Stopping power for MeV 12 C ions in solids

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1 Nuclear Instruments and Methods in Physics Research B 35 (998) 69±74 Stopping power for MeV C ions in solids Zheng Tao, Lu Xiting *, Zhai Yongjun, Xia Zonghuang, Shen Dingyu, Wang Xuemei, Zhao Qiang Department of Technical Physics and Institute of Heavy Ion Physics, Peking University, Beijing 0087, People's Republic of China Abstract The stopping powers for 0.3±6.4 MeV C ions in C, Al, Ti, Cu, Nb and Ag have been measured with the transmission method. The experimental data on stopping power are compared with evaluated values using LSS theory, ZBL semiempirical model predictions and previous experimental data. The results show that there is signi cant discrepancy between present work and LSS theory; for C in Al, ZBL calculations quite agree with our measurements, yet for C in other stoppers, those cannot reproduce most of present experimental data; our work consists mostly with previous measurements. Moreover, present stopping power data exhibit apparent Z -oscillation. Ó 998 Elsevier Science B.V. PACS: Bw Keywords: Stopping power; C ion; Transmission technique; Z -oscillation. Introduction Stopping powers in materials are of interest in many research elds, such as in nuclear physics, atomic physics, solid-state physics, radiation dosimetry and nuclear technique applications. During the last two decades, it has attracted a great deal of attention. However, the experimental information on low energy heavy ions is still scarce and sometimes contains large discrepancies. It is the purpose of this study to determine the stopping powers for 0.3±6.4 MeV C ions in C, Al, Ti, Cu, Nb and Ag foils using transmission technique. It is a continuation of our systematic * Corresponding author. Tel.: ; fax: ; xtlu@ihipms.ihip.pku.edu.cn. study of stopping powers in various solids []. In this paper our results are compared to the LSS theory [,3] and ZBL model calculations [4], great discrepancy has been observed. We also compare them with previous experimental stopping data and discuss Z -oscillation of present stopping power data. Our experimental results can be well described by an empirical formula.. Experimental The C ion beams were generated by the.7 MV tandem accelerator of Peking University. The schematic arrangement of transmission technique is showed in Fig.. The ions scattered by 60 penetrated foil placed in front of a 5-mm diam. silicon barrier detector (SBD). In this way X/98/$9.00 Ó 998 Elsevier Science B.V. All rights reserved. PII S X ( 9 7 )

2 70 T. Zheng et al. / Nucl. Instr. and Meth. in Phys. Res. B 35 (998) 69±74 3. Results and discussion Fig.. Schematic arrangement of transmission technique. the ion ux could be reduced to a reasonable level and direct beam exposure of the foils was avoided. The C, Al, Ti, Cu, Nb and Ag foils were xed on target frames which could be moved up and down by a handle. The energies for ions directly coming from the gold scatterer and for those having passing through the foil were measured, respectively. The energy calibration of the detector system was carried out by using scattered carbon ion beams of known energies, which was de ned by the magnetic eld of the accelerator analyzing magnet. In this way, corrections include e ects due to detector window thickness, pulse height defect and any nonlinear energy response of the detector system for carbon ion beams. A 50 nm or 4 nm gold lm on a silicon substrate was used to scatter the incident ions from the accelerator. The energy loss of the ions transmitted through the foil could then be determined by the shift of leading edge of the energy spectra for thick gold layer or by the change of spectrum peak-position for thin gold layer. The foils studied were analyzed by using MeV a-rbs and 3.05 MeV a resonance scattering. No obvious impurities were found in the foils. To extract stopping powers from the energy loss data, the area densities of the foils were determined from the energy loss of 3.9, 4. and 4.5 MeV alpha particles in the foils, because of the high accuracy of stopping data for alpha particles from the ZBL calculations in this energy region. Alpha energy loss was measured by using the same geometry and at the same spot on the foils as the carbon ion energy loss. We measured the stopping power of 0.5±6.4 MeV C in C, Al, Cu and Ag, a 50 nm gold lm on a silicon substrate used as a scatterer, and measured the stopping power of 0.3±6.3 MeV C in Ti and Nb, the scatterer being a thin gold layer of 4 nm. The average energy E ˆ E E = is the corresponding energy of the measured stopping power, where E and E are the energies of the scattered ions entering and passing through the foils, respectively. Present results on stopping power are shown in Table and Fig.. The uncertainty of our stopping data is about 3%, which mainly includes the error of determining the thickness of foils and the energy shift of the backscattering spectra on gold layer. The ZBL semiempirical calculations are also shown in Table and Fig. for comparison. Previous measurements are shown in Fig. as well. The stopping powers shown in Table and Fig. are electronic stopping powers S e, which have been corrected by experimental stopping power S exp minus the nuclear stopping power S n. For this correction, the nuclear S n values are taken from ZBL calculations. The ratio of nuclear S n to electronic S e stopping value S n /S e is small and always less than % in our measuring energy region. To quantify the energy dependence of the measured stopping powers, the experimental electronic stopping data have been adjusted to the following empirical formula. S e ˆ ; a E b a a 3 E b where a, a, a 3, b and b are the tted coe cients, which are listed in Table. The unit of MeV cm / mg is taken for S e and that of MeV for E. The tted curves are shown in Fig. as well. 3.. Comparison to ZBL calculations and previous data In most part of the measured energy region, there are no previous experimental data. In the region where previous data are available, present data t well with them. From Fig. we can see that for C in Al foil, present measurements are gener-

