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u Fe, Kr and I ions in ten metals
Radiation Physics and Chemistry 59 (2000) 249±253
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Slowing down of 1.3±3.5 MeV/u Fe, Kr and I ions in ten metals T. Alanko*, J. HyvoÈnen, V. KylloÈnen, S. MuÈller, J. RaÈisaÈnen, A. Virtanen Department of Physics, University of JyvaÈskylaÈ, P.O. Box 35, FIN-40351 JyvaÈskylaÈ, Finland Received 23 November 1999; accepted 10 February 2000
Abstract Stopping powers for 1.3±3.5 MeV/u 56Fe, 80, 84Kr and 127I ions in Mg, V, Fe, Co, Ni, Cu, Nb, Sn, Ta and Au have been determined by a transmission technique exposing the metallic sample foils to the direct ion beam. No previous data have been published for Mg, V, Fe, Co, Nb, Sn or Ta stopping media with these ion energies. The experimental results are compared with parametrizations of the stopping powers found in the literature (SRIM-2000 and Hubert's parametrization). Discrepancies as high as 21 and 16% are observed for SRIM and Hubert's parametrization, respectively. However, there is agreement between the present results and other experimental data available at corresponding ion velocities for 84Kr and 56Fe in Ni, Cu, and Au. 7 2000 Elsevier Science Ltd. All rights reserved. PACS: 34.50.Bw Keywords: Stopping power; Energy loss;
56
Fe;
80
Kr;
84
Kr;
127
I
1. Introduction Accurate knowledge of ion energy losses is essential in nuclear physics experiments where ion beams are guided through solid targets, gas target windows, and in the detection of ®ssion fragments. Accurate stopping power values are equally important in dierent characterization methods based on ion beam techniques in which heavy ions have recently gained more signi®cance (Davies et al., 1998). The accuracy of the characterization method depends generally directly on the accuracy of the stopping-power values used. For heavy
* Corresponding author. Tel.: +358-14-2602-390; fax: +358-14-2602-351. E-mail address: [email protected].® (T. Alanko).
ions only a limited number of experimental data can be found in the literature. When experimental stopping-power values are not available, theoretical predictions must be used. Experimental data are needed for the development of semiempirical parametrizations for predicting energy losses and the validity of these calculations for heavy ions needs to be further investigated. We have determined stopping powers of ten dierent metals (Mg, V, Fe, Co, Ni, Cu, Nb, Sn, Ta and Au) for three heavy ions (Fe, Kr and I) at three ion energies. The measurements were carried out by using a transmission method. The purpose of the present study is to collect more experimental data for the needs of applications and development of theoretical parametrizations. A comparison with a widely used parametrization and model for stopping powers is presented. Also, a comparison with existing experimental data is pre-
0969-806X/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 0 ) 0 0 2 6 6 - 8
250
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253
sented. This work is a continuation of our extensive series of accurate measurements of heavy-ion stopping powers for havar (Alanko et al., 1999a, 1999b). 2. Experimental procedure and analysis The ion beams were supplied by the K130 cyclotron at the Accelerator laboratory of the University of JyvaÈskylaÈ. Measurements were carried out in the scattering chamber used for radiation tests of electronics (Virtanen et al., 1999). A PIN diode (area 100 mm2, thickness 300 mm) was used for particle detection. The ion beam spot size on the sample foil was limited to 5 mm in diameter by using collimating slits and apertures. Distance between the sample foils and the detector was 30 cm. A geometry where the sample foil is exposed to the direct ion beam was used in the experiments. The detector was placed at 08 to the beam, and the sample foil was placed perpendicular to the ion beam in front of the detector. The energy losses of ions were deduced from measurements of the beam energy before and after the foil. All foils were attached to a linear movement assembly which made it possible to do all measurements without breaking the vacuum of the chamber. The areal densities of the foils were determined by measuring the energy loss of 4He ions from a 226Ra radioactive source and using reference stopping powers (Ziegler, 1999). Also, the areal densities were checked for several foils by weighing. The independently obtained areal-density values were in fairly good agreement with each other; within 2% for the uniform foils. The values determined by 4He ion energy loss were adopted as the reference values for this study because they represent best the foil positions used in the actual measurements. The V, Nb, Sn, Ta and Au foils were
