- Email: [email protected]
Stopping power of Au for protons from 3 to 8 MeV
Nuclear Instruments and Methods North-Holland, Amsterdam
STOPPING
Research
B2 (1984) 141-144
POWER OF Au FOR PROTONS
R. ISHIWARI, Department
in Physics
N. SHIOMI
141
FROM 3 TO 8 MeV
and N. SAKAMOTO
of Physics, Nara Women’s University, Nara 630, Japan
Stopping powers of Au for protons from 3 to 8 MeV have been measured with a surface barrier silicon detector. The results have been presented in the form of Bichsel’s X-variable. The experimental X-value points fit very well with the theoretical X-value curve using the Bonderup shell correction and the mean excitation energy, I, of 745.4 eV. If we use Bichsel’s shell correction, Z-value of 824 eV reproduces fairly well the experimental X-value points. In the range from 3 to 8 MeV, it is difficult to determine which shell correction represents the experimental situation better. However, if we experiment in the range from 8 to 20 MeV, it may be possible to judge which shell correction better represents the experimental points.
1. Introduction The accurate value of the stopping power of matter is of interest in many fields of physics, such as nuclear physics, radiation dosimetry, surface analysis, ion implantation and the electronic structure of the atom and so on. One can obtain the mean excitation energy I of matter from an accurate measurement of the stopping power by the use of the Bethe-Bloch formula. In previous experiments [1,2], stopping powers of 21 kinds of metallic elements for 6.5 MeV protons were measured with an accuracy of f 0.3%. The mean excitation energies were extracted by using the Bonderup shell correction 131. According to a recent work of Berger [4], if we use Bichsel’s shell correction [5], the extracted mean excitation energies agree fairly well with those obtained using the Bonderup shell correction for atomic numbers up to - 50. For heavier elements Bichsel’s shell correction gives systematically higher I-values than the Bonderup shell correction. In the present experiment, stopping powers of Au for protons from 3 to 8 MeV have been measured using a surface barrier silicon detector with an accuracy of &0.3%. Then, the mean excitation energy Z has been extracted using both the Bonderup shell correction and Bichsel’s shell correction.
2. Experimental The analyzed beam of protons from the tandem Van de Graaf accelerator of Kyoto University was used in the present experiment. The experiemtnal procedure to determine the energy loss of protons in the sample target is the same as our recent experiment [2] in which 0168-583X/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
stopping powers of Zr, Pd, Cd, In and Pb for 6.75 MeV protons were determined. The analyzed beam of protons was scattered by a thin gold foil of 180 pg/cm* at the center of the scattering chamber. The beam scattered at an angle of 15” was used for the measurement. The scattered beam was collimated by a double slit system, the diameters of which were 1.5 mm each and 7.8 cm apart. Then protons were passed through the target and all the protons that passed through the target were detected by a surface barrier silicon detector. In order to determine the energy loss of protons in the target, the pulse height of protons that passed through the target and the pulse height of protons that did not pass through the targei were recorded by a 4096 channel pulse height analyzer simultaneously in one exposure. To achieve this, a special device was used for mounting the target. This device is shown in fig. 1. The part indicated by A is essentially an ammeter. When ac power is supplied, the hand indicated by B makes a metronomic motion. A double frame indicated by C is fixed to the hand B. The target is fixed to one part of the double frame and the other frame is left empty. When ac power is supplied and the hand B makes a metronomic motion, the incident beam traverses the two frames. Therefore, protons that pass through the target and protons that do not pass through the target hit the detector alternately. Thus, the pulse heights of protons with and without the target are recorded simultaneously in one exposure. The pulses from the detector were amplified and recorded by the 4096 channel pulse height analyzer. By taking the average values for both peaks with and without the target, the difference between the pulse heights was determined. Because the effect of the gain drift of the amplifier was eliminated automatically by this method, the different between the pulse heights was III. ENERGY
LOSS
142
R. Ishiwari et al. / Stopping power of Au for protons
the present results have been reduced to a round number energy by assuming that the stopping power is proportional to (In u2)/u2 in a narrow velocity range. From the above-mentioned uncertainties of the energy loss and the target thickness, the uncertainty of the stopping power is calculated to be +0.25X. Making allowance for unexpected errors, the final uncertainty of the present results was assigned to be &0.3X.
