tantalum foils of only 2 µm thickness [6]. The target mass is only 10 g cm−2 , compared to the usual mass of ∼ 100 g cm−2. As in all the tests, the standard ISOLDE tungsten thermal ionizer was used. It would have been advantageous to reduce its delay time by altering the geometry [7], but this was not possible for practical reasons.
Fig. 1. Cross section of the tantalum target, Ta129.
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3. The measurements The target was tested during a week in April 1999 and again in September 1999. During the first test, the yield of 11 Li was measured by counting the delayed neutrons [7]. The release curves of 7 Li (stable) were measured using a sensitive current meter at several target temperatures [8]. Also, the release curve of 8 Li was measured by counting the beta decays using a tape drive system. In the second test the yield measurement of 11 Li was repeated and yields of 12 Be, 14 Be, 23 Na and 27 Na were measured. The release curves of 8 Li and 11 Be were taken using the tape drive. Laser ionization in the tungsten thermal ionizer was used for the beryllium beams. Unfortunately, the laser ionization system was so unstable during the measurements of 11 Be that it was not possible to obtain a reasonably smooth release curve. The 11 Li and beryllium beams were deposited onto a Kapton foil and neutron and beta decays were counted in 0.1 ms time bins [7]. This gives an integral of the release function, p(t), as a function of time, I (t) = e
−λt
t p(t) dt.
(1)
0
The integral method [9] of measuring release curves provides very good data in general, is quick and easy to use and makes use of all the information from each pulse. Using small time intervals is particularly valuable where the release curve is changing rapidly with time.
4. Results Table 1 shows the yield measurements. The yield of 11 Li was much larger than had been measured previously with the standard ISOLDE roll foil tantalum targets despite the small target mass. Also the yield of 12 Be was much larger than had been found previously with uranium carbide targets. However, the yield of 14 Be was not much improved over previous measurements. Table 1 Yields of short-lived isotopes of lithium, beryllium and sodium from target Ta129. The values in brackets indicate previous yields from uranium carbide (UC) and standard ISOLDE roll foil tantalum (Ta) targets Run date
Particle
April 1999 September 1999
11 Li 11 Li 12 Be 14 Be 23 Al 32 Al 33 Al
Yield particles (µC) 7000 (500 Ta) 3000–1000 50 000 (4000 UC) 7 (4 UC) not detected not detected 10
Particle 29 Na 30 Na 31 Na 32 Na
Yield particles (µC) 6400 (1200 Ta) 300 (230 Ta) – (12 Ta) 8
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Table 2 Calculated release parameters found by fitting the mathematical model to the measured data. The release times for 11 Li in the April run are scaled from 8 Li by the square root of their masses Particle Isotope τ ms 8 Li
No.
Target Release parameters Temperature d h D E τD (K) (µm) (cm) (cm2 s−1 ) (cm2 s−1 ) (s)
1218 Ta050 2258
12.5
10
1E-8
τE (s)
τs (s)
εt (%)
389
63
0.1
0.015
8
528 285 –
0.67 0.2 0.23
0.043 0.08 0.09
0.005 0.006 0.007
100 84 2
April 1999 run on Ta129 7 Li 8 Li 11 Li
∞ Ta129 2423 1218 Ta129 2423 13 Ta129 2423
1 1 1
7.5 7.5 7.5
0.6E-8 2E-8 –
September/October 1999 run on Ta129 8 Li 11 Li 12 Be 14 Be
1218 13 34 6.3
Ta129 Ta129 Ta129 Ta129
2423 2423 2448 2448
1 1 1 1
7.5 7.5 7.5 7.5
0.9E-8 – – –
2280 – – –
0.46 0.001 ∼ 0.5 ∼ 0001 ∼ 0.01 ∼ 0.08 ∼ 0.01 ∼ 0.08
0.006 83 0.005 6 0.015 0.186 0.013 0.015
Fig. 2. Integral release curve for 11 Li. The circles are the measured points and the line is the approximately calculated fit.
Table 2 shows the calculated release parameters found by fitting the mathematical model to the measured release and integral release curves, see Fig. 2. Also shown in Table 2 is some lithium data from Ta050. Unfortunately, the integral release curves for the very shortlived isotopes, 11 Li (see Fig. 2), 12 Be and 14 Be are so dominated by the decay, that the time constants for diffusion, τD , and effusion through the target, τE , are largely indeterminate. They are calculated to lie within limits of a factor of ∼ 0.01 to ∼ 100 of the values shown in Table 2. However, the value of the ionizer time constant, τs is well-defined. Beryllium
J.R.J. Bennett et al. / Nuclear Physics A 701 (2002) 327c–333c
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would appear to have a higher diffusion coefficient than lithium but a lower effusion, presumably because it is more sticky, but all values must be taken with caution. The diffusion coefficients of isotopes of the same element should scale with the square root of their masses. The release parameters of 11 Li have been calculated on this basis from those of 8 Li.