3 T. Zheng et al. / Nucl. Instr. and Meth. in Phys. Res. B 35 (998) 69±74 7 Fig.. Stopping power of C in C (a), Al (b), Ti (c), Cu (d), Nb (e), Ag (f). Present data and comparison with ZBL and data of Refs [5± 0]. ally consistent with the ZBL calculations, but for Ti, Cu, Nb, Ag, in the region of 3±6 MeV, ZBL calculated data are lower than those of our measurements; for C in C, ZBL calculated data are higher than those of our measurements when the energy is below 3 MeV. It should be noted that in most of our energy range no previous experimental data of stopping power exist to our knowledge in the literature for carbon ions in these six stoppers. 3.. Comparison to LSS theory Linhard and Schar published a formula to calculate the stopping cross section of heavy ions, which was called LSS formula.

4 7 T. Zheng et al. / Nucl. Instr. and Meth. in Phys. Res. B 35 (998) 69±74 Table Stopping power of C in C, Al, Cu, Ti, Nb, Ag (unit: MeV cm /mg) Carbon Aluminum Copper Titanium Niobium Silver E Se Se-ZBL

5 T. Zheng et al. / Nucl. Instr. and Meth. in Phys. Res. B 35 (998) 69±74 73 Table Fitted coe cients of C electronic stopping power Sample b b a a a 3 Fitting range C ) ±6.36 Al ) ±6.33 Ti ) ±6.6 Cu ) ±6. Nb ) ±6.5 Ag ±6.6 S e ˆ 8pe Z 7=6 a 0 Z 3= v v 0 ; v < v 0 ; where v is the velocity of incident ion; a 0 and v 0 are Bohr radius and Bohr velocity, respectively; Z and Z are the atomic number of incident ion and target material. According to LSS theory, the stopping power of low velocity heavy ions can be calculated as follows: de ˆ NS e ˆ 8pNe Z 7=6 Z v a 0 dx 3= ; e v 0 v < v 0 ; 3 where N is the atom density of the target. So the stopping power of low velocity heavy ions is directly proportional to the velocity. For C, this formula can be used in the energy range E < 3.7 MeV. We make a comparison between the experimental data and the calculated values of LSS theory. De ning the reduced velocity v red v= v 0 ; can be written as: S e ˆ 8pe Z =6 Z a 0 3= v red Z =6 Z ˆ 9:45 3= v red 0 5 ev cm ; v red < : 4 We also de ne the reduced electronic stopping cross section as: Fig. 3. Comparison of present results and LSS theory. 3 6 Z =6 Z 7 S red S e 4 3= 5 ; 5 so the LSS formula can be expressed as S red ˆ 9:45v red 0 5 ev cm ; v red < : 6 In Fig. 3 our experimental data are compared with that of LSS theory. For C in C, Al, Cu, present results t LSS theory well, but for C in Ti, Nb, Ag, there are great deviations, some of them have di erences around 50%, the theory greatly underestimates the stopping cross section. Although no previous data of Ti and Nb can o er testimony, the experimental measurements of Abdesselam et al. [7,8] and Porat et al. [5] for C