ABSTRACTS EFFECT

OF

PROTON

OPERATION

OF

IRRADIATION

A SCINTILLATION

ON T H E COUNTER

B . V. G u b i n s k i i , E . M. I o v e n k o , V. A . K u z ' m i n , V. G. M i k u t s k i i , a n d V. N. N i k o l a e v

UDC 539.1.074.3

The effects of proton i r r a d i a t i o n (Ep = 18 MeV, flux eb = 6 -1019 and 6.109 c m -2, density 2.104 c m -2 9see -1 and Ep = 360 MeV, 9 = 106, 8.106,-and 1.46.10 T c m -2, density 1.05 "10s c m -2 -see -z) on an NaI(T1) c r y s t a l were studied. The changes taking place in the counting c h a r a c t e r i s t i c s , the differential s p e c t r u m , and the position of the photopeak c o r r e s p o n d i n g to the 1,-radiation of ~37Cs (recorded before and a f t e r i r r a d i a t i o n of the crystal) were estimated. The original counting c h a r a c t e r i s t i c s were d e t e r m i n e d for an e n e r g y - d i s c r i m i n a tion threshold of Ug = 20, 40, and 60 keV. F i g u r e s 1 and 2 show the counting c h a r a c t e r i s t i c s m e a s u r e d before and a time At after i r r a d i a t i o n of the c r y s t a l s and the c h a r a c t e r of the changes taking place in these c h a r a c t e r i s t i c s respectively.

8

/4

z

r

f400

1600

1000

8

1200

1400

1600

Fig. 1

1800

Uphotomult, V

Uphotomult, V Fig. 2

Fig. 1. Counting c h a r a c t e r i s t i c s of an FI~U-70 + NaI(T1) scintillation counter before and after i r r a d i a t i o n of the c r y s t a l s : e) c h a r a c t e r i s t i c s before i r r a d i a tion V) At = 6 min, Ep = 360 MeV, 4~ = 8 -106 c m -2, Ug = 40 keV (No. 580); • At = 6 min, E p = 3 6 0 M e V , r = 10 ~ e m -2, U g = 4 0 k e V (No. 592); A) A t = 4 m i n , E o = i00 MeV, 9 = 4.1.10 -7 c m -2, Ug = 20 keV (No. 624); 9 At = 8 min, Ep ='18 MeV, 4~ = 6.109 c m -2, Ug = 40 keV (No. 712). Fig. 2. Counting c h a r a c t e r i s t i c s of an FI~U-70 + NaI(T1) scintillation counter obtained at various t i m e s At after the i r r a d i a t i o n of c r y s t a l No. 605 with 300 MeV protons at a flux of 1.46 -107 cm-2: O) original; [5, e , A, x) At = 8; 35; 80; 270 rain respectively. t

Translated f r o m Atomnaya Energiya, Vol. 38, No. 6, pp. 411-417, June, 1975.

9 19 75 Plenum Publishing Corporation, 227 West 1 7th Street, New York, N. Y. 10011. No part o f this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission o f the publisher. A copy o f this article is available from the publisher for $15.00.

524

A n a l y s i s of the r e s u l t a n t data shows that a f t e r proton i r r a d i a t i o n the m o s t i m p o r t a n t change which o c c u r s in the counting c h a r a c t e r i s t i c is an upward d i s p l a c e m e n t of the l a t t e r . This m a y be a s s o c i a t e d with the d e v e l o p m e n t of induced activity ( c h a r a c t e r i z e d by the e m i s s i o n of ? - q u a n t a and f l - p a r t i c l e s with a m e a n e n e r g y of the o r d e r of 1 MeV and a m e a n half life of 30-40 min) in the c r y s t a l and the sheath around it. The r a d i o a c t i v e nuclei a r i s i n g in the c r y s t a l may be identified, f o r e x a m p l e , on the b a s i s of the p r o b a b i l i t y of s t a r f o r m a t i o n at the heavy and light nuclei under the influence of the protons. T h e s e nuclei include 122I, 1211, 12~Sb' 12SSn' 123Sn' 24Na' 18F, 29AI, 12o8. Thus f o r the i r r a d i a t i o n fluxes studied the change in the slope of the plateau is v e r y slight, and has no s e r i o u s effect on the o p e r a t i o n of the scintillation c o u n t e r . The counting e r r o r a s s o c i a t e d with i r r a d i a tion d i m i n i s h e s with t i m e and is no g r e a t e r than about 5% s o m e 2-3 h a f t e r the end of i r r a d i a t i o n , depending on the p a r t i c u l a r s a m p l e . The change fluctuates c o n s i d e r a b l y f o r different c r y s t a l s a m p l e s . Original a r t i c l e s u b m i t t e d M a r c h 27, 1974