of commercial origin and the others were produced by rolling at our laboratory, the foil speci®cations are given in Table 1. As a ®rst step in the analysis, gaussian curves were ®tted to the peaks in the spectra to obtain the peak positions. The uncertainty of the ®tted peak position was 0.1±0.3 channels. Measurements without the foils were used for energy calibration of the detection system featuring linear energy dependence. The initial ion energy was calculated from the accelerator parameters and was estimated to have an uncertainty of less than 1%. The most probable energy loss of the ions transmitted through the foil was determined from the reduction of the ion energy observed through the shift of the peak position. According to the spectra obtained, the dierence between the average energy loss and the most probable energy loss was negligible. The stopping power at mean ion energy (Eav) was calculated by dividing the energy loss in the foil by the foil areal density rDx), where r represents mass density, Dx the foil thickness, and Eav Ei Ef =2 for initial Ei and ®nal Ef ion energy. To account for the non-linear dependence on ion energy of stopping powers, a small correction to the mean energy Eav was applied (RaÈisaÈnen et al., 1996). As a result, the mass stopping power S ÿ 1=r dE=dx (dierential energy loss per unit areal density of path) is taken as DE=rDx at an eective ion energy, Eeff : The estimated errors in the energy loss values are 2.2±2.6%, including the uncertainties due to the inaccuracy of the beam energy, energy calibration procedure and the peak position. The uncertainty of the adopted areal density values is 2.9±4.6%. This range arises from possible uncertainties in the 4He stoppingpower values, and in the non-uniformity of the foils. When a quadratic combination of these errors is assumed, a standard deviation of 3.7±5.3% in the stopping powers is obtained.
Table 1 Speci®cations of the used sample foilsa foil
Dx (mg/cm2)
3. Results and discussion
Mg V Fe Co Ni Cu Nb Sn Ta Au
0.9420.04 2.7020.12 0.4620.01 2.8320.13 0.5020.02 0.8620.04 3.8020.17 4.3320.20 2.9020.13 3.4420.16
The experimental results are summarised in Tables 2±4 where the stopping-power values are presented as a function of the eective ion energy. The results for 3.3 MeV/u 84Kr ions are also presented in Fig. 1 together with experimental data found in the literature (Bimbot et al., 1978) and the commonly used parametrizations (Ziegler, 1999; Ziegler, 1992). Experimental values by Bimbot et al., obtained only for 3.3 MeV/u 84 Kr ions, and the present results agree within error limits for elements heavier than vanadium. Experimental values extracted from the ®gures of Anthony and Lanford (1982) for Fe ions are in good agreement with
a The error limits in the thickness values include uncertainties caused by foil inhomogenity.
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253 Table 2 Stopping powers for
127
I ions in units of MeV/(mg/cm2) as a function of energy in MeV/u
127 16+
127 18+
I
127 21+
I
I
Foil
Ee
Present results
SRIM
Ee
Present results
SRIM
Mg V Fe Co Ni Cu Nb Sn Ta Au
1.77 1.50 1.97 1.53 1.97 1.92 1.48 1.47 1.76 1.75
7724 50.322.6 53.322.1 45.222.3 48.022.4 43.722.3 36.521.9 32.421.7 25.621.3 22.621.2
65.7 48.4 46.8 44.1 47.0 44.4 36.0 30.8 25.8 24.2
2.33 2.06 2.54 2.07 2.54 2.48 2.03 2.02 2.31 2.31
8124 52.122.7 54.822.1 49.122.5 50.022.5 47.622.5 38.622.0 34.721.8 27.821.4 23.721.2
66.0 50.0 47.3 45.7 48.1 45.4 37.8 32.6 27.2 25.6
