⇦Chinese Physics Letters, 2017, Vol. 34, No. 10, Article code 102501 Charge-Changing Cross Sections of 736 A MeV $^{28}$Si on Carbon Targets * Jun-Sheng Li(李俊生)1**, Ying-Hua Dang(党英华)1, Dong-Hai Zhang(张东海)1, Jin-Xia Cheng(程锦霞)2, S. Kodaira3, N. Yasuda4 Affiliations 1Institute of Modern Physics, Shanxi Normal University, Linfen 041004 2College of Electric and Information Engineering, Beifang Ethnic University, Yinchuan 750021 3Radiation Measurement Research Section, National Institute of Radiological Sciences, Chiba 263-8555, Japan 4Research Institute of Nuclear Engineering, University of Fukui, Fukui 914-0055, Japan Received 4 May 2017 *Supported by the National Natural Science Foundation of China under Grant Nos 11075100, 11347198 and 11565001, and the Shanxi Provincial Science Foundation under Grant No 2011011001-2.
**Corresponding author. Email: lijs@sxnu.edu.cn Citation Text: Li J S, Dang Y H, Zhang D H, Cheng J X and Kodaira S et al 2017 Chin. Phys. Lett. 34 102501 Abstract The total and partial charge-changing cross sections of $^{28}$Si on carbon targets at 736 and 723 A MeV are studied by CR-39 plastic nuclear track detectors using the HSP-1000 microscope system and the PitFit track measurement software. The values of the total charge-changing cross section are $\sigma_{\rm tot}=(1179\pm50)$ mb and $\sigma_{\rm tot}=(1186\pm42)$ mb at 736 and 723 A MeV, respectively. The result is compared with the ones obtained by other experimental and theoretical results. The odd–even effect of the partial charge-changing cross section is observed. DOI:10.1088/0256-307X/34/10/102501 PACS:25.70.Mn, 25.75.-q, 25.70.-z © 2017 Chinese Physics Society Article Text The knowledge of heavy ion fragmentation at intermediate and high energies from several hundreds of A MeV to several A GeV is very necessary in nuclear physics, astrophysics, radiobiology and applied physics, etc. Understanding the interaction mechanism at intermediate and high energy nuclear collisions is very important to estimate the radiation damage to the equipment of space vehicles, to calculate the transport of the heavy ions in the galactic cosmic rays (GCR) through the interstellar medium, and to understand the effects of these components of cosmic rays.[1-3] Hence, it is necessary to have accurate knowledge of fragmentation cross section of heavy ions at different energies in various target media. The charge-changing cross section provides a way to clarify the reaction mechanisms in heavy ion collisions and the distribution of valence protons, particularly for neutron-rich projectiles. Until now, the projectile fragmentation charge-changing cross section has been explored by many research groups at relativistic energy with various targets.[4-32] Yamaguchi et al. introduced a phenomenological way to relate point proton distribution radii ($r_{\rm p}$) to charge-changing cross sections($\sigma _{\rm cc}$) in carbon target.[4] Recently, the charge-changing cross section has been measured to obtain the information on the $r_{\rm p}$ of some unstable nuclei.[15-21] When free-space doses from GCR heavy ions are plotted as a function of atomic number, the contribution of silicon to dose equivalent in free space is second only to that of iron.[8] Therefore the fragmentation cross sections of silicon ions on various targets are of considerable importance. At present, the results of the total and partial charge-changing cross sections of $^{28}$Si ion beam in different targets using the CR-39 detector are relatively less, and the results of different research groups do not agree well with each other.