EXPERIMENTAL

DETERMINATION

TEMPERATURE

DEPENDENCE

CONDUCTIVITY

OF

CONDITIONS

OF

URANIUM

REACTOR

OF

OF THE

DIOXIDE

THE THERMAL UNDER

IRRADIATION

B . V. S a m s o n o v , Yu. G. Spiridonov, N. A. Fomin, and V. A. Tsykanov

UDC 621.039.542.34(063)

E x p e r i m e n t a l data r e l a t i n g to a d e t e r m i n a t i o n of the t h e r m a l conductivity of uranium dioxide at 02800~ b a s e d on the radial heat-flow method a r e p r e s e n t e d . The m e a s u r e m e n t s w e r e c a r r i e d out on f u e l e l e m e n t s a m p l e s containing c o m p a c t u r a n i u m dioxide with a density of 10.4-10.7 g / c m 3 and an oxygen c o e f ficient of 2.01• V in a s t a i n l e s s steel can 32.5 x 1 m m in d i a m e t e r . The t e m p e r a t u r e of the s u r f a c e and c e n t e r of the c o r e w e r e m e a s u r e d with V R h / V R 2 0 t h e r m o c o u p l e s c a l i b r a t e d o v e r the whole range of working t e m p e r a t u r e s . In o r d e r to find ~ (T) at t e m p e r a t u r e s above 2300~ i . e . , a f t e r the c e n t r a l t h e r m o couple bad failed, e x p e r i m e n t s w e r e c a r r i e d out using a molten c e n t r a l zone of the fuel, with c o r r e s p o n d ing a n a l y s i s a f t e r r e m o v a l f r o m the r e a c t o r . The p o w e r of the fuel e l e m e n t w a s d e t e r m i n e d c a l o r i m e t r i c a l l y , using a c a l i b r a t e d e l e c t r i c h e a t e r . The d e p r e s s i o n of the neutron flux in the fuel e l e m e n t s was found f r o m the f i s s i o n density m e a s u r e d with 90%-enriched metallic uranium i n d i c a t o r s . The distribution of the neutron flux with r e s p e c t to the height of the fuel e l e m e n t was d e t e r m i n e d f r o m the activation of c o p p e r i n d i c a t o r s . We found that in the t e m p e r a t u r e r a n g e 0-2800~ the t h e r m a l conductivity of uranium dioxide w a s d e s c r i b e d to an e r r o r no g r e a t e r than 5% by the equation ;+(T) --- +5~0 - 55 - - - F - ~ 0.942.i0-~eT~, W/(cm. "C). The r e s u l t a n t ~ (T) r e l a t i o n s h i p is r e c o m m e n d e d f o r use in t h e r m o p h y s i o a l c a l c u l a t i o n s of fuel e l e m e n t s b a s e d on c o m p a c t uranium dioxide fuel made by the technology employed f o r VVI~R-440 r e a c t o r s . Original a r t i c l e submitted April 21, 1974

525

MECHANICAL

STRENGTH

OF

URANIUM

FIELD-EMITTERS A. L . S u v o r o v , G. M. K u k a v a d z e , D. M. S k o r o v , B. A. K a l i n , A . F . B o b k o v , V. A. F e d o r c h e n k o , B . V. S h a r o v , a n d G. N. S h i s h k i n