the present results for Au and in fairly good agreement for Cu, Table 5. The other parametrization included in Fig. 1 is Trim-92 (version 92.04, Ziegler, 1992) based on the work of Ziegler et al. (1985). The latest parametrization by the same author is SRIM-2000 (v.09, Ziegler, 1999), which is based on a revised scaling law from 1995. Comparing these two parametrizations presented in Fig. 1, one can see that the dierences are mainly in the stopping power magnitudes, Trim-92 values being systematically slightly higher. In general the Trim-92 parametrization agrees better with the present results than does SRIM-2000. However, the dierences between the two parametrizations are minor, and they both underestimate slightly the present stopping powers for medium to high atomic-number stopping media. For low atomic-number media, a strong discrepancy is observed, the experimental values being higher than the SRIM and Trim values. For Fe ions the deviations from SRIM values are mainly less than 6% (Mg Table 3 Stopping powers for
251
Hubert
50.6 49.2
Ee
Present results
SRIM
Hubert
3.29 3.00 3.50 3.00 3.49 3.43 2.95 2.93 3.24 3.23
8324 54.522.8 55.622.2 51.422.7 52.522.6 48.522.5 41.622.2 37.321.9 30.321.6 26.221.4
65.2 50.4 47.5 46.3 48.9 45.7 38.6 33.5 28.4 26.9
73.0 51.7 50.7 47.5 33.9 27.0 25.3
being an exception for which the deviations are up to 18%, see Table 4). Also, for I and Kr ions the parametrization yields results which are in reasonable agreement, with deviations of typically 2±8% (Tables 2±3). The maximum deviations with these ions are obtained for Mg, namely 21%. In Tables 2 and 3 the stopping power values for ion energies above 2.5 MeV/u obtained by ®tting a curve to the table values of Hubert et al. (1990), are also presented. The values of the Hubert tables are based on a-particle stopping powers and on heavy-ion eective charge parametrization deduced from experimental stopping-power values. Stopping powers for a-particles have been taken from Ziegler (1977). The parametrization is valid for 36 solids and for ions with atomic number 2 R Z R 103 at energies of 2.5 R E/A R 500 MeV/u. As can be seen from Tables 2±4, the values obtained from the Hubert parametrization are generally closer to the present experimental results for elements lighter
80, 84
Kr ions in units of MeV/(mg/cm2) as a function of energy in MeV/u
80
Kr10+
84
Kr12+
84
Kr14+
Foil
Ee
Present results
SRIM
Ee
Present results
SRIM
Mg V Fe Co Ni Cu Nb Sn Ta Au
1.69 1.39 1.91 1.39 1.91 1.84 1.37 1.35 1.68 1.66
54.522.8 34.521.8 37.321.5 33.021.7 34.921.7 32.021.7 25.321.3 23.121.2 17.920.9 15.920.8
44.0 32.8 31.3 29.7 31.4 29.6 24.3 20.9 17.3 16.2
2.33 2.04 2.55 2.03 2.54 2.48 2.01 2.00 2.31 2.30
55.122.8 35.621.8 33.621.3 34.321.7 33.421.6 31.921.6 26.421.3 23.621.2 18.720.9 16.320.8
43.8 33.3 31.1 30.4 31.5 29.9 25.3 21.8 18.0 16.9
Hubert
32.2 31.4
Ee
Present results
SRIM
Hubert
3.31 3.01 3.52 3.02 3.52 3.46 2.97 3.00 3.27 3.26
53.122.7 36.421.9 34.321.3 34.221.8 33.121.6 30.921.6 27.521.4 23.321.2 19.521.0 17.120.9
41.9 32.7 30.4 30.1 31.2 29.3 25.1 21.8 18.3 17.3
44.4 32.0 31.4 29.6 21.7 17.2 16.1
252
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253
Table 4 Stopping powers for 56
56
Fe ions in units of MeV/(mg/cm2) as a function of energy in MeV/u
Fe7+
56
Fe8+
Foil
Ee
Present results
SRIM
Ee
Present results
SRIM
Mg V Fe Co Ni Cu Nb Sn Ta Au
1.69 1.39 1.92 1.40 1.91 1.85 1.33 1.33 1.66 1.64
37.822.0 24.421.3 25.021.0 23.121.2 23.621.2 21.721.1 18.921.0 16.720.9 13.220.7 11.720.6
32.7 25.2 22.6 22.8 22.6 21.5 18.8 16.1 12.7 11.9
2.32 2.01 2.54 2.01 2.54 2.47 1.95 1.96 2.27 2.26
37.221.9 24.921.3 23.720.9 23.621.2 22.321.1 22.021.1 19.221.0 16.720.9 13.820.7 12.120.6
30.7 24.0 21.6 21.8 21.9 20.8 18.2 15.7 12.7 11.9
than copper (Z R 29). The SRIM values are in better agreement for elements heavier than Cu. The average deviation of the values obtained by the Hubert parametrization is 7.1% while the maximum deviation is 16%. The respective values for the SRIM predictions are 6.7 and 21%. Ouichaoui et al. (1995) have tested the validity of the Hubert parametrization for energies below 2.5 MeV/u. We made a similar test with the present data, so that the Hubert values were calculated also for ion energies below 2.5 MeV/u. For I, Kr and Fe ions and targets lighter than Cu, the Hubert values and the pre-
Fig. 1. Stopping powers of 3.3 MeV/u
84
Hubert
21.3 20.8
sent results deviate less than 12% (excluding Mg). For heavier targets and lower energies the deviations are more signi®cant. The present comparison con®rms the validity limits of the Hubert parametrization de®ned by Ouichaoui et al. (1995) as 210% uncertainty at energies below 2.5 MeV/u. 4. Conclusions We have determined the stopping powers of several metals (Z = 12±79) for 56Fe, 80, 84Kr and 127I ions at
Kr ions as a function of atomic-number of the stopping medium.
