1. No category

PRO CEE DINGS SERIES
BIOPHYSICAL ASPECTS
OF RADIATION QUALITY
PROCEEDINGS O F A SYMPOSIUM ON
BIOPHYSICAL ASPECTS OF RADIATION QUALITY
H E L D BY T H E
INTERNATIONAL ATOMIC ENERGY AGENCY
IN L U C A S H E I G H T S , A U S T R A L I A , 8 - 1 2 M A R C H 1971
INTERNATIONAL ATOMIC ENERGY AGENCY
VIENNA, 1971
CONTENTS
PHYSICAL PHENOMENA (MICRODOSIMETRY, TRACK-THEORY
( S e s s i o n s I a n d II)
Survey Paper:
C H C T e M a T H K a 3aÄaH R03MMeTpHH
H BOnpOCbl
MHKpOfl03HMeTpHH
(IAEA-SM-145/2)
B . H . HßaHOB
Discussion
T r a c k t h e o r y and r a d i a t i o n quality ( I A E A - S M - 1 4 5 / 9 )
R . Katz
Discussion
P a r t i c l e slowing-down p r o c e s s and l i n e a r e n e r g y t r a n s f e r (LET)
spectra (IAEA-SM-145/15)
M. C . E . P e t e r s e n
Discussion
T h e o r y o f w a l l - e f f e c t s in m i c r o d o s i m e t r i c m e a s u r e m e n t s
(IAEA-SM-145/6)
A.M. K e l l e r e r
Discussion
ETC.)
3
9
11
23
25
43
45
52
Survey P a p e r :
M e a n i n g a n d a s s e s s m e n t of r a d i a t i o n q u a l i t y for r a d i a t i o n
protection (IAEA-SM-145/3)
55
J.E. T u r n e r
Discussion
77
M i c r o d o s i m e t r y of l o w - e n e r g y e l e c t r o n s ( I A E A - S M - 1 4 5 / 8 )
79
A. E . S . G r e e n , J . J . O l i v e r o , R . W . S t a g a t
Discussion
97
A n a l y s i s of d o s e - e f f e c t r e l a t i o n s h i p s b a s e d on t h e m i c r o d o s e c o n c e p t
(SM-145/47)
'
99
N . O d a , T . N u m a k u n a i , S. Ohtani
D e t e r m i n a t i o n du d e b i t d e d o s e a u t o u r d f u n e s o n d e de C r o w e
p a r la methode photographique (IAEA-SM-145/24)
119
J. G a r s o u , R . B o n i v e r
O $ J i y K T y a u [ H H X $ y H K U H H p a c n p e a e J i e H H H BepOHTHOCTH /JJIH S H e p r H H ,
nepeflaHHOö 3 a ^ a H H O M y o 6 i > e M y H O H H 3 H p y i o m H M H 3 J i y n e H H e M
(IAEA-SM-145/49)
H.ü. K a ^ a i n H H K O B , B . C . P e M H 3 0 B H M , M . H . P H 3 a H O B
I T K a H e a K B H B a a e H T H f c i e n p o n o p u n o H a J i b H b i e cneTHHKH B M H K p o ^ o 3 H -
MeTpHH ( I A E A - S M - 1 4 5 / 5 1 )
II.H.
B . A.
B e J i O H o r u H , B . M . HßaHOB,
ÜHTKeBHM,
Discussion
A.n.
