Stopping powers of mylar for protons from 0.40 to 3.25 MeV

Nuclear Instruments and Methods in Physics Research B 129 ( 1997) l-4

NOM B

Beam Interactions with Materials & Atoms ELSEVIER

Stopping powers of mylar for protons from 0.40 to 3.25 MeV N. Shiomi-Tsuda,

N. Sakamoto, Depariment

of Physics.

H. Ogawa, M. Tanaka, M. Saito, U. Kitoba Nara

Women s Univcrsiry

Nara

630, Japan

Received 16 December 1996; revised form received 18 February 1997

Abstract Stopping powers of mylar have been measured for protons of 0.40 to 3.25 MeV from the accelerator at Nara Women’s University. The experimental setup and procedure are quite similar to those of the previous experiments [e.g., Nucl. Ins&. and Meth. B 103 (1995) 225; Nucl. Ins&. and Meth. B 47 (1990) Ill]. The results agree well with the calculated values of the ICRU Report 49 for protons above 1.50 MeV. For protons under 1.50 MeV, however, our results are higher as the energies decrease. The mean excitation energy, viz., the I-value, for mylar has been extracted from the measured stopping power data. The Z-values extracted with Bonderup’s [K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 35 (1967) no. 171 and Bichsel’s [UCRL Report No. 17538 ( 1967); ICRU Report 37 (1984)] shell corrections are 81.7 and 80.8 eV, respectively, and agree well within their uncertainties. They are also in good agreement with the previous I-values of 80.8 and 80.2 eV [Nucl. Instr. and Meth. B 103 ( 1995) 2551 obtained from measurements at 4.0-l 1.5 MeV with the respective shell corrections and also with the value recommended in ICRU Reports 37 and 49, 78.7 eV, the uncertainty of which is stated to be 5-10%. The Z-values obtained by combining the previous data and present stopping power data are 81.8 and 80.9 eV with the respective Bonderup’s and Bichsel’s shell corrections.

1. Introduction Stopping powers of mylar previously were measured for 4.0-l 1.5 MeV protons from the tandem Van de Graaff accelerator at Kyoto University [ 11. The results agreed well with the tabulated values of the ICRU Report 49 [ 21. Using the modified Bethe-Bloch formula and the Bragg additivity rule for the stopping power of compounds [ 31, the effective mean excitation energy (hereafter we call it the I-value) for mylar has been extracted from the experimental results. The extracted I-values were in good agreement with the recommended value in ICRU Reports 37 [ 41 and 49 [ 21. In the experiment reported here, the stopping powers of mylar have been measured for protons from 0.40 to 3.25 MeV from the 1.7MV tandem Van de Graaff accelerator at Nara Women’s University (hereafter, “Naraaccelerator”). Furthermore, the I-values of mylar have been determined from the stopping power data by the same analysis as that used in previous experiments [ 1,5].

2.

Experimental

procedure

The energy of the protons from the Nara-accelerator was determined with a 90’ beam analyzing magnet of the radius of curvature 1 m. The magnet was calibrated using the resonances of the elastic scattering of alpha particles by 160( cy,(Y)I60 at 3034 f 4 keV [ 61 and by ‘*C( (Y,cy)‘*C at 0168-583X/97/$17.00 @ 1997 Elsevier Science B.V. All rights reserved PIISO168-583X(97)00144-4

4265 f 5 keV [ 71. The experimental setup and procedure were quite similar to those described in detail in previous papers [ 1.5.81. Therefore, we give here a short description of them. Fig. 1 shows the experimental setup. The analyzed beam of protons passed a double slit system (Sl and S2) and baffle through and then entered the scattering chamber. The beam scattered at an angle of 15” by a thin gold foil of 172 pg/cm* mounted at the center of the scattering chamber was used for the energy loss measurement. After being collimated with a double slit system (S3 and S4), the beam was brought to a target mounting device shown in the inset of Fig. 1. By using the device which could make metronomic motion, we could detect protons that passed the target through and incident protons that did not pass the target through simultaneously in one exposure, with a surface barrier silicon detector. The proton pulses from the detector were amplified and were recorded on a 4096 channel pulse height analyzer. From the pulse height difference of the protons with and without the target, the absolute energy loss of protons in the target in keV was determined by the very same method as that of Ref. [ 11. Mylar films used in the present experiment were supplied by ‘Toray’ Co., Ltd. The chemical structure is given by CH20H[CloHs04]nOHCH2, the mean value of n being 95. Because the proton energies used in the present experiment range from 0.40 to 3.25 MeV, about one order of magnitude, three thicknesses of mylar film 1.5, 6 and 11.5 pm were

N. Shiomi-Tsuda et al./Nucl.

Analyzed Beam .

Sl 1 I

2mm xl0mm

Instr. and Meth. in Phys. Res. B 129 (1997) 1-4

Au 220 “i”

555

/

/ -. 2mm

,5”

\

8mm Baffle

8-c s3 -K/

, Fig. 1. A schematic diagram of the experimental setup for the energy loss measurement using the “metronomic technique”.