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253 Table 5 Present and corresponding literature stopping powers for Fe ions in units of MeV/(mg/cm2) Stopping media
Ee
Present results
Literature data
Cu
1.85
21.7
2.47
22.0
1.64
11.7
2.26
12.1
21.5a 20.9b 20.8a 19.6b 11.9a 11.8b 11.9a 12.1b
Au
a b
SRIM. Anthony and Lanford (1982).
1.3±3.5 MeV/u energies. The total uncertainty in the experimental values is about 5%. Comparison with two parametrizations based on the works of Ziegler et al. and Hubert et al. shows fairly good agreement with present results. For all stopping media it can be noted that the SRIM-2000 predictions nearly always underestimate the present results. Also, the Hubert parametrization systematically underestimates the present stopping power values. Acknowledgements The work has been partly funded by the Academy of Finland under the contract 43983. References Alanko, T., HyvoÈnen, J., KylloÈnen, V., RaÈisaÈnen, J.,
253
Virtanen, A., 1999a. Stopping powers of havar for 1.6, 2.3 and 3.2 MeV/u heavy ions, Nucl. Instr. and Methods B (to be published). Alanko, T., HyvoÈnen, J., KylloÈnen, V., RaÈisaÈnen, J., Virtanen, A., 1999b. Stopping powers of havar and eective charge for 1.4±3.2 MeV/u 127I-ions, Nucl. Instr. and Methods B (to be published). Anthony, J.M., Lanford, W.A., 1982. Stopping power and eective charge of heavy ions in solids. Phys. Rev. A 25, 1868±1879. Bimbot, R., Della Negra, S., Gardes, D., Gauvin, H., Fleury, A., Hubert, F., 1978. Stopping power measurements for 4±5 MeV/nucleon 16O, 40Ar, 63Cu and 84Kr in C, Al, Ni, Ag and Au. Nucl. Instr. and Methods 153, 161±169. Davies, J.A., Forster, J.S., Walker, S.R., 1998. Elastic recoil detection analysis with heavy ion beams. Nucl. Instr. and Methods B 136±138, 594±602. Hubert, F., Bimbot, R., Gauvin, H., 1990. Range and stopping-power tables for 2.5±500 MeV/nucleon heavy ions in solids. Atomic Data and Nuclear Data Tables 46, 1±213. Ouichaoui, S., Rosier, L., Hourany, E., Bimbot, R., Redjdal, N., Beaumevieille, H., 1995. Stopping powers of Al, Cu, Ag and Au media for 1.47 MeV/u 127I, 2 MeV/u 32S and 79 Br ions. Nucl. Instr. and Methods B 95, 463±469. RaÈisaÈnen, J., WaÈtjen, U., Plompen, A.J.M., Munnik, F., 1996. Stopping power determinations by the transmission technique. Nucl. Instr. and Methods B 118, 1±6. Virtanen, A., HyvoÈnen, J., Ranttila, K., Rekikoski, I., Tuppurainen, J., 1999. Heavy ion and proton test site at JYFL-accelerator laboratory. Nucl. Instr. and Methods A 426, 68±71. Ziegler, J.F., 1977. Helium Stopping Powers and Ranges in All Elements. Pergamon Press, NY. Ziegler, J.F., Biersack, J.P., Littmark, U., 1985. In: Ziegler, J.F. (Ed.), The Stopping and Range of Ions in Solids. Pergamon Press, NY. Ziegler, J.F., 1992. Trim-92 computer code, private communication. Ziegler, J.F., 1999. SRIM-2000 computer code, private communication.