T H 6 a H oB
E.C.Ky3bMHH,
127
139
168
M E C H A N I S M S O F C E L L D E A T H ( S e s s i o n III, P a r t 1)
Survey Paper:
C e l l d e a t h a n d i t s m o d i f i c a t i o n : T h e r o l e s of p r i m a r y l e s i o n s
in m e m b r a n e s a n d DNA ( I A E A - S M - 1 4 5 / 1 )
Tikvah Alp er
Discussion
171
183
BIOLOGICAL ACTION O F IONIZING RADIATION
AT THE MOLECULAR L E V E L
( S e s s i o n III, P a r t 2, S e s s i o n IV, P a r t 1)
D N A s y n t h e s i s in m a m m a l i a n c e l l s e x p o s e d t o c o m b i n e d i o n i z i n g
and n o n - i o n i z i n g r a d i a t i o n ( I A E A - S M - 1 4 5 / 1 7 )
J.K. B r o w n
Discussion
S t r u c t u r a l a n d f u n c t i o n a l c h a n g e s in i r r a d i a t e d D N A
(IAEA-SM-145/20)
H . J u n g , M . U l l r i c h , H . Kröger,
E. P e t e r s e n , U. H a g e n
Discussion
G a m m a i r r a d i a t i o n of E . c o l i r i b o s o m e s ( I A E A - S M - 1 4 5 / 3 6 )
C.J. R e i n e c k e
Discussion
R e l a t i v e b i o l o g i c a l e f f e c t i v e n e s s of h i g h - e n e r g y b r e m s s t r a h l u n g
in t h e G e V ränge ( I A E A - S M - 1 4 5 / 4 5 )
H . A . Künkel, F . Z y w i e t z
Discussion
L i n o l e a t e m i c e l l e s a s m o d e l s for r a d i o b i o l o g i c a l e f f e c t s
(IAEA-SM-145/46)
J.M. G e b i c k i
Discussion
187
197
199
206
207
215
217
226
229
238
C E L L U L A R K I N E T I C S ( S e s s i o n IV, P a r t 2, S e s s i o n V, P a r t i )
I n a c t i v a t i o n of m a m m a l i a n c e l l s at d i f f e r e n t s t a g e s of t h e
c e l l c y c l e a s a f u n c t i o n of r a d i a t i o n l i n e a r e n e r g y
transfer (IAEA-SM-145/5)
R. B i r d , J . B u r k i
Discussion
A c o r r e l a t i o n b e t w e e n d i v i s i o n d e l a y and l o s s of c o l o n y - f o r m i n g
a b i l i t y in c u l t u r e d C h i n e s e h a m s t e r c e l l s ( I A E A - S M - 1 4 5 / 2 6 )
D . V . C o r m a c k , G. F r o e s e
Discussion
P r o b l e m e s d o s i m e t r i q u e s p o s e s p a r la d e t e r m i n a t i o n de l ' E B R
d a n s u n l a r g e d o m a i n e d * e n e r g i e ( e l e c t r o n s d e 15 a 34 M e V ,
p h o t o n s d e 55 k V a 20 M V ) ( I A E A - S M - 1 4 5 / 5 2 )
A. W a m b e r s i e , A n d r e e D u t r e i x
Discussion
241
249
251
259
261
272
C h r o m o s o m e a b e r r a t i o n s in C h i n e s e h a m s t e r c e l l s f o l l o w i n g
e x p o s u r e t o X - r a y and u l t r a v i o l e t r a d i a t i o n ( I A E A - S M - 1 4 5 / 1 8) . . . .