3. Results
Fig. 1. The device for mounting the target. The part indicated as A is essentially an ammeter. When ac power is supplied, the hand indicated as B makes a metronomic motion. A double frame indicated as C is fixed to the hand B. The target is fixed to one of the double frames and the other frame is left empty. When ac power is supplied and the hand B makes a metronomic motion, the incident beam traverses the two frames.
determined with an accuracy of +0.15%. The energy calibration of the pulse height spectrum was made with a very high precision pulse generator (ORTEC 448). The ionization defect of the silicon detector was investigated in the previous experiment [I] and has turned out to be substantially zero for 6.5 MeV protons. In the present experiment, it was assumed that the ionization defect of the detector is zero for protons from 3 to 8 MeV. The accuracy of the energy loss was estimated to be f0.28. The target was manufacture by the Ishifuku Metal Industry Co., Ltd and the purity was 99.95%. Two foils of (10.549 f 0.016)mg/cm2 and (21.007 f 0.032)mg/cm2 were used. The thickness of the target was determined by measuring its weight and area. The weight was measured by a Mettler ME 30/36 electro-microbalance which has an absolute accuracy of 11 fig. The area was measured by a Tiyoda LTG bi-AI1 microscope which can read to 1 pm. In the present experiment, the proton beam traverses the target during the measurement. So the possible nonuniformity of the target thickness is automatically averaged and the observed energy loss corresponds to the average thickness of the target, that is the thickness obtained by the weight per area method. In general, the observed energy loss divided by the average path length of protons in the target, A E/AX, corresponds, to a good approximation, to the stopping power, -d E/d X, at the average energy defined by J!?= E, - d E/2, where E, is the incident energy. The incident energy was chosen such that the average energy is very nearly a round number. For convenience when comparing the present results with other experiments,
The results are shown in table 1 and are compared with the Riser data of Sorensen and Andersen [6]. The results have been expressed in the form of Bichsel’s X-variable [7]. We use Bichsel’s notation to represent the Bethe-Bloch formula of stopping power [8]. dE -----as dX
where @ is the Bloch correction [9,10], L,Z, is the Z:-correction [lo-121 and C/Z, is the shell correction. The value of f( j3) has been tabulated by Bichsel[8]. The other symbols have their usual meanings. The X-variables, Xtheo and X_,, are defined as; X ,heo=lnI+C/Zz-@-LL,Z,,
In fig. 2, the present X-variable.
(2)
results are shown using Bichsel’s
Table 1 Comparison of the Nara data with the R&la data (keV/mg cm-*) E
Nara
[email protected]
Rise
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
36.71 f 0.11 33.78 + 0.10 31.30 * 0.09 29.29 + 0.09 21.56 f 0.08 26.04 * 0.08 24.67 f 0.07 23.52 + 0.07 22.45 f 0.07 21.50*0.06 20.66 f 0.06
36.73 33.75 31.30 29.25 27.51 25.99 24.65 23.48 22.43 21.49 20.63
37.10f0.11 34.09 f 0.10
31.62 + 0.09 29.55 f0.09 27.79 f 0.08 26.25 f 0.08 24.90* 0.07 23.72 f 0.07 22.66 +-0.07 21.71* 0.07 20.84 + 0.06
R. Ishiwari et al. / Stopping power of Au for protons
s.soL 0
I 5
I
I
I 20
10 Ed7
MeV 1
Fig. 2. The results represented by Bichsel’s X-variable. The solid curve is Xthco using Bonderup shell correction and I = 745.4 eV. The dot and dash curve are Berger’s results using Bichsel’s shell correction and I = 790 eV. The dashed curve is X ,,,_, using Bichsel’s shell correction and I = 824 eV. The open circle is the point reduced from Burkig and MacKenzie’s relative stopping power measurements taking Al as standard material.