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Slowing down of 1.3±3.5 MeV/u Fe, Kr and I ions in ten metals T. Alanko*, J. HyvoÈnen, V. KylloÈnen, S. MuÈller, J. RaÈisaÈnen, A. Virtanen Department of Physics, University of JyvaÈskylaÈ, P.O. Box 35, FIN-40351 JyvaÈskylaÈ, Finland Received 23 November 1999; accepted 10 February 2000
Abstract Stopping powers for 1.3±3.5 MeV/u 56Fe, 80, 84Kr and 127I ions in Mg, V, Fe, Co, Ni, Cu, Nb, Sn, Ta and Au have been determined by a transmission technique exposing the metallic sample foils to the direct ion beam. No previous data have been published for Mg, V, Fe, Co, Nb, Sn or Ta stopping media with these ion energies. The experimental results are compared with parametrizations of the stopping powers found in the literature (SRIM-2000 and Hubert's parametrization). Discrepancies as high as 21 and 16% are observed for SRIM and Hubert's parametrization, respectively. However, there is agreement between the present results and other experimental data available at corresponding ion velocities for 84Kr and 56Fe in Ni, Cu, and Au. 7 2000 Elsevier Science Ltd. All rights reserved. PACS: 34.50.Bw Keywords: Stopping power; Energy loss;
56
Fe;
80
Kr;
84
Kr;
127
I
1. Introduction Accurate knowledge of ion energy losses is essential in nuclear physics experiments where ion beams are guided through solid targets, gas target windows, and in the detection of ®ssion fragments. Accurate stopping power values are equally important in dierent characterization methods based on ion beam techniques in which heavy ions have recently gained more signi®cance (Davies et al., 1998). The accuracy of the characterization method depends generally directly on the accuracy of the stopping-power values used. For heavy
* Corresponding author. Tel.: +358-14-2602-390; fax: +358-14-2602-351. E-mail address: [email protected].® (T. Alanko).
ions only a limited number of experimental data can be found in the literature. When experimental stopping-power values are not available, theoretical predictions must be used. Experimental data are needed for the development of semiempirical parametrizations for predicting energy losses and the validity of these calculations for heavy ions needs to be further investigated. We have determined stopping powers of ten dierent metals (Mg, V, Fe, Co, Ni, Cu, Nb, Sn, Ta and Au) for three heavy ions (Fe, Kr and I) at three ion energies. The measurements were carried out by using a transmission method. The purpose of the present study is to collect more experimental data for the needs of applications and development of theoretical parametrizations. A comparison with a widely used parametrization and model for stopping powers is presented. Also, a comparison with existing experimental data is pre-
0969-806X/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 0 ) 0 0 2 6 6 - 8
250
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253
sented. This work is a continuation of our extensive series of accurate measurements of heavy-ion stopping powers for havar (Alanko et al., 1999a, 1999b). 2. Experimental procedure and analysis The ion beams were supplied by the K130 cyclotron at the Accelerator laboratory of the University of JyvaÈskylaÈ. Measurements were carried out in the scattering chamber used for radiation tests of electronics (Virtanen et al., 1999). A PIN diode (area 100 mm2, thickness 300 mm) was used for particle detection. The ion beam spot size on the sample foil was limited to 5 mm in diameter by using collimating slits and apertures. Distance between the sample foils and the detector was 30 cm. A geometry where the sample foil is exposed to the direct ion beam was used in the experiments. The detector was placed at 08 to the beam, and the sample foil was placed perpendicular to the ion beam in front of the detector. The energy losses of ions were deduced from measurements of the beam energy before and after the foil. All foils were attached to a linear movement assembly which made it possible to do all measurements without breaking the vacuum of the chamber. The areal densities of the foils were determined by measuring the energy loss of 4He ions from a 226Ra radioactive source and using reference stopping powers (Ziegler, 1999). Also, the areal densities were checked for several foils by weighing. The independently obtained areal-density values were in fairly good agreement with each other; within 2% for the uniform foils. The values determined by 4He ion energy loss were adopted as the reference values for this study because they represent best the foil positions used in the actual measurements. The V, Nb, Sn, Ta and Au foils were
