- Email: [email protected]
Target element dependence in the elastic and inelastic energy loss of fast heavy ions
ARTICLE IN PRESS
Radiation Physics and Chemistry 76 (2007) 537–541 www.elsevier.com/locate/radphyschem
Target element dependence in the elastic and inelastic energy loss of fast heavy ions O¨nder Kabadayi, Hasan Gu¨mu¨s-, M. C - ag˘atay Tufan Physics Department, Faculty of Arts and Sciences, Ondokuz Mayıs University, Samsun-Turkey Received 31 August 2005; accepted 10 February 2006
Abstract The target atomic number dependence of elastic and inelastic stopping power has been investigated by using theoretical stopping power formulations from literature. The stopping powers for target elements with atomic numbers from 3 to 92 are calculated on the basis of the model of Montenegro et al. and the nuclear stopping power is calculated using the formulation of Wilson et al.. The target atomic number dependence of the electronic and nuclear stopping power is examined for some light and heavy projectiles by comparing the stopping powers for all considered targets. It is observed that there is a strong target atomic number oscillation for helium, nickel and silver ions in nuclear and electronic stopping as a result of varying densities of neighboring elements. We have also determined the target materials, which apply a maximum total stopping force for some incident ions. r 2006 Elsevier Ltd. All rights reserved. PACS: 34.50.Bw; 61.18.Bn Keywords: Stopping power; Heavy ions; Energy loss
1. Introduction The energy loss of electrons, protons and heavy ions in matter has received considerable interest due to its various applications over decades. However, measurements of the stopping power experimentally for all ion–target combinations and for all energy intervals is impossible task to complete from experimental point of view; besides experimental studies are focused only on a limited number of ion–target combination. Therefore, theoretical analysis is essential in examining the stopping power variations for all ion and target combinations for all energies; but this is a hard task even from theoretical point of view because of the large data to be processed to complete stopping power calculations, e.g., 92 89 element combinations over the energy range 1 eV–1 GeV.
Corresponding author. Tel.: +90 362 4576020/5259; fax: +90 362 4576081. E-mail address: [email protected] (O¨. Kabadayi).
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2006.02.017
The target atomic number dependence (Z2) in the electronic stopping power is a well-known phenomenon and principally arises from the variations of the density for atoms of the neighboring elements (Gertner et al., 1980). There have been studies on Z2 dependence of the electronic stopping power in the literature (Gertner et al., 1980; Kaneko, 1984; Chu and Powers, 1972; Wilson et al., 1971; Ishikawa et al., 1992). However, most of the studies deal with a specific ion on a restricted energy value only and the target elements in consideration are restricted, and this fact makes a complete analysis of the phenomena impossible. E.g. Cowern et al. (1984) examined Z1 dependence of the stopping power for He, Li and C ions in a carbon target, Gertner et al. (1980) studied the Z2 oscillations for protons and alpha particles for target atomic numbers up to 54, but only for a few energy values. The Z2 dependence of stopping power was investigated theoretically for MeV helium and hydrogen ions by Kaneko (1984). Besides, there is a lack of investigation on Z2 dependence of nuclear stopping power in the literature because all of the above studies deal with
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electronic stopping power. In the present work, however, we take into consideration all of the target-projectile combinations (89 92) in a wide projectile energy range to investigate Z2 dependence of the electronic and nuclear stopping power. The purpose of this study is essentially to determine Z2 dependence of the elastic and inelastic stopping power by calculating the stopping powers for a complete set of ion and target elements. Moreover, we are also able to obtain the target material with a maximum stopping power for projectiles helium, nickel and silver projectiles. For this purpose, we have calculated the electronic stopping power for 89 different target elements over a large range of energies for the projectiles, He, Ni and Ag. It is also aimed here to find an ion– target combination that yields the biggest stopping power for a given energy value among the all ion and target combinations.
