TECHNICAL JOURNAL. 3 (1976) 6 - 16

DETERMINATION OF TOTAL CROSS SECTION AND BUILDUP FACTOR OF COAL FOR Cs-137 AND Co-60 GAMMA RAYS.

0. ÖZDEMİR - C. ÖZMUTLU

Ankara Nuclear Research and Training Center

ABSTRACT

The total cross sections of coal for Cs-137 and C o-60 gamma rays have been determined theoretically and experimentaly. The differences between the experimental and theoretical results were found about 6 %. The total cross sections were measu­red by means of the ratios of the full energy peak areas which correspond to the different thicknesses of coal. The number buildup factors for the thickness range of 0-80 mg/mm2 have been determined as the ratio of the counts of scattered and unscattered photons to the count of unscattered photons. The determination of effective atomic number for coal has been found by using the effective — Z — method [2 -3 ]. The curves for the dose buildup factor of Ca versus /zx for various photon energy have been used to find the dose buildup factor of coal.

ÖZET

Kömür’ün Cs-137 ve C o-60 gamaları için toplam tesir kesiti, deneysel ve teorik olarak tayin edilmiştir. Deneysel ve teorik değerler arasında 6 % farklılık bulunmuştur. Toplam tesir kesiti çeşitli kömür kalınlıkları için ölçülen tüm-enerji pik alanları ora­nından yararlanılarak ölçülmüştür. 0-80 mg/mm2 arasındaki kalınlıklar için number- buildup faktörü, saçılmış ve saçılmamış foton sayısının saçılmamış foton sayısına ora­nından elde edilmiştir. Ca’un çeşitli foton enerjisi için /zx’e bağımlı dose-buildup faktörü eğrileri kömür’ün dose-buildup faktörünün elde edilmesinde kullanılmıştır.

INTRODUCTION

Since not ali gamma interactions are absorptive and some scatte­red radiation may ultimately penetrate a shield, a numerical correction is commonly used in attenuation calculations. The uncollided flux is calculated using total cross sections, and then multiplied by the approp­riate buildup factor to give a more realistic value of the transmitted flux. The important orders of magnitude which are involved in the design of shields against gamma radiations, such as, for example, the biologi­cal dose D, the heat generated in the shield and the energy flux I, are functions of the gamma particle flux in the shield.

DETERMINATION OF TOTAL CROSS SECTION AND BUILDUP FACTOROF COAL FOR Cs - 137 AND Co - 60 GAMMA RAYS.

g

BUILDUP FACTORS

Within the scope of the point kernel theory, [1,7] the flux 0 (P',E) at a point P' of a homegeneous and infinite medium, is given by

0 (P'.Eo)= /

V

B.S(P.Eo) dV ( 1)

where, V is the volume of all points constituting the source region (cm3),

P a general source point of V,

S(P,E0)

P'

Intensity of the source of gammas of energy E0 in point P per unit of volume (cm3 sec ’)

the «detector» point, or the point in which either the dose or the heat generated by the gammas is to be calculated

X= (P-P ')

Pt (E0)

B

the distance between the source point and the detector point (cm),

Total absorption coefficient of the medium for a collima­ted beam (cm'1)

Buildup factor

In particular, if the value to be found by means of 0 (P',E0) is the biological dose, B represents the dose-buildup factor, BD, on the other hand, if the heat generated in the shield is to be calculated, B represents the absorbed energy buildup factor, BA, If the energy flux is of interest, B represents the energy buildup factor, BE, finally if the gamma flux is of interest, B will indicate the number buildup factor, BN.

The buildup factors are functions of the initial energy of the gammas Eo, the number of relaxation lengths px and the atomic number of the shield material (Z).

Except for a few substances, such as water and concrete, most of the buildup calculations have been made for single elements [1 -3 ] It frequently happens that shielding materials will consist of homogeneous mixtures of a number of elements, and it is important to be able to pre­dict their behavior from the available computations, it is usually possible to find an equivalent single element having the same gamma-ray inte­raction properties as the mixture.

10 Ü. ÖZDEMİR — C. ÖZMUTLU

EFFECTIVE-Z-METHOD

The total cross section could be found for a mixture or compound of some elements using fallowing expression.

Here, a, and pit are the weight fraction and total cross section of the i th element respectively. For finding the effective Z for the mixture, to compare the value of pT of the mixture with the corresponding pT values for individual elements, the ratios of Pt/ ps (scattering cross section) vs. E are plotted for the mixture and the elements to find a reasonable match over the energy region of interest. The atomic number of the ele­ment which provides the match can be taken as effective — Z— of the mixture. However, if the values of the ratio pT/ps for the mixture and an element are equal to each other for the individual energies in the energy region of interest, and the pT curves have same shape, the atomic num­ber of the element can also be taken as effective — Z— . That element is known as equivalent element. The buildup factors for the equivalent element can then be found from the tables by simple interpolation in Z [2 -5 ],

EXPERIMENT

The experimental set-up, consists of the fallowing main parts: 3 "X 3 " Na (Tl) scintillation detector, a linear amlifier and a 4096 channel PHA. Thin coal tablets 72 mm in diameter, were prepared by using 100 tons capacity hydrolic press. In order to fixed experimental conditions a cylindrical glass tube in 1 mm thickness, placed between the source detector. The detector side of the tube was covered by the mylar films in 0.03 mm thickness and a plexiglass ring was placed on the other side for supporting the standart point gamma sources. The shape of the glass tube and tablets are given in. Fig. 1.

