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n 24Mg in light targets
Radiation Measurements 45 (2010) 856e860
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Technical note
Fragmentation of 370 MeV/n
20
Ne and 470 MeV/n
24
Mg in light targets
A.N. Golovchenko a, L. Sihver b, c, d, *, S. Ota e, f, J. Skvar c g, N. Yasuda f, S. Kodaira f, G.N. Timoshenko a, h M. Giacomelli a
Laboratory of Radiation Biology, Joint Institute for Nuclear Research, 141980 Dubna, Russia Chalmers University of Technology, Nuclear Engineering, Applied Physics, SE-412 96 Göteborg, Sweden c Roanoke College, Department of Mathematics, Computer Science and Physics, Salem, VA 24153, USA d Texas A&M University, Department of Nuclear Engineering, TAMU-3133, College Station, TX 77843-3133, USA e Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan f Fundamental Technology Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555, Japan g Isaac Newton Group of Telescopes, Apartado de correos 321, E-38700 Santa Cruz de la Palma, Canary Islands, Spain h Slovenian Nuclear Safety Administration, Division of Radiation Safety and Materials, P.O. Box 5759, 1001 Ljubljana, Slovenia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 August 2009 Received in revised form 13 March 2010 Accepted 30 March 2010
Total charge-changing cross sections and cross sections for the production of projectile-like fragments were determined for fragmentation reactions induced by 370 MeV/n 20Ne ions in water and lucite, and 490 MeV/n 24Mg ions in polyethylene, carbon and aluminum targets sandwiched with CR-39 plastic nuclear track detectors. An automated microscope system and a track-to-track matching algorithm were used to count and recognize the primary and secondary particles. The measured cross sections were then compared with published cross sections and predictions of different models. Two models and the threedimensional Monte Carlo Particle Heavy Ion Transport Code System (PHITS) were used to calculate total charge-changing cross sections. Both models agreed within a few percent for the system 24Mg þ CH2, however a deviation up to 20% was observed for the systems 20Ne þ H2O and C5H8O2, when using one of the models. For all the studied systems, PHITS systematically underestimated the total charge-changing cross section. It was also found that the partial fragmentation cross sections for 24Mg þ CH2 measured in present and earlier works deviated up to 20% for Z ¼ 6e11. Measured cross sections for the production of fragments (Z ¼ 4e9) for 20Ne þ H2O and C5H8O2 were compared with predictions of three different semiempirical models and JQMD which is used in the PHITS code. The calculated cross sections differed from the measured data by 10e90% depending on which fragment and charge was studied, and which model was used. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Heavy ions Nuclear fragmentation Total and partial cross sections CR-39
1. Introduction Heavy ions are used in various fields of nuclear physics, medical physics and material science. There are applications within accelerator and reactor science, space and medicine, especially light ion radiation therapy. Accurate knowledge of the physics of interaction of high energetic heavy ions is therefore necessary for these applications, but also for estimating radiation damage due to Single Event Upsets (SEU) in electronic devises on space vehicles. Concern about the biological effects of space radiation and space dosimetry is increasing rapidly due to the perspectives of long-term manned missions outside the Earth’s protective magnetosphere. While * Corresponding author. Chalmers University of Technology, Nuclear Engineering, Applied Physics, SE-412 96 Göteborg, Sweden. Tel.: þ46 31 772 2921; fax: þ46 31 772 3079. E-mail address: [email protected] (L. Sihver). 1350-4487/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2010.03.006
minimal shield optimization was required in the initial low-Earthorbit vehicles, optimization will and should be a major factor in the design of vehicles for prolonged solar system travel. Galactic Cosmic Rays (GCR) and Solar Particle Events (SPE) will be the dominant source of the radiation dose for crews on long-term missions outside the earth’s magnetic field and this poses a major risk to these space flights. Even if energetic heavy ions (Z 2) only comprise a small fraction of GCR, their charge, penetrating power and interactions will make them a significant source of risk to astronaut health during long-duration crewed missions outside the Earth’s protective magnetosphere. To perform risk assessments, it is therefore essential to be able to estimate the absorbed dose, dose equivalents and biological effects of the ionization radiation. However, heavy ion transport includes many complex processes and to perform measurements for all possible systems would be both impractical and too expensive; e.g. direct measurements of dose equivalents inside critical organs in humans cannot be
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860 800
857
cut-off peak of Ne O F
N / 0.2 µ m
600
C
N
400
B
200 Be
0 5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Track radius, µm Fig. 1. Spectrum of Ne and fragments tracks at a depth of 7 cm in the lucite stack.
performed. The characterization of the outer space craft radiation field could be achieved with appropriate measurements, but the radiation field is modified by passage through the hulls of the space craft, materials in the space craft, and when passing through the human tissue. Reliable particles and heavy ion transport codes are therefore essential tools when performing the risk assessment for the personnel on space stations and space vehicles. There are a number of one-dimensional (1-D) and three-dimensional (3-D) particle and heavy ion transport codes available today, such as PHITS, HETC-HEDS, SHIELD-HIT, GEANT4, FLUKA, MARS, and MCNPX. A careful comparison of most of these codes is found in Sihver et al. (2008) and Sihver and Mancusi (2008). Most of these codes use semi-empirical models for calculating the total inelastic cross section. Since the total inelastic cross section deduces the mean free path of the nucleus in the material used in the Monte Carlo simulation and, therefore, also acts as a scaling parameter for the partial cross sections, it is important that this quantity is calculated as accurate as possible. To certify the accuracy, comparisons with measurements are necessary (see for instance, Heinbockel et al., 2006). We have, therefore, performed measurements of the total charge-changing cross sections (sTCC) and the partial cross sections for the production of projectile-like fragments (sPCC) for the interactions of 370 MeV/n 20Ne on water and lucite and 470 MeV/n 24Mg on polyethylene and carbon. The measured results are presented together with model predictions and previously published measurements. 2. Experiments Two stacks, 4 4 cm2 in area, consisting of water and lucite targets (thicknesses ranged from 1 to 5 cm) interleaved with w0.7 mm thick CR-39 sheets (Intercast Co., Parma, Italy) were perpendicularly bombarded by a 400 MeV/n 20Ne beam at the Heavy Ion Medical Accelerator (HIMAC) at the National Institute of Radiological Sciences (NIRS), Chiba, Japan. In Fig. 1, a spectrum of Ne
Fig. 3. The energy dependence of the total charge-changing cross section for 20 Ne þ lucite.