J.K. B r o w n
Discussion
L o c a l i z e d a p p l i c a t i o n of D N A p r e c u r s o r s f o r s t u d y i n g r a d i a t i o n
e f f e c t s in c e l l p o p u l a t i o n k i n e t i c s ( I A E A - S M - 1 4 5 / 4 2 )
I . S . J e n k i n s o n , S. G e o r g e , W . K . A . P a v e r
Discussion
R a d i a t i o n d a m a g e t o l y m p h o c y t e s : I t s e x p r e s s i o n in t h e k i n e t i c s
of s h o r t - t e r m c u l t u r e ( I A E A - S M - 1 4 5 / 4 1 )
P.L.T. I l b e r y , A.B. R i c k i n s o n
Discussion
V a r i o u s e x a m p l e s f r o m cellular kinetics showing how radiation
q u a l i t y c a n b e a n a l y s e d and c a l c u l a t e d b y t h e t w o - c o m p o n e n t
t h e o r y of r a d i a t i o n ( I A E A - S M - 1 4 5 / 4 4 )
R. Wideröe
Discussion
273
285
287
295
297
308
311
329
M E C H A N I S M S O F BIOLOGICAL D A M A G E BY RADIATION AND
R A D I A T I O N Q U A L I T Y ( S e s s i o n V, P a r t 2 and S e s s i o n VI)
Dual r a d i a t i o n injury and its c o n s e q u e n c e s ( I A E A - S M - 1 4 5 / 1 0 )
H.H. Ro s si
Discussion
P r e d i c t i o n of b i o l o g i c a l d a m a g e f r o m s t o p p i n g - p o w e r t h e o r y :
3HTdR studies (IAEA-SM-145/16)
D.R. D a v y
Discussion
R a d i a t i o n e f f e c t s of t r i t i a t e d t h y m i d i n e s t u d i e d i n p r e g n a n t r a t s
and their offspring ( I A E A - S M - 1 4 5 / 4 8 )
T.M. F l i e d n e r , J. C h a u d h u r i , R.J. H a a s ,
H . Knör r - G a e r t n e r , W . S c h r e m l
Discussion
B i o l o g i c a l e f f e c t s of v e r y h i g h e n e r g y n u c l e i of h i g h Z
(IAEA-SM- 145/12)
V.P. Bond
Discussion
L o c a l e n e r g y d e p o s i t i o n in t h y r o i d c e l l s d u e t o t h e i n c o r p o r a t i o n
of 1 2 5 I ( I A E A - S M - 1 4 5 / 3 0 )
Y . F e i g e , A. G a v r o n , E . L u b i n , Z . L e w i t u s ,
M . B e n - P o r a t h , G. G r o s s , E . L o e w i n g e r
Discussion
D i f f e r e n c e s in t h e r a d i o b i o l o g i c a l a c t i o n of 1 2 5 I a n d 1 3 1 I i n t h e
thyroid cell (IAEA-SM- 145/31)
Z . L e w i t u s , M . B e n - P o r a t h , Y. F e i g e , E . L u b i n ,
J. R e c h n i c , Y. L a o r
B i o l o g i c a l t o x i c i t y a s s o c i a t e d w i t h t h e A u g e r effect
(IAEA-SM-145/22)
L.E. F e i n e n d e g e n , H.H. E r t l , V.P. B o n d
Discussion
333
340
343
353
355
367
369
381
383
404
405
419
429
C o m p a r a t i v e e f f e c t s of n e u t r o n s and X - r a y s on C h i n e s e
h a m s t e r cells (IAEA-SM-145/14)
M. K e y
Discussion
E f f i c a c i t e b i o l o g i q u e r e l a t i v e e n f o n c t i o n du t r a n s f e r t d ' e n e r g i e
lineique pour le c r i t e r e cataracte chez le lapin
(IAEA-SM-145/29)
G. L e g e a y , C. H a y e , J . D r o u e t , J . P . B a z i n
Discussion
D i s t r i b u t i o n de la dose obtenue p a r P a s s o c i a t i o n de faisceaux
d ! e l e c t r o n s et d e p h o t o n s ( I A E A - S M - 1 4 5 / 4 0 )
H. G h a r b i , J. D u t r e i x
I n v e s t i g a t i o n s of e a r l y r a d i a t i o n c h e m i c a l e f f e c t s a n d t h e i r
s i g n i f i c a n c e i n b i o l o g i c a l Systems ( I A E A - S M - 1 4 5 / 1 9)
D. F . S a n g s t e r
Discussion
431
444
445
460
461
481
495
MODIFICATIONS O F RADIOSENSITIVITY AND
R A D I A T I O N P R O T E C T I O N ( S e s s i o n VII)
R o l e of s h o r t - l i v e d t r a n s i e n t s in r a d i o s e n s i t i z a t i o n of b a c t e r i a l
cells by chemicals (IAEA-SM-145/33)
A. R. G o p a l - A y e n g a r , M . A . S h e n o y , B . B . S i n g h