[4-14] In this study, using CR-39 detectors, the total and partial charge-changing cross sections of 736 and 723 A MeV $^{28}$Si on carbon targets are calculated, aiming at filling the gap in the profile of experimental cross sections of fragmentation productions and giving a further study on the dependence of the charge-changing cross sections on the energies. The experimental results are compared with other experimental results and theoretical models. The carbon targets were exposed by an 800 A MeV $^{28}$Si ion beam at the heavy ion medical accelerator in Chiba (HIMAC) at the Japanese national institute of radiological sciences (NIRS). The beam fluence is about 1250 ions/cm$^{2}$. A type of HARZLAS TD-1 CR-39 sheet manufactured by Fukuvi Chemical Industry Co., LTD. is placed before and after the targets. The typical configuration of the stack for this experiment is shown in Fig. 1. Using this configuration, we can obtain the charge-changing cross sections of $^{28}$Si on carbon targets at different energies. In this work, we focus on the interactions of $^{28}$Si on carbon targets at 736 and 723 A MeV because of the lack of the charge-changing cross sections of $^{28}$Si on carbon targets at energies of 550–750 A MeV. The thickness of the targets and CR-39 detectors were about 5 mm and 0.783 mm, respectively. The beam energy at the first target upper surface is 788 A MeV. The total and partial charge-changing cross sections of $^{28}$Si in the first target have been calculated in our previous work.[12] The CR-39 detectors were etched in 7N NaOH aqueous solution at 70$^{\circ}\!$C. The etching time is 15 h. Then, the beam ions and their fragments in the CR-39 manifest as etch-pit cones (tracks) on both sides of CR-39 sheets. After etching, the tracks were scanned and analyzed using the HSP-1000 microscope system and the PitFit track measurement software.[33] Figure 2 shows the images of ion tracks scanned by the HSP-1000 microscope system. The spot A is the track of $^{28}$Si, the spots B and C are the tracks of projectile fragments (PFs). Using PitFit software, we can obtain the geometric information of the tracks, such as the area of etched track spot on CR-39 surfaces, the position coordinates and other information. Figure 3 shows the base-area distribution of etched tracks of 736 A MeV $^{28}$Si and their fragments in CR-39 detector after carbon target. The charge of PFs is identified by the base area distribution. Multi Gaussian fittings are made in the base-area distribution. It is clear that the base-area distribution of $^{28}$Si ions and their fragments with charge from 5 to 13 manifests a better and more resolution capability of the CR-39 detector. The trajectories of $^{28}$Si and the ones of PFs are reconstructed in the scanned stack. Details of track tracing and reconstruction, identification of charge of PFs can be found in our recent works.[24-26]
cpl-34-10-102501-fig1.png
Fig. 1. The typical configuration of the stacks for this experiment.
cpl-34-10-102501-fig2.png
Fig. 2. Tracks of charged particles on CR-39.
The total charge-changing cross section is calculated by using the following relation[11] $$\begin{align} \sigma _{\rm tot} =\frac{A_{\rm T} \ln(N_{\rm in} /N_{\rm out})}{\rho _{\rm T} tN_{\rm AV}},~~ \tag {1} \end{align} $$ where $A_{\rm T}$, $\rho _{\rm T}$, $t$ and $N_{\rm AV}$ are the nuclear mass of the target, target density, thickness of the target, and the Avogadro number, respectively, $N_{\rm in}$ is the number of $^{28}$Si ions before the target, and $N_{\rm out}$ is the number of $^{28}$Si ions after the target. The systematic error in counting the number of $^{28}$Si ions after the target and the PFs is less than 2%. The Bradt–Peters cross section is also calculated using the relation[34] $$\begin{align} \sigma _{\rm tot}=\pi r_0^2(A_{\rm T}^{1/3} +A_{\rm p}^{1/3} -b_0)^2,~~ \tag {2} \end{align} $$ where $r_0 =1.35$ fm, $b_0 =0.94$, $A_{\rm p}$ is the projectile mass number, and $A_{\rm T}$ is the target mass number. The experimental total charge-changing cross sections and theoretical prediction are listed in Table 1. Figure 4 presents the dependence of the total charge-changing cross sections of $^{28}$Si on carbon targets on the energy. It is found that our experimental data are in agreement with the results of other ones and theoretical prediction within experimental uncertainties and do not show any obvious energy dependence.
cpl-34-10-102501-fig3.png
Fig. 3. Base-area distribution of etched tracks of 736 A MeV $^{28}$Si and their fragments in CR-39 detector after C target.
cpl-34-10-102501-fig4.png
Fig. 4. Dependence of the total charge-changing cross sections on the energy.
cpl-34-10-102501-fig5.png
Fig. 5. The dependence of the partial cross sections of fragment production on the charge of fragment in interactions of $^{28}$Si in C targets.