and fragments at a depth of 7 cm in the Lucite stack is shown. Another two stacks (up to 7 7 cm2 in area) of similar configuration and with polyethylene and carbon targets (1.5e4 cm thick) were exposed to a 500 MeV/n 24Mg beam at the Nuclotron accelerating facility (Joint Institute for Nuclear Research, Dubna, Russia). Fig. 2 presents a typical design of the stack (targets were made of carbon) irradiated with Mg ions. After slowing down in the materials preceding the samples, the beam energies in front of the stacks were measured and calculated to be w370 MeV/n and w470 MeV/n for Ne and Mg ions, respectively. Two detector sheets were placed in front of each stack to monitor the primary beam and accompanying particles (produced in materials preceding the stack). The fluences of the incoming particles were measured to be on the average w103 cm2. Chemical etching in 7 M NaOH at 70 C was applied to the detector sheets to develop the latent tracks to visible etch pits. The time of etching was different from stack to stack depending on the fluence. Effort was made to avoid etch pit overlapping as much as possible and to reveal the lowest detectable fragment. Then the tracks were scanned by an automated microscope system TRACOS (Skvar c, 1993) at the Jozef Stefan Institute (Ljubljana, Slovenia) and by a High Speed Imaging Microscope (HSP-1000) developed at NIRS and Seiko Precision Instruments (Japan) (Yasuda et al., 2005). After automatic counting, the tracks originating from primary and secondary particles and measurements of their parameters (average brightness, minor and major axes of the etch pit etc.) were matched (Skvar c and Golovchenko, 2001) on the upper and bottom surfaces
Fig. 2. Carbon stack configuration for a Mg beam.
858
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860
Table 1 Measured total charge-changing cross sections (sTCC,exp) for
20
Ne þ H2O together with model predictions (sTCC,mod).
sTCC, exp (mb)
Energy (MeV/n)
285 (85)
sTCC, mod (mb)
This work
Schall et al. (1996)
Sihver et al. (1993, 1998)
Tripathi et al. (1996)
PHITSc (Iwase et al., 2002)
1882 (29)a
1800 (43) [4.4%]b
1606 [15%]b
1776 [5.6%]b
1567 [16%]b
a
Values in parenthesis are statistical errors. Percents in brackets are difference between the results of this work and those from previous experiments and models i.e. (sTCC, exp sTCC, mod)/sTCC, exp. c In PHITS calculation, total charge-changing cross section (sTCC) was obtained from total reaction cross section (sTRC) non-charge-changing cross section (sNCC). The sTRC was calculated by Tripathi’s model and sNCC was calculated by Cugnon new INC model (Cugnon et al., 1981).Thereafter, all the cross sections in the subsequent tables were calculated in the same way including errors and percents in brackets. b
Table 2 Measured total charge-changing cross section (sTCC,exp) for Energy (MeV/n)
24
Mg þ C and
sTCC, exp (mb) This work
Mg þ CH2 experiments together with model predictions (sTCC,mod).
24
sTCC, mod (mb) Webber et al. (1990a)
Sihver et al. (1993, 1998)
Tripathi et al. (1996)
PHITS (Iwase et al., 2002)
1097 (11)
1128 (11) 1120 (11)
1092 1112 1149 1170 1146
1087 1091 1105 1116 1166
989 [10%] 980 [13%] 992 [11%] 998 [12%] 1040 [7%]
1725 (18)
1632 [5.4%]
1774 [2.8%]
1679 [0.4%] 1698 [1.4%] 1716 [2.4%]
1789 [6.2%] 1798 [4.4%] 1806 [2.7%]
1736 1749 1762 1850
1818 1829 1839 1946
24
Mg þ C 309 (71) 345 (25) 424 (44) 481 (59) 739 (51)
1129 (91) 1116 (42)
[0.5%] [1.5%] [3.0%] [3.7%] [2.3%]
[0.9%] [3.4%] [1.0%] [1.1%] [4.1%]
24
Mg þ CH2 309 (71) 343 (38) 363 (23) 385 (45) 408 (22) 432 (34) 437 (51) 459 (29) 481 (59) 739 (51)
1703 1685 1722 1759 1750 1774 1784
(58) (101) (49) (96) (50) (51) (57) 1800 (18) 1826 (18)
[2.1%] [2.0%] [2.1%] [1.3%]
of the detector sheets. Thus, unwanted events (fragments produced in the body of the detector, bubbles, radon induced tracks etc.) were rejected. The charge resolution (1s) was about 0.1e0.3 elementary charge units. The energy losses of primaries and fragments along the stacks could not be measured directly in this experiment, but were calculated using a computer code derived from the work of Henke and Benton (1967). The peaks on each individual detector are clearly separated (see for instance Fig. 1). Knowing that the highest peak with the biggest tracks was due to Ne or Mg, all subsequent peaks could only be from the nuclei with lower atomic number (the charge pick-up cross section is negligibly small). No absolute calibration is needed. In other words, the peaks of lower Z ions are resolved relative to the largest right-hand peak of primary ions. Different etching times do therefore not affect the resolution of the detector. Table 3 Measured partial cross sections (sPCC,exp) for Energy (MeV/n)
Z
20
Ne þ H2O and
1472 [15%] 1476 [14%] 1484 [12%] 1494 [13%] 1502 [15%] 1514 [13%] 1518[14%] 1528 [14%] 1540 [14%] 1667 [8.7%]
[2.5%] [2.5%] [2.2%] [6.6%]
3. Results The total charge-changing cross sections (sTCC) were obtained from the numbers of matched tracks corresponding to the peaks of primaries in front of and behind a given target using the conventional exponential absorption equation. To calculate the partial cross sections (sPCC), the formula included in the article by Golovchenko et al. (2002) was used. This formula accounts for the number of fragments in front of the target (when using several targets in the stack) but still assumes that sTCC values are equal for the primaries and secondaries. It was shown that if the total charge-changing cross section of a given fragment is within 20% of that of a primary ion, the number of fragments does not change by more than w2%. Note, that sTCC and sPCC were calculated per molecular mass of the complex target i.e. water, polyethylene and lucite.
Ne þ C5H8O2 experiments together with model predictions (sPCC,mod).
