LITERATURE CITED D. Wiles and R. Tomlinson, Phys. Rev., 99, 188 (1955). F. Brown, G. Hail. and A. Walter, J. Inorg. and Nucl. Chem., 1, 241 (1958). M.P. Glazunov et al., Atomnaya ~nergiya, 1._O0,6,622 (1961). H. Farrar, A. Dasgupta, and R. Tomlinson, Canad. J. Chem., 3_.99,3, 681 (1961). F. Hayes, Internat. J. Appl. RaG and Isotopes, _1, 46 (1986). T_ Steyn, Proc. Phys. 8oc., A69,, 865 (1956). K. Flinn and L. Glendenin, Phys. Rev.. 116, 744 (1956). D.G. Fleishman and V. V. Gtazunov, Atomnaya ~nergiya, 1_.22,4, 320 (1962). B.S. D~helepov and L, K. Peker, Decay Schemes of Atomic Nuclei [in Russian] (Izd. AN 8SSR, 1958). C. Crouthamel, Applied Gamma-Ray Spectrometry (Pergamon Press, London, 1960),

1. 2. 3. 4. 5. 6. % 8. 9. 10.

CALCULATING GAMMA

D. L. B r o d e r ,

BUILDUP FACTORS IN HETEROGENEOUS MEDIA

Yu. P. K a y u r i n ,

a n d A. A. K u t u z o v

Translated from Atomnaya ~nergiya, Vol. 13, No. 6, pp. 593-598, December, 1962 Original article submitted May 4, 1962

A semiempirical formula is proposed in [1] for computing Co6~ gamma-ray buildup factors in heterogeneous media. In this note, we report on a study of the appiicability of that formula to the region of higher energies, viz. 2.76 and 6.4 MeV. The gamma-ray source, yielding 2.76 MeV photons, was the radioactive isotope Na~. We treated only two principal lines, 2.76 MeV and 1.38 Me V (in 1 : 1 ratio) in our work. The facility, detector, and materials were identical to those in [1]. The gamma-ray attenuation coefficients for energies 2.'/6 and 1.38 MeV were taken from [2]. The dose rate from the Na ~4 source, in the absence of shielding, was DNa

r ) 2 , 7 6 ~ r)1,38 = ~0 ~ ~0 '

TABLE 1. Experimental and Theoretical Values of Gamma-Ray Buildup Factors in Heterogeneous Media for 2.76-MeV Gamma Quanta Mixture

taxi

P~§

2,266 4,493 4,493 4,493 7,271 7,271 7,27i t,500 3,000 3,000 3,000 4,500 4,800 4,800 8,250 2,899

Al

The same >)

>>

))

>)

AI@Pb The same ))

))

~)

Fe4-AI Alq-Pbq-AI Pbq-A1 q-Fe Fo-}-AI@Pb

1226

-3,007 4,490 2,899

u2x~.

u~x8

6,750 3,000 4,500 6,750 l, 500 2,250 3,000 7,27i 2,294 4,503 7,271 4,047 3,157 2,266 0,862 t, 500 2,266 3,000 3,000 i,382 1,500 2,2?2 w

B exp Bmix 7,32 4,69 5,67 8,21 5,t8 5,36 5,95 4,93 3,7i 4,64 5,89 6,34 5,98 5,85 8,06 4,00 6,32 6,ii 4,67

7,45 5,i5 6,42 8,45 5,13 5,78 6,39 5,03 4,03 L

TABLE 2. Theoretical and Experimental Values of Buildup Factors in Homogeneous Media for ~6.4-MeV Gamma Quanta Material

Polyethylene

Aluminum

5,02 1 6,431 6,25 i

~X

Btheor

Bexp

0,254 0,685 0,94C 1,420

t,12 t,30 1,4t t,62

t,19 1,40 t,48 1,66

0i2i5 0,860 t,506 3 1t9

1,08 .i,34 t,60 t,93 2,23

t,11 1,43 1,69 2,06 2,36

t,i5 t,48 2,05 2,47 3,63

i,09 t,33 2,04 2,24 3,50

1,26 1,73

t,it 1,6t 2,40 3,09

2,366

6,05[' 5,68 I 7,88 I

Iron

0,488 t,443 2,941 3,910 6,361

4,67

Lead

i,456 3,395 5,329 7,253

~,05 I 6,44 I 6,26 }

2;40 3,4t

TABLE 3. Computed and Experimental Values of Buildup Factors in Heterogeneous Mixtures for 9-'6.4- MeV Gamma Quanta Mixture Fe-] Pb Fe I-A1,

ltqxl 6,361 6,361 2,420 2,42O 3,227 3,227 3,227 3,227 2,438 2,438 4,795 4,795 4,795 4.795 2.438 2.438 7.253 4.815 2.458 t.016 O, 508 0.685