UDC 535.82:546.791

The mechanical p r o p e r t i e s of thin a c i c u l a r tungsten and G-uranium samples were studied with the aid of a f i e l d - e m i s s i o n ion m i c r o s c o p e . The chief aim was to determine the limiting strength and the mode of deformation of the uranium samples; the experiments with tungsten were treated as standards. The samples were loaded directly in the f i e l d - e m i s s i o n m i c r o s c o p e , using the s t r o n g electric field required to f o r m images of the sample s u r f a c e s . The technique of p r e p a r i n g the uranium f i e l d - e m i s s i o n samples was described in [1]. Since one cause of sample deformation and rupture in the f i e l d - e m i s s i o n m i c r o s c o p e was the a s y m m e t r y of the sample, the sample profiles were carefully monitored, f i r s t in the optical m i c r o scope, and after f i e l d - e m i s s i o n i o n - m i c r o s c o p e analysis in the electron m i c r o s c o p e . Rupture of the samples was indicated by a sharp change in the c o n t r a s t of the f i e l d - e m i s s i o n ion image (or the complete disappearance of the latter). Calculation of the s t r e s s e s c~K c o r r e s p o n d i n g to rupture was based on the equation ~ = F2/8% where F is the electric field strength, proportional tu the sample potential. The resultant aK values for tungsten and a - u r a n i u m were respectively (1.31 9 0.15) -101~ and (1.13 ~: 0.20) .10 ~~ N / m 2 (sample orientiation along the [011] and [010] directions respectively). The mean d i a m e t e r s of the samples were ~ 1000 A. The tungsten samples analyzed numbered 18 and the uranium 10 (altogether 50 uranium samples were examined in various imaging gases; only eight were ruptured by the field). The c o r r e s p o n d i n g value of aK for tungsten obtained in [2] using an analogous technique was (2.06 =~0.18) .101~ N / m 2, which a g r e e s with the results of the p r e s e n t investigation within the limits of experimental e r r o r . The values of the normal s t r e s s e s % in the samples on imaging in various imaging gases are p r e sented in Table 1, together with the c o r r e s p o n d i n g deformations e. A c o m p a r i s o n between the theoretical strengths a T of tungsten and ~ - u r a n i u m calculated f r o m the equation a T = ~G, where ~? = 0.133 f r o m [3], G is the s h e a r modulus (for tungsten G = 14.85 -109, for ~ uranium G = 7.35-10 s N / m 2) shows that these are respectively 1.98.109 and 0.97.109 N / m 2. Thus the r e sults here obtained lend weight to the a s s e r t i o n that the true theoretical strength is realized in such c r y s t a l s (whiskers); this situation is p r o m i s i n g f r o m the point of view of verifying theory and also for the extensive practical use of the whiskers for example, as a base for modern composite m a t e r i a l s . TABLE 1. Calculated Values of Various P a r a m e t e r s Imaging gas I-[o, Ar Ne He Evaporation mode

o0,N/m 2 2 , 2 84

3,5 4,4 5,7 (W) 4,35 (a-U) LITERATURE

1.

2. 3.

2,i.i0s 5,3. t0s 8,4.t0s

t ,4t. 109 (W)

8,2.10s (a-U) }

~,% W

~-U

0,63 i,6 2,5 4,2

1,9 4,8 7,5 7,4

CITED

A. L. Suvorov et al., At. ]~nerg., 36, No. 1, 14 (1974). R. I. G a r b e r , Zh. I. Dranova, and I. M. Mikhailovskii, Dokl. Akad. Nauk SSSR, 174, 1044 (1967). J. Hirth, Relative Structure and Mechanical P r o p e r t i e s of Metals, Vol. 1, London (1963), p. 218. Original article submitted July 1, 1974 revision submitted J a n u a r y 28, 1975

