- Email: [email protected]
u light ions
Nuclear Instruments and Methods in Physics Research B 354 (2015) 96–99
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Forward–backward correlated secondary electron emission depending on the emergence angle of 1 MeV/u light ions H. Ogawa a,⇑, S. Amano b, K. Ishii a, T. Kaneko c a
Dept. of Physics, Nara Women’s Univ., Nara 630-8506, Japan Graduate School of Hum. and Sci., Nara Women’s Univ., Nara 630-8506, Japan c Graduate School of Science, Okayama Univ. of Science, Okayama 700-0005, Japan b
a r t i c l e
i n f o
Article history: Received 4 July 2014 Received in revised form 29 August 2014 Accepted 12 September 2014 Available online 3 October 2014 Keywords: Secondary electron Emission statistics Energy loss
a b s t r a c t The statistical distributions of the number of forward- and backward-emitted secondary electrons (SE’s) from a thin carbon foil have been measured simultaneously in coincidence with foil-transmitted 1H+, 4 He2+ and 6Li3+ at a fixed velocity of 1 MeV/u. The emergence angles of the projectiles, hem , were varied from 0 to 2 [mrad] for H+ and from 0 to 1 [mrad] for He2+ and Li3+ ions. Irrespective of ion species, measured total SE yields, that is, the average number of simultaneous emitted electrons per projectile, increase with increasing hem both in the forward and backward directions. This trend is consistent with the calculated hem -dependent energy losses of protons penetrating a thin carbon foil. As for the forwardor backward-emitted SE yields, we have obtained a negative forward–backward(F–B) correlation, except for the hem ¼ 0:0 [mrad] emergence of H+ projectiles where a positive correlation has been observed. The negative F–B correlation becomes prominent with increasing the atomic number of the projectile, Z p . In addition, this correlation appears to become slightly stronger with increasing hem . The observed F–B correlation and its Z p - and hem -dependences are interpreted from the point of view of production of high energy internal SE’s. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Kinetic emission of secondary electrons (SE’s) from solid surface under fast ion bombardments has been studied intensively for a long time [1,2]. Sternglass has proposed the following three-step model for this phenomenon; First, the creation of excited electrons via collisions of projectiles with target atoms in the solid. Second, the transport of liberated electrons through the bulk to the surface including higher order ionizations by high energy internal SE’s (cascade multiplication). Finally, the transmission through the surface potential barrier [3]. According to this scenario, the SE yields c, that is the average number of the emitted SE’s per projectile, is proportional to the electronic stopping power Se as
c ¼ K Se
ð1Þ
where K is the so-called material parameter that depends only on the target material. As far as the proton-incidence on carbon foils is concerned, it was experimentally certified by the conventional current measurement that K is constant over a wide energy range from 0.02 to 10 MeV [4]. ⇑ Corresponding author. Tel./fax: +81 742 20 3380. E-mail address: [email protected] (H. Ogawa). http://dx.doi.org/10.1016/j.nimb.2014.09.025 0168-583X/Ó 2014 Elsevier B.V. All rights reserved.
As for the method to measure the SE emission, the measurement of the emission statistics is an alternative one that was firstly employed by Krebs [5]. It can also determine the probability of n SE emission and has been applied to the basic research on ion-surface interactions [6–8]. Especially, the simultaneous measurement of emitted SEs from both the beam-entrance (refer to as ‘‘backward’’ hereafter) and -exit (refer to as ‘‘forward’’ hereafter) surfaces of a thin foil may bring about quite a valuable information on the forward–backward correlation (refer to as ‘‘F–B correlation’’ hereafter) characterizing specific collisions in the foil. There also exists an experiment by Barrué et al. that investigates the correlation between the energy loss and the SE emission directly. They measured the number distributions of forward and backward emitted SEs in coincidence with the energy loss and the outgoing charge state of the projectile heavy ions in channeling and also in random incidence [9]. By the way, it is well known that the energy losses of the incident particles in a target foil depend on the emergent-angle, hem , of them due to the impact parameter dependence of the energy loss [10–17]. Judging from a close relation between the energy loss and the SE emission [4], it is easily predictable that the SE emission also depends on the impact parameter or, in other word, the scattering angle of the incident ions. This expectation has been
H. Ogawa et al. / Nuclear Instruments and Methods in Physics Research B 354 (2015) 96–99