For calculating the partial charge-changing cross section of the fragment with charge $Z_{\rm f}$, we can use the following relation[11] $$\begin{align} \sigma _{Z_{\rm i} \to Z_{\rm f} } =\frac{A_{\rm T} }{\rho _{\rm T} tN_{\rm AV} }\Big(\frac{N_{\rm out}^{\rm f} }{N_{\rm out}^{\rm p} }-\frac{N_{\rm in}^{\rm f} }{N_{\rm in}^{\rm p} }\Big),~~ \tag {3} \end{align} $$ where $\sigma _{Z_{\rm i} \to Z_{\rm f}}$ is the partial charge-changing cross section of a beam ion $Z_{\rm i}$ into $Z_{\rm f}$, $N_{\rm in}^{\rm f}$ and $N_{\rm out}^{\rm f}$ are the numbers of PFs with charge $Z_{\rm f}$ before and after the target, $N_{\rm in}^{\rm p}$ and $N_{\rm out}^{\rm p}$ are the numbers of beam ions before and after the target, $A_{\rm T}$, $\rho _{\rm T}$, $t$ and $N_{\rm AV}$ are the nuclear mass of the target, target density, thickness of the target, and the Avogadro number, respectively. The formula is valid if the thickness of the target is smaller compared with the mean free path of the fragments in that material. Table 2 lists the experimental partial charge-changing cross sections for PFs with charges of $5\le Z\le13$ produced in the interactions of $^{28}$Si projectiles in C targets at various energies. Figure 5 presents the variation of the partial cross sections with the charge of PFs for the interactions of $^{28}$Si with the C target. An obvious odd–even effect is observed in the PFs production in all interactions. The odd–even effect is mainly affected by the pairing energy and the Wigner energy in the statistical decay process.[35-37] The partial cross section for $Z=5$ is relatively small because of the low statistics. The partial cross section for $Z=13$ is relatively large due to the fact that there are mixed events in the statistical distinction.[9,25,26]
Table 1. The total charge-changing cross sections for interactions of $^{28}$Si on C targets.
Energy (A MeV) $\sigma_{\rm tot}$ (mb) NUCFRG2 Bradt–Peters References
144 1195$\pm$12 Ref. [4]
208 1138$\pm$17 Ref. [4]
270 1131$\pm$34 1112 Ref. [8]
309 1119$\pm$8 Ref. [4]
352 1125$\pm$16 1115 Ref. [8]
467 1136.4$\pm$12.8 Ref. [5]
503 1176$\pm$12 Ref. [13]
550 1142$\pm$16 1154 Ref. [8]
723 1186$\pm$42 This work
736 1179$\pm$50 1037 This work
765 1110$\pm$14 1196 Ref. [8]
770 1183$\pm$12 Ref. [13]
788 1127$\pm$42 1037 Ref. [12]
1000 1117$\pm$62 Ref. [11]
1150 1100$\pm$16 1208 Ref. [8]
14500 1185.0$\pm$30.0 Ref. [14]
Table 2. Experimental partial charge-changing cross sections for the production of $^{28}$Si projectiles for C targets.
Beam energy (A MeV)
$Z_{\rm f}$ 344[8] 467[5] 560[8] 723 (This work) 736 (This work) 770[8] 788[12] 1000[11] 1147[8] 14500[14]
13 122$\pm$4 125.3$\pm$4.7 118$\pm$3 205$\pm$20 254$\pm$24 157$\pm$2 225$\pm$19 293$\pm$18 103$\pm$3 107.0$\pm$7.4
12 143$\pm$4 129.5$\pm$4.8 134$\pm$3 131$\pm$16 131$\pm$17 163$\pm$2 154$\pm$15 177$\pm$12 109$\pm$4 116.7$\pm$6.9
11 80$\pm$3 66.7$\pm$3.4 74$\pm$2 58$\pm$11 65$\pm$12 64$\pm$2 92$\pm$12 123$\pm$11 61$\pm$2 56.2$\pm$4.7
10 86$\pm$3 77.1$\pm$3.5 80$\pm$2 75$\pm$12 100$\pm$15 63$\pm$2 75$\pm$11 122$\pm$11 64$\pm$2 65.1$\pm$5.1
9 45$\pm$2 37.8$\pm$2.4 42$\pm$1 33$\pm$8 65$\pm$12 30$\pm$2 49$\pm$9 62$\pm$8 38$\pm$2 42.0$\pm$4.1
8 93$\pm$6 79.4$\pm$3.5 86$\pm$5 58$\pm$11 100$\pm$15 65$\pm$2 92$\pm$12 117$\pm$11 73$\pm$5 76.8$\pm$5.6
7 71$\pm$5 61.5$\pm$3.1 65$\pm$4 62$\pm$11 89$\pm$14 48$\pm$1 55$\pm$9 83$\pm$9 59$\pm$5 54.2$\pm$5.2
6 104$\pm$7 84.6$\pm$3.6 98$\pm$6 81$\pm$13 104$\pm$16 74$\pm$2 107$\pm$13 90$\pm$10 88$\pm$7 65.7$\pm$11.4
5 21$\pm$7 50$\pm$9