526

DOSE

DISTRIBUTION

MEDIUM

FROM

ALPHA-PARTICLE

IN A TISSUE-EQUIVALENT

A PLANE

THIN

ISOTROPIC

SOURCE UDC 621.039,538.7

D. P . O s a n o v , V. P . P a n o v a , Y u . N. P o d s e v a l o v , a n d ]~. B .

Ershov

A general method is p r e s e n t e d for calculating the dose distribution in a tissue-equivalent medium f r o m a plane thin isotropic s o u r c e of alpha p a r t i c l e s of e n e r g y E 0 _~ 9 MeV having a surface s o u r c e strength The dose rate at point A (Fig. 1) due to all alpha p a r t i c l e s reaching it with residual energy between 0 and E(x) is E (x)

P(x)=k ~ dN(x) (E dE (E)dE, ) --~T~

(i)

0

w h e r e N(x) is the flux density of alpha p a r t i c l e s at depth x, and the c o n v e r s i o n f a c t o r k depends on the choice of units. It is obvious that dN(x) = ( o / 2 ) ( p d p / r 2) = ( ( r / 2 ) ( d r / r ) . Then E (x)

i" J

E (x)

dE ==k ~._ ~ dE 2 J n.(Eo)-R wi'

O

(2)

0

w h e r e R(E0) and R(E) a r e r e s p e c t i v e l y the total and residual alpha particle r a n g e s . Equation (2) can also be derived by s t a r t i n g f r o m the definition of dose rate as the derivative of the e n e r g y flux density with r e s p e c t to the depth of the a b s o r b e r P(x) = d W / d x . The determination of the dose function P(x) is reduced to the c o r r e c t determination of R(E) f o r a tissue-equivalent material. We have found that o u r results on the e n e r g y dependence of alpha particle ranges in a t i s s u e - e q u i valent material and the data cited in the l i t e r a t u r e a r e best approximated by the e x p r e s s i o n s

R(E)=6.3E, 0 < E < 3,5 IvleV; R (E) = t3.5E-- 25.5, 3.5 < E < 9 MeV,

(3)

By substituting (3) into (2) and integrating we obtain P(x)=c(~ln R(ED x

x>[R(Eo)--22],

[l;

]J ' x<[R(Eo)--22], ~. P (z) = ca [ln ...... R (Eo) . (Eo--22) . x . .~-.0.47.in R

(4)

Here c = 2 8 ( r a d / m i n ) -(em2/pCi), (~ is in p C i / c m 2, and x and r a r e in p. The a c c u r a c y of Eq. (4) was tested experimentally for 2~gPu alpha p a r t i c I e s . The dose distribution f r o m a piano thin alpha particle s o u r c e in d i r e c t contact with a tissue-equivalent a b s o r b e r was determined

7~ "" 50 -~. z{o

Fig. 1. D i a g r a m for d e r i v a tion of formula.

0 5 ~0 15 zo z5 Jo J5 x, Fig. 2. C o m p a r i s o n of calculated (Eq. (4)) and m e a s u r e d dose distributions f o r 239Pu alpha p a r t i c l e s : 9 s e m i c o n d u c t o r d e t e c t o r ; e) scintillation detector.

527

by m e a s u r i n g the s p e c t r u m of alpha particles (dN(x)/(dE))(E)penetratingvarious depths (x) of the a b s o r b e r . The m e a s u r e m e n t s were made with a silicon semiconductor surface b a r r i e r detector and a CsI(T1) scintillation c r y s t a l 70p thick on a light pipe. The energy resolution for 5.14 MeV alpha p a r t i c l e s was 2.2% f o r the s e m i c o n d u c t o r and 6% for the scintillation s p e c t r o m e t e r . The total energy r e l e a s e rate W(x) behind an a b s o r b e r of thickness x was determined by the m e a s u r e d functions (dN(x)/(dE))(E) E (~)

dN (x) W (x)= j ~ (E) E dE.

(5)

0

It is c l e a r that P(x) = --dW(x)/dx. The calculated and experimental results are in good a g r e e m e n t (Fig. 2). Thus the absorbed dose rate in biological t i s s u e s f r o m plane thin s o u r c e s of alpha p a r t i c l e s of energy E 0 _~ 9 MeV can be calculated f r o m Eq. (4) using the alpha particle ranges given by (3). The e r r o r in d e t e r m i n i n g the dose rate does not exceed 15%. The dose rate in tissue-equivalent material f r o m a thick tissue-equivalent alpha particle source can be calculated f r o m Eq. (4) by using the method described e a r l i e r . LITERATURE 1.