2. Electronic stopping power The average energy loss per unit path length, electronic stopping power, has long been studied to investigate the interaction of charged particles with matter. There have been a variety of models and formulas to calculate stopping powers for collisions with ions at high (E41 MeV/ nucleon), intermediate (100 keV/nucleon) and low (Eo10 keV/nucleon) energy ions (Bloch, 1933; Lindhard and Scharff, 1953; Sugiyama, 1981; Firsov, 1959). Montenegro et al. (1982) developed an analytic expression from a semi-phenomenological approach based on the theoretical and experimental results of the electronic stopping power for ions. Although this equation was obtained through a semi-phenomenological analysis of different mechanisms, its final form does not depend on any adjustable parameters and is valid for all the energy region: au 1=6aue2au 2 2 ½1 e Se ¼ Z1 (1) Sp , ½1 eu 1=6ue2u 2
a ¼ 8pa30 I H Z 2 .
2 2 2 e ¼ 3b2 d=ðZ 1:4 2 bd þ b þ d Þ,
f ¼ ce3 =d, g ¼ 2b=3c, c ¼ ab, u ¼ v=v0 ,
ð4Þ
where Z 2 is the number of external electrons in the target atom with the orbital velocity of the order of v0. However, O¨ztu¨rk et al. (1989) found out the wrong derivation of d and gave the correct form as d ¼ K=c þ b=2 þ Z 2 =9bZ2 .
(5)
They found b in the last term in the original expression for d of Montenegro et al. (1982) is missing. The change of coefficient d will also affect the derivation of e and f. Their revision of the equation led to a difference of stopping power values up to 30% compared to previous results. They found that their formulation and experimental values agree well with experiment for their formulation and the formula has been widely used by many researchers. In this work, we have used the corrected version of formulas of Montenegro et al. as given by O¨ztu¨rk et al. (1989) for calculating electronic stopping powers for all ion and target elements. In calculating the stopping powers, SCOEF03 data within SRIM program (Ziegler, 2003) is employed for densities and atomic mass of all elements.
3. Nuclear stopping power
ð2Þ (3)
Sn ðEÞ ¼ sðÞ
S p ¼ Kueu þ au2 lnð1 þ bu2 Þ cð1 þ du2 Þ1
b ¼ 4I H =hIi;
d ¼ K=c þ b=2 þ Z 2 =9Z2 ,
The theory of nuclear stopping power is based on Bohr’s (Bohr, 1948) pioneering work. However, a number of semiempirical and theoretical formulations have been presented over the decades. In fact, the main difference in these formulations comes from the evaluation of interatomic potential. Among these formulations, a formula by Wilson et al. (1977) is frequently used in the literature and this step produce results in good agreement with the experiment. The nuclear stopping power for any projectile energy in this formula is given by
where Sp is the proton stopping cross section given by
þ fu4 ð1 þ eu2 Þ3 bðgu2 Þ3=2 ð1 þ gu2 Þ4 =6b2 ,
coefficients in Eq. (2) are
Here we have b ¼ a=ð9:5616Z 2 Þ, Z1 is the projectile 2=3 atomic number, a ¼ Z 1 , and u ¼ v=v0 , v is the velocity of the ion and v0 is the Bohr velocity. The constant K in Eq. (2) is obtained from Montenegro et al. while a and b are obtained from The Bethe (1930) theory. Z2 is the target atomic number, a0 is the Bohr radius, /IS is the mean ionization potential for the target atom and IH is the hydrogen atom ionization energy. Other
8:462Z1 Z2 M 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , 2=3 2=3 ðM 1 þ M 2 Þ Z1 þ Z2
(6)
where the reduced projectile energy is given by ¼
32:53M 2 E qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . 2=3 2=3 Z1 Z 2 ðM 1 þ M 2 Þ Z 1 þ Z 2
(7)
In this equation, M1 and M2 are projectile and target masses and Z1 and Z2 are projectile and target atomic
ARTICLE IN PRESS O¨. Kabadayi et al. / Radiation Physics and Chemistry 76 (2007) 537–541
539
numbers. The reduced stopping power is given by sðÞ ¼
1 lnð1 þ Þ . 2 ð þ 0:107180:37544 Þ
(8)
E is the energy of incoming ion in keV units. 4. Results and discussion Based on the formulas presented above, we have investigated target atomic number dependence of the electronic and nuclear stopping power. In Fig. 1 a plot of the electronic stopping power is given for helium ions in all target materials. The electronic stopping power for helium is calculated on the basis of corrected Montenegro et al. formula for 89 different target materials from Z 2 ¼ 3–92 for energies up to 5 MeV/nucleon. An inspection of Fig. 1 reveals that well-known Z2 oscillations occurs as a result of varying densities and the other properties such as ionization potential of neighboring atoms. It is also found that the electronic stopping power has five peak values at Z2 ¼ 92U, 76Os, 43Tc, 28Ni, and 5B, among the other target materials. We are able to determine the material that causes a maximum stopping power value for helium ions by comparing the data obtained for the stopping power of all targets. The result of this comparison shows that the stopping power for helium projectile is the largest for osmium target, which is the densest naturally occurring element. Fig. 2 shows a 3D plot of the nuclear stopping power for helium ions in all elemental targets. A comparison of data in Fig. 2 shows that the maximum stopping power occurs for Boron target. However, the other large stopping values are obtained at elements 76Os and 28Ni. It is evident from comparison of Figs. 1 and 2 that the oscillations are small in the case of nuclear stopping power when they are compared with the electronic stopping power.