4. Discussion As can be seen from table 1, the present results agree very well with the values of the Rise’ data X0.99. This trend agrees with the Aarhus data of Andersen et al. [ 131 for Al, Cu and Ag. The Aarhus stopping power valuFs for Al, Cu and Ag are lower by - 1% than the Rise data [6] of Sorensen and Andersen. We have analyzed the data using the Bonderup shell correction [3]. The values of the Bonderup shell correction have been calculated using x = 1.358, where x is the constant that appears in the statistical model of the atom and is usually taken as 2”‘. The values of the Z:-correction have been calculated by the theory of Ashley et al. [lo-121 using x = 1.358 and b = 1.3 + 0.2. These values of constants, x and b, were determined in previous experiments [l]. The value of the mean excitation energy, I, has been taken as a free parameter and determined by the method of least squares to fit the X_ points. The best fit was obtained with Z = 745.4 eV. This value agrees very well with the value of 746 eV obtained from the measurement for 6.5 MeV protons [l]. The curve of Xtheo with Z = 745.4 eV is shown in fig. 2 by a solid curve. The curve represents the X cxp points very well. This point is the essential difference of our data from the revised Aarhus data for Au of Andersen and Nielsen [14]. Andersen and Nielsen say that the Bonderup shell correction curve does not agree with the experimental shell correction curve in the energy range from 1 to 7 MeV.
143
The open circle shows the reduced X value of Au obtained from the relative stopping power measurements of Burkig and Mackenzie [15] at 19.8 MeV taking Al as standard. First, we obtained the absolute value of the stopping power of Al for 20 MeV protons from eq. (1) taking Z= 167.4 eV and using the Bonderup shell correction [3] and Z:-correction calculated by the theory of Ashley et al. [lo-121. The Z value of 167.4 eV was obtained in our previous experiments [l]. Next, multiplying the relative value of stopping power of Burkig and MacKenzie with the stopping power for Al, we obtained the absolute value of the stopping power of Au for 20 MeV protons. Then, using eq. (3) we obtained the X-value of Au at 20 MeV. The open circle falls very near to the solid curve. Recently, Berger [4] has analyzed many experimental data using Bichsel’s shell correction [5] taking into account the Bloch correction and the Z:-correction. In Bichsel’s method of calculating the shell correction, it is assumed that the higher correction term than the M shell has the same shape as the L shell correction of Walske [16]. Then, two free parameters are multiplied with the energy value and the shell correction value. Berger has obtained the Z value for Au as (790 + 30) eV. In fig. 2, Berger’s curve using Bichsel’s shell correction and an Z value of 790 eV is shown by a dot and dash curve. As can be clearly seen, Berger’s curve lies much lower than our curve using the Bonderup shell correction. As is shown in eq. (2). the Xtheo curve can be shifted up and down by changing the value of Z without changing the shape of the curve. We have taken the value of Z as a free parameter. Using Bichsel’s shell correction we have fitted the Xtheo curve with our X exp points by the method of least squares. The best fit has been obtained with the Z value of 824 eV. This curve is also shown in fig. 2 by a dashed curve. As can be seen from the figure, this curve also fits the XexP points fairly well. Therefore, it is difficult to determine exactly which shell correction represents the experimental points better from the present experiment. However, as is shown in fig. 2, Bonderup’s curve with Z = 745.4 eV and Bichsel’s curve with Z = 824 eV diverge from each other from 8 up to 20 MeV. Therefore, if we make stopping power measurement in the range from 8 to 20 MeV, it may be possible to judge which shell correction better represents the experimental points. The stopping power measurements in the range from 8 to 20 MeV have actually been performed using the tandem Van de Graaf accelerator of the University of Tsukuba in cooperation with Drs K. Shima and T. Ishihara. The preliminary results of this experiment appear to show that the experimental X value points fall in between the two theoretical curves. Detailed results will be soon published [17]. III. ENERGY LOSS
144
R. Ishiwari et al. / Stopping power of Au for protons
The authors would like to thank the late Professor J. Muto and Professor S. Kobayashi for their kind support throughout the experiment. Thanks are also due to Drs K. Takimoto and M. Nakamura for their kind cooperation.