The gamma - ray spectrum of the Co - 60 (1,17 - 1,33 MeV) and Cs -137 (0.662 MeV) were taken using the experimental apparatus for each coal tablet thickness. The counting time was chosen 200 sec. for each spect­rum, The net full energy-peak areas versus coal thickness plotted and the total cross sections were determined using the ratio of the full energy-peak areas. To find the total cross sections, the least squares method was applied to the Eq.3, by a computer program.

(2)

V-T =

In N (o) — In N (Xj(3)

X

DETERMINATION OF TOTAL CROSS SECTION AND BUILDUP FACTOROF COAL FOR Cs - 137 AND Co - 60 GAMMA RAYS.

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Standartsource

Fig. 1. Experimental set-up

Here N (X) is the full energy-peak areas for the point X in the shield

slab, N (o) is the incident full energy-peak areas.

As it is known the number buildup factor BN(px) is defined as [6].

Bn((xx) (4)N (X) D

Where N(Xj Dis undeflected or direct component of the total number of gammas at point X, N (x)t 's the total number of gammas at point X and defines the sum of the direct and scattered number of gammas;

N (X)T = N ( X ) D + N ( X ) S 151

The number buildup factor BN(px) was found by calculating N(X)T by use of measured total net spectrum areas and dividing this by N(X)0

calculated by use of Lambert’s law N(X)D = N(0) e _ t̂X.

12 Ü. ÖZDEMİR — C. OZMUTLU

Fig. 2. Total net spectrum areas, N (x)T and calculated undeflected compenent, N (x)ü of N( x ) t versus coal thickness, x. (mg/mm2)

The curve of the N(X)T and N(X)D is plotted againts coal thickness in Fig. 2, and the number buildup factors are plotted in Fig. 3, as a function of coal thickness. The dose buildup factors were found by using the effective Z method for Co-60 and Cs-137 gamma energies. As it seen from Fig. 4, the total cross section curves of coal have the same shape with Ca. The ratios of p.T/p.s of Ca and Coal have been compared for energies of Co - 60 and Cs-137 gamma’s. The maximum difference was found 0.4 % for these reason Ca has been accepted as equivalent element.

DETERMINATION OF TOTAL CROSS SECTION AND BUILDUP FACTOR OF COAL FOR Cs - 137 AND Co - 60 GAMMA RAYS.

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Fig. 3. Buildup factors of coal as a function of thickness for Cs-137 and Co -60 gamma rays.

The dose-buildup factor data taken from the tables of reference 2 and 3, are plotted against Z. Then the values for Ca are obtained from this curve by simple interpolation in Z and plotted in Fig. 5, as a functionof [IX.

In Table - 1 the values of total cross section, pT of coal are given for the gammas of Co-60 and Cs-137.

14 Ü. ÖZDEMİR — C. ÖZMUTLU

Fig. 4. Total cross section versus gamma ray energy for main individual elements in coal.

CONCLUSION

As it is seen from the Table-1. the experimental values of total cross sections are too close to the theoretical results. The main source of the error on the values of experimental pT are statistical evaluation on counts of the full energy - peaks. The error on the experimental p.T value is characterized by introducing the standart evaluation of least square fitting.

DETERMINATION OF TOTAL CROSS SECTION AND BUILDUP FACTOROF COAL FOR Cs - 137 AND Co - 60 GAMMA RAYS.

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Fig. 5. Dose buildup factors versus gamma ray energy for Ca [3 ].

16 Cl. ÖZDEMİR — C. ÖZMUTLU

TABLE— 1. Total cross sections of coal for Cs-137 and C o-60 gamma rays.

GammaSource

Experimental /iT (c m 1)

Theoric /*T (cm ') DIFFERENCE % DIFFERENCE

Cs-137 0.1159 0.1233 0.0074 5.2

C o-60 0.0856 0.0903 0.0047 6

Due to the very small difference between the two gamma energy of Co -60 gammas, the average energy is assumed as 1.25 MeV in deter­mination of the dose-buildup factors for Co-60 gammas. The other assumption is that, the intrinsic efficiency will change very slightly for the energies of Co-60 gamma rays.

The changes in the absolute efficiencies of 3x3 inch Nal(TI) detec­tor used in experiment had been checked [7] for the gamma energies. It was found that, relative deviations in absolute efficiencies for the gamma energies 1.17-1.33 MeV. are about 4 % in our experiment.

REFERENCES

[1 ] Buscaglino, S. and Manzini, R., Buildup Factors Coefficients of the Equation ot J. J. Taylor. Report ORNL-TR-80 (Rev), (1965).

[2 ] Goldstein, H., Fundamental Aspects of Reactor Shielding, Addison - Wesley Pub­lishing Company (1971).

[3 ] Blizard, E. P.t Chilton, A. B., Jaeger, R. G., Grotenhuis, M., Honig, A., Eisenlohr, H. H., Engineering Compendium on Radiation Shielding Vol. 1, Springer-Verlag Berlin Heidelberg NeW-York (1968).

[4 ] Kazanskii, Yu. A., Kukhtevich, V. I., Matusevich, E. S., Sinitsyn, B. I., Tsypin, S. G. Physics of Reactor Shielding, Atomizdat Moskva (1969).

[5 ] Dennis, R.f Purohit, S. N., Brownell, L. E., Procedures For Shielding Calculations, AECU-3510 (1957).

[6 ] Schaeffer, N. M., Reactor Shielding For Nuclear Engineers (1974).

[7 ] Heath, R. L., Scintillation Spectrometry Gamma - Ray Spectrum Catalogue, Phillips Petroleum C. Atomic Energy Division Idaho Operations Office, U. S. Atomic Energy Commission (1957).