certified as correct by our measurement of the hem -dependent SE yields of foil-transmitted protons [18]. As an extension of the above work, the forward and backward emitted SEs have been measured simultaneously in coincidence with the foil-transmitted protons in order to investigate the hem -dependent F–B correlations [19]. In the present work, a similar measurement has been carried out with 4He2+ and 6Li3+ beams of 1 MeV/u in order to examine how the F–B correlation and its hem -dependence varies with the atomic number of the projectile, Zp . 2. Experiment The experiment was performed using 1 MeV/u 1H+, 4He2+ and Li3+ ions obtained with a 1.7-MV tandem Van de Graaff accelerator at Nara Women’s University. The beam was transported to a target carbon foil using the method described in Ref. [20]. The incident beam was collimated with two diaphragms of 0.2 mm in diameter and 224 cm apart. A baffle of 1.2 mm in diameter was placed about 5 cm behind the second diaphragm to prevent edge-scattered particles from hitting the target. The target foil was placed 7 cm behind the baffle and tilted by 45° relative to the normal angle of incidence. The foil was floated at a potential of 30 kV. The emitted electrons were accelerated to a grounded electrode that was parallel to the foil and 40 mm apart from the target. At the grounded electrode a solid-state Si detector (SSD) of 100 mm2 sensitive area faced the target foil. The thickness of the carbon target foil was determined by measuring the transmitted fraction of 2.5 MeV H0, while accounting for the electron loss and capture cross sections involved [21]. The thickness of the present carbon was found to be 4.0 ± 0.2 l g/cm2. This pffiffiffi value is that tilted by 45° from the normal to the surface and is 2 times of that for the normal incidence which is estimated to be 2.8 ± 0.2 lg/cm2. The same system as our previous work was employed for the detection of foil-transmitted protons as a function of hem [20]. We have used independently movable vertical and horizontal slits, the widths of which were about 0.3 mm. Thus, the hem -resolved projectiles were detected by a Si photo diode (PD) of 800 mm2 sensitive area. The measurement with He2+ and Li3+ beams were carried out from hem = 0.0 to 1.0 [mrad] by 0.5 [mrad] step. In this connection, the measurement with proton beams was carried out from hem = 0.0 to 2.0 [mrad] by 1.0 [mrad] step [19]. In the center of mass frame, the impact parameter b and the scattering angle hcm satisfy the following relation,
97
statistics [22]. With these probabilities, the forward (backward) SE yields, cF ðnB Þ (cB ðnF Þ), gated by nB (nF ) are given as nF;max
cF ðnB Þ ¼
X
nF PðnF ; nB Þ
ð5Þ
nB PðnF ; nB Þ
ð6Þ
nF ¼1
nB;max
cB ðnF Þ ¼
X
nB ¼1
where nF;max (nB;max ) denotes the maximum number of forward(backward-) emitted SEs per projectile observed in the spectra. In the present case, typical numbers of nF;max and nB;max were about 15, 20 and 25 for H+, He2+ and Li3+, respectively.
6
b¼
Z p Z T e2 cotðhcm =2Þ mv 2
3. Results and discussion Before discussing the F–B correlation of the SE emission and its hem -dependence, the calculated angular distribution of 1 MeV/u projectiles transmitted through a carbon foil of 4.0 lg/cm2 are shown in Fig. 1. Black, red and blue solid curves represent the results for H+, He2+ and Li3+, respectively evaluated by the theory of multiple scattering by Sigmund and Winterbon [23]. It should be noted that the distributions for 4He2+ and 6Li3+ ions of the same velocity agree completely with each other because they have the same ratio of the charge to the mass number. Corresponding dashed curves are those calculated for a single scattering by a screening potential of the following form,
VðrÞ ¼
Z P Z T e2 r exp aTF r
ð7Þ
where e and aTF denote the elementary charge and the Thomas– Fermi screening radius, respectively. Here, we have to mention that the scattering yields calculated by using Eq. (7) are quite rough estimations. As is clear from this figure, hem of projectiles exiting at angles larger than 0.5 [mrad] are determined substantially by a single collision of a small impact parameter in the foil for 1 MeV/u He2+ and Li3+, although they suffer multiple scattering in the foil. Combining this result with that given in Fig. 4 of Ref. [19], not only H+ but also He2+ and Li3+ ions observed at
ð2Þ
where Z T ; m and v denote the atomic number of the target atom, the reduced mass of the projectile and the target atom and the velocity of the projectile, respectively. Furthermore, when hcm 1, the scattering angle in the laboratory frame, hlab , can be related to hcm as
hlab ¼
m hcm Mp
ð3Þ
Therefore the following relation holds,
b hlab /
Zp Mp
ð4Þ
Therefore the present experiments with He and Li ions have investigated the same impact parameter region as that with the 1 MeV proton. For the quantitative comparison of the F–B correlation, we have evaluated the emission probability, PðnF ; nB Þ, for nF and nB electrons emitted simultaneously in the forward and backward directions, respectively, from the two-dimensional spectra of the emission
Fig. 1. The angular distribution due to multiple scattering of 1 MeV/u 4He2+ and 6 3+ Li ions penetrating a carbon foil of 4.0 ± 0.2 lg/cm2 in thickness. Solid curves are obtained with a theory of the multiple scattering by Sigmund and Winterbon [23]. For comparison, the scattering yields assuming a single scattering by a screened Coulomb potential given by Eq. (3) are also presented by the corresponding dashed curves.