~x~

~t~x~

Bmi x

0,947 2,922

4,20 5,73

:l,076

2,29

3,227 -2,420 i - 4,863 -0,947 -4,795 -1,223 --

3,18 3,43 A I --I-Fe 4,8i 2,60 A1 t-Pb 41,45 t,98 4,638 -3,69 Pb-]- Fe l, 223 -2,78 4,875 -5,i3 t,076 -2,65 3;227 --3,59 Pb -]--AI 3,227 -2,82 t,6t3 -2,t3 1,0t61 - 3,77 Pb-~ PE* 1,2701 - 2,67 1,422 -2,i7 2,458 -2,15 PE-[- Pb 4,8t5 2,60 2,372 -2,t8 PE-~- Fe 1.021 2,372 -2,36 2,372 0,685 2, i0 Fe-~ PE 2,372 t,02t t - 2,23 Fe-~- Pb-[- Fe 2.439 2,397 1,472 3,35 Fe--t~ Pb q- A l 2.439 2,397 2,15t1 3,52 t~b-l- AI ~-Pb 2. 397 2,15t 2,357[ 3,42 At-I Fe I-Pb 2.151 2,439 2,357 3,{H PE --~-Pb !- PE 0. 594 4,815 10,594 2,60

Bexp 4,03 6, t6 2,16 3, if)

3,40 4,58 2,49 4,t9 1,81 3,57 2,75 4,95 2,47 3,491 2,7l I 2,04 3,53

2,5t I

2,14 2,07 2,47 1

where D~0"76 is the dose rate due to the 2.76-MeV line; D~0"as is the dose rate due to the 1.38-MeV line. The gamma constants for those lines are 11.9 and 7.15 r / h . respectively, i.e., D2'76

tl,9

D~, 38

7,t5 :

Then D~o"'t6= 0.625 DNa and D~0"m = 0.375 DNa, In the presence of n shielding layers, the total dose on the far side of the shielding is DNa ~1,38DI,38 __~ t 38~ \ , x =~x ~0 exp ( bti ' -,i}~ti=t -V'~xn2'76r~2'76 - ~ exp 0 (

~ P~2'76xt ~ i "!

And, accordingly. DNa •

3r Ix

x

•0•375B•

•• •

- DONa --

(

exp ~ - -

s i= I

,

i/ , (1)

n

0,625 exp ~f -

2 "2'76 ~i xi. i=t 2,27. where B2.~ x and B1.~ x are the gamma build-up factors in a 2,08 given heterogeneous medium for energies 2.76 and 1.38 I 2,09 MeV, respectively. Blx"~ was calculated from the semitl 3,32 empirical formula stated in [1] for each heterogeneous [ 3,49 medium. Control measurements of the buildup factors for [ 3,17 such homogeneous media as lead, iron, and aluminum, 3,88 under conditions close to "infinite" geometry, were also 2,41 done. Experimental buildup factor values obtained from * P E s t a n d s for p o l y e t h y l e n e [ - P u b l i s h e r ' s Note'~., Eq. (1) are found to agree within :t10% with theoretically calculated values [3]. The experimental results onheterogeneous mixtures are listed in Table 1. The table presents the materials included in the heterogeneous mixture (beginning with the source), and the layer thicknesses in terms of mean free path lengths. Bexp denotes the experimental buildup factor computed from Eq. (1) and averaged over three separate measurements; Bmi x denotes the buildup factor for a mixture, these buildup factors being obtained on the basis of the semiempirical formula reported in [1].