in Ag support our conclusion Z -oscillation Our results clearly state that, similar to proton and a ion, the stopping power of low velocity heavy ion also changes frequently with the atomic number Z. The dependence of 3 MeV C electronic stopping power on the target atomic number Z is depicted in Fig. 4. The results of ZBL (solid curve) and LSS (dotted curve) calculations are also depicted. It is seen that in our stopping data appears a strong Z -oscillation. The ZBL calculation curve agrees with the experimental results quite well. The LSS calculation curve shows that the electronic stopping power S e changes with Z

6 74 T. Zheng et al. / Nucl. Instr. and Meth. in Phys. Res. B 35 (998) 69±74 Acknowledgements We would like to thank Xu Guoji for preparing the high quality foils. References Fig. 4. Dependence of C ion on Z. in a monotonous way. This is one of the shortcomings of the LSS theory. In conclusion, we measured the stopping powers for MeV carbon ions in Z ˆ 6±47 six targets using transmission technique. The data are compared with the predictions of ZBL semiempirical model. Better agreement was observed for Al target, while discrepancies were found for C, Ti, Cu, Nb and Ag stopping media. Compared with the LSS theory, for C in C, Al, Cu, present results t LSS theory well, but for C in Ti, Nb, Ag, there are great deviations. A strong Z -oscillation has been seen in the discussion, ZBL model can reproduce this phenomenon, but LSS theory cannot explain it. [] Z.Q. Wu, X.T. Lu, C.W Jin, Z.H. Xia, H.T. Liu, D.X. Jiang, Y.L. Ye, Chin. Phys. Lett. (9) (994) 537. [] J. Lindhard, M. Schar, H.E. Schiùtt, K. Dan. vidensk. selsk. Mat. Fys. Medd. 33 (963) 4. [3] J. Lindhard, M. Schar, Phys. Rev. 4 (96) 8. [4] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, vol., Pergamon Press, New York, 985; J.F. Ziegler, TRIM-9, IBM-Research, Yorktown, New York. [5] D.I. Porat, K. Ramavataram, Proc. Phys. Soc. London 77 (96) 97. [6] D.C. Santry, R.D. Werner, Nucl. Instr. and Meth. B 53 (99) 7. [7] M. Abdesselam, J.P. Stoquert, M. Hage-Ali, J.J. Grob, P. Si ert, Nucl. Instr. and Meth. B 73 (993) 5. [8] M. Abdesselam, J.P. Stoquert, G. Guillaume, M. Hage- Ali, J.J. Grob, P. Si ert, Nucl. Instr. and Meth. B 6 (99) 385. [9] C.W. Jin, X.T. Lu, X.J. Huang, Y.L. Ye, D.X. Jiang, H.T. Liu, Z.H. Xia, Nucl. Sci. and Tech. 4 (993) 4. [0] C.W. Jin, X.T. Lu, Z.H. Xia, H.T. Liu, D.X. Jiang, Y.L. Ye, Chin. Phys. Lett. 8 (99) 65.

The limits of volume reflection in bent crystals

The limits of volume reflection in bent crystals V.M. Biryukov Institute for High Energy Physics, Protvino, 142281, Russia Abstract We show that theory predictions for volume reflection in bent crystals