Fig. 2. Nuclear stopping power for helium in targets Z2 ¼ 3 to 92 for energies up to 10 keV/nucleon.
Fig. 3. Electronic and nuclear stopping power for energies up to 10 keV/ nucleon. Gray and white colors show nuclear and electronic stopping powers for helium projectiles, respectively.
Fig. 1. Electronic stopping power for helium for targets Z2 ¼ 3 to 92.
In Fig. 3, we plot the nuclear and electronic stopping powers for helium ions on the same graph for comparison. The results are drawn for energies up to 5 keV/nucleon since the nuclear stooping power is important only at small
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Fig. 5. Electronic and nuclear stopping power of silver ions for energies up to 3 MeV/nucleon. Gray and white colors show nuclear and electronic stopping powers, respectively. Fig. 4. Electronic and nuclear stopping power of nickel ions for energies up to 1 MeV/nucleon. Gray and white colors show nuclear and electronic stopping powers, respectively.
energies and electronic energy loss dominates at higher energies. It can be seen in Fig. 3 that the electronic stopping is dominant even in low energies for targets with atomic numbers larger than 38. However, it is seen that the nuclear stopping power is larger than the electronic stopping power for energies lesser than 10 keV and for targets with atomic numbers lesser than 38. In Fig. 4, we plot the electronic and nuclear stopping power, together for nickel ions, to compare these for low energies. It is clear that the electronic stopping power dominates at higher energies. However, the nuclear stopping power dominates for all targets at low energies and this situation is different from that we found in the case of helium projectiles. In Fig. 5, the electronic and nuclear stopping powers for silver projectiles are given for varying energies and target atomic numbers. It is seen from Fig. 5 that nuclear stopping power is larger than electronic stopping power for all targets at low energies. The nuclear stopping power decreases with increasing energy after passing through a maximum. The oscillations in the nuclear and electronic stopping powers are similar in a way that maximum and minimum values of oscillations occur at the same target materials for both stopping powers. In Fig. 6, we plot the electronic and nuclear stopping power for all Z1 projectiles in all Z2 targets in a constant energy of any projectile. It is evident from Fig. 6 that oscillations in the electronic and nuclear stopping power for various targets are similar for all Z1 projectiles. From analysis of the data in Fig. 6, it is also possible to determine the ion–target combination that yields the biggest stopping
Fig. 6. All Z1 ions in all Z2 targets at a fixed energy value of 500 MeV/ nucleon. Gray and white colors show nuclear and electronic stopping powers, respectively.