20
sPCC, exp (mb)
sPCC, mod (mb)
This work
[1]
[2]
[3]a
PHITS
258 [37%] 263 [25%] 194 [31%] 125 [57%] 74 [37%] 37 [36%]
161 [15%] 141 [60%] 130 [54%] 115 [60%] 82 [31%] 41 [29%]
235 [24%] 271 [23%] 184 [34%] 199 [32%] 60 [49%] 58 [0%]
1324 [11%] 1358 [23%] 1003 [31%] 650 [48%] 394 [45%] 216 [49%]
859 754 692 613 438 251
1129 [5%] 1501 [15%] 1035 [29%] 1165 [21%] 370 [48%] 366 [14%]
20
Ne þ H2O 285 (85)
9 8 7 6 5 4
189 350 280 291 118 58
(6) (9) (7) (7) (5) (3)
211 274 160 121 106 112
[12%] [22%] [43%] [58%] [10%] [93%]
9 8 7 6 5 4
1189 1772 1455 1472 718 426
(20) (25) (20) (24) (15) (12)
1110 [6.6%] 1423 [20%] 846 [42%] 918 [38%] 631 [12%] 718 [69%]
20
Ne þ C5H8O2 267 (103)
a
All the partial cross sections calculated with EPAX [3] are energy independent.
[28%] [57%] [52%] [58%] [39%] [41%]
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860 Table 4 Measured partial cross sections (sPCC,exp) for predictions (sPCC,mod).
Mg þ CH2 together with model
sPCC, exp (mb)
sPCC, mod (mb)
sPCC, exp (mb)
sPCC, mod (mb)
PHITS
Cor 2
PHITS
11 10 9 8
310 259 149 275
(17) (16) (12) (15)
302 [2.6%] 228 [12%] 89 [40%] 145 [47%]
300 248 138 252
(16) (16) (11) (14)
302 [0.7%] 228 [8.1%] 89 [36%] 145 [42%]
11 10 9 8
230 255 91 205
(8) (9) (5) (8)
300 [30%] 225 [12%] 89 [2.2%] 144 [30%]
227 251 88 196
(8) (8) (5) (8)
300 [32%] 225 [10%] 89 [1.1%] 144 [27%]
Z
343 (38)
432 (34)
charge-changing cross section for 20Ne on lucite, measured in this work in comparison with model calculations. The experimental results together with the calculated ones for w370 MeV/n 20Ne ions in water and lucite, and for w470 MeV/n 24Mg ions in polyethylene and carbon are presented in Tables 1 and 2. The energy values (E) in each Table are averages of those in front of and behind the target, while the values in parenthesis are deviations from these averages. In Tables 3e6, the partial cross sections measured in this work are compared with the results of three models (Sihver et al., 1993, 1998; Tsao et al., 1993; and EPAX2 by Summerer and Blank, 2000) enumerated as [1], [2] and [3], respectively, and PHITS (Iwase et al., 2002). Z denotes the charge of the fragment. In Tables 4e6, in the “Cor 1” column the measured partial cross sections are tabulated with a correction for secondaries created in the detectors/targets using the procedure given in Golovchenko et al. (2002). The next column presents calculated results using PHITS. The figures inside the brackets show deviation from the measured cross sections tabulated in the “Cor 1” column. In the “Cor 2” column the measured partial cross sections are corrected for the secondaries created in the detectors/targets using Sihver’s semi-empirical model (Sihver et al., 1993, 1998). The next column tabulates calculated results using PHITS and shows deviations from the measured cross sections corrected with Sihver’s formula, tabulated in the second column. Figs. 4 and 5 present the energy dependence of the total charge-changing cross section for 24Mg in polyethylene
24
Cor 1
Energy (MeV/n)
When comparing the measured total charge-changing cross sections with model calculations, the total reaction cross sections were first calculated using two different models 1) an enhanced version (Sihver et al., 1998, 2008) of the total reaction cross section model developed by Sihver et al. (1993), and 2) a model developed by Tripathi et al. (1996, 1997, 1999). The non-charge-changing parts of the reaction cross sections (neutron removal) were then calculated with the enhanced version of the semi-empirical model originally developed by Sihver et al. (1993), which takes advantage of the experimentally verified weak factorization property (Olson et al., 1983). Fig. 3 presents the energy dependence of the total Table 5 Measured partial cross sections (sPCC,exp) for
sPCC, exp (mb)
sPCC, mod (mb)
sPCC, exp (mb)
sPCC, mod (mb)
PHITS
Cor 2
PHITS
11 10 9 8 7 6 5
161 142 33 172 115 203 124
(23) (20) (16) (21) (19) (22) (13)
92 [43%] 105 [26%] 47 [42%] 82 [52%] 84 [27%] 103 [49%] 40 [68%]
151 135 26 158 104 183 116
(22) (20) (15) (21) (19) (21) (13)
92 [39%] 105 [22%] 47 [81%] 82 [48%] 84 [19%] 103 [44%] 40 [66%]
11 10 9 8 7 6 5
113 112 64 125 100 151 75
(8) (7) (5) (7) (6) (7) (5)
91 [19%] 100 [11%] 45 [30%] 78 [38%] 81 [19%] 101 [33%] 40 [47%]
110 109 62 120 96 141 70
(8) (6) (5) (7) (6) (7) (5)
91 [17%] 100 [8.3%] 45 [27%] 78 [35%] 81 [16%] 101 [28%] 40 [43%]
Z
345 (25)
424 (44)
a
Mg þ C together with model predictions (sPCC,mod).
24
Cor 1
Energy (MeV/n)
859
sPCC, exp (mb)
Energy (MeV/n)
Webber et al. (1990b),a
Webber et al. (1990b),a
309 (71)
148 (2) [8%] 133 (2) [6%] 58 (2) [76%] 137 (2) [20%] 90 (3) [22%] 114 (3) [44%] 40 (1) [68%]
148 (2) [2.0%] 133 (2) [1.5%] 58 (2) [123%] 137 (2) [13%] 90 (3) [13%] 114 (3) [38%] 40 (1) [65%]
481 (59)
124 (2) [10%] 111 (2) [0.9%] 56 (2) [13%] 120 (2) [4%] 89 (3) [11%] 120 (3) [21%] 48 (1) [36%]
124 (2) [13%] 111 (2) [1.8%] 56 (2) [10%] 120 (2) [0.0%] 89 (3) [7.3%] 120 (3) [15%] 48 (1) [31%]
Values in brackets in two last columns of this table are comparisons with Cor 1 and Cor 2.