98
H. Ogawa et al. / Nuclear Instruments and Methods in Physics Research B 354 (2015) 96–99
non-zero hem have been supposed to penetrate deeply inside the Kshell electron cloud of the carbon atom in the foil. Hereafter we move on to the discussion on the F–B correlation of the SE emission observed in the present results. Fig. 2(a) and (b) represents the cF ðnB Þ and cB ðnF Þ, respectively, obtained by the present experiment with 1 MeV/u He2+ ions. Similarly, Fig. 3(a) and (b) shows those with 1 MeV/u Li3+ ions. In this connection the corresponding results for 1 MeV proton are presented in Fig. 5(a) and (b) of Ref. [19]. In these figures, squares, circles and triangles represent the data for hem = 0.0, 0.5 and 1.0 [mrad], respectively. The associated error of each data point includes only the statistical one. In order to make the variation of cF ðnB Þ (cB ðnF Þ) with nB (nF ) conspicuous, the measured value of cF ðnB Þ (cB ðnF Þ) were least square fitted on trial with a linear function of nB (nF ) assuming the following relation as,
cF ðnB Þ ¼ aF þ bF nB
ð8Þ
and
cB ðnF Þ ¼ aB þ bB nF :
ð9Þ
For He and Li ions, cF ðnB Þ and cB ðnF Þ exhibit a negative correlation(i.e. bF ; bB < 0) at every hem observed. As is discussed in our previous paper [24], the sign of the F–B correlation seems to be quite
Fig. 3. Same as Fig. 2 except that the projectiles are 1 MeV/u 6Li3+. Solid lines represent the least square fittings to (a) cF ðnB Þ of nB = 2 to 10 and (b) cB ðnF Þ of nF = 2 to 10 for each hem .
Fig. 2. The hem -dependence of the F–B correlation in the measured SE emission from a carbon foil of 4.0 ± 0.2 lg/cm2 induced by 1 MeV/u 4He2+ penetration. (a) The forward SE yields, cF ðnB Þ, as a function of nB , and (b) the backward SE yields, cB ðnF Þ, as a function of nF . Solid squares, circles and triangles are the results for hem = 0.0, 0.5 and 1.0 [mrad], respectively. Solid lines represent the least square fittings to (a) cF ðnB Þ and (b) cB ðnF Þ for each hem .
sensitive to the ratio of the range of the internal high energy SEs to the target thickness. The binary electrons that have a range comparable to or larger than the foil thickness can bring about the positive FB correlation by cascading ionization. On the other hand, those with a range significantly smaller than the foil thickness can participate only in the forward or backward SE emission depending on the position of its production. For the projectile velocity of 1 MeV/ u, the contribution of the latter seems to be predominant and the negative correlation comes out. In this connection, the correlation is expected to change from negative to positive(i.e. bF ; bB > 0) with increasing the projectile velocity [24]. In order to examine the obtained F–B correlation quantitatively, values of bB and bF are presented for H+, He2+ and Li3+ ions in Fig. 4(a) and (b), respectively as a function of hem . In these figures, squares, circles and triangles represent the values for H+, He2+ and Li3+ ions, respectively. In order to make the hem -dependence clear, the values of bF and bB at hem = 0 [mrad] are presented with horizontal lines. From these figures, it is clear that the negative correlation becomes more prominent with increasing Z p . Furthermore, the negative correlation also appears to be stronger with increasing hem . Both of these trend may be explained by the fact that the high energy secondary electrons produced in the foil bring about the observed negative correlation and that the amount of these electrons increases both with Z p and with hem for a given Z p .
H. Ogawa et al. / Nuclear Instruments and Methods in Physics Research B 354 (2015) 96–99
99
of SE emitted in the opposite direction. At every hem , a negative F–B correlation was observed and this correlation is becoming pronounced with increasing the projectile atomic number Z p . Furthermore, the increase of hem seems to make this correlation outstanding. Acknowledgments The authors would like to acknowledge J. Karimata for his assistance in the operation of the accelerator. This work is partially supported financially by Nara Women’s University Intramural Grant for Project Research, 2013. References
Fig. 4. Coefficients (a) bF in Eq. (8) and (b) bB in Eq. (9) as a function of hem ., The values of bF and bB at hem = 0 [mrad] are presented with horizontal lines, in order to make the hem -dependence clear.