power for the given energy value. The electronic stopping power is found to be the largest for Z 1 ¼ 20 (calcium) and Z2 ¼ 76 (osmium) at 12.5 MeV/nucleon. It is also seen from Fig. 6 that the electronic stopping power is increasing with Z1 and after passing through a maximum decreases with increasing projectile atomic number; besides there have been some small oscillations in the electronic stopping power for different Z1’s. 5. Conclusion The results on target element dependence of the electronic and nuclear stopping power are presented by
ARTICLE IN PRESS O¨. Kabadayi et al. / Radiation Physics and Chemistry 76 (2007) 537–541
calculating stopping powers for all ion–target combinations. It is found that strong Z2 oscillations occur in the electronic and nuclear stopping power for all considered energies. The behaviors of the electronic and nuclear stopping power are similar with respect to Z2 variations. However, the electronic stopping shows small oscillations with Z1, especially near the stopping power maximum. It is found that for ions nickel and silver, the nuclear stopping power is larger than the electronic stopping power at low energies. However, it is interesting to observe that the electronic stopping power is larger than the nuclear stopping power even in the low energies for helium ions for targets with atomic numbers larger than 38. References Bethe, H.A., 1930. Zur theorie des durchangs schneller korpuskularstrahlen durch materie. Ann. Phys. 5, 325–400. Bloch, F., 1933. Zur bremsung rasch bewegter teilchen beim durchgang durch materie. Ann. Phys. 16, 285–320. Bohr, N., 1948. The penetratıon of atomic particles through matter. K. Dan Vidensk Selsk Mat. Fys. Medd. 18, 8. Chu, W.K., Powers, D., 1972. Z2 dependence of stopping cross section for low-energy alpha partiles. Phys. Lett. A 38 (4), 267–268. Cowern, N.E.B., Read, P.M., Soifeld, C.J., Bridwell, L.B., Lucas, M.W., 1984. Charge-chaning energy loss, higher order Z1 dependence, and
541
pre-equilibrium behavior in the stopping power for energetic ions in solids. Phys. Rev. A 30 (4), 1682–1691. Firsov, O.B., 1959. Qualitative interpretation of the mean electron excitation energy in atomic collisions. Zh. Ekzo. Teor. Fiz. 36, 1571 (Sov. Phys. JET, 1076–1080. p. 36). Gertner, I., Meron, M., Rosner, B., 1980. Z2 oscillations and target– structure effects in the electronic stopping cross section of heavy ions in solids. Phys. Rev. A 21 (4), 1191–1195. Ishikawa, H., Misu, A., Koyama, A., et al., 1992. Z2-dependence of energy-spectra of electrons excited by fast heavy ions incident at grazing angle. Nucl. Instr. Meth. B 67 (1–4), 160–163. Kaneko, T., 1984. Z2 dependence of the stopping power and the effective charge for MeV helium-ion beams. Phys. Rev. A 30 (4), 1714–1720. Lindhard, J., Scharff, M., 1953. Energy loss in matter by fast particles of low charge. K. Dan Vidensk Selsk Mat. Fys. Medd. 27 (15), 1–31. Montenegro, E.C., Cruz, S.A., Vargas-Aburto, C., 1982. A universal equation for the electronic stopping of ions in solids. Phys. Lett. 92A (4), 195–202. O¨ztu¨rk, N., Williamson, W., Antolak, A.J., 1989. Electronic stopping power of ions in solids. Phys. Lett. A 139, 507–508. Sugiyama, H., 1981. Electronic stopping power formula for intermediate energies. Radiat. Eff. 56, 205–211. Wilson, W.D., Hatcher, R.D., Bisson, C.L., 1971. Z2 dependence of alphaparticle electronic stopping. Bull. Am. Phys. Soc. 16 (3), 333–335. Wilson, W.D., Haggmark, L.G., Biersack, J.P., 1977. Calculations of nuclear stopping, ranges, and straggling in low energy region. Phys. Rev. B 5 (15), 2458–2468. Ziegler, J.F., 2003. SRIM2003 program, Stopping and Ranges Ions in Matter. version 2003.26, /www.srim.orgS.
Radiation Physics and Chemistry 76 (2007) 537–541 www.elsevier.com/locate/radphyschem
Target element dependence in the elastic and inelastic energy loss of fast heavy ions O¨nder Kabadayi, Hasan Gu¨mu¨s-, M. C - ag˘atay Tufan Physics Department, Faculty of Arts and Sciences, Ondokuz Mayıs University, Samsun-Turkey Received 31 August 2005; accepted 10 February 2006
Abstract The target atomic number dependence of elastic and inelastic stopping power has been investigated by using theoretical stopping power formulations from literature. The stopping powers for target elements with atomic numbers from 3 to 92 are calculated on the basis of the model of Montenegro et al. and the nuclear stopping power is calculated using the formulation of Wilson et al.. The target atomic number dependence of the electronic and nuclear stopping power is examined for some light and heavy projectiles by comparing the stopping powers for all considered targets. It is observed that there is a strong target atomic number oscillation for helium, nickel and silver ions in nuclear and electronic stopping as a result of varying densities of neighboring elements. We have also determined the target materials, which apply a maximum total stopping force for some incident ions. r 2006 Elsevier Ltd. All rights reserved. PACS: 34.50.Bw; 61.18.Bn Keywords: Stopping power; Heavy ions; Energy loss
1. Introduction The energy loss of electrons, protons and heavy ions in matter has received considerable interest due to its various applications over decades. However, measurements of the stopping power experimentally for all ion–target combinations and for all energy intervals is impossible task to complete from experimental point of view; besides experimental studies are focused only on a limited number of ion–target combination. Therefore, theoretical analysis is essential in examining the stopping power variations for all ion and target combinations for all energies; but this is a hard task even from theoretical point of view because of the large data to be processed to complete stopping power calculations, e.g., 92 89 element combinations over the energy range 1 eV–1 GeV.