References
[l] R. Ishiwari, N. Shiomi and N. Sakamoto, Nucl. Instr. and Meth. 194 (1982) 61. [2] R. Ishiwari, N. Shiomi and N. Sakamoto, these Proceedings (ACIS-IO), p. 195. [3] E. Bonderup, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 35 (1967) no. 17. (41 M.J. Berger, private communication (August 1982). [5] H. Bichsel, UCRL-17538 (University of California, 1967). [6] H. Sorensen and H.H. Andersen, Phys. Rev. B8 (1973) 1854.
[7] H. Bichsel, Natl. Acad. Sci.-Natl. Res. Council Publ. 1133
(1964) p. 17. [8] H. Bichsel, American Institute of Physics Handbook 3rd ed. (McGraw-Hill, New York, 1972). [9] J. Lindhard, Nucl. Instr. and Meth. 132 (1976) 1. [lo] R.H. Ritchie and W. Brandt, Phys. Rev. Al7 (1978) 2102. [ll] J.C. Ashley, R.H. Ritchie and W. Brandt, Phys. Rev. B5 (1972) 2393. 112) J.C. Ashley, R.H. Ritcbie and W. Brand& Phys. Rev. A8 (1973) 2402. [13] H.H. Andersen, J.F. Bak, H. Knudsen and B.R. Nielsen, Phys. Rev. Al6 (1977) 1929. 1141 H.H. Andersen and B.R. Nielsen, Nucl. Instr. and Meth. 191 (1981) 475. 1151 V.C. Burkig and K.R. MacKenzie, Phys. Rev. 106 (1957) 848. (161 M.C. Walske, Phys. Rev. 101 (1956) 940. 1171 R. Ishiwari, N. Sbiomi, N. Sakamoto, K. Shima and T. Ishihara, to be published.
STOPPING
Research
B2 (1984) 141-144
POWER OF Au FOR PROTONS
R. ISHIWARI, Department
in Physics
N. SHIOMI
141
FROM 3 TO 8 MeV
and N. SAKAMOTO
of Physics, Nara Women’s University, Nara 630, Japan
Stopping powers of Au for protons from 3 to 8 MeV have been measured with a surface barrier silicon detector. The results have been presented in the form of Bichsel’s X-variable. The experimental X-value points fit very well with the theoretical X-value curve using the Bonderup shell correction and the mean excitation energy, I, of 745.4 eV. If we use Bichsel’s shell correction, Z-value of 824 eV reproduces fairly well the experimental X-value points. In the range from 3 to 8 MeV, it is difficult to determine which shell correction represents the experimental situation better. However, if we experiment in the range from 8 to 20 MeV, it may be possible to judge which shell correction better represents the experimental points.
1. Introduction The accurate value of the stopping power of matter is of interest in many fields of physics, such as nuclear physics, radiation dosimetry, surface analysis, ion implantation and the electronic structure of the atom and so on. One can obtain the mean excitation energy I of matter from an accurate measurement of the stopping power by the use of the Bethe-Bloch formula. In previous experiments [1,2], stopping powers of 21 kinds of metallic elements for 6.5 MeV protons were measured with an accuracy of f 0.3%. The mean excitation energies were extracted by using the Bonderup shell correction 131. According to a recent work of Berger [4], if we use Bichsel’s shell correction [5], the extracted mean excitation energies agree fairly well with those obtained using the Bonderup shell correction for atomic numbers up to - 50. For heavier elements Bichsel’s shell correction gives systematically higher I-values than the Bonderup shell correction. In the present experiment, stopping powers of Au for protons from 3 to 8 MeV have been measured using a surface barrier silicon detector with an accuracy of &0.3%. Then, the mean excitation energy Z has been extracted using both the Bonderup shell correction and Bichsel’s shell correction.