CITED

D. P. Osanov et al., Meditsinskaya Radiologiya, 5, 44 (1971). Original article submitted August 19, 1974

RECOVERY

OF

NEUTRONS

IN THE

BY T H E

THE

INTEGRATED ENERGY

EXTRAPOLATION

SPECTRUM

RANGE

0.1-3

OF

MeV

METHOD

R . D. V a s i l ' e v , E. I. Grigor'ev, G. B. T a r n o v s k i i , a n d V. P . Y a r y n a

UDC 621.039.57

The proposed extrapolation method of r e c o v e r i n g the integrated s p e c t r u m of neutrons in the range 0.1-3 MeV is based on the use of, f i r s t , experimental information on the s p e c t r u m of neutrons in the range 0.5-3 MeV obtained by means of a collection of threshold d e t e c t o r s and, second, a priori information on the used s p e c t r u m in the range 0.1-3 MeV, which makes it possible to extrapolate the s p e c t r u m into the region in which information is not available. The integrated s p e c t r u m was r e c o v e r e d by an approximation by the method of l e a s t squares. An optimal approximating function was obtained: g(E) = 9> E (E)/(D s (where (9> E (E) is the energy dependence of the integrated neutron flux density; egs is the integrated flux density of neutrons with energy g r e a t e r than the effective reaction threshold 32S (n,p)32P) in the f o r m g(E) = alf(E) + a2, where as and a 2 are p a r a m e t e r s which must be determined; f(E) is a function specified with allowance f o r the r e a c t o r type as follows: f o r the fields of a w a t e r - m o d e r a t e d w a t e r - c o o l e d r e a c t o r f(E) = exp (--0.8 E), for the fields of graphite and h e a v y - w a t e r r e a c t o r s and also for neutron fields with gNp > 11 and gNp < 6 f (E) = exp [-- (lg E-~ 2,2) 2.0.i5],

and for the remaining c a s e s f ( E ) = exp (--0,8E) E0"0~(gNp-7"5)9"-0"35;

here, the neutron energy is expressed in m e g a e l e c t r o n volts; gNp = ~ N P / ~ s c o r r e s p o n d s to the reaction 237Np (n, f). F o r m e a s u r e m e n t s , one is r e c o m m e n d e d to use the neutron activation sets developed and supplied by the All-Union Scientific Research Institute of Physieotechnical and Radiotechnical M e a s u r e m e n t s . These

528

include five n d e t e c t o r - - s o u r c e ~ activation sets: l~ in a c a d m i u m screen. ~15In--hlCr, 199Hg--139Ce, 58Ni--58Co, ~2S--32P and one " d e t e c t o r - - d e t e c t o r of fission f r a g m e n t s " fissile set: 237Np--mica. We investigated the problem of d e t e r m i n i n g the e r r o r of the spectral coefficient g(0, 1) for the energy 0.1 MeV and f o r m u l a s are given for its calculation. The main advantage of the extrapolation method is that it e n s u r e s a c o r r e c t result when a s p e c t r u m is r e c o v e r e d on the b a s i s of little information. This is confirmed by c o m p a r i s o n of the results of m e a s u r e ments obtained by this method and o t h e r methods for different types of static and pulse r e a c t o r s . At the p r e s e n t time, the extrapolation method has been standardized and is used to solve applied problems of solid-state physics. Original article submitted August 19, 1974