4. Conclusions The forward and backward SE emission from a thin carbon foil by the penetration of 1 MeV/u 1H+, 4He2+ and 6Li3+ projectiles were measured as a function of hem of the foil-transmitted projectiles. In both directions, the SE yields increase with increasing hem irrespective of projectile. This trend is quite understandable since the emergence at the larger angle is due to the close collision with a target carbon nucleus leading to the ejection of target K-shell electrons. In order to examine the F–B correlation, the forward and backward SE yields were represented as a function of the number
[1] J. Devooght, J.C. Dehaes, A. Dubus, M. Cailler, J.P. Ganachaud, M. Roesler, W. Brauer, in: G. Hoehler, E.A. Niekisch (Eds.), Particle Induced Electron Emission I, Springer Tracts in Modern Physics, vol. 122, Springer, Berlin, 1991. [2] D. Hasselkamp, H. Rothard, K.O. Groeneveld, J. Kemmler, P. Varga, H. Winter, in: G. Hoehler, E.A. Niekisch (Eds.), Particle Induced Electron Emission II, Springer Tracts in Modern Physics, vol. 123, Springer, Berlin, 1991. [3] E.J. Sternglass, Phys. Rev. 108 (1975) 1. [4] H. Rothard, D. Dauvergne, M. Fallavier, K.O. Groeneveld, R. Kirsch, J.-C. Poizat, J. Remillieux, J.P. Thomas, Radiat. Eff. Defects Solids 126 (1993) 373. [5] K.H. Krebs, Ann. Phys. 10 (1962) 213. [6] G. Lakits, F. Aumayr, H. Winter, Rev. Sci. Instr. 60 (1989) 3151. [7] A.A. Kozochkina, V.B. Leonas, M. Witte, Nucl. Instr. Meth. B 62 (1991) 51. [8] Y. Yamazaki, K. Kuroki, Nucl. Instr. Meth. A 262 (1987) 118; Y. Yamazaki, K. Kuroki, T. Azuma, K. Komaki, H. Watanabe, N. Kakutani, T. Hasegawa, M. Sekiguchi, T. Hattori, Phys. Rev. Lett. 70 (1993) 2702. [9] F. Barrué, M. Chevallier, D. Dauvergne, R. Kirsch, J.C. Poizat, C. Ray, L. Adoui, A. Cassimi, H. Rothard, M. Toulemonde, C. Cohen, A. L’Hoir, D. Vernhet, C. Demonchy, L. Giot, W. Mittig, S. Pita, P. Roussel-Chomaz, A. Billebaud, Phys. Rev. A 70 (2004) 032902. [10] R. Ishiwari, N. Shiomi-Tsuda, N. Sakamoto, H. Ogawa, Nucl. Instr. Meth. B 51 (1991) 209. [11] N. Sakamoto, H. Ogawa, N. Shiomi-Tsuda, R. Ishiwari, Nucl. Instr. Meth. B 69 (1992) 84. [12] G.A. Iferov, V.A. Khodyrev, E.I. Sirotinin, Yu.N. Zhukova, Phys. Lett. A 97 (1983) 283. [13] J.C. Eckard, G.H. Lantschner, M.M. Jakas, V.H. Ponce, Nucl. Instr. Meth. B 2 (1984) 168. [14] G.H. Lantschner, J.C. Eckardt, M.M. Jakas, N.E. Capuj, H. Ascolani, Phys. Rev. A 36 (1987) 4667. [15] G.A. Iferov, Yu. N. Zhukova, V. Ya. Chumanov, O.V. Chumanova, N.M. Kabachnic, Nucl. Instr. Meth. B 48 (1990) 43. [16] H. Geissel, W.N. Lennard, H.R. Andrews, D.P. Jackson, I.V. Mitchell, D. Phillips, D. Ward, Nucl. Instr. Meth. B 12 (1985) 38. [17] H. Geissel, K.B. Winterbon, W.N. Lennard, Nucl. Instr. Meth. B 27 (1987) 333. [18] H. Ogawa, H. Tsuchida, N. Sakamoto, Phys. Rev. A 68 (2003) 052901. [19] H. Ogawa, K. Sorai, S. Amano, K. Ishii, T. Kaneko, J. Phys. B 47 (2014) 85201. [20] H. Ogawa, H. Tsuchida, N. Sakamoto, Nucl. Instr. Meth. B 193 (2002) 85. [21] H. Ogawa, N. Sakamoto, H. Tsuchida, Nucl. Instr. Meth. B 164–165 (2000) 279. [22] P. Sigmund, K.B. Winterbon, Nucl. Instr. Meth. 119 (1974) 541. [23] H. Ogawa, M. Sonoda, Y. Inoue, K. Ishii, T. Kaneko, Nucl. Instr. Meth. B 267 (2009) 2612. [24] H. Ogawa, A. Shimada, M. Kiuchi, M. Hagihara, Y. Inoue, K. Ishii, T. Kaneko, Phys. Rev. A 82 (2010) 012902.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Forward–backward correlated secondary electron emission depending on the emergence angle of 1 MeV/u light ions H. Ogawa a,⇑, S. Amano b, K. Ishii a, T. Kaneko c a
Dept. of Physics, Nara Women’s Univ., Nara 630-8506, Japan Graduate School of Hum. and Sci., Nara Women’s Univ., Nara 630-8506, Japan c Graduate School of Science, Okayama Univ. of Science, Okayama 700-0005, Japan b
a r t i c l e
i n f o
Article history: Received 4 July 2014 Received in revised form 29 August 2014 Accepted 12 September 2014 Available online 3 October 2014 Keywords: Secondary electron Emission statistics Energy loss