Table 6 Measured partial cross sections from the
Mg þ CH2 experiments (sPCC,exp).
24
sPCC, exp (mb)
Energy (MeV/n)
Energy (MeV/n)
Z
Cor 1
Cor 2
343 (38)
11 10 9 8
310 259 149 275
(17) (16) (12) (15)
300 248 138 252
(16) (16) (11) (14)
432 (34)
11 10 9 8
230 255 91 205
(8) (9) (5) (8)
227 251 88 196
(8) (8) (5) (8)
459 (29)
11 10 9 8 7 6
298 272 136 267 186 257
(11) (10) (7) (10) (8) (9)
sPCC, exp (mb) Webber et al. (1990b)
Webber et al. (1990b)
309 (71)
309 263 105 253
(8) (7) (3) (6)
309 263 105 253
(8) (7) (3) (6)
481 (59)
295 239 113 239 161 201
(15) [1.0%] (12) [12%] (6) [17%] (12) [10%] (8) [13%] (10) [22%]
295 239 113 239 161 201
(15) [1.0%] (12) [12%] (6) [17%] (12) [10%] (8) [13%] (10) [22%]
This work in comparison with the measurements performed by Webber et al. (1990b).
[0.3%] [2%] [30%] [8%]
[3.0%] [6.0%] [24%] [0.4%]
Total charge-changing cross section (mb)
860
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860
sections calculated with the JQMD model in PHITS can differ from the measured values with up to more than 80% for some systems. The deviations between the calculated and measured cross sections show that more exact measurements of cross sections are needed to benchmark the total and partial reaction cross sections models used in both one-dimensional deterministic and three-dimensional Monte Carlo particle and heavy ion transport codes.
This work Webber et al. (1990a) Sihver et al. (1993, 1998) Tripathi et al. (1996) PHITS
2000
1900
1800
1700
Acknowledgements 1600
1500 0
200
400
600
800
1000
Energy (MeV/n)
Total charge-changing cross section (mb)
Fig. 4. The energy dependence of the total charge-changing cross section for Mg on CH2.
This work Webber et al. (1990a) Sihver et al. (1993, 1998) Tripathi et al. (1996) PHITS
1300
1200
References
1100
1000
900
0
200
400
L. Sihver would like to acknowledge, with much gratitude, the support from the Japan Society for the Promotion of Science (JSPS), which made it possible for him to spend two very fruitful and interesting months as a short term JSPS Fellow at NIRS, during 2009. A.N. Golovchenko appreciates the support of NIRS and Jozef Stefan Institute (Slovenia). S. Ota appreciates the support by Practical Training Program for Doctoral Students at Waseda University, which made it possible for him to work five months in L. Sihver research group at Chalmers University of Technology in Sweden.
600
800
1000
Energy (MeV/n) Fig. 5. The energy dependence of the total charge-changing cross section for Mg on C.
and carbon, respectively, measured in this work in comparison with model calculations. 4. Discussion and conclusions As can be seen from Tables 1e6, the measurements of both the total and partial charge-changing cross sections presented in this paper agree well with previously measured data. Both the semiempirical total reaction model developed by Tripathi et al. (1996, 1997, 1999) and the enhanced version (Sihver et al., 1998, 2008) of the semi-empirical model developed by Sihver et al. (1993), were corrected for the non-charge-changing parts of the reaction cross sections (neutron removal) using the enhanced version of the semiempirical model developed by Sihver et al. After the correction, the cross sections calculated with the model developed by Tripathi et al., agreed with the measured one within 5e10%, and the cross sections calculated with the model developed by Sihver et al., models agreed within 15e20%. When comparing the measured partial cross sections with the calculated results using three semiempirical models (Sihver et al., 1993, 1998; Tsao et al., 1993; and EPAX2 by Summerer and Blank, 2000), and the JQMD model used in PHITS, the model by Sihver et al. (1998) gives the best overall agreement. The total charge-changing cross sections calculated with PHITS are always underestimated, which is in agreement with previous studies (Sihver et al., 2008). The calculated partial cross
Cugnon, J., Mizutani, T., Vandermeulen, J., 1981. Equilibration in relativistic nuclear collisions. A Monte Carlo calculation. Nucl. Phys. A352, 505e534. Golovchenko, A.N., Skvar c, J., Yasuda, N., Giacomelli, M., Tretyakova, S.P., Ili c, R., Bimbot, R., Toulemonde, M., Murakami, T., 2002. Total charge-changing and partial cross-section measurements in the reactions of w110e250 MeV/ nucleon 12C in carbon, paraffin, and water. Phys. Rev. C 66, 014609. Heinbockel, J.H., Wilson, J.W., Blattnig, S.R., Qualls, C.D., Badavi, F.F., Cucinotta, F.A., 2006. HZE ion fragmentation cross-section sensitivity and propagated errors on HZE exposure estimates. Radiat. Meas. 41, 1103e1114. Henke, R.P., Benton, E.V., 1967. U.S. Naval Radiological Laboratory (San Francisco). Report USN-RDL-TR-67-122. Iwase, H., Niita, K., Nakamura, T., 2002. Development of a general-purpose particle heavy ion transport Monte Carlo code. J. Nucl. Sci. Technol. 39, 1142e1146. Olson, D.L., Berman, B.B., Greiner, D.E., Heckman, H.H., Lindstrom, P.J., Crawford, H.J., 1983. Phys. Rev. C 28, 1602. Schall, I., Schardt, D., Geissel, H., Irnich, H., Kankeleit, E., Kraft, G., Magel, A., Mohar, M.F., Munzenberg, G., Nickel, F., Scheidenberger, C., Schwab, W., 1996. Charge-changing nuclear reactions of relativistic light-ion beams (5 Z 10) passing through thick absorbers. Nucl. Instr. and Meth. B 117, 221e234. Sihver, L., Mancusi, D., 2008. HIBRAC: a 1-D deterministic heavy-ion transport code optimised for radiotherapy. Radiat. Meas 44 (2009), 38e46. Sihver, L., Tsao, C.H., Silberberg, R., Kanai, T., Barghouty, A.F., 1993. Total reaction and partial cross section calculations in proton-nucleus (Zt 26) and nucleusnucleus reactions (Zp and Zt 26). Phys. Rev. C 47, 1225e1236. Sihver, L., Schardt, D., Kanai, T., 1998. Depth-dose distributions of high-energy carbon, oxygen and neon beams in water. Jpn. J. Med. Phys. 18, 1e22. Sihver, L., Mancusi, D., Niita, K., Sato, T., Townsend, L., Farmer, C., Pinsky, L., Ferrari, A., Cerutti, F., Gomese, I., 2008. Benchmarking of calculated projectile fragmentation cross-sections using the 3-D, MC codes PHITS, FLUKA, HETCHEDS, MCNPX_HI, and NUCFRG2. Acta Astronaut. 