of commercial origin and the others were produced by rolling at our laboratory, the foil speci®cations are given in Table 1. As a ®rst step in the analysis, gaussian curves were ®tted to the peaks in the spectra to obtain the peak positions. The uncertainty of the ®tted peak position was 0.1±0.3 channels. Measurements without the foils were used for energy calibration of the detection system featuring linear energy dependence. The initial ion energy was calculated from the accelerator parameters and was estimated to have an uncertainty of less than 1%. The most probable energy loss of the ions transmitted through the foil was determined from the reduction of the ion energy observed through the shift of the peak position. According to the spectra obtained, the dierence between the average energy loss and the most probable energy loss was negligible. The stopping power at mean ion energy (Eav) was calculated by dividing the energy loss in the foil by the foil areal density rDx), where r represents mass density, Dx the foil thickness, and Eav Ei Ef =2 for initial Ei and ®nal Ef ion energy. To account for the non-linear dependence on ion energy of stopping powers, a small correction to the mean energy Eav was applied (RaÈisaÈnen et al., 1996). As a result, the mass stopping power S ÿ 1=r dE=dx (dierential energy loss per unit areal density of path) is taken as DE=rDx at an eective ion energy, Eeff : The estimated errors in the energy loss values are 2.2±2.6%, including the uncertainties due to the inaccuracy of the beam energy, energy calibration procedure and the peak position. The uncertainty of the adopted areal density values is 2.9±4.6%. This range arises from possible uncertainties in the 4He stoppingpower values, and in the non-uniformity of the foils. When a quadratic combination of these errors is assumed, a standard deviation of 3.7±5.3% in the stopping powers is obtained.
Table 1 Speci®cations of the used sample foilsa foil
Dx (mg/cm2)
3. Results and discussion
Mg V Fe Co Ni Cu Nb Sn Ta Au
0.9420.04 2.7020.12 0.4620.01 2.8320.13 0.5020.02 0.8620.04 3.8020.17 4.3320.20 2.9020.13 3.4420.16
The experimental results are summarised in Tables 2±4 where the stopping-power values are presented as a function of the eective ion energy. The results for 3.3 MeV/u 84Kr ions are also presented in Fig. 1 together with experimental data found in the literature (Bimbot et al., 1978) and the commonly used parametrizations (Ziegler, 1999; Ziegler, 1992). Experimental values by Bimbot et al., obtained only for 3.3 MeV/u 84 Kr ions, and the present results agree within error limits for elements heavier than vanadium. Experimental values extracted from the ®gures of Anthony and Lanford (1982) for Fe ions are in good agreement with
a The error limits in the thickness values include uncertainties caused by foil inhomogenity.
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253 Table 2 Stopping powers for
127
I ions in units of MeV/(mg/cm2) as a function of energy in MeV/u
127 16+
127 18+
I
127 21+
I
I
Foil
Ee
Present results
SRIM
Ee
Present results
SRIM
Mg V Fe Co Ni Cu Nb Sn Ta Au
1.77 1.50 1.97 1.53 1.97 1.92 1.48 1.47 1.76 1.75
7724 50.322.6 53.322.1 45.222.3 48.022.4 43.722.3 36.521.9 32.421.7 25.621.3 22.621.2
65.7 48.4 46.8 44.1 47.0 44.4 36.0 30.8 25.8 24.2
2.33 2.06 2.54 2.07 2.54 2.48 2.03 2.02 2.31 2.31
8124 52.122.7 54.822.1 49.122.5 50.022.5 47.622.5 38.622.0 34.721.8 27.821.4 23.721.2
66.0 50.0 47.3 45.7 48.1 45.4 37.8 32.6 27.2 25.6
the present results for Au and in fairly good agreement for Cu, Table 5. The other parametrization included in Fig. 1 is Trim-92 (version 92.04, Ziegler, 1992) based on the work of Ziegler et al. (1985). The latest parametrization by the same author is SRIM-2000 (v.09, Ziegler, 1999), which is based on a revised scaling law from 1995. Comparing these two parametrizations presented in Fig. 1, one can see that the dierences are mainly in the stopping power magnitudes, Trim-92 values being systematically slightly higher. In general the Trim-92 parametrization agrees better with the present results than does SRIM-2000. However, the dierences between the two parametrizations are minor, and they both underestimate slightly the present stopping powers for medium to high atomic-number stopping media. For low atomic-number media, a strong discrepancy is observed, the experimental values being higher than the SRIM and Trim values. For Fe ions the deviations from SRIM values are mainly less than 6% (Mg Table 3 Stopping powers for