a b s t r a c t The statistical distributions of the number of forward- and backward-emitted secondary electrons (SE’s) from a thin carbon foil have been measured simultaneously in coincidence with foil-transmitted 1H+, 4 He2+ and 6Li3+ at a fixed velocity of 1 MeV/u. The emergence angles of the projectiles, hem , were varied from 0 to 2 [mrad] for H+ and from 0 to 1 [mrad] for He2+ and Li3+ ions. Irrespective of ion species, measured total SE yields, that is, the average number of simultaneous emitted electrons per projectile, increase with increasing hem both in the forward and backward directions. This trend is consistent with the calculated hem -dependent energy losses of protons penetrating a thin carbon foil. As for the forwardor backward-emitted SE yields, we have obtained a negative forward–backward(F–B) correlation, except for the hem ¼ 0:0 [mrad] emergence of H+ projectiles where a positive correlation has been observed. The negative F–B correlation becomes prominent with increasing the atomic number of the projectile, Z p . In addition, this correlation appears to become slightly stronger with increasing hem . The observed F–B correlation and its Z p - and hem -dependences are interpreted from the point of view of production of high energy internal SE’s. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Kinetic emission of secondary electrons (SE’s) from solid surface under fast ion bombardments has been studied intensively for a long time [1,2]. Sternglass has proposed the following three-step model for this phenomenon; First, the creation of excited electrons via collisions of projectiles with target atoms in the solid. Second, the transport of liberated electrons through the bulk to the surface including higher order ionizations by high energy internal SE’s (cascade multiplication). Finally, the transmission through the surface potential barrier [3]. According to this scenario, the SE yields c, that is the average number of the emitted SE’s per projectile, is proportional to the electronic stopping power Se as
c ¼ K Se
ð1Þ
where K is the so-called material parameter that depends only on the target material. As far as the proton-incidence on carbon foils is concerned, it was experimentally certified by the conventional current measurement that K is constant over a wide energy range from 0.02 to 10 MeV [4]. ⇑ Corresponding author. Tel./fax: +81 742 20 3380. E-mail address: [email protected] (H. Ogawa). http://dx.doi.org/10.1016/j.nimb.2014.09.025 0168-583X/Ó 2014 Elsevier B.V. All rights reserved.
As for the method to measure the SE emission, the measurement of the emission statistics is an alternative one that was firstly employed by Krebs [5]. It can also determine the probability of n SE emission and has been applied to the basic research on ion-surface interactions [6–8]. Especially, the simultaneous measurement of emitted SEs from both the beam-entrance (refer to as ‘‘backward’’ hereafter) and -exit (refer to as ‘‘forward’’ hereafter) surfaces of a thin foil may bring about quite a valuable information on the forward–backward correlation (refer to as ‘‘F–B correlation’’ hereafter) characterizing specific collisions in the foil. There also exists an experiment by Barrué et al. that investigates the correlation between the energy loss and the SE emission directly. They measured the number distributions of forward and backward emitted SEs in coincidence with the energy loss and the outgoing charge state of the projectile heavy ions in channeling and also in random incidence [9]. By the way, it is well known that the energy losses of the incident particles in a target foil depend on the emergent-angle, hem , of them due to the impact parameter dependence of the energy loss [10–17]. Judging from a close relation between the energy loss and the SE emission [4], it is easily predictable that the SE emission also depends on the impact parameter or, in other word, the scattering angle of the incident ions. This expectation has been
H. Ogawa et al. / Nuclear Instruments and Methods in Physics Research B 354 (2015) 96–99
certified as correct by our measurement of the hem -dependent SE yields of foil-transmitted protons [18]. As an extension of the above work, the forward and backward emitted SEs have been measured simultaneously in coincidence with the foil-transmitted protons in order to investigate the hem -dependent F–B correlations [19]. In the present work, a similar measurement has been carried out with 4He2+ and 6Li3+ beams of 1 MeV/u in order to examine how the F–B correlation and its hem -dependence varies with the atomic number of the projectile, Zp . 