63, 865e877. Skvar c, J., 1993. Automatic image analysis system TRACOS. Informacije MIDEM 23, 201e205. Skvarc, J., Golovchenko, A.N., 2001. A method of trajectory tracing of Z 10 ions in the energy region below 300 MeV/u. Radiat. Meas. 34, 113e118. Summerer, K., Blank, B., 2000. Modified empirical parametrization of fragmentation cross sections. Phys. Rev. C 61, 034607. Tripathi, R.K., Cucinotta, F.A., Wilson, J.W., 1996. Accurate universal parameterization of absorption cross sections. Nucl. Instr. and Meth. B 117, 347e349. Tripathi, R.K., Wilson, J.W., Cucinotta, F.A., 1997. Accurate universal parameterization of absorption cross sections II e neutron absorption cross sections. Nucl. Instr. and Meth. B 129, 11e15. Tripathi, R.K., Cucinotta, F.A., Wilson, J.W.,1999. Accurate universal parameterization of absorption cross sections III e light systems. Nucl. Instr. and Meth. B 155, 349e356. Tsao, C.H., Silberberg, R., Barghouty, A.F., Sihver, L., Kanai, T., 1993. Scaling algorithm to calculate heavy-ion spallation cross sections. Phys. Rev. C 47, 1257e1262. Webber, W.R., Kish, J.C., Schrier, D.A., 1990a. Total charge and mass changing cross sections of relativistic nuclei in hydrogen, helium, and carbon targets. Phys. Rev. C 41, 520e532. Webber, W.R., Kish, J.C., Schrier, D.A., 1990b. Individual charge changing fragmentation cross sections of relativistic nuclei in hydrogen, helium, and carbon targets. Phys. Rev. C 41, 533e546. Yasuda, N., Namiki, K., Honma, Y., Umeshima, Y., Marumo, Y., Ishii, H., Benton, E.R., 2005. Development of a high speed imaging microscope and new software for nuclear track detector analysis. Radiat. Meas. 40, 384e388.
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Technical note
Fragmentation of 370 MeV/n
20
Ne and 470 MeV/n
24
Mg in light targets
A.N. Golovchenko a, L. Sihver b, c, d, *, S. Ota e, f, J. Skvar c g, N. Yasuda f, S. Kodaira f, G.N. Timoshenko a, h M. Giacomelli a
Laboratory of Radiation Biology, Joint Institute for Nuclear Research, 141980 Dubna, Russia Chalmers University of Technology, Nuclear Engineering, Applied Physics, SE-412 96 Göteborg, Sweden c Roanoke College, Department of Mathematics, Computer Science and Physics, Salem, VA 24153, USA d Texas A&M University, Department of Nuclear Engineering, TAMU-3133, College Station, TX 77843-3133, USA e Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan f Fundamental Technology Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555, Japan g Isaac Newton Group of Telescopes, Apartado de correos 321, E-38700 Santa Cruz de la Palma, Canary Islands, Spain h Slovenian Nuclear Safety Administration, Division of Radiation Safety and Materials, P.O. Box 5759, 1001 Ljubljana, Slovenia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 August 2009 Received in revised form 13 March 2010 Accepted 30 March 2010
Total charge-changing cross sections and cross sections for the production of projectile-like fragments were determined for fragmentation reactions induced by 370 MeV/n 20Ne ions in water and lucite, and 490 MeV/n 24Mg ions in polyethylene, carbon and aluminum targets sandwiched with CR-39 plastic nuclear track detectors. An automated microscope system and a track-to-track matching algorithm were used to count and recognize the primary and secondary particles. The measured cross sections were then compared with published cross sections and predictions of different models. Two models and the threedimensional Monte Carlo Particle Heavy Ion Transport Code System (PHITS) were used to calculate total charge-changing cross sections. Both models agreed within a few percent for the system 24Mg þ CH2, however a deviation up to 20% was observed for the systems 20Ne þ H2O and C5H8O2, when using one of the models. For all the studied systems, PHITS systematically underestimated the total charge-changing cross section. It was also found that the partial fragmentation cross sections for 24Mg þ CH2 measured in present and earlier works deviated up to 20% for Z ¼ 6e11. Measured cross sections for the production of fragments (Z ¼ 4e9) for 20Ne þ H2O and C5H8O2 were compared with predictions of three different semiempirical models and JQMD which is used in the PHITS code. The calculated cross sections differed from the measured data by 10e90% depending on which fragment and charge was studied, and which model was used. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Heavy ions Nuclear fragmentation Total and partial cross sections CR-39
1. Introduction Heavy ions are used in various fields of nuclear physics, medical physics and material science. There are applications within accelerator and reactor science, space and medicine, especially light ion radiation therapy. Accurate knowledge of the physics of interaction of high energetic heavy ions is therefore necessary for these applications, but also for estimating radiation damage due to Single Event Upsets (SEU) in electronic devises on space vehicles. Concern about the biological effects of space radiation and space dosimetry is increasing rapidly due to the perspectives of long-term manned missions outside the Earth’s protective magnetosphere. While * Corresponding author. Chalmers University of Technology, Nuclear Engineering, Applied Physics, SE-412 96 Göteborg, Sweden. Tel.: þ46 31 772 2921; fax: þ46 31 772 3079. E-mail address: [email protected] (L. Sihver). 1350-4487/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2010.03.006
minimal shield optimization was required in the initial low-Earthorbit vehicles, optimization will and should be a major factor in the design of vehicles for prolonged solar system travel. Galactic Cosmic Rays (GCR) and Solar Particle Events (SPE) will be the dominant source of the radiation dose for crews on long-term missions outside the earth’s magnetic field and this poses a major risk to these space flights. Even if energetic heavy ions (Z 2) only comprise a small fraction of GCR, their charge, penetrating power and interactions will make them a significant source of risk to astronaut health during long-duration crewed missions outside the Earth’s protective magnetosphere. To perform risk assessments, it is therefore essential to be able to estimate the absorbed dose, dose equivalents and biological effects of the ionization radiation. However, heavy ion transport includes many complex processes and to perform measurements for all possible systems would be both impractical and too expensive; e.g. direct measurements of dose equivalents inside critical organs in humans cannot be
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860 800
857
cut-off peak of Ne O F
N / 0.2 µ m
600
C
N
400
B
200 Be
0 5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Track radius, µm Fig. 1. Spectrum of Ne and fragments tracks at a depth of 7 cm in the lucite stack.