2. Experimental The analyzed beam of protons from the tandem Van de Graaf accelerator of Kyoto University was used in the present experiment. The experiemtnal procedure to determine the energy loss of protons in the sample target is the same as our recent experiment [2] in which 0168-583X/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
stopping powers of Zr, Pd, Cd, In and Pb for 6.75 MeV protons were determined. The analyzed beam of protons was scattered by a thin gold foil of 180 pg/cm* at the center of the scattering chamber. The beam scattered at an angle of 15” was used for the measurement. The scattered beam was collimated by a double slit system, the diameters of which were 1.5 mm each and 7.8 cm apart. Then protons were passed through the target and all the protons that passed through the target were detected by a surface barrier silicon detector. In order to determine the energy loss of protons in the target, the pulse height of protons that passed through the target and the pulse height of protons that did not pass through the targei were recorded by a 4096 channel pulse height analyzer simultaneously in one exposure. To achieve this, a special device was used for mounting the target. This device is shown in fig. 1. The part indicated by A is essentially an ammeter. When ac power is supplied, the hand indicated by B makes a metronomic motion. A double frame indicated by C is fixed to the hand B. The target is fixed to one part of the double frame and the other frame is left empty. When ac power is supplied and the hand B makes a metronomic motion, the incident beam traverses the two frames. Therefore, protons that pass through the target and protons that do not pass through the target hit the detector alternately. Thus, the pulse heights of protons with and without the target are recorded simultaneously in one exposure. The pulses from the detector were amplified and recorded by the 4096 channel pulse height analyzer. By taking the average values for both peaks with and without the target, the difference between the pulse heights was determined. Because the effect of the gain drift of the amplifier was eliminated automatically by this method, the different between the pulse heights was III. ENERGY
LOSS
142
R. Ishiwari et al. / Stopping power of Au for protons
the present results have been reduced to a round number energy by assuming that the stopping power is proportional to (In u2)/u2 in a narrow velocity range. From the above-mentioned uncertainties of the energy loss and the target thickness, the uncertainty of the stopping power is calculated to be +0.25X. Making allowance for unexpected errors, the final uncertainty of the present results was assigned to be &0.3X.
3. Results
Fig. 1. The device for mounting the target. The part indicated as A is essentially an ammeter. When ac power is supplied, the hand indicated as B makes a metronomic motion. A double frame indicated as C is fixed to the hand B. The target is fixed to one of the double frames and the other frame is left empty. When ac power is supplied and the hand B makes a metronomic motion, the incident beam traverses the two frames.
determined with an accuracy of +0.15%. The energy calibration of the pulse height spectrum was made with a very high precision pulse generator (ORTEC 448). The ionization defect of the silicon detector was investigated in the previous experiment [I] and has turned out to be substantially zero for 6.5 MeV protons. In the present experiment, it was assumed that the ionization defect of the detector is zero for protons from 3 to 8 MeV. The accuracy of the energy loss was estimated to be f0.28. The target was manufacture by the Ishifuku Metal Industry Co., Ltd and the purity was 99.95%. Two foils of (10.549 f 0.016)mg/cm2 and (21.007 f 0.032)mg/cm2 were used. The thickness of the target was determined by measuring its weight and area. The weight was measured by a Mettler ME 30/36 electro-microbalance which has an absolute accuracy of 11 fig. The area was measured by a Tiyoda LTG bi-AI1 microscope which can read to 1 pm. In the present experiment, the proton beam traverses the target during the measurement. So the possible nonuniformity of the target thickness is automatically averaged and the observed energy loss corresponds to the average thickness of the target, that is the thickness obtained by the weight per area method. In general, the observed energy loss divided by the average path length of protons in the target, A E/AX, corresponds, to a good approximation, to the stopping power, -d E/d X, at the average energy defined by J!?= E, - d E/2, where E, is the incident energy. The incident energy was chosen such that the average energy is very nearly a round number. For convenience when comparing the present results with other experiments,
The results are shown in table 1 and are compared with the Riser data of Sorensen and Andersen [6]. The results have been expressed in the form of Bichsel’s X-variable [7]. We use Bichsel’s notation to represent the Bethe-Bloch formula of stopping power [8]. dE -----as dX
where @ is the Bloch correction [9,10], L,Z, is the Z:-correction [lo-121 and C/Z, is the shell correction. The value of f( j3) has been tabulated by Bichsel[8]. The other symbols have their usual meanings. The X-variables, Xtheo and X_,, are defined as; X ,heo=lnI+C/Zz-@-LL,Z,,
In fig. 2, the present X-variable.