Corresponding author. Tel.: +90 362 4576020/5259; fax: +90 362 4576081. E-mail address: [email protected] (O¨. Kabadayi).
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2006.02.017
The target atomic number dependence (Z2) in the electronic stopping power is a well-known phenomenon and principally arises from the variations of the density for atoms of the neighboring elements (Gertner et al., 1980). There have been studies on Z2 dependence of the electronic stopping power in the literature (Gertner et al., 1980; Kaneko, 1984; Chu and Powers, 1972; Wilson et al., 1971; Ishikawa et al., 1992). However, most of the studies deal with a specific ion on a restricted energy value only and the target elements in consideration are restricted, and this fact makes a complete analysis of the phenomena impossible. E.g. Cowern et al. (1984) examined Z1 dependence of the stopping power for He, Li and C ions in a carbon target, Gertner et al. (1980) studied the Z2 oscillations for protons and alpha particles for target atomic numbers up to 54, but only for a few energy values. The Z2 dependence of stopping power was investigated theoretically for MeV helium and hydrogen ions by Kaneko (1984). Besides, there is a lack of investigation on Z2 dependence of nuclear stopping power in the literature because all of the above studies deal with
ARTICLE IN PRESS O¨. Kabadayi et al. / Radiation Physics and Chemistry 76 (2007) 537–541
538
electronic stopping power. In the present work, however, we take into consideration all of the target-projectile combinations (89 92) in a wide projectile energy range to investigate Z2 dependence of the electronic and nuclear stopping power. The purpose of this study is essentially to determine Z2 dependence of the elastic and inelastic stopping power by calculating the stopping powers for a complete set of ion and target elements. Moreover, we are also able to obtain the target material with a maximum stopping power for projectiles helium, nickel and silver projectiles. For this purpose, we have calculated the electronic stopping power for 89 different target elements over a large range of energies for the projectiles, He, Ni and Ag. It is also aimed here to find an ion– target combination that yields the biggest stopping power for a given energy value among the all ion and target combinations.
2. Electronic stopping power The average energy loss per unit path length, electronic stopping power, has long been studied to investigate the interaction of charged particles with matter. There have been a variety of models and formulas to calculate stopping powers for collisions with ions at high (E41 MeV/ nucleon), intermediate (100 keV/nucleon) and low (Eo10 keV/nucleon) energy ions (Bloch, 1933; Lindhard and Scharff, 1953; Sugiyama, 1981; Firsov, 1959). Montenegro et al. (1982) developed an analytic expression from a semi-phenomenological approach based on the theoretical and experimental results of the electronic stopping power for ions. Although this equation was obtained through a semi-phenomenological analysis of different mechanisms, its final form does not depend on any adjustable parameters and is valid for all the energy region: au 1=6aue2au 2 2 ½1 e Se ¼ Z1 (1) Sp , ½1 eu 1=6ue2u 2
a ¼ 8pa30 I H Z 2 .
2 2 2 e ¼ 3b2 d=ðZ 1:4 2 bd þ b þ d Þ,
f ¼ ce3 =d, g ¼ 2b=3c, c ¼ ab, u ¼ v=v0 ,
ð4Þ
where Z 2 is the number of external electrons in the target atom with the orbital velocity of the order of v0. However, O¨ztu¨rk et al. (1989) found out the wrong derivation of d and gave the correct form as d ¼ K=c þ b=2 þ Z 2 =9bZ2 .