DETERMINATION PURE

METALS

A. F . A. P.

OF BY

TRACES

GAMMA

OF

NITROGEN

IN

ACTIVATION

Gorenko, A. S. Z a d v o r n y i , Klyucharev, a n d N. A . S k a k u n

UDC 539.172.3: 543.064:621.039.32

The most sensitive method available at the p r e s e n t time for determining the mean content of nitrogen i m p u r i t i e s in r e p r e s e n t a t i v e s a m p l e s (5-10 g) of various pure metals is T - a c t i v a t i o n analysis. After i r radiation of the samples the radioactive isotope 13N is separated, this being the product of the nuclear r e a c tion 14N (7, n) t3N (T1/2 = 10.1 min, fl+); selective deposition and a m e a s u r e m e n t of the isotope activity follows. In this operation the influence of activities induced in other i m p u r i t i e s and the matrix by the ~,i r r a d i a t i o n is eliminated. Samples of Be, Y, V, and Nb were i r r a d i a t e d with v - q u a n t a obtained by the retardation of 25 MeV e l e c t r o n s (at a c u r r e n t of 18p A) in a tungsten c o n v e r t e r 2 m m thick. The metals were packed in aluminum cans and t r a n s p o r t e d to and f r o m the i r r a d i a t i o n site by pneumatic post. A standard with a known N content was i r r a d i a t e d at the same time as the samples. The 13N isotope was separated f r o m the i r r a d i a t e d samples and standards in a furnace at T = 1200~C. Using a helium flow, the ~3N and other gases were passed to a zeolite trap cooled with liquid nitrogen. In the path of the flow was a s o l i d - p a r t i c l e filter followed by c o p p e r shavings heated to 500~C in which the nitrogen oxides were deoxidized. Absorption of halides took place o v e r s i l v e r shavings heated to 350~ The activity deposited in the zeolite was r e c o r d e d by means of a fast--slow coincidence scintillation s p e c t r o m e t e r with an efficiency of 1-2~. The absorption of ~1C~502 took place in a s c a r i t e . The efficiency of the absorption of 13N f r o m the gas flow passing through the zeolite was a l m o s t 100%. The following t r a c e s of nitrogen were found (wt.%): Be (10-3-10-5), Nb ~ 10 -3, Y ~ 10 -5 and V ~ 10 -3. These c h a r a c t e r i s t i c s of the method influencing the a c c u r a c y and reproducibility of the results are d i s cussed. Original article submitted September 24, 1974

529

MICROSCOPIC EVENTS

DISTRIBUTION

I N AN I R R A D I A T E D

CHARACTERISTIC IONIZING

OF IONIZATION

OF

MEDIUM

THE

QUALITY

AS A OF

RADIATION

I. B. Keirim-Markus, a n d I. V. F i l y u s h k i n

A. K.

Savinskii,

UDC 539.12.08

The traditional way of c h a r a c t e r i z i n g the quality of the radiation by the average linear energy loss of charged particles (L) is today recognized as inadequate [1]. In this connection, one seeks new p a r a m e t e r s and functions which more adequately d e s c r i b e the spatial distribution of energy t r a n s f e r r e d to a medium. Of the functions of such kind one already knows the radial distribution of the energy t r a n s f e r r e d to the medium in the t r a c k s of c h a r g e d p a r t i c l e s [2], which in c o n t r a s t to the linear energy l o s s gives an idea of the two-dimensional spatial distribution of the t r a n s f e r r e d energy. As a f u r t h e r c h a r a c t e r i s t i c one can take the spatial microdistribution of events of ionization (excitation) in the i r r a d i a t e d medium, which enables one to take into account the volume distribution of the t r a n s f e r r e d energy in small regions within the track. One seeks the average distribution (or mathematical expectation) of the initial distances between the ionization (excitation) events when a charged particle p a s s e s through the medium. The required d i s t r i b u tion AP (p, E) is the conditional probability of finding an ionization eventin unit volume of a thin spherical l a y e r of radius p with c e n t e r coinciding with an a r b i t r a r y ionization event. It can be r e p r e s e n t e d in the form 2~

,

0

1

2~

E~ X D (p,

0

E6, r) dr dE5,

(I)

where E and L(E) are the energy and linear energy loss of the charged particle; D(r,E) is the value of the radial distribution of the transferred energy of the particle at distance r from the track axis; D(O, E, r) is the mean value of the radial distribution of the transferred energy on a sphere of radius p with center at distance r from the track axis (the same notation with E replaced by E 5 applies to 5 electrons); f(E, E 6) is the spectrum of the 6 electrons generated by the first particle in all generations. Calculations of Ap (p, E) for particles with effective charge Z* from I to 8 and energies up to 100 MeV showed in particular that the function ~:(p) = 4~rp2Ap(p, E) depends solely on the ratio of the effective charge of the particle to its velocity, Z*/fi. In Fig. 1 these functions are shown for a set of values of the parameter.