performed. The characterization of the outer space craft radiation field could be achieved with appropriate measurements, but the radiation field is modified by passage through the hulls of the space craft, materials in the space craft, and when passing through the human tissue. Reliable particles and heavy ion transport codes are therefore essential tools when performing the risk assessment for the personnel on space stations and space vehicles. There are a number of one-dimensional (1-D) and three-dimensional (3-D) particle and heavy ion transport codes available today, such as PHITS, HETC-HEDS, SHIELD-HIT, GEANT4, FLUKA, MARS, and MCNPX. A careful comparison of most of these codes is found in Sihver et al. (2008) and Sihver and Mancusi (2008). Most of these codes use semi-empirical models for calculating the total inelastic cross section. Since the total inelastic cross section deduces the mean free path of the nucleus in the material used in the Monte Carlo simulation and, therefore, also acts as a scaling parameter for the partial cross sections, it is important that this quantity is calculated as accurate as possible. To certify the accuracy, comparisons with measurements are necessary (see for instance, Heinbockel et al., 2006). We have, therefore, performed measurements of the total charge-changing cross sections (sTCC) and the partial cross sections for the production of projectile-like fragments (sPCC) for the interactions of 370 MeV/n 20Ne on water and lucite and 470 MeV/n 24Mg on polyethylene and carbon. The measured results are presented together with model predictions and previously published measurements. 2. Experiments Two stacks, 4 4 cm2 in area, consisting of water and lucite targets (thicknesses ranged from 1 to 5 cm) interleaved with w0.7 mm thick CR-39 sheets (Intercast Co., Parma, Italy) were perpendicularly bombarded by a 400 MeV/n 20Ne beam at the Heavy Ion Medical Accelerator (HIMAC) at the National Institute of Radiological Sciences (NIRS), Chiba, Japan. In Fig. 1, a spectrum of Ne
Fig. 3. The energy dependence of the total charge-changing cross section for 20 Ne þ lucite.
and fragments at a depth of 7 cm in the Lucite stack is shown. Another two stacks (up to 7 7 cm2 in area) of similar configuration and with polyethylene and carbon targets (1.5e4 cm thick) were exposed to a 500 MeV/n 24Mg beam at the Nuclotron accelerating facility (Joint Institute for Nuclear Research, Dubna, Russia). Fig. 2 presents a typical design of the stack (targets were made of carbon) irradiated with Mg ions. After slowing down in the materials preceding the samples, the beam energies in front of the stacks were measured and calculated to be w370 MeV/n and w470 MeV/n for Ne and Mg ions, respectively. Two detector sheets were placed in front of each stack to monitor the primary beam and accompanying particles (produced in materials preceding the stack). The fluences of the incoming particles were measured to be on the average w103 cm2. Chemical etching in 7 M NaOH at 70 C was applied to the detector sheets to develop the latent tracks to visible etch pits. The time of etching was different from stack to stack depending on the fluence. Effort was made to avoid etch pit overlapping as much as possible and to reveal the lowest detectable fragment. Then the tracks were scanned by an automated microscope system TRACOS (Skvar c, 1993) at the Jozef Stefan Institute (Ljubljana, Slovenia) and by a High Speed Imaging Microscope (HSP-1000) developed at NIRS and Seiko Precision Instruments (Japan) (Yasuda et al., 2005). After automatic counting, the tracks originating from primary and secondary particles and measurements of their parameters (average brightness, minor and major axes of the etch pit etc.) were matched (Skvar c and Golovchenko, 2001) on the upper and bottom surfaces
Fig. 2. Carbon stack configuration for a Mg beam.
858
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860
Table 1 Measured total charge-changing cross sections (sTCC,exp) for
20
Ne þ H2O together with model predictions (sTCC,mod).
sTCC, exp (mb)
Energy (MeV/n)
285 (85)
sTCC, mod (mb)
This work
Schall et al. (1996)
Sihver et al. (1993, 1998)
Tripathi et al. (1996)
PHITSc (Iwase et al., 2002)
1882 (29)a
1800 (43) [4.4%]b
1606 [15%]b
1776 [5.6%]b
1567 [16%]b
a
Values in parenthesis are statistical errors. Percents in brackets are difference between the results of this work and those from previous experiments and models i.e. (sTCC, exp sTCC, mod)/sTCC, exp. c In PHITS calculation, total charge-changing cross section (sTCC) was obtained from total reaction cross section (sTRC) non-charge-changing cross section (sNCC). The sTRC was calculated by Tripathi’s model and sNCC was calculated by Cugnon new INC model (Cugnon et al., 1981).Thereafter, all the cross sections in the subsequent tables were calculated in the same way including errors and percents in brackets. b
Table 2 Measured total charge-changing cross section (sTCC,exp) for Energy (MeV/n)
24
Mg þ C and
sTCC, exp (mb) This work
Mg þ CH2 experiments together with model predictions (sTCC,mod).