E S R s t u d i e s o n s h o r t - l i v e d t r a n s i e n t s of r a d i o s e n s i t i z e r s
(IAEA-SM-145/32)
B . B . S i n g h , N. C. V e r m a , A . R . G o p a l - A y e n g a r
Discussion
M o d i f i c a t i o n of b a c t e r i a l s e n s i t i v i t y t o r a d i a t i o n b y t r e a t m e n t w i t h
a keto-aldehyde (IAEA-SM-145/35)
R . A l c a n t a r a G o m e s , R. S. A. P i n h e i r o ,
A . C . Leitäo, L . R . C a l d a s
M e t a b o l i e c h a n g e s in m i c e a f t e r m o d i f i c a t i o n of r a d i o s e n s i t i v i t y
(IAEA-SM-145/21)
C. S t r e f f e r
Discussion
R a d i a t i o n p r o t e c t i v e s t u d i e s w i t h c o m b i n a t i o n s of c y s t e a m i n e a n d
penicillamine (IAEA-SM-145/27)
G.A. G r a n t , B. B r a c e l a n d
Discussion
C h a i r m e n of S e s s i o n s and S e c r e t a r i a t of t h e S y m p o s i u m
L i s t of P a r t i c i p a n t s
Author Index
T r a n s l i t e r a t i o n Index
I n d e x of P r e p r i n t S y m b o l s
499
507
515
517
525
537
539
551
553
554
559
560
561
IAEA-SM-145/6
THEORY OF W A L L - E F F E C T S
IN MICRODOSIMETRIC MEASUREMENTS*
A.M. KELLERER
Department of Radiology,
College of Physicians and Surgeons,
Columbia University,
New York, N.Y.,
United States of America
Abstract
THEORY OF WALL-EFFECTS IN MICRODOSIMETRIC MEASUREMENTS.
Microdosimetric data and the experimental assessment of radiation quality are based upon measurements
with proportional counters. The Simulation of microscopic tissue regions by cavities filled with tissue
equivalent gas is, however, limited by the fact that scaling relations are not preserved when a particle
track has multiple intersections with a boundary between regions of different density. This limitation has
forced various attempts to replace conventional proportional counters with wall-less constructions. In spite
of its practical irnportance to microdosimetry there is as yet no satisfactory analysis of the problem.
General theorems which allow a quantitative determination of the wall-effects can, however, be derived.
First one can extend Fano's theorem from a Statement on the fluence spectrum at a point to a Statement
on the spectrum of track segments in extended domains. As a second step one can then evaluate those
changes in the Statistical correlation of track segments which are brought about by density variations in the
irradiated medium. Finally one can give a generalization of Cauchy's theorem on the mean chord length
in convex bodies to curved and finite tracks and their secondaries. These results make it possible to assess
the differences between energy deposition spectra in conventional counters and wall-less instruments.
1.
INTRODUCTION
An i n c r e a s i n g number o f s t u d i e s on r a d i a t i o n q u a l i t y i s being based
on m i c r o d o s i m e t r i c concepts and q u a n t i t i e s . While microdosimetry has developed i n t o an e f f i c i e n t t o o l of r a d i o b i o l o g y , one aspect has, however,
remained l a r g e l y unresolved. T h i s i s the problem o f the s o - c a l l e d w a l l e f f e c t s . Wall e f f e c t s are d i s t o r t i o n s i n the s t a t i s t i c s o f energy dep o s i t i o n which occur i f microscopic t i s s u e regions are simulated by gasf i l l e d cavities.
Rossi and h i s co-workers have drawn a t t e n t i o n to these
d i s t o r t i o n s e a r l y i n the development of microdosimetry (1,2); subsequently
w a l l - l e s s p r o p o r t i o n a l counters have been constructed i n order to overcome the e f f e c t i n microdosimetric measurements (3,4,5,6).