(5)
They found b in the last term in the original expression for d of Montenegro et al. (1982) is missing. The change of coefficient d will also affect the derivation of e and f. Their revision of the equation led to a difference of stopping power values up to 30% compared to previous results. They found that their formulation and experimental values agree well with experiment for their formulation and the formula has been widely used by many researchers. In this work, we have used the corrected version of formulas of Montenegro et al. as given by O¨ztu¨rk et al. (1989) for calculating electronic stopping powers for all ion and target elements. In calculating the stopping powers, SCOEF03 data within SRIM program (Ziegler, 2003) is employed for densities and atomic mass of all elements.
3. Nuclear stopping power
ð2Þ (3)
Sn ðEÞ ¼ sðÞ
S p ¼ Kueu þ au2 lnð1 þ bu2 Þ cð1 þ du2 Þ1
b ¼ 4I H =hIi;
d ¼ K=c þ b=2 þ Z 2 =9Z2 ,
The theory of nuclear stopping power is based on Bohr’s (Bohr, 1948) pioneering work. However, a number of semiempirical and theoretical formulations have been presented over the decades. In fact, the main difference in these formulations comes from the evaluation of interatomic potential. Among these formulations, a formula by Wilson et al. (1977) is frequently used in the literature and this step produce results in good agreement with the experiment. The nuclear stopping power for any projectile energy in this formula is given by
where Sp is the proton stopping cross section given by
þ fu4 ð1 þ eu2 Þ3 bðgu2 Þ3=2 ð1 þ gu2 Þ4 =6b2 ,
coefficients in Eq. (2) are
Here we have b ¼ a=ð9:5616Z 2 Þ, Z1 is the projectile 2=3 atomic number, a ¼ Z 1 , and u ¼ v=v0 , v is the velocity of the ion and v0 is the Bohr velocity. The constant K in Eq. (2) is obtained from Montenegro et al. while a and b are obtained from The Bethe (1930) theory. Z2 is the target atomic number, a0 is the Bohr radius, /IS is the mean ionization potential for the target atom and IH is the hydrogen atom ionization energy. Other
8:462Z1 Z2 M 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , 2=3 2=3 ðM 1 þ M 2 Þ Z1 þ Z2
(6)
where the reduced projectile energy is given by ¼
32:53M 2 E qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . 2=3 2=3 Z1 Z 2 ðM 1 þ M 2 Þ Z 1 þ Z 2
(7)
In this equation, M1 and M2 are projectile and target masses and Z1 and Z2 are projectile and target atomic
ARTICLE IN PRESS O¨. Kabadayi et al. / Radiation Physics and Chemistry 76 (2007) 537–541
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numbers. The reduced stopping power is given by sðÞ ¼
1 lnð1 þ Þ . 2 ð þ 0:107180:37544 Þ
(8)
E is the energy of incoming ion in keV units. 4. Results and discussion Based on the formulas presented above, we have investigated target atomic number dependence of the electronic and nuclear stopping power. In Fig. 1 a plot of the electronic stopping power is given for helium ions in all target materials. The electronic stopping power for helium is calculated on the basis of corrected Montenegro et al. formula for 89 different target materials from Z 2 ¼ 3–92 for energies up to 5 MeV/nucleon. An inspection of Fig. 1 reveals that well-known Z2 oscillations occurs as a result of varying densities and the other properties such as ionization potential of neighboring atoms. It is also found that the electronic stopping power has five peak values at Z2 ¼ 92U, 76Os, 43Tc, 28Ni, and 5B, among the other target materials. We are able to determine the material that causes a maximum stopping power value for helium ions by comparing the data obtained for the stopping power of all targets. The result of this comparison shows that the stopping power for helium projectile is the largest for osmium target, which is the densest naturally occurring element. Fig. 2 shows a 3D plot of the nuclear stopping power for helium ions in all elemental targets. A comparison of data in Fig. 2 shows that the maximum stopping power occurs for Boron target. However, the other large stopping values are obtained at elements 76Os and 28Ni. It is evident from comparison of Figs. 1 and 2 that the oscillations are small in the case of nuclear stopping power when they are compared with the electronic stopping power.
Fig. 2. Nuclear stopping power for helium in targets Z2 ¼ 3 to 92 for energies up to 10 keV/nucleon.