24
sTCC, mod (mb) Webber et al. (1990a)
Sihver et al. (1993, 1998)
Tripathi et al. (1996)
PHITS (Iwase et al., 2002)
1097 (11)
1128 (11) 1120 (11)
1092 1112 1149 1170 1146
1087 1091 1105 1116 1166
989 [10%] 980 [13%] 992 [11%] 998 [12%] 1040 [7%]
1725 (18)
1632 [5.4%]
1774 [2.8%]
1679 [0.4%] 1698 [1.4%] 1716 [2.4%]
1789 [6.2%] 1798 [4.4%] 1806 [2.7%]
1736 1749 1762 1850
1818 1829 1839 1946
24
Mg þ C 309 (71) 345 (25) 424 (44) 481 (59) 739 (51)
1129 (91) 1116 (42)
[0.5%] [1.5%] [3.0%] [3.7%] [2.3%]
[0.9%] [3.4%] [1.0%] [1.1%] [4.1%]
24
Mg þ CH2 309 (71) 343 (38) 363 (23) 385 (45) 408 (22) 432 (34) 437 (51) 459 (29) 481 (59) 739 (51)
1703 1685 1722 1759 1750 1774 1784
(58) (101) (49) (96) (50) (51) (57) 1800 (18) 1826 (18)
[2.1%] [2.0%] [2.1%] [1.3%]
of the detector sheets. Thus, unwanted events (fragments produced in the body of the detector, bubbles, radon induced tracks etc.) were rejected. The charge resolution (1s) was about 0.1e0.3 elementary charge units. The energy losses of primaries and fragments along the stacks could not be measured directly in this experiment, but were calculated using a computer code derived from the work of Henke and Benton (1967). The peaks on each individual detector are clearly separated (see for instance Fig. 1). Knowing that the highest peak with the biggest tracks was due to Ne or Mg, all subsequent peaks could only be from the nuclei with lower atomic number (the charge pick-up cross section is negligibly small). No absolute calibration is needed. In other words, the peaks of lower Z ions are resolved relative to the largest right-hand peak of primary ions. Different etching times do therefore not affect the resolution of the detector. Table 3 Measured partial cross sections (sPCC,exp) for Energy (MeV/n)
Z
20
Ne þ H2O and
1472 [15%] 1476 [14%] 1484 [12%] 1494 [13%] 1502 [15%] 1514 [13%] 1518[14%] 1528 [14%] 1540 [14%] 1667 [8.7%]
[2.5%] [2.5%] [2.2%] [6.6%]
3. Results The total charge-changing cross sections (sTCC) were obtained from the numbers of matched tracks corresponding to the peaks of primaries in front of and behind a given target using the conventional exponential absorption equation. To calculate the partial cross sections (sPCC), the formula included in the article by Golovchenko et al. (2002) was used. This formula accounts for the number of fragments in front of the target (when using several targets in the stack) but still assumes that sTCC values are equal for the primaries and secondaries. It was shown that if the total charge-changing cross section of a given fragment is within 20% of that of a primary ion, the number of fragments does not change by more than w2%. Note, that sTCC and sPCC were calculated per molecular mass of the complex target i.e. water, polyethylene and lucite.
Ne þ C5H8O2 experiments together with model predictions (sPCC,mod).
20
sPCC, exp (mb)
sPCC, mod (mb)
This work
[1]
[2]
[3]a
PHITS
258 [37%] 263 [25%] 194 [31%] 125 [57%] 74 [37%] 37 [36%]
161 [15%] 141 [60%] 130 [54%] 115 [60%] 82 [31%] 41 [29%]
235 [24%] 271 [23%] 184 [34%] 199 [32%] 60 [49%] 58 [0%]
1324 [11%] 1358 [23%] 1003 [31%] 650 [48%] 394 [45%] 216 [49%]
859 754 692 613 438 251
1129 [5%] 1501 [15%] 1035 [29%] 1165 [21%] 370 [48%] 366 [14%]
20
Ne þ H2O 285 (85)
9 8 7 6 5 4
189 350 280 291 118 58
(6) (9) (7) (7) (5) (3)
211 274 160 121 106 112
[12%] [22%] [43%] [58%] [10%] [93%]
9 8 7 6 5 4
1189 1772 1455 1472 718 426
(20) (25) (20) (24) (15) (12)
1110 [6.6%] 1423 [20%] 846 [42%] 918 [38%] 631 [12%] 718 [69%]
20
Ne þ C5H8O2 267 (103)
a
All the partial cross sections calculated with EPAX [3] are energy independent.
[28%] [57%] [52%] [58%] [39%] [41%]
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860 Table 4 Measured partial cross sections (sPCC,exp) for predictions (sPCC,mod).
Mg þ CH2 together with model
sPCC, exp (mb)
sPCC, mod (mb)
sPCC, exp (mb)
sPCC, mod (mb)
PHITS
Cor 2
PHITS
11 10 9 8
310 259 149 275
(17) (16) (12) (15)
302 [2.6%] 228 [12%] 89 [40%] 145 [47%]
300 248 138 252
(16) (16) (11) (14)
302 [0.7%] 228 [8.1%] 89 [36%] 145 [42%]
11 10 9 8
230 255 91 205
(8) (9) (5) (8)
300 [30%] 225 [12%] 89 [2.2%] 144 [30%]
227 251 88 196
(8) (8) (5) (8)
300 [32%] 225 [10%] 89 [1.1%] 144 [27%]
Z
343 (38)
432 (34)
charge-changing cross section for 20Ne on lucite, measured in this work in comparison with model calculations. The experimental results together with the calculated ones for w370 MeV/n 20Ne ions in water and lucite, and for w470 MeV/n 24Mg ions in polyethylene and carbon are presented in Tables 1 and 2. The energy values (E) in each Table are averages of those in front of and behind the target, while the values in parenthesis are deviations from these averages. In Tables 3e6, the partial cross sections measured in this work are compared with the results of three models (Sihver et al., 1993, 1998; Tsao et al., 1993; and EPAX2 by Summerer and Blank, 2000) enumerated as [1], [2] and [3], respectively, and PHITS (Iwase et al., 2002). Z denotes the charge of the fragment. In Tables 4e6, in the “Cor 1” column the measured partial cross sections are tabulated with a correction for secondaries created in the detectors/targets using the procedure given in Golovchenko et al. (2002). The next column presents calculated results using PHITS. The figures inside the brackets show deviation from the measured cross sections tabulated in the “Cor 1” column. In the “Cor 2” column the measured partial cross sections are corrected for the secondaries created in the detectors/targets using Sihver’s semi-empirical model (Sihver et al., 1993, 1998). The next column tabulates calculated results using PHITS and shows deviations from the measured cross sections corrected with Sihver’s formula, tabulated in the second column. Figs. 4 and 5 present the energy dependence of the total charge-changing cross section for 24Mg in polyethylene
24
Cor 1
Energy (MeV/n)
When comparing the measured total charge-changing cross sections with model calculations, the total reaction cross sections were first calculated using two different models 1) an enhanced version (Sihver et al., 1998, 2008) of the total reaction cross section model developed by Sihver et al. (1993), and 2) a model developed by Tripathi et al. (1996, 1997, 1999). The non-charge-changing parts of the reaction cross sections (neutron removal) were then calculated with the enhanced version of the semi-empirical model originally developed by Sihver et al. (1993), which takes advantage of the experimentally verified weak factorization property (Olson et al., 1983). Fig. 3 presents the energy dependence of the total Table 5 Measured partial cross sections (sPCC,exp) for
sPCC, exp (mb)
sPCC, mod (mb)
sPCC, exp (mb)
sPCC, mod (mb)
PHITS
Cor 2
PHITS
11 10 9 8 7 6 5
161 142 33 172 115 203 124
(23) (20) (16) (21) (19) (22) (13)
92 [43%] 105 [26%] 47 [42%] 82 [52%] 84 [27%] 103 [49%] 40 [68%]
151 135 26 158 104 183 116
(22) (20) (15) (21) (19) (21) (13)
92 [39%] 105 [22%] 47 [81%] 82 [48%] 84 [19%] 103 [44%] 40 [66%]
11 10 9 8 7 6 5
113 112 64 125 100 151 75
(8) (7) (5) (7) (6) (7) (5)
91 [19%] 100 [11%] 45 [30%] 78 [38%] 81 [19%] 101 [33%] 40 [47%]
110 109 62 120 96 141 70
(8) (6) (5) (7) (6) (7) (5)
91 [17%] 100 [8.3%] 45 [27%] 78 [35%] 81 [16%] 101 [28%] 40 [43%]
Z
345 (25)
424 (44)
a
Mg þ C together with model predictions (sPCC,mod).