T h i s paper contains a Synopsis of r e l e v a n t concepts and o f geometrical
theorems which are u s e f u l as a b a s i s f o r a theory o f w a l l e f f e c t s .
Such a
theory i s d e s i r a b l e because c r i t e r i a are needed to decide whether i n any
p a r t i c u l a r case conventional p r o p o r t i o n a l counters are a p p l i c a b l e , or w a l l l e s s Instruments must be used.
In order to give a b r i e f survey i t w i l l be necessary to draw together
r e s u l t s without d e t a i l e d d e r i v a t i o n s . Proof o f the v a r i o u s r e l a t i o n s are
given i n more t e c h n i c a l i n v e s t i g a t i o n s ( 7 , 8 ) .
* Based on work performed under Contract AT-(30-1)-2740 for the USAEC and Grant No.EC-74
for the National Institutes of Health.
45
KELLERER
46
FIG. l. Definition of the concept track segment.
2.
2.1
CHARACTERIZATION OF WALL
EFFECTS
D e f i n i t i o n o f Concepts
S e v e r a l concepts w i l l be needed throughout the d i s c u s s i o n . The f i r s t
concept i s that o f an energy d e p o s i t i o n event. The terra s i g n i f i e s energy
d e p o s i t i o n i n the r e g i o n , U,of i n t e r e s t by a charged p a r t i c l e and/or i t s
secondaries. An event can a l s o i n v o l v e two charged p a r t i c l e s s e t i n motion
by the same uncharged p a r t i c l e . Two energy depositions belong to d i f f e r e n t
events i f they are s t a t i s t i c a l l y independent, that i s i f they cannot be
traced back to a common quantum a c t . The term event w i l l be used i n a
somewhat more general c o n n o t a t i o n which a l s o includes passage o f a charged
p a r t i c l e without a c t u a l energy d e p o s i t i o n i n U. The d i s t i n c t i o n can be
neglected except f o r very s m a l l regions and s p a r s e l y i o n i z i n g p a r t i c l e s .
A charged p a r t i c l e t r a c k i s the l i n e o f motion of a charged p a r t i c l e
together w i t h the branches and subbranches formed by i t s s e c o n d a r i e s . Track
length i s the t o t a l length o f the t r a c k i n c l u d i n g i t s branches. A t r a c k
segment i s a continuous p o r t i o n o f a t r a c k l y i n g i n s i d e the r e g i o n , U.
Two segments may belong to the same t r a c k , as f o r example the segments A
and B i n F i g . l .
Event m u l t i p l i c i t y , M, i s the raean number of segments per event i n
U. I f the frequency o f segments i n U per u n i t dose i s 4> and * i s the
frequency o f events, then the m u l t i p l i c i t y i s :
g
M - * /*
s
2.2
(1)
Types o f Wall E f f e c t s
Wall e f f e c t s are due to the f a c t that the c a v i t y f i l l e d with low
density gas i s surrounded by h i g h d e n s i t y
raaterial.
In the w a l l s the
charged p a r t i c l e t r a c k s are s h o r t as compared to the dimensions o f the
cavity.
The boundary o f the c a v i t y as seen from the o u t s i d e o f the
c a v i t y then appears as a p l a n e . T h i s leads to the f a c t that t r a c k
segments can occur s i m u l t a n e o u s l y which would i n the S t a n d a r d case
1
With the commonly eraployed c a v i t y s i z e s the c o n d i t i o n holds f o r e l e c t r o n s
up to 1 MeV and f o r h e a v i e r p a r t i c l e s o f much higher energy. Other cases
are excluded from t h i s d i s c u s s i o n .
48
KELLERER
( i . e . , when the region U i s surrounded by m a t e r i a l o f the same d e n s i t y )
be s t a t i s t i c a l l y independent. Three p r i n c i p a l processes can be d i s tinguished.
In the Standard case a primary p a r t i c l e may t r a v e r s e U while a
6 ray formed o u t s i d e U does not enter the region but traverses the
plane, T, which i s t a n g e n t i a l to U at the entrance point of the primary
particle.