2. Experiment The experiment was performed using 1 MeV/u 1H+, 4He2+ and Li3+ ions obtained with a 1.7-MV tandem Van de Graaff accelerator at Nara Women’s University. The beam was transported to a target carbon foil using the method described in Ref. [20]. The incident beam was collimated with two diaphragms of 0.2 mm in diameter and 224 cm apart. A baffle of 1.2 mm in diameter was placed about 5 cm behind the second diaphragm to prevent edge-scattered particles from hitting the target. The target foil was placed 7 cm behind the baffle and tilted by 45° relative to the normal angle of incidence. The foil was floated at a potential of 30 kV. The emitted electrons were accelerated to a grounded electrode that was parallel to the foil and 40 mm apart from the target. At the grounded electrode a solid-state Si detector (SSD) of 100 mm2 sensitive area faced the target foil. The thickness of the carbon target foil was determined by measuring the transmitted fraction of 2.5 MeV H0, while accounting for the electron loss and capture cross sections involved [21]. The thickness of the present carbon was found to be 4.0 ± 0.2 l g/cm2. This pffiffiffi value is that tilted by 45° from the normal to the surface and is 2 times of that for the normal incidence which is estimated to be 2.8 ± 0.2 lg/cm2. The same system as our previous work was employed for the detection of foil-transmitted protons as a function of hem [20]. We have used independently movable vertical and horizontal slits, the widths of which were about 0.3 mm. Thus, the hem -resolved projectiles were detected by a Si photo diode (PD) of 800 mm2 sensitive area. The measurement with He2+ and Li3+ beams were carried out from hem = 0.0 to 1.0 [mrad] by 0.5 [mrad] step. In this connection, the measurement with proton beams was carried out from hem = 0.0 to 2.0 [mrad] by 1.0 [mrad] step [19]. In the center of mass frame, the impact parameter b and the scattering angle hcm satisfy the following relation,
97
statistics [22]. With these probabilities, the forward (backward) SE yields, cF ðnB Þ (cB ðnF Þ), gated by nB (nF ) are given as nF;max
cF ðnB Þ ¼
X
nF PðnF ; nB Þ
ð5Þ
nB PðnF ; nB Þ
ð6Þ
nF ¼1
nB;max
cB ðnF Þ ¼
X
nB ¼1
where nF;max (nB;max ) denotes the maximum number of forward(backward-) emitted SEs per projectile observed in the spectra. In the present case, typical numbers of nF;max and nB;max were about 15, 20 and 25 for H+, He2+ and Li3+, respectively.
6
b¼
Z p Z T e2 cotðhcm =2Þ mv 2
3. Results and discussion Before discussing the F–B correlation of the SE emission and its hem -dependence, the calculated angular distribution of 1 MeV/u projectiles transmitted through a carbon foil of 4.0 lg/cm2 are shown in Fig. 1. Black, red and blue solid curves represent the results for H+, He2+ and Li3+, respectively evaluated by the theory of multiple scattering by Sigmund and Winterbon [23]. It should be noted that the distributions for 4He2+ and 6Li3+ ions of the same velocity agree completely with each other because they have the same ratio of the charge to the mass number. Corresponding dashed curves are those calculated for a single scattering by a screening potential of the following form,
VðrÞ ¼
Z P Z T e2 r exp aTF r
ð7Þ
where e and aTF denote the elementary charge and the Thomas– Fermi screening radius, respectively. Here, we have to mention that the scattering yields calculated by using Eq. (7) are quite rough estimations. As is clear from this figure, hem of projectiles exiting at angles larger than 0.5 [mrad] are determined substantially by a single collision of a small impact parameter in the foil for 1 MeV/u He2+ and Li3+, although they suffer multiple scattering in the foil. Combining this result with that given in Fig. 4 of Ref. [19], not only H+ but also He2+ and Li3+ ions observed at
ð2Þ
where Z T ; m and v denote the atomic number of the target atom, the reduced mass of the projectile and the target atom and the velocity of the projectile, respectively. Furthermore, when hcm 1, the scattering angle in the laboratory frame, hlab , can be related to hcm as
hlab ¼
m hcm Mp
ð3Þ
Therefore the following relation holds,
b hlab /
Zp Mp
ð4Þ
Therefore the present experiments with He and Li ions have investigated the same impact parameter region as that with the 1 MeV proton. For the quantitative comparison of the F–B correlation, we have evaluated the emission probability, PðnF ; nB Þ, for nF and nB electrons emitted simultaneously in the forward and backward directions, respectively, from the two-dimensional spectra of the emission
Fig. 1. The angular distribution due to multiple scattering of 1 MeV/u 4He2+ and 6 3+ Li ions penetrating a carbon foil of 4.0 ± 0.2 lg/cm2 in thickness. Solid curves are obtained with a theory of the multiple scattering by Sigmund and Winterbon [23]. For comparison, the scattering yields assuming a single scattering by a screened Coulomb potential given by Eq. (3) are also presented by the corresponding dashed curves.
