IL NUOVO CIMENTO VOL. 100 A, N. 3 Settembre 1988

Stopping Powers of Protons in Some Organic Materials in the Energy Range 0.1 MeV to 200 MeV (*).

R. PRASAD

Department of Natural Sciences, Mutah University, P.O. Box 7 - Mutah, Karak, Jordan

(ricevuto il 30 Marzo 1988)

Summary. -- The study of the energy loss phenomenon of low- hand high- energy protons in organic materials is of great physical importance. In the present paper, a simple computational method has been described and used to compute the mass stopping powers of protons from 0.1 MeV to 200 MeV in some important organic (polymeric) materials.

PACS 29.70.Gn - Energy loss and energy range relations.

1. - I n t r o d u c t i o n .

Organic materials, more specifically polymers or plastics, have for many years been replacing traditional materials in scientific research and industries. Recent discoveries, still at laboratory stage, that some polymers can be turned in to good conductors, envisage their potential applications (1) in research and industries. In the present paper, a simple computational method has been described and used to derive the mass stopping powers of protons from 0.1 to 200 MeV in polymeric materials, v/z. polyacetal, diacetate cellulose, polystrene, polythene, polyvinylchloride (PVC), teflone and polymethylmethacrylate. Further, the meted described here can also be employed to study the energy loss of low- and high-energy protons in biological materials. Since the stopping power of protons is directly related to the linear energy transfer, such studies can be of paramount importance for the trace element analysis by proton-induced X-rays and also in the radiotherapeutical applications.

(*) To speed up publication, the author of this paper has agreed to not receive the proofs for correction. (1) D. BLOOR: Spectrum, 188, 8 (1984).

435

436 R. PRASAD

2. - C o m p u t a t i o n a l m e t h o d .

The relativistic expression for the mass stopping power of heavy charged particles in a material is well known and can be expressed (=) in the desired form a s

dE z~ e4 No(Z/A) (1) S (E)= - d---~ -= 4=~moV 2 [ln2moV2/I-ln(1 -[9) - [ 9 - Co/Z -r

where z is the effective charge of the charged particle (for proton, z --- 1), e is the electronic charge, No is Avogadro's number, Z and A are the atomic number and the atomic weight, respectively, of the stopping material, mo is the rest mass of the electron, eo is the permittivity of the free space, V is the velocity of the projectile (proton), I is the mean excitation potential of the atoms in the medium and fl = V/C is the relativistic velocity ratio for proton. The terms Co/Z and ~(fl) account for various inner shell corrections and density correction, respectively. It is imperative to mention that these last two terms in eq. (1) are insignificant for the present energy range and hence can be neglected. Also, it is worth mentioning that the relationship between the mass per unit area and the thickness x (in cm) of the stopping material is, of course, 5 = xp, where p is the density of the material.

Thus eq. (1) takes the form

z2 e4 No(Z/A) [ 2fl2moC 2 ] (2) S(E)= 4~omoC2 f l n I ( l _ / ~ ) /~ '

where moC 2 is the rest mass energy of the electron. Further, the relativistic velocity ratio fl, of a particle, is expressed as

(3) f12 = [1 - (1 + E/mC'Z)-~,

where E is the kinetic energy and mC 2 is the rest mass energy of the particle. For proton, eq. (3) transforms as

(4) f12 = E 2 + 1 8 7 6 . 5 2 E (938.26 + E ) 2 "

Now, using eq. (4) and substituting the numerical values for various physical constants, eq. (2) for the mass stopping power (MeV cm 8 g-l) of protons reduces to

(5) S(E) = (Z /A )(X/Y)[In 1.161Y - In I] - O. 307 Z /A ,

(') H.A. ENGE: Introduction to Nuclear Physics (Addison-Wesley Pub. Co., Reading, Mass., 1981).

STOPPING POWERS OF PROTONS IN SOME ORGANIC MATERIAI~ ETC. 437

where

(6) X = (0.307E 2 + 576.09E + 270261.87),

(7) Y = E 2 + 1876.52E

and E is the proton energy in MeV. The unknown parameters in eq. (5) are Z/A and In I, which can be calculated

using Bragg's additivity rule (~) for a material composed of i types of different species of atoms. Thus the average values of Z / A and In I, following Bragg~s additivity rule, can .be written as

(8) (Z/A) = Z W,(Z,/AJ i

and

W i Z i l n l i / A i (9) ( l n I ) = E, ( Z / A ) '

TABLE I. - The values of W (percentage composition by weight), I and the average values of Z/A and In I of the organic materials in question.

Materials Constituents W % (Z/A) (In I)

1) polyacetil C 40.0 0.532 4.305 H 6.66 0 53.33

2) diacetate cellulose C 43.75 0.530 4.309 H 6.25 0 50.0

3) polystyrene C 92.307 0.537 4.167 H 7.692

4) polythene C 85.714 0.570 4.015 H 14.285

5) polyvinylchloride (PVC) C 38.709 0.512 4.641 H 4.838 CI 56.451

6) teflone C 24.0 0.480 4.677 F 76.0

7) polymethylmethacrylate C 60.0 0.539 4.227 H 8.0 0 32.0

(8) H. BICHSEL: Radiation Dosimetry, Vol. 1, edited by F. H. A~'rIx and W. C. ROESCH (Academic Press, New York, N.Y., 1968).