In conclusion, the total and partial charge-changing cross sections for 736 and 723 A MeV$^{28}$Si ion beams on the C target have been measured using CR-39 detectors. The total charge-changing cross sections of our experimental result are in agreement with other experimental data and the theoretical predictions. The total charge-changing cross sections in the present work do not show any obvious energy dependence. The partial cross sections show an obvious odd–even effect for the fragments with charges of 5$\le$Z$\le$12. We gratefully acknowledge the staff of the HIMAC for providing the beam to expose the stacks. References Nuclear fragmentation database for GCR transport code developmentEnergy-dependent charge-changing cross sections and proton distribution of Si 28 Projectile fragmentation of silicon ions at 490 A MeVTrends of total reaction cross sections for heavy ion collisions in the intermediate energy rangeProton-nucleus total inelastic cross sections - an empirical formula for E greater than 10 MeVFragmentation cross sections of 28Si at beam energies from toFragmentation cross-section of 600 A MeV Si14+ ions in thick polyethylene targetFragmentation cross sections and search for nuclear fragments with fractional charge in relativistic heavy ion collisionsFragmentation cross sections of Fe26+, Si14+ and C6+ ions of 0.3–10 on polyethylene, CR39 and aluminum targetsFragmentation cross sections of 788A MeV 28Si on carbon and polyethylene targetsIndividual charge changing fragmentation cross sections of relativistic nuclei in hydrogen, helium, and carbon targetsFragmentation cross sections of Si 28 at 14.5 GeV/nucleonParameter-free calculation of charge-changing cross sections at high energyScaling of Charge-Changing Interaction Cross Sections and Point-Proton Radii of Neutron-Rich Carbon IsotopesProton radius of 14Be from measurement of charge-changing cross sectionsProton Radii of B 12 – 17 Define a Thick Neutron Surface in B 17 Proton Distribution Radii of C 12 – 19 Illuminate Features of Neutron HalosCharge-changing cross sections of Ne 30 , Na 32 , 33 with a proton targetInvestigations of charge-changing processes for light proton-rich nuclei on carbon and solid-hydrogen targetsFragmentation Cross Sections of 158 AGeV Pb ProjectilesFragmentation studies of high-energy ions using CR39 nuclear track detectorsThe fragmentation of 20 Ne at 400 A MeVProjectile fragmentation of 471 A MeV 56Fe in polyethylene, carbon and aluminum targetsProjectile fragment emission in the fragmentation of 56 Fe on C, Al and CH 2 targets at 471 A MeVInteractions in hydrogen of relativistic neon to nickel projectiles: Total charge-changing cross sectionsTotal charge and mass changing cross sections of relativistic nuclei in hydrogen, helium, and carbon targetsTotal and Partial Fragmentation Cross-Section of 500 MeV/nucleon Carbon Ions on Different Target MaterialsNuclear fragmentation cross-sections of 400AMeV 36Ar and 40Ar in collisions with light and heavy target nucleiRelativistic Energy Pb Projectile Fragmentation with Heavy Target NucleiSecondary Beam Fragments Produced by 200 and 400 MeV/ u 12 C 6+ Ions in WaterTracking method for the measurement of projectile charge changing cross-section using CR-39 detector with a high speed imaging microscopeThe Heavy Nuclei of the Primary Cosmic RadiationOdd–even and nonequilibrium effects in multifragmentation of 56Fe on C, Al targets at 471 A MeVThe odd–even effect of fragmentation cross sections for 36 Ar and 40 ArComplex nuclear-structure phenomena revealed from the nuclide production in fragmentation reactions
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