10

Fig. 1. Microdistribution of d i s tances between events in the t r a c k s of c h a r g e d p a r t i c l e s of a r b i t r a r y species and energy in a t i s s u e equivalent medium.

D 1O-J

530

J 10-z

l

10-I

p,

It follows f r o m g e o m e t r i c a l a r g u m e n t s that r - - 2L(E) as p - - ,o (we ignore the v a r i a t i o n of L along the track). In this connection, the function r f o r l a r g e p m u s t b e c o m e equal to unity. It can be seen f r o m the figure that indeed r = 1 f o r p ~ 300 4 , i . e . , at such d i s t a n c e s the p r o p o s e d c h a r a c t e r i s t i c of the quality of the radiation no longer gives additional information c o m p a r e d with the l i n e a r e n e r g y l o s s . At s h o r t e r d i s t a n c e s , down to i n t e r a t o m i c d i s t a n c e s , the r e q u i r e d distribution is different f o r diff e r e n t p a r t i c l e s and is d e t e r m i n e d by the p a r a m e t e r Z * / f l . The distribution r at d i s t a n c e s ~ 16 A has a m a x i m u m , whose value is the l a r g e r , the s m a l l e r is Z * / 3 . T h i s f o r m of the function is due to the contribution of the concentration of ionization events in the cloud of 6 e l e c t r o n s which surround the c o r e of the c h a r g e d p a r t i c l e ' s t r a c k . This distribution together with the existing l i n e a r e n e r g y l o s s and radial distribution of the t r a n s f e r r e d e n e r g y can s e r v e as an additional c h a r a c t e r i s t i c of the quality of the radiation when one c o n s i d e r s radiation events c h a r a c t e r i z e d by i n t e r a c t i o n lengths ( 300 A. LITERATURE I. 2.

CITED

ICRU, Rep. No. 16, Washington (1970). I. K. Kalugina et al., At. ]~nerg., 34, No. 4, 298 (1973). Original a r t i c l e submitted J a n u a r y 24, 1974

ALLOWANCE

FOR

IRRADIATION ACTIVE O.

FLUCTUATIONS

DOSE

OF

LUNGS

IN THE

BY HIGHLY

PARTICLES M. Z a r a e v

and

B.

N.

Rakhmanov

UDC 621.039.7

In r e a l conditions one o b s e r v e s c a s e s when s e v e r a l o r just one highly active a e r o s o l p a r t i c l e is r e tained in the b r e a t h i n g o r g a n s . The existing methods enable one to c a l c u l a t e the dose a v e r a g e d o v e r a l a r g e n u m b e r o f individuals. To choose a nrisk c r i t e r i o n " of internal i r r a d i a t i o n in such situations one r e q u i r e s the distribution of d o s e s within individuals. To e s t i m a t e the potential d a n g e r of r a d i o a c t i v e a e r o s o l s one m u s t take into account two independent p r o c e s s e s : 1) a e r o s o l p a r t i c l e s r e a c h i n g the windpipe and being r e t a i n e d in different p a r t s of the b r e a t h i n g o r g a n s ; 2) the r e m o v a l of a e r o s o l p a r t i c l e s f r o m the b r e a t h i n g o r g a n s . In the d e v e l o p m e n t of a method of p r o b a b i l i s t i c e s t i m a t i o n o f d o s e s o f i n t e r n a l i r r a d i a t i o n i t w a s a s s u m e d , f i r s t , that the ~history" of each p a r t i c l e is independent of the " h i s t o r y " of the o t h e r p a r t i c l e s and, second, the m a t e r i a l is r e m o v e d d y n a m i c a l l y , i.e., the r a t e of r e m o v a l is p r o p o r t i o n a l to the amount of retained m a t e r i a l . I f n p a r t i c l e s a r e r e t a i n e d in the b r e a t h i n g o r g a n s , the p r o b a b i l i t y of t h e i r being r e moved in t i m e t n is