Fig. 2. Stopping power ratios of the present results and experimental data of Rauhala and RI&ten to the tabulated values of ICRU Report 49 plotted against the proton energy. The previously reported results (Ref. [ 11) for 4.0- 11.5 MeV protons also am shown.

used to measure the stopping powers in the three proton energy ranges of 0.40-0.80, 0.70-2.00 and 1.50-3.25 MeV, respectively. The respective mass thicknesses were 0.2140, 0.8808 and 1.622 mg/cm*. Because the mylar films tend to adsorb moisture from the ambient atmosphere, special attention was paid to estimating their weights when the energy loss of the protons was measured in the scattering chamber, as described in detail in Ref. [ 11. The thickness uncertainty is largest for the 1.5 ,um thick film, which crumples easily. The final results for each overlapped proton energy were obtained by averaging.

3. Results The observed energy loss divided by the average path length of protons in the target, AE/Ax, corresponds, to a good approximation, to the stopping power, dE/dx, at the average energy defined by E = & - AE/2 where & is the incident proton energy, if the energy loss does not exceed

20% of E+ For the energy loss which exceeded it, the stopping power at the average energy B was obtained by using Eqs. (4)) (5) and (6) in Ref. [ 51. Table 1 shows the present results in keV/ (mg/cm*) and compares them with the tabulated values from ICRU Report 49 [ 21 (the ICRU values). The experimental data of Rauhala and Rtiis&nen [ 91 for the common energy intervals also are given together with the ICRU values [ 21. To show the differences among each data set clearly, Fig. 2 gives the stopping power ratios of the present results and the experimental data of Ref. [ 93 to the ICRU values [ 21. The previous data [ 1 ] reported for 4.011.5 MeV protons also are shown in Fig. 2. In the higher energy range of 1.50-3.25 MeV, the experimental uncertainty of the present stopping power values was estimated to be f0.35% by the method described in Ref. [ 11. The uncertainties for the energy ranges of 0.70-2.00 and 0.400.80 MeV were estimated as f0.40% and f0.45%, respectively. These differences are due mainly to the accuracy of the mass thickness measurements of the mylar films used.

N. Shiomi-Tsuda

et al./Nucl.

Instr. and Merh. in Phys. Res. Li 129 (1997) l-4

3

Table I The present stopping power data given in keVl(mg/cm2) and compared with the tabulated values in ICRU Report 49. The experimental data of Rauhala and RtWnen for the common energy intervals also are given together with the values from ICRU Report 49. Stopping powers

E (MeV) Present data 0.336 0.393 0.4 0.457 0.5 0.509 0.525 0.6 0.648 0.7 0.730 0.75 0.8 0.879 0.9 0.940 1.00 1.096 1.148 1.25 1.311 1.355 1.50 1.519 1.552 1.725 1.75 1.762 1 933 1.966 2.00 2.136 2.25 2.339 2 370 2 50 2 75 2.840 2.910 300 3 25 3 340

Ref. [81

Ref. [21

462 432

485.9 439.4 434.4 398.6 376.5 372.3 365.1 335.3 319.1 303.5 295.2 290.0 211.9 260.9 256.8 249.4 239.1 224.5 217.4 204.9 198.2 193.7 180.3 178.7 176.0 163.2 161.5 160.7 150.3 148.4 146.6 139.7 134.5 130.7 129.4 124.4 115.9 113.1 111.1 108.6 102.3 100.2

441.4 f 2.0 410 381.9 f 1.7 370 374 339.0 f 1.5 325 306.0 f 1.2 288 292.6 f 1.3 279.4 f 1.0 260 258.0 f 1.0 241 240.1 f 1.0 224 214 205.6 f 0.8 194 187 180.3 f 0.6 176 173 163 161.5 f 0.6 158 146 142 146.6 f 0.5 139 134.5 f 0.5 131 127 124.2 f 0.4 115.7 f 0.4 114 115 108.3 f 0.4 101.9 f 0.4 104

4. Discussion

As seen in Fig. 2 and Table 1 the present results for protons above 1SO MeV agree well with the ICRU values [ 21 and also connect smoothly with the previous reported values [ 11. For protons below 1SO MeV, however, the present results rise as the energy decreases. The values of Rauhala and Raisanen [9] show a wide scatter, leading to a large uncertainty of f3%. The Z-value for mylar was extracted from the stopping power data using a modification of Bichsel’s X variable [ lo]

4.42

~

Bonderup

I = 81.7 eV

2

1 Proton

1

3

Energy (MeV)

Fig. 3. X,,, points and Xb curves with the best fit I-values. Solid circles are the X,,, points obtained from the present stopping power data. The solid and dashed lines show the X,b curves obtained respectively with Bonderup’s and Bicbsel’s shell corrections.

4.50.