Fig. 3. Electronic and nuclear stopping power for energies up to 10 keV/ nucleon. Gray and white colors show nuclear and electronic stopping powers for helium projectiles, respectively.
Fig. 1. Electronic stopping power for helium for targets Z2 ¼ 3 to 92.
In Fig. 3, we plot the nuclear and electronic stopping powers for helium ions on the same graph for comparison. The results are drawn for energies up to 5 keV/nucleon since the nuclear stooping power is important only at small
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Fig. 5. Electronic and nuclear stopping power of silver ions for energies up to 3 MeV/nucleon. Gray and white colors show nuclear and electronic stopping powers, respectively. Fig. 4. Electronic and nuclear stopping power of nickel ions for energies up to 1 MeV/nucleon. Gray and white colors show nuclear and electronic stopping powers, respectively.
energies and electronic energy loss dominates at higher energies. It can be seen in Fig. 3 that the electronic stopping is dominant even in low energies for targets with atomic numbers larger than 38. However, it is seen that the nuclear stopping power is larger than the electronic stopping power for energies lesser than 10 keV and for targets with atomic numbers lesser than 38. In Fig. 4, we plot the electronic and nuclear stopping power, together for nickel ions, to compare these for low energies. It is clear that the electronic stopping power dominates at higher energies. However, the nuclear stopping power dominates for all targets at low energies and this situation is different from that we found in the case of helium projectiles. In Fig. 5, the electronic and nuclear stopping powers for silver projectiles are given for varying energies and target atomic numbers. It is seen from Fig. 5 that nuclear stopping power is larger than electronic stopping power for all targets at low energies. The nuclear stopping power decreases with increasing energy after passing through a maximum. The oscillations in the nuclear and electronic stopping powers are similar in a way that maximum and minimum values of oscillations occur at the same target materials for both stopping powers. In Fig. 6, we plot the electronic and nuclear stopping power for all Z1 projectiles in all Z2 targets in a constant energy of any projectile. It is evident from Fig. 6 that oscillations in the electronic and nuclear stopping power for various targets are similar for all Z1 projectiles. From analysis of the data in Fig. 6, it is also possible to determine the ion–target combination that yields the biggest stopping
Fig. 6. All Z1 ions in all Z2 targets at a fixed energy value of 500 MeV/ nucleon. Gray and white colors show nuclear and electronic stopping powers, respectively.
power for the given energy value. The electronic stopping power is found to be the largest for Z 1 ¼ 20 (calcium) and Z2 ¼ 76 (osmium) at 12.5 MeV/nucleon. It is also seen from Fig. 6 that the electronic stopping power is increasing with Z1 and after passing through a maximum decreases with increasing projectile atomic number; besides there have been some small oscillations in the electronic stopping power for different Z1’s. 5. Conclusion The results on target element dependence of the electronic and nuclear stopping power are presented by
ARTICLE IN PRESS O¨. Kabadayi et al. / Radiation Physics and Chemistry 76 (2007) 537–541
calculating stopping powers for all ion–target combinations. It is found that strong Z2 oscillations occur in the electronic and nuclear stopping power for all considered energies. The behaviors of the electronic and nuclear stopping power are similar with respect to Z2 variations. However, the electronic stopping shows small oscillations with Z1, especially near the stopping power maximum. It is found that for ions nickel and silver, the nuclear stopping power is larger than the electronic stopping power at low energies. However, it is interesting to observe that the electronic stopping power is larger than the nuclear stopping power even in the low energies for helium ions for targets with atomic numbers larger than 38. References Bethe, H.A., 1930. Zur theorie des durchangs schneller korpuskularstrahlen durch materie. Ann. Phys. 5, 325–400. Bloch, F., 1933. Zur bremsung rasch bewegter teilchen beim durchgang durch materie. Ann. Phys. 16, 285–320. Bohr, N., 1948. The penetratıon of atomic particles through matter. K. Dan Vidensk Selsk Mat. Fys. Medd. 18, 8. Chu, W.K., Powers, D., 1972. Z2 dependence of stopping cross section for low-energy alpha partiles. Phys. Lett. A 38 (4), 267–268. Cowern, N.E.B., Read, P.M., Soifeld, C.J., Bridwell, L.B., Lucas, M.W., 1984. Charge-chaning energy loss, higher order Z1 dependence, and
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