i04~

-

Fig. 1. Maximal i r r a d i a t i o n dose of a lung f o r which the p r o b a b i l i t y of being exceeded is 0.05% for different d a , p : 1) 0.4; 2) 0.8; 3) 1.0; 4) 2.0; 5) 4.0; 6)

6.0; 7) 8.0; 8) I0.0.

r

,+0-+11 +I1

+1

19"t~

10"8

II

I I+1 t0 8

+ 10~"

,,, I0"~

+

,

10~

,

10 z

a, rel.untts

531

(~ ' n ) n

n- l -}~nt

where X is the constant for the removal of the radioisotope f r o m the breathing o r g a n s . With a probability of 99.95% one can a s s e r t that the removal time of one particle exceeds by not more than 7.6 times the average removal time of the same amount of radioactive material uniformly distributed among many p a r t i c l e s . The mathematical model developed applies to any o r g a n f r o m which the removal is d e s c r i b e d by an exponential law. As the risk c r i t e r i o n when a relatively small number of radioactive p a r t i c l e s get into the breathing o r g a n s one must evidently take the s o - c a l l e d local absorbed dose, i.e., the radiation energy absorbed in l g of the i r r a d i a t e d tissue. The radiation danger cannot be estimated by the f o r m a l c o m p a r i s o n of this dose with the maximally allowed dose since the l a t t e r is essentially the tissue a v e r a g e , i.e., it r e f e r s to unit m a s s of the complete organ. In this connection, it is desirable to determine the t i s s u e - a v e r a g e d absorbed doses f r o m radioactive particles calculated on the b a s i s of the one-component variant of the exponential model of their removal with effective constant ~eff and with allowance for the statistical nature of the p r o c e s s e s of a r r i v a l and removal of the aerosol p a r t i c l e s . The p r o c e s s e s of deposition and removal of the particles are independent. The probability that the m e a n - t i s s u e dose absorbed in part ] of the breathing s y s t e m a f t e r the inhaling of an aerosol during time with mean number N of particles that a r r i v e is the quantity D, equal to V (D) = Ecoi (n) W~ (D), where ~j (n) =

n!

--

c h a r a c t e r i z e s the p r o c e s s of inhaling of the p a r t i c l e s and their deposition [ ~eff~ D 7~-1

in part j of the breathing system; W,~(D) = \~](n----~. exp(--~'effD/P~ ql) c h a r a c t e r i z e s the p r o c e s s of removal of the particles; D is the maximal i r r a d i a t i o n dose of the lung; Pj is the probability of deposition of a particle in part j of the breathing system; P~ is the power of the m e a n - t i s s u e dose f r o m a source with activity l p C i ; ql is the activity of one particle. The average dose adsorbed in part j of the breathing s y s t e m is oo

o--

eff

0

Here, D does not depend on the number of retained p a r t i c l e s but is entirely determined by the total amount of the radioisotope retained in part ]. Figure I shows universal c u r v e s which enable one to calculate the maximal i r r a d i a t i o n dose of the breathing o r g a n s of an individual as a function of the number of radioisotopes that a r r i v e averaged for the complete contingent of w o r k e r s . F o r convenience, Q and Dma x are given in relative units a and b, which are related to the c o r r e s p o n d i n g absolute values through the p a r a m e t e r s of the a e r o s o l p a r t i c l e s by --

q!

Q= a - - ~ , q--~,

~Ci ;

Dmax = b Vp ~'eff

relTl 9

The linear sections of these dependences c o r r e s p o n d to the a r r i v a l amounts at which the fluctuation of the doses has no practical importance. Original article submitted J a n u a r y 31, 1975

532