24
Cor 1
Energy (MeV/n)
859
sPCC, exp (mb)
Energy (MeV/n)
Webber et al. (1990b),a
Webber et al. (1990b),a
309 (71)
148 (2) [8%] 133 (2) [6%] 58 (2) [76%] 137 (2) [20%] 90 (3) [22%] 114 (3) [44%] 40 (1) [68%]
148 (2) [2.0%] 133 (2) [1.5%] 58 (2) [123%] 137 (2) [13%] 90 (3) [13%] 114 (3) [38%] 40 (1) [65%]
481 (59)
124 (2) [10%] 111 (2) [0.9%] 56 (2) [13%] 120 (2) [4%] 89 (3) [11%] 120 (3) [21%] 48 (1) [36%]
124 (2) [13%] 111 (2) [1.8%] 56 (2) [10%] 120 (2) [0.0%] 89 (3) [7.3%] 120 (3) [15%] 48 (1) [31%]
Values in brackets in two last columns of this table are comparisons with Cor 1 and Cor 2.
Table 6 Measured partial cross sections from the
Mg þ CH2 experiments (sPCC,exp).
24
sPCC, exp (mb)
Energy (MeV/n)
Energy (MeV/n)
Z
Cor 1
Cor 2
343 (38)
11 10 9 8
310 259 149 275
(17) (16) (12) (15)
300 248 138 252
(16) (16) (11) (14)
432 (34)
11 10 9 8
230 255 91 205
(8) (9) (5) (8)
227 251 88 196
(8) (8) (5) (8)
459 (29)
11 10 9 8 7 6
298 272 136 267 186 257
(11) (10) (7) (10) (8) (9)
sPCC, exp (mb) Webber et al. (1990b)
Webber et al. (1990b)
309 (71)
309 263 105 253
(8) (7) (3) (6)
309 263 105 253
(8) (7) (3) (6)
481 (59)
295 239 113 239 161 201
(15) [1.0%] (12) [12%] (6) [17%] (12) [10%] (8) [13%] (10) [22%]
295 239 113 239 161 201
(15) [1.0%] (12) [12%] (6) [17%] (12) [10%] (8) [13%] (10) [22%]
This work in comparison with the measurements performed by Webber et al. (1990b).
[0.3%] [2%] [30%] [8%]
[3.0%] [6.0%] [24%] [0.4%]
Total charge-changing cross section (mb)
860
A.N. Golovchenko et al. / Radiation Measurements 45 (2010) 856e860
sections calculated with the JQMD model in PHITS can differ from the measured values with up to more than 80% for some systems. The deviations between the calculated and measured cross sections show that more exact measurements of cross sections are needed to benchmark the total and partial reaction cross sections models used in both one-dimensional deterministic and three-dimensional Monte Carlo particle and heavy ion transport codes.
This work Webber et al. (1990a) Sihver et al. (1993, 1998) Tripathi et al. (1996) PHITS
2000
1900
1800
1700
Acknowledgements 1600
1500 0
200
400
600
800
1000
Energy (MeV/n)
Total charge-changing cross section (mb)
Fig. 4. The energy dependence of the total charge-changing cross section for Mg on CH2.
This work Webber et al. (1990a) Sihver et al. (1993, 1998) Tripathi et al. (1996) PHITS
1300
1200
References
1100
1000
900
0
200
400
L. Sihver would like to acknowledge, with much gratitude, the support from the Japan Society for the Promotion of Science (JSPS), which made it possible for him to spend two very fruitful and interesting months as a short term JSPS Fellow at NIRS, during 2009. A.N. Golovchenko appreciates the support of NIRS and Jozef Stefan Institute (Slovenia). S. Ota appreciates the support by Practical Training Program for Doctoral Students at Waseda University, which made it possible for him to work five months in L. Sihver research group at Chalmers University of Technology in Sweden.
600
800
1000
Energy (MeV/n) Fig. 5. The energy dependence of the total charge-changing cross section for Mg on C.
and carbon, respectively, measured in this work in comparison with model calculations. 4. Discussion and conclusions As can be seen from Tables 1e6, the measurements of both the total and partial charge-changing cross sections presented in this paper agree well with previously measured data. Both the semiempirical total reaction model developed by Tripathi et al. (1996, 1997, 1999) and the enhanced version (Sihver et al., 1998, 2008) of the semi-empirical model developed by Sihver et al. (1993), were corrected for the non-charge-changing parts of the reaction cross sections (neutron removal) using the enhanced version of the semiempirical model developed by Sihver et al. After the correction, the cross sections calculated with the model developed by Tripathi et al., agreed with the measured one within 5e10%, and the cross sections calculated with the model developed by Sihver et al., models agreed within 15e20%. When comparing the measured partial cross sections with the calculated results using three semiempirical models (Sihver et al., 1993, 1998; Tsao et al., 1993; and EPAX2 by Summerer and Blank, 2000), and the JQMD model used in PHITS, the model by Sihver et al. (1998) gives the best overall agreement. The total charge-changing cross sections calculated with PHITS are always underestimated, which is in agreement with previous studies (Sihver et al., 2008). The calculated partial cross
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