98
H. Ogawa et al. / Nuclear Instruments and Methods in Physics Research B 354 (2015) 96–99
non-zero hem have been supposed to penetrate deeply inside the Kshell electron cloud of the carbon atom in the foil. Hereafter we move on to the discussion on the F–B correlation of the SE emission observed in the present results. Fig. 2(a) and (b) represents the cF ðnB Þ and cB ðnF Þ, respectively, obtained by the present experiment with 1 MeV/u He2+ ions. Similarly, Fig. 3(a) and (b) shows those with 1 MeV/u Li3+ ions. In this connection the corresponding results for 1 MeV proton are presented in Fig. 5(a) and (b) of Ref. [19]. In these figures, squares, circles and triangles represent the data for hem = 0.0, 0.5 and 1.0 [mrad], respectively. The associated error of each data point includes only the statistical one. In order to make the variation of cF ðnB Þ (cB ðnF Þ) with nB (nF ) conspicuous, the measured value of cF ðnB Þ (cB ðnF Þ) were least square fitted on trial with a linear function of nB (nF ) assuming the following relation as,
cF ðnB Þ ¼ aF þ bF nB
ð8Þ
and
cB ðnF Þ ¼ aB þ bB nF :
ð9Þ
For He and Li ions, cF ðnB Þ and cB ðnF Þ exhibit a negative correlation(i.e. bF ; bB < 0) at every hem observed. As is discussed in our previous paper [24], the sign of the F–B correlation seems to be quite
Fig. 3. Same as Fig. 2 except that the projectiles are 1 MeV/u 6Li3+. Solid lines represent the least square fittings to (a) cF ðnB Þ of nB = 2 to 10 and (b) cB ðnF Þ of nF = 2 to 10 for each hem .
Fig. 2. The hem -dependence of the F–B correlation in the measured SE emission from a carbon foil of 4.0 ± 0.2 lg/cm2 induced by 1 MeV/u 4He2+ penetration. (a) The forward SE yields, cF ðnB Þ, as a function of nB , and (b) the backward SE yields, cB ðnF Þ, as a function of nF . Solid squares, circles and triangles are the results for hem = 0.0, 0.5 and 1.0 [mrad], respectively. Solid lines represent the least square fittings to (a) cF ðnB Þ and (b) cB ðnF Þ for each hem .
sensitive to the ratio of the range of the internal high energy SEs to the target thickness. The binary electrons that have a range comparable to or larger than the foil thickness can bring about the positive FB correlation by cascading ionization. On the other hand, those with a range significantly smaller than the foil thickness can participate only in the forward or backward SE emission depending on the position of its production. For the projectile velocity of 1 MeV/ u, the contribution of the latter seems to be predominant and the negative correlation comes out. In this connection, the correlation is expected to change from negative to positive(i.e. bF ; bB > 0) with increasing the projectile velocity [24]. In order to examine the obtained F–B correlation quantitatively, values of bB and bF are presented for H+, He2+ and Li3+ ions in Fig. 4(a) and (b), respectively as a function of hem . In these figures, squares, circles and triangles represent the values for H+, He2+ and Li3+ ions, respectively. In order to make the hem -dependence clear, the values of bF and bB at hem = 0 [mrad] are presented with horizontal lines. From these figures, it is clear that the negative correlation becomes more prominent with increasing Z p . Furthermore, the negative correlation also appears to be stronger with increasing hem . Both of these trend may be explained by the fact that the high energy secondary electrons produced in the foil bring about the observed negative correlation and that the amount of these electrons increases both with Z p and with hem for a given Z p .
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of SE emitted in the opposite direction. At every hem , a negative F–B correlation was observed and this correlation is becoming pronounced with increasing the projectile atomic number Z p . Furthermore, the increase of hem seems to make this correlation outstanding. Acknowledgments The authors would like to acknowledge J. Karimata for his assistance in the operation of the accelerator. This work is partially supported financially by Nara Women’s University Intramural Grant for Project Research, 2013. References
Fig. 4. Coefficients (a) bF in Eq. (8) and (b) bB in Eq. (9) as a function of hem ., The values of bF and bB at hem = 0 [mrad] are presented with horizontal lines, in order to make the hem -dependence clear.