29 - II Nubvo Cimen~ A.

438 R. PRASAD

where W is the percen tage weight of a par t icular type of a tom in a given mater ia l and the subscr ipt i s tands for the different types of a toms in a given composition. The values of I , the excitat ion ene rgy for different e lements , can be t aken f rom the more realistic compilation work of Ziegler (4).

TABLE II. - M a s s stopping powers (MeVcm2g -2) ofproton,s in organic materials 1) to 7) as referred in table I.

E (MeV) S(E)

1) 2) 3) 4) 5) 6) 7)

0.1 826.643 820.481 941.158 1123.8 547.761 488.634 898.079 0.2 678.957 674.877 738.72 846.526 529.51 483.968 718.175 0.4 472.383 469.843 503.522 565.68 392.643 361.877 493.746 0.6 366.81 364.921 388.062 432.727 311.686 288.054 381.737 0.8 302.753 301.232 318.956 354.175 260.361 240.973 314.315 1.0 259.38 258.099 272.507 301.752 224.812 208.269 268.857 2.0 156.475 155.734 163.3 179.594 138.165 128.281 161.571 3.0 114.848 114.314 119.502 131.025 102.232 95.009 118.387 4.0 91.789 91.367 95.337 104.335 82.104 76.347 94.52 5.0 76.97 76.619 79.845 87.268 69.082 64.262 79.204 6.0 66.574 66.273 68.996 75.336 59.902 55.74 68.469 7.0 58.843 58.578 60.938 66.485 53.052 49.377 50.492 8.0 52.82 58.612 54.698 59.639 47.726 44.428 54.312 9.0 48.056 47.841 49.71 54.172 43.456 40.46 49.371

10.0 44.127 43.93 45.626 49.698 39.951 37.201 45.323 15.0 31.731 31.591 32.758 35.623 28.847 26.874 32.562 20.0 25.094 24.983 25.88 28.115 22.872 21.314 25.736 25.0 20.92 20.828 21.56 23.404 19.102 17.805 21.447 30.0 18.037 17.959 18.58 20.157 16.493 15.376 18.486 35.0 15.92 15.851 16.392 17.776 14.574 13.588 16.312 40.0 14.295 14.233 14.713 15.95 13.098 12.213 14.644 45.0 13.006 12.95 13.383 14.503 11.927 11.122 13.322 50.0 11.958 11.906 12.301 13.327 10.973 10.233 12.246 60.0 10.353 10.308 10.645 11.527 9.51 8.871 10.599 70.0 9.179 9.139 9.435 10.213 8.44 7.873 9.396 80.0 8.281 8.246 8.51 9.209 7.62 7.109 8.476 90,0 7.572 7.54 7.779 8.416 6.972 6.504 7.749

100.0 6.997 6.967 7.187 7.774 6.446 6.014 7.16 120.0 6.121 6.095 6.284 6.795 5.644 5.266 6.261 140.0 5.483 5.46 5.629 6.084 5.06 4.722 5.609 160.0 4.999 4,978 5.13 5.544 4.615 4.307 5.112 180.0 4.618 4.598 4.738 5.119 4.266 3.981 4.722 200.0 4.311 4.293 4.422 4.777 3.984 3.718 4.408

(') J. F. ZIEGLER: Nucl. Instrum. Methods, 168, 17 (1980).

STOPPING POWERS OF PROTONS IN SOME ORGANIC MATERIALS ETC. 439

3. - R e s u l t s a n d d i s c u s s i o n .

The composition of polymeric materials under consideration along with the percentage composition by weight of their constituent elements are presented in table I. Also, the values of (Z/A) and ( lnI ) as calculated from eqs. (8) and (9), respectively, are shown in table I.

The mass stopping powers of proton in the materials in question have been computed using eq. (5) and are presented in table II. The main source of error in the computation of mass stopping powers in such materials of complex composition lies in the determination of the percentage weights of their constituent elements. Also, the error associated with the determination of I, the mean excitation energy, plays an important role.

Thus these are the two main sources of error which might affect the results of this calculation. Since we have not come across (to the best of my knowledge) any experimental results for the mass stopping powers of proton in these materials, a comparison with experimental values has not been possible. However, the calculated values by the present method may differ within about 10% from those quoted elsewhere in the literature.

@ RIASSUNTO (*)

Lo studio del fenomeno della perdita d'energia dei protoni a baasa e alta energia nei materiali organici 6 di notevole importanza fisica. Nel presente lavoro si 6 descritto e usato un semplice modello di calcolo per calcolare i poteri di rallentamento della massa dei protoni da 0.1 MeV a 200 MeV in alcuni importanti materiali organiei (polimerici).

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