(2)
results are shown using Bichsel’s
Table 1 Comparison of the Nara data with the R&la data (keV/mg cm-*) E
Nara
[email protected]
Rise
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
36.71 f 0.11 33.78 + 0.10 31.30 * 0.09 29.29 + 0.09 21.56 f 0.08 26.04 * 0.08 24.67 f 0.07 23.52 + 0.07 22.45 f 0.07 21.50*0.06 20.66 f 0.06
36.73 33.75 31.30 29.25 27.51 25.99 24.65 23.48 22.43 21.49 20.63
37.10f0.11 34.09 f 0.10
31.62 + 0.09 29.55 f0.09 27.79 f 0.08 26.25 f 0.08 24.90* 0.07 23.72 f 0.07 22.66 +-0.07 21.71* 0.07 20.84 + 0.06
R. Ishiwari et al. / Stopping power of Au for protons
s.soL 0
I 5
I
I
I 20
10 Ed7
MeV 1
Fig. 2. The results represented by Bichsel’s X-variable. The solid curve is Xthco using Bonderup shell correction and I = 745.4 eV. The dot and dash curve are Berger’s results using Bichsel’s shell correction and I = 790 eV. The dashed curve is X ,,,_, using Bichsel’s shell correction and I = 824 eV. The open circle is the point reduced from Burkig and MacKenzie’s relative stopping power measurements taking Al as standard material.
4. Discussion As can be seen from table 1, the present results agree very well with the values of the Rise’ data X0.99. This trend agrees with the Aarhus data of Andersen et al. [ 131 for Al, Cu and Ag. The Aarhus stopping power valuFs for Al, Cu and Ag are lower by - 1% than the Rise data [6] of Sorensen and Andersen. We have analyzed the data using the Bonderup shell correction [3]. The values of the Bonderup shell correction have been calculated using x = 1.358, where x is the constant that appears in the statistical model of the atom and is usually taken as 2”‘. The values of the Z:-correction have been calculated by the theory of Ashley et al. [lo-121 using x = 1.358 and b = 1.3 + 0.2. These values of constants, x and b, were determined in previous experiments [l]. The value of the mean excitation energy, I, has been taken as a free parameter and determined by the method of least squares to fit the X_ points. The best fit was obtained with Z = 745.4 eV. This value agrees very well with the value of 746 eV obtained from the measurement for 6.5 MeV protons [l]. The curve of Xtheo with Z = 745.4 eV is shown in fig. 2 by a solid curve. The curve represents the X cxp points very well. This point is the essential difference of our data from the revised Aarhus data for Au of Andersen and Nielsen [14]. Andersen and Nielsen say that the Bonderup shell correction curve does not agree with the experimental shell correction curve in the energy range from 1 to 7 MeV.