4. Conclusions The forward and backward SE emission from a thin carbon foil by the penetration of 1 MeV/u 1H+, 4He2+ and 6Li3+ projectiles were measured as a function of hem of the foil-transmitted projectiles. In both directions, the SE yields increase with increasing hem irrespective of projectile. This trend is quite understandable since the emergence at the larger angle is due to the close collision with a target carbon nucleus leading to the ejection of target K-shell electrons. In order to examine the F–B correlation, the forward and backward SE yields were represented as a function of the number
[1] J. Devooght, J.C. Dehaes, A. Dubus, M. Cailler, J.P. Ganachaud, M. Roesler, W. Brauer, in: G. Hoehler, E.A. Niekisch (Eds.), Particle Induced Electron Emission I, Springer Tracts in Modern Physics, vol. 122, Springer, Berlin, 1991. [2] D. Hasselkamp, H. Rothard, K.O. Groeneveld, J. Kemmler, P. Varga, H. Winter, in: G. Hoehler, E.A. Niekisch (Eds.), Particle Induced Electron Emission II, Springer Tracts in Modern Physics, vol. 123, Springer, Berlin, 1991. [3] E.J. Sternglass, Phys. Rev. 108 (1975) 1. [4] H. Rothard, D. Dauvergne, M. Fallavier, K.O. Groeneveld, R. Kirsch, J.-C. Poizat, J. Remillieux, J.P. Thomas, Radiat. Eff. Defects Solids 126 (1993) 373. [5] K.H. Krebs, Ann. Phys. 10 (1962) 213. [6] G. Lakits, F. Aumayr, H. Winter, Rev. Sci. Instr. 60 (1989) 3151. [7] A.A. Kozochkina, V.B. Leonas, M. Witte, Nucl. Instr. Meth. B 62 (1991) 51. [8] Y. Yamazaki, K. Kuroki, Nucl. Instr. Meth. A 262 (1987) 118; Y. Yamazaki, K. Kuroki, T. Azuma, K. Komaki, H. Watanabe, N. Kakutani, T. Hasegawa, M. Sekiguchi, T. Hattori, Phys. Rev. Lett. 70 (1993) 2702. [9] F. Barrué, M. Chevallier, D. Dauvergne, R. Kirsch, J.C. Poizat, C. Ray, L. Adoui, A. Cassimi, H. Rothard, M. Toulemonde, C. Cohen, A. L’Hoir, D. Vernhet, C. Demonchy, L. Giot, W. Mittig, S. Pita, P. Roussel-Chomaz, A. Billebaud, Phys. Rev. A 70 (2004) 032902. [10] R. Ishiwari, N. Shiomi-Tsuda, N. Sakamoto, H. Ogawa, Nucl. Instr. Meth. B 51 (1991) 209. [11] N. Sakamoto, H. Ogawa, N. Shiomi-Tsuda, R. Ishiwari, Nucl. Instr. Meth. B 69 (1992) 84. [12] G.A. Iferov, V.A. Khodyrev, E.I. Sirotinin, Yu.N. Zhukova, Phys. Lett. A 97 (1983) 283. [13] J.C. Eckard, G.H. Lantschner, M.M. Jakas, V.H. Ponce, Nucl. Instr. Meth. B 2 (1984) 168. [14] G.H. Lantschner, J.C. Eckardt, M.M. Jakas, N.E. Capuj, H. Ascolani, Phys. Rev. A 36 (1987) 4667. [15] G.A. Iferov, Yu. N. Zhukova, V. Ya. Chumanov, O.V. Chumanova, N.M. Kabachnic, Nucl. Instr. Meth. B 48 (1990) 43. [16] H. Geissel, W.N. Lennard, H.R. Andrews, D.P. Jackson, I.V. Mitchell, D. Phillips, D. Ward, Nucl. Instr. Meth. B 12 (1985) 38. [17] H. Geissel, K.B. Winterbon, W.N. Lennard, Nucl. Instr. Meth. B 27 (1987) 333. [18] H. Ogawa, H. Tsuchida, N. Sakamoto, Phys. Rev. A 68 (2003) 052901. [19] H. Ogawa, K. Sorai, S. Amano, K. Ishii, T. Kaneko, J. Phys. B 47 (2014) 85201. [20] H. Ogawa, H. Tsuchida, N. Sakamoto, Nucl. Instr. Meth. B 193 (2002) 85. [21] H. Ogawa, N. Sakamoto, H. Tsuchida, Nucl. Instr. Meth. B 164–165 (2000) 279. [22] P. Sigmund, K.B. Winterbon, Nucl. Instr. Meth. 119 (1974) 541. [23] H. Ogawa, M. Sonoda, Y. Inoue, K. Ishii, T. Kaneko, Nucl. Instr. Meth. B 267 (2009) 2612. [24] H. Ogawa, A. Shimada, M. Kiuchi, M. Hagihara, Y. Inoue, K. Ishii, T. Kaneko, Phys. Rev. A 82 (2010) 012902.