In the c a v i t y case t r a v e r s a l o f the t a n g e n t i a l plane, T,
means entrance i n t o the c a v i t y . The S i t u a t i o n i s s c h e m a t i c a l l y r e presented i n Fig.2a.
The simultaneous entrance o f the primary and the
secondary p a r t i c l e i s c a l l e d d e l t a ray e f f e c t .
A s i m i l a r process i s represented i n Fig.2b.
The e f f e c t i s due to
the back s c a t t e r i n g o f the charged p a r t i c l e a f t e r i t has t r a v e r s e d the
c a v i t y . T h i s re-entry e f f e c t i s s i g n i f i c a n t only f o r e l e c t r o n s with
their curled tracks.
A t h i r d type of w a l l e f f e c t i s the V - e f f e c t . This e f f e c t i s r e presented i n Fig.2c.
The V-shaped track o f two n u c l e a r fragments formed
i n a n o n e l a s t i c n u c l e a r c o l l i s i o n has a higher p r o b a b i l i t y f o r s i m u l taneous passages through the c a v i t y than through the a c t u a l m i c r o s c o p i c
region.
2.3
Increase
of M u l t i p l i c i t y
A common c h a r a c t e r i s t i c o f the d i f f e r e n t types of w a l l e f f e c t s i s
that they i n c r e a s e event m u l t i p l i c i t y . The shape and the r e l a t i v e f r e quency o f t r a c k segments i n the region, U, i s not a f f e c t e d by the d e n s i t y
of the w a l l s ; t h i s i s true under the c o n d i t i o n s o f Fano's theorem ( 9 ) ,
and i t follows from t h i s theorem. I t i s merely the S t a t i s t i c a l c o u p l i n g
between segments which depends on the density of the m a t e r i a l surrounding
U.
Assume that the r e g i o n U i s convex. Then one obtains m u l t i p l i c i t y
1 i n the f r e e Space case, i . e . , when U i s p o s i t i o n e d i n vacuo. In the
Standard case the m u l t i p l i c i t y i s near 1, i f one deals with s m a l l r e g i o n s .
In the c a v i t y case one has maximal m u l t i p l i c i t y .
Estimates of the numeric a l values are given i n s e c t i o n 3.
2.4
Event Frequency and Mean Event Size
I f a convex r e g i o n of volume V and surface S i s randomly t r a v e r s e d
by i n f i n i t e s t r a i g h t l i n e s ( F i g . 3 a ) , then the mean chord l e n g t h , £, i n
the region i s equal to 4V/S. This i s the soj-called theorem o f Cauchy.
I f the t r a c k s a r e f i n i t e and o f mean ränge r , then one can show that the
mean segment length i n the r e g i o n i s :
_ -1
s + 1/r)
(2)
T h i s i s the g e n e r a l i z a t i o n o f Cauchy's theorem to the S i t u a t i o n represented i n Fig.3b.
The g e n e r a l i z a t i o n goes, however, f u r t h e r than t h a t . Eq.
(2) holds even i n the case where one deals with an I s o t r o p i e f i e l d of
t r a c k s which a r e c u r l e d and branched (10). This complete g e n e r a l i z a t i o n
i s i n d i c a t e d i n F i g . 3 c . The q u a n t i t y Ä i s equal t o 4V/S, the mean ränge
i s the mean length o f t r a c k s i n c l u d i n g t h e i r branches, and s i s the mean
length o f segments as defined i n 2.1.
FIG. 3. Diagram for the Cauchy theorem and its generalizations.
(a) Infinite, straight random tracks
(b) Finite, straight random tracks
(c) Finite, curved, and branched random tracks
The general Cauchy theorem leads to the f o l l o w i n g formula f o r the
segment frequency per r a d :
4>
G
=
(1 + rfü)
.062
V/E
Q
(3)
E
(keV) i s the mean i n i t i a l energy of the charged p r i m a r i e s , r t h e i r
mean t r a c k length i n c l u d i n g d e l t a r a y s . V(pra^) i s the volume of the
r e g i o n , and i t i s assumed that t h i s region has d e n s i t y 1.