143
The open circle shows the reduced X value of Au obtained from the relative stopping power measurements of Burkig and Mackenzie [15] at 19.8 MeV taking Al as standard. First, we obtained the absolute value of the stopping power of Al for 20 MeV protons from eq. (1) taking Z= 167.4 eV and using the Bonderup shell correction [3] and Z:-correction calculated by the theory of Ashley et al. [lo-121. The Z value of 167.4 eV was obtained in our previous experiments [l]. Next, multiplying the relative value of stopping power of Burkig and MacKenzie with the stopping power for Al, we obtained the absolute value of the stopping power of Au for 20 MeV protons. Then, using eq. (3) we obtained the X-value of Au at 20 MeV. The open circle falls very near to the solid curve. Recently, Berger [4] has analyzed many experimental data using Bichsel’s shell correction [5] taking into account the Bloch correction and the Z:-correction. In Bichsel’s method of calculating the shell correction, it is assumed that the higher correction term than the M shell has the same shape as the L shell correction of Walske [16]. Then, two free parameters are multiplied with the energy value and the shell correction value. Berger has obtained the Z value for Au as (790 + 30) eV. In fig. 2, Berger’s curve using Bichsel’s shell correction and an Z value of 790 eV is shown by a dot and dash curve. As can be clearly seen, Berger’s curve lies much lower than our curve using the Bonderup shell correction. As is shown in eq. (2). the Xtheo curve can be shifted up and down by changing the value of Z without changing the shape of the curve. We have taken the value of Z as a free parameter. Using Bichsel’s shell correction we have fitted the Xtheo curve with our X exp points by the method of least squares. The best fit has been obtained with the Z value of 824 eV. This curve is also shown in fig. 2 by a dashed curve. As can be seen from the figure, this curve also fits the XexP points fairly well. Therefore, it is difficult to determine exactly which shell correction represents the experimental points better from the present experiment. However, as is shown in fig. 2, Bonderup’s curve with Z = 745.4 eV and Bichsel’s curve with Z = 824 eV diverge from each other from 8 up to 20 MeV. Therefore, if we make stopping power measurement in the range from 8 to 20 MeV, it may be possible to judge which shell correction better represents the experimental points. The stopping power measurements in the range from 8 to 20 MeV have actually been performed using the tandem Van de Graaf accelerator of the University of Tsukuba in cooperation with Drs K. Shima and T. Ishihara. The preliminary results of this experiment appear to show that the experimental X value points fall in between the two theoretical curves. Detailed results will be soon published [17]. III. ENERGY LOSS
144
R. Ishiwari et al. / Stopping power of Au for protons
The authors would like to thank the late Professor J. Muto and Professor S. Kobayashi for their kind support throughout the experiment. Thanks are also due to Drs K. Takimoto and M. Nakamura for their kind cooperation.
References
[l] R. Ishiwari, N. Shiomi and N. Sakamoto, Nucl. Instr. and Meth. 194 (1982) 61. [2] R. Ishiwari, N. Shiomi and N. Sakamoto, these Proceedings (ACIS-IO), p. 195. [3] E. Bonderup, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 35 (1967) no. 17. (41 M.J. Berger, private communication (August 1982). [5] H. Bichsel, UCRL-17538 (University of California, 1967). [6] H. Sorensen and H.H. Andersen, Phys. Rev. B8 (1973) 1854.
[7] H. Bichsel, Natl. Acad. Sci.-Natl. Res. Council Publ. 1133
(1964) p. 17. [8] H. Bichsel, American Institute of Physics Handbook 3rd ed. (McGraw-Hill, New York, 1972). [9] J. Lindhard, Nucl. Instr. and Meth. 132 (1976) 1. [lo] R.H. Ritchie and W. Brandt, Phys. Rev. Al7 (1978) 2102. [ll] J.C. Ashley, R.H. Ritchie and W. Brandt, Phys. Rev. B5 (1972) 2393. 112) J.C. Ashley, R.H. Ritcbie and W. Brand& Phys. Rev. A8 (1973) 2402. [13] H.H. Andersen, J.F. Bak, H. Knudsen and B.R. Nielsen, Phys. Rev. Al6 (1977) 1929. 1141 H.H. Andersen and B.R. Nielsen, Nucl. Instr. and Meth. 191 (1981) 475. 1151 V.C. Burkig and K.R. MacKenzie, Phys. Rev. 106 (1957) 848. (161 M.C. Walske, Phys. Rev. 101 (1956) 940. 1171 R. Ishiwari, N. Sbiomi, N. Sakamoto, K. Shima and T. Ishihara, to be published.