4.46 a, P $

4.46.

x 4.44

442

1

t : 0.4

06

0.6

1.0

1.5 2 3 4 Proton Energy (MeV)

56

8

10

1:

Fig. 4. The X variable for protons from 0.40 to 1I.5 MeV on a logarithmic scale. Open circles show the Xexp points obtained from reported stopping power data. The other symbols and description are the same as in Fig. 3.

in the same as the previous report [ 11. As given in Bqs. ( 13) and ( 14) in the report [ 11, the experimental and theoretical X variables, Xexpand X,b respectively are defined as Xexp= 10

2mv2

( > P2 1

_

p

-

mu2 1 -4~Zfe~Na(Z2/A)

and Xh=lnI+

(

c z2

>

-Z~(EI)--4,

(2)

where the quantities within the brackets ( ) denote the effective values for the composite material on the assumption of the Bragg additivity rule [3]. The other symbols have

4

N. Shiomi-Tsuda

Ed ol./Nucl.

Instr. and Meth. in Phys. Rex B 129 (1997)

their usual meanings (e.g., Ref. [I]). In the calculations of the X,b, we used the theory of Ashley et al. [ 11,121 to estimate the Barkas correction, and Bondet-up’s [ 131 and Bichsel’s [ 14,4] shell corrections. Adjustable parameter values contained in the Barkas correction of Ashley et al. and in the Bondetup shell correction were the same as those of the previous report [ 1J, i.e., y = 1.336 and b = 1.32 [ 151. Adjustable parameter values of Bichsel’s shell correction were taken from the ICRU Report 37 [4], the same as Ref. [ 11. Taking the Z-value as an adjustable parameter, we compared the Xtko values with the XexPvalues. The method of least squares was used to obtain the best fit values of I. The best fit i-values are 81.7 * 3.4 eV with Bonderup’s shell correction and 80.8 f 3.6 eV with Bichsel’s shell correction. The uncertainties were estimated from the theoretical accuracy of the shell corrections (~t20%) and from the experimental uncertainty of the stopping powers. Fig. 3 shows the Xexppoints obtained with the present experimental data and X,b curves with the best fit I-values. The solid and dashed lines show the Xh curves obtained with Bonderup’s and Bichsel’s shell corrections, respectively. As seen in this figure, the X[heocurve obtained with Bonderup’s shell correction fits the Xerp points well. The XkO curve obtained with Bichsel’s shell correction also can be regarded as well reproducing the experimental situation within the uncertainties. Both the present I-values for mylar, 81.7 f 3.4 and 80.8 f 3.6 eV agree well within the uncertainties. They agree well within the uncertainties with the reported I-values [ 1] obtained with Bonderup’s and Bichsel’s shell corrections, respectively 80.8 f 1.7 and 80.2 f 1.7 eV and also are in good agreement with the value recommended in Refs. [4,2], 78.7 eV, the uncertainty of which is stated to be 5-10%. Results of X variables obtained by the combination of the present and

14

reported [ 1] stopping power data are given in Fig. 4. The best&Z-valuesare81.8f3.1 and80.9f3.2eVrespectively for Bonderup’s and Bichsel’s shell corrections and are very similar to those extracted from the present data for 0.403.25 MeV protons within the same shell corrections.

References [ I ] N. Shiomi-Tsuda, N. Sakamoto and H. Ogawa, Nucl. Instr. and Meth. B 103 (1995) 255. 121 ICRU Report 49, Stopping Powers and Ranges for Protons and Alpha Particles (International Commission on Radiation Units and Measurements, 1993 ) 131 W.H. Bragg and R.K. Kleeman, Philos. Mag. 10 (1905) 318. 14) ICRU Report 37, Stopping Powers for Electrons and Positrons (International Commission on Radiation Units and Measurements, 1984). [ 51 R. Ishiwti, N. Shiomi-Tsuda, N. Sakamoto and H. Ogawa, Nucl. Instr. and Meth. B 47 ( 1990) 111. 161 J.A. LeavitS L.C. McIntyre, Jr., M.D. Ashbaugh, J.G. Oder, Z. Lin and B. Dezfouly-Arjomandy, Nucl. Instr. and Meth. B 44 ( 1990) 260. [7] J.A. Leavitt, L.C. McIntyre, Jr., P. Stoss, J.G. Oder, M.D. Ashbaugh, B. Dezfouly-Arjomandy, Z-M. Yang and 2. Lin, Nucl. Insu. and Meth. B 40/41 (1989) 776. [ 81 R. Ishiwari, N. Shiomi-Tsuda and N. Sakamoto, Nucl. Ins& and Meth. B 31 (1988) 503. [91 E. Rauhala and J. RGsXnen, Nucl. Instr. and Meth. B 35 (1988) 130. I IO] H. Bichsel, A Critical Review of Experimental Stopping Power and Range Data, in: National Academy of Science-National Research Council, Pobl. 1133, Studies in Penetration of Charged Particles in

Matter (1964) p. 17. J.C. Ashley, R.H. Ritchie and W. Brandt, Phys. Rev. B 5 (1972) 2393. 1121J.C. Ashley, R.H. Ritchie and W. Brandt, Phys. Rev. A 8 (1973) 2402. 1131 E. Bonderup, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 35 ( 1967) “0.17. [141 H. Bichsel, UCRL Report No. 17538 (1967) (unpublished). [ill

[I51 N. Shiomi-Tsuda.

N. Sakamoto, H. Ogawa and R. Ishiwari, Radiat.

Eff. and Defects in Solids 117 (1991) 185.