2,tll

The pig(p, a)Ol0 reaction was used to obtain g a m m a photons of about 6.4 MeV energy. The protons were accelerated on a linear accelerator to 0.88 MeV and aimed at a CaFz Crystal shaped close to a sphere of about 10 m m diameter. The g a m m a quanta of the three principal energies emitted in the course of the reaction: 6.13, 6.9, and q.1 MeV, at relative intensities 0.76, 0.025, and 0.21, respectively, were taken into account in the calculations. range.

Buildup factors and absorption coefficients of various substances vary slightly over the 6.13-7.1 MeV energy We therefore used the mean effective energy 6.4 MeV. The estimate of over-all experimental error is 17%.

Table 2 lists experimentally derived buildup factors for gamma radiation emitted in the Ft9(p. a ) O l* reaction. For purposes of comparison, the tabulated material includes theoretically computed values of the gamma-radiation buildup factors borrowed from [3]. Some of the results derived from experiments on heterogeneous mixtures appear in Table 3. The computed values are obtained from a formula cited in [1]. The results of the experimental data and the experimental results from [1] demonstrate that the formula in [1] m a y be successfully applied in calculations of g a m m a - r a y buildup factors in the 1-6.5 MeV g a m m a energy interval. There is no reason to doubt that this formula will be valid even at higher g a m m a energies. Calculations based on that formula and on an empirical formula suggested individually by Goldstein [3] for the mixture Pb + HzO differ by

122'/

not more than 3%, both for 3-MeV energy and for 10-MeV (in each case, the calculations apply to nine different assemblies). For energies below 1 MeV and thicknesses greater than 15 mean free path lengths, no information is yet available. The authors express their acknowledgments to V. A. Shalin for his valuable participation in the performance and processing of all the experiments and resulting data. 1. 2. 3.

LITERATURE CITED D.L. Broder, Yu. P. Kayurin, and A. A. Kutuzov, Atomnaya ~nergiya, 1__22,1, 30 (1962). U. Fano. Nucleonics, 11, 8, 8 (1958). H. Goldstein, Fundamental Aspects of Reactor Shielding (Addison-Wesley, Reading, Mass., 1959).

TECHNETIUM

B U I L D U P IN T H E R M A L R E A C T O R S

B. S. K i r ' y a n o v ,

A. P. S m i r n o v - A v e r i n ,

and

V. I. G a l k o v

Translated from Atomnaya Energiya, Vol. 13, No. 6, pp. 595-597, December, 1962 Original article submitted March 17, 1962

The considerable amount of interest being shown in technetium is due to its good inhibiting properties [1], which make it useful in various branches of engineering, in particular with semiconductors. This element was first separated from molybdenum, which had been irradiated with deuterons in a cyclotron [2]. However, this method does not make it possible to get appreciable quantities of the long-lived isotope of technetium. This has only become possible with the development of atomic energy. In investigating the isotopic composition of spent fuel elements from the first atomic electric station, Tc 90 was separated in ponderable amounts. The principal source of technetium buildup in the fuel element is U2~ fission. However, with prolonged operation of a fuel element in the reactor, considerable quantities of Pu2m and Pu z~ build up, which on fission become additional sources of technetium. The formation of technetium from molybdenum contained in the fuel element by the reaction 87% [ ----~Tc.99m.

M~ (n' ') M~ - f ~

1 t3% lisomerictransition15....

>Tc99

-)~ RI199

2,12.105 yr

may be neglected, since it does not exceed 1%. The amount of technetium in a spent fuel element, considering buildup from uranium and plutonium fission, may be calculated from the following formula: 9 235

NT c ~

To.

99.40zN235~235(l_~_~)6Tc[t_e-~% -cry *

o

.t

6,02-i023- 100 (oc-235 _ _ov-Tc')

't

)~]e

_

Tc

%' ~t)t mg/IkgU, (I)

where N~ ~ is the number of U 2~ nuclei per kg of uranium, o 2~ e and o2~ are the capture and fission cross sections of

Y A239,241 U2~, averaged over the reactor neutron spectra, /3 = ~ is the ratio of the number of Puz3s and Pu241 fissions to

the number of U~-~ fissions, 6 Te is the technetium yield in U2~ fission, percent [3], and ~t is the integrated neutron flUX.

1228