251
Hubert
50.6 49.2
Ee
Present results
SRIM
Hubert
3.29 3.00 3.50 3.00 3.49 3.43 2.95 2.93 3.24 3.23
8324 54.522.8 55.622.2 51.422.7 52.522.6 48.522.5 41.622.2 37.321.9 30.321.6 26.221.4
65.2 50.4 47.5 46.3 48.9 45.7 38.6 33.5 28.4 26.9
73.0 51.7 50.7 47.5 33.9 27.0 25.3
being an exception for which the deviations are up to 18%, see Table 4). Also, for I and Kr ions the parametrization yields results which are in reasonable agreement, with deviations of typically 2±8% (Tables 2±3). The maximum deviations with these ions are obtained for Mg, namely 21%. In Tables 2 and 3 the stopping power values for ion energies above 2.5 MeV/u obtained by ®tting a curve to the table values of Hubert et al. (1990), are also presented. The values of the Hubert tables are based on a-particle stopping powers and on heavy-ion eective charge parametrization deduced from experimental stopping-power values. Stopping powers for a-particles have been taken from Ziegler (1977). The parametrization is valid for 36 solids and for ions with atomic number 2 R Z R 103 at energies of 2.5 R E/A R 500 MeV/u. As can be seen from Tables 2±4, the values obtained from the Hubert parametrization are generally closer to the present experimental results for elements lighter
80, 84
Kr ions in units of MeV/(mg/cm2) as a function of energy in MeV/u
80
Kr10+
84
Kr12+
84
Kr14+
Foil
Ee
Present results
SRIM
Ee
Present results
SRIM
Mg V Fe Co Ni Cu Nb Sn Ta Au
1.69 1.39 1.91 1.39 1.91 1.84 1.37 1.35 1.68 1.66
54.522.8 34.521.8 37.321.5 33.021.7 34.921.7 32.021.7 25.321.3 23.121.2 17.920.9 15.920.8
44.0 32.8 31.3 29.7 31.4 29.6 24.3 20.9 17.3 16.2
2.33 2.04 2.55 2.03 2.54 2.48 2.01 2.00 2.31 2.30
55.122.8 35.621.8 33.621.3 34.321.7 33.421.6 31.921.6 26.421.3 23.621.2 18.720.9 16.320.8
43.8 33.3 31.1 30.4 31.5 29.9 25.3 21.8 18.0 16.9
Hubert
32.2 31.4
Ee
Present results
SRIM
Hubert
3.31 3.01 3.52 3.02 3.52 3.46 2.97 3.00 3.27 3.26
53.122.7 36.421.9 34.321.3 34.221.8 33.121.6 30.921.6 27.521.4 23.321.2 19.521.0 17.120.9
41.9 32.7 30.4 30.1 31.2 29.3 25.1 21.8 18.3 17.3
44.4 32.0 31.4 29.6 21.7 17.2 16.1
252
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253
Table 4 Stopping powers for 56
56
Fe ions in units of MeV/(mg/cm2) as a function of energy in MeV/u
Fe7+
56
Fe8+
Foil
Ee
Present results
SRIM
Ee
Present results
SRIM
Mg V Fe Co Ni Cu Nb Sn Ta Au
1.69 1.39 1.92 1.40 1.91 1.85 1.33 1.33 1.66 1.64
37.822.0 24.421.3 25.021.0 23.121.2 23.621.2 21.721.1 18.921.0 16.720.9 13.220.7 11.720.6
32.7 25.2 22.6 22.8 22.6 21.5 18.8 16.1 12.7 11.9
2.32 2.01 2.54 2.01 2.54 2.47 1.95 1.96 2.27 2.26
37.221.9 24.921.3 23.720.9 23.621.2 22.321.1 22.021.1 19.221.0 16.720.9 13.820.7 12.120.6
30.7 24.0 21.6 21.8 21.9 20.8 18.2 15.7 12.7 11.9
than copper (Z R 29). The SRIM values are in better agreement for elements heavier than Cu. The average deviation of the values obtained by the Hubert parametrization is 7.1% while the maximum deviation is 16%. The respective values for the SRIM predictions are 6.7 and 21%. Ouichaoui et al. (1995) have tested the validity of the Hubert parametrization for energies below 2.5 MeV/u. We made a similar test with the present data, so that the Hubert values were calculated also for ion energies below 2.5 MeV/u. For I, Kr and Fe ions and targets lighter than Cu, the Hubert values and the pre-
Fig. 1. Stopping powers of 3.3 MeV/u
84
Hubert
21.3 20.8
sent results deviate less than 12% (excluding Mg). For heavier targets and lower energies the deviations are more signi®cant. The present comparison con®rms the validity limits of the Hubert parametrization de®ned by Ouichaoui et al. (1995) as 210% uncertainty at energies below 2.5 MeV/u. 4. Conclusions We have determined the stopping powers of several metals (Z = 12±79) for 56Fe, 80, 84Kr and 127I ions at
Kr ions as a function of atomic-number of the stopping medium.