5. Discussion The run in September 1999 showed that the yields were considerably lower than those taken in April. It is believed that this is due to the deterioration of the target; subsequently, the target was cut open and the foils were found to have fused together and in parts melted. Consequently the effective foil thickness increases and the diffusion time increases. Conversely, the effusion time decreases since there is little release from within the foil structure but mainly from the outer surface. Measurements of the release curve of 8 Li in September (see Table 2) show this clearly; τD has more than doubled while τE has decreased by nearly 2 orders of magnitude compared to the corresponding measurements in April. The low yield of 11 Li (between 1000 and 3000 atoms per µC of protons) in September is explained by this and means that the effective target mass is reduced by a factor of 6–20. This can also explain the low yield of 8 Li (∼ 20 times lower than in April) in September, despite the unchanged release efficiency (see Table 2). Fig. 3 shows the calculated diffusion coefficients, D and E, on an Arrhenius plot. D increases with temperature as would be expected. E also increases, but at a much faster rate than the expected square root of the temperature (i.e., the particle velocity). It is assumed that the difference is due to the more rapid change in sojourn time. Hence, the temperature can be very important for sticky particles. Since the target temperature remains almost constant, τs is unchanged at ∼ 10 ms for lithium. The value calculated from the conductance is ∼ 1 ms. Again, this difference is assumed to be due to the lithium being sticky. At the end of the run in April 1999, the release of stable 7 Li was measured [10] for a single pulse of protons on the target at several temperatures. It will be seen from Fig. 3, that the values of D are lower and E higher than for the corresponding values of 8 Li. It is likely that the fusion of the foils was already taking place at this time. The measured yield of 11 Li from the RIST disc target, Ta126, with 100 µm thick tantalum foils, was 2500 particles per µC. Scaling this with the expected release parameters of Ta129, gives a prediction of the yield of 11 Li which is almost exactly in agreement with the measured value. This shows the power of the model in predicting the performance of targets when the basic release parameters are known. The apparently low yield of 14 Be is simply explained. The ratio of the release efficiencies (Table 2) for 12 Be and 14 Be is 0.070. The corresponding ratio of the cross sections, calculated using Silberberg and Tsao [11], is 0.0022. Multiplying the measured yield of 12 Be by these ratios gives the yield of 14 Be as 9 atoms per µC, in almost exact agreement with the measurement of 7 atoms per µC.
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Fig. 3. Arrhenius plots of D and E for lithium.
Acknowledgements Grateful thanks are given to everyone who helped in performing the experiments at ISOLDE, including the PS staff.
References [1] R.J. Bennett, C.J. Densham, P.V. Drumm, W.R. Evans, M. Holding, G.R. Murdoch, V. Panteleev, Nucl. Instrum. Methods B 126 (1997) 117. [2] P.V. Drumm, J.R.J. Bennett, C.J. Densham, W.R. Evans, M. Holding, G.R. Murdoch, A.H. Evenson, E. Kugler, J. Lettry, H. Ravn, O. Tengblad, P. Van Duppen, R. Catherall, O. Jonsson, J. Kay, D.D. Warner, M. Harder, C. Thwaites, J. Honsi, R. Page, J. Billowes, S.J. Freeman, I.S. Grant, S. Schwebel, G. Smith, C. Bishop, P.M. Walker, Nucl. Instrum. Methods B 126 (1997) 121. [3] E. Kugler, D. Fiander, B. Jonson, H. Haas, A. Prewloka, H.L. Ravn, D.J. Simon, K. Zimmer, Nucl. Instrum. Methods B 70 (1992) 41. [4] J.R.J. Bennett, in: K.W. Shepard (Ed.), Proceedings of the Eight International Conference on Heavy Ion Accelerator Technology, Argonne National Laboratory, Chicago, 5–9 October 1998, AIP Conference Proceedings, Vol. 473, AIP, New York, 1999, p. 490.
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[5] J.R.J. Bennett, Nucl. Phys. A 701 (2002), proceedings of this conference. [6] J.R.J. Bennett, P.V. Drumm, R. Catherall, O.C. Jonsson, J. Lettry, T. Nilsson, H.L. Ravn, H. Simon and Members of the ISOLDE Collaboration, Nucl. Instrum. Methods B 155 (1999) 515. [7] U.C. Bergman, L. Axelsson, M.J.G. Borge, V.N. Fedoseyev, C. Forssén, H.O.U. Fynbo, S. Grévy, P. Hornshøj, Y. Jading, B. Jonson, U. Köster, K. Markenroth, F.M. Marqués, V.I. Mishin, I. Mukha, T. Nilsson, G. Nyman, A. Oberstedt, H.L. Ravn, K. Riisager, G. Schrieder, V. Sebastian, H. Simon, O. Tengblad, F. Wenander, K. Wilhelmsen Rolander, Nucl. Phys. A 658 (1999) 129. [8] J. Lettry, private communication. [9] Proceedings of European Particle Accelerator Conference, 22–26 June 1998, IOP, Bristol, 1998, p. 2383. [10] J. Lettry, private communication. [11] R. Silberberg, C.H. Tsao, Cross Sections of Proton–Nucleus Interactions at High Energies, Naval Research Laboratory, NRL report 7593, 1973.