T. Alanko et al. / Radiation Physics and Chemistry 59 (2000) 249±253 Table 5 Present and corresponding literature stopping powers for Fe ions in units of MeV/(mg/cm2) Stopping media
Ee
Present results
Literature data
Cu
1.85
21.7
2.47
22.0
1.64
11.7
2.26
12.1
21.5a 20.9b 20.8a 19.6b 11.9a 11.8b 11.9a 12.1b
Au
a b
SRIM. Anthony and Lanford (1982).
1.3±3.5 MeV/u energies. The total uncertainty in the experimental values is about 5%. Comparison with two parametrizations based on the works of Ziegler et al. and Hubert et al. shows fairly good agreement with present results. For all stopping media it can be noted that the SRIM-2000 predictions nearly always underestimate the present results. Also, the Hubert parametrization systematically underestimates the present stopping power values. Acknowledgements The work has been partly funded by the Academy of Finland under the contract 43983. References Alanko, T., HyvoÈnen, J., KylloÈnen, V., RaÈisaÈnen, J.,
253
Virtanen, A., 1999a. Stopping powers of havar for 1.6, 2.3 and 3.2 MeV/u heavy ions, Nucl. Instr. and Methods B (to be published). Alanko, T., HyvoÈnen, J., KylloÈnen, V., RaÈisaÈnen, J., Virtanen, A., 1999b. Stopping powers of havar and eective charge for 1.4±3.2 MeV/u 127I-ions, Nucl. Instr. and Methods B (to be published). Anthony, J.M., Lanford, W.A., 1982. Stopping power and eective charge of heavy ions in solids. Phys. Rev. A 25, 1868±1879. Bimbot, R., Della Negra, S., Gardes, D., Gauvin, H., Fleury, A., Hubert, F., 1978. Stopping power measurements for 4±5 MeV/nucleon 16O, 40Ar, 63Cu and 84Kr in C, Al, Ni, Ag and Au. Nucl. Instr. and Methods 153, 161±169. Davies, J.A., Forster, J.S., Walker, S.R., 1998. Elastic recoil detection analysis with heavy ion beams. Nucl. Instr. and Methods B 136±138, 594±602. Hubert, F., Bimbot, R., Gauvin, H., 1990. Range and stopping-power tables for 2.5±500 MeV/nucleon heavy ions in solids. Atomic Data and Nuclear Data Tables 46, 1±213. Ouichaoui, S., Rosier, L., Hourany, E., Bimbot, R., Redjdal, N., Beaumevieille, H., 1995. Stopping powers of Al, Cu, Ag and Au media for 1.47 MeV/u 127I, 2 MeV/u 32S and 79 Br ions. Nucl. Instr. and Methods B 95, 463±469. RaÈisaÈnen, J., WaÈtjen, U., Plompen, A.J.M., Munnik, F., 1996. Stopping power determinations by the transmission technique. Nucl. Instr. and Methods B 118, 1±6. Virtanen, A., HyvoÈnen, J., Ranttila, K., Rekikoski, I., Tuppurainen, J., 1999. Heavy ion and proton test site at JYFL-accelerator laboratory. Nucl. Instr. and Methods A 426, 68±71. Ziegler, J.F., 1977. Helium Stopping Powers and Ranges in All Elements. Pergamon Press, NY. Ziegler, J.F., Biersack, J.P., Littmark, U., 1985. In: Ziegler, J.F. (Ed.), The Stopping and Range of Ions in Solids. Pergamon Press, NY. Ziegler, J.F., 1992. Trim-92 computer code, private communication. Ziegler, J.F., 1999. SRIM-2000 computer code, private communication.