$
i s equal to the event frequency f o r the f r e e space case. For
s m a l l regions i t i s also n e a r l y equal to the event frequency i n the
Standard case. In the c a v i t y case i t can be markedly l a r g e r than the
event frequency, and one must d i v i d e i t by the a p p r o p r i a t e m u l t i p l i c i t y
to o b t a i n the event frequency or i t s i n v e r s e , the mean event s i z e .
s
3.
3.1
NUMERICAL ESTIMATES
Heavy P a r t i c l e s
The 6 rays of heavy charged p a r t i c l e s are s h o r t as compared to
the l e n g t h of the primary t r a c k . Therefore the p r o b a b i l i t y i s very
s m a l l that a 6 ray enters the c a v i t y while the primary t r a c k does not
enter i t .
Consequently the i n d i r e c t events, i . e . , those events where
the primary p a r t i c l e passes o u t s i d e the r e g i o n , U, and merely i n j e c t s
one o r s e v e r a l of i t s 6 rays i n t o U are suppressed i n the c a v i t y case.
I f t $ / t p i s the 6 r*y t r a c k l e n g t h per u n i t primary t r a c k l e n g t h then
the m u l t i p l i c i t y i s :
M - 1 + t /t
6
p
The very short 6 rays lead to double events even i n the Standard case.
In o r d e r to o b t a i n an estimate of the w a l l e f f e c t s one must t h e r e f o r e
exclude these short 6 rays from t<5. A reasonable approximation i s to
exclude a l l 6 rays whose ränge i s l e s s than the e q u i v a l e n t diameter o f
the r e g i o n U.
Table I gives the 6 ray length per u n i t primary t r a c k l e n g t h
f o r protons at various e n e r g i e s . The m u l t i p l i c i t y i n c r e a s e due to the
(4)
KELLERER
50
T A B L E I. D E L T A R A Y R A N G E P E R U N I T L E N G T H O F
PRIMARY TRACK
Proton
energy (MeV)
All
6 rays
6 rays
> .1 um
6 rays
> 1 ym
0.48
0.20
—
5
0.33
0.22
0.10
10
0.26
0.20
0.14
20
0.21
0.18
0.15
50
0.17
0.16
0.15
100
0.15
0.14
0.13
2
6 ray e f f e c t i s o f the order of .15 i n the t y p i c a l case of an e q u i v a l e n t
diameter o f 1 ym; i . e . about 15% of a l l p u l s e s observed i n a c o n v e n t i o n a l
t i s s u e equivalent p r o p o r t i o n a l counter are too l a r g e due to 6 ray I n f l u x .
The event frequency i s reduced by about 15% and the mean event s i z e i s
increased correspondingly.
The suppressed i n d i r e c t events are on the average much sraaller
than the d i r e c t events (4) . The f r a c t i o n o f energy involved i n the
d i s t o r t i o n i s t h e r e f o r e s i g n i f i c a n t l y s m a l l e r than 15%. Numerical
v a l u e s f o r charged p a r t i c l e s and f o r neutron f i e l d s are given i n r e f .
(8).
For h e a v i e r p a r t i c l e s o f atomic number Z at given energy per nuc l e o n one has to m u l t i p l y the values i n Table I by Z^. This means that
most of the events can be d i s t o r t e d due to the 6 ray e f f e c t . The f r a c t i o n
of energy i n v o l v e d i n the d i s t o r t i o n s i s , however, the same as that f o r
protons.
The V - e f f e c t can be an a p p r e c i a b l e p a r t of the w a l l e f f e c t s , i f
the neutrons o r charged p a r t i c l e s have enough energy that a s i g n i f i c a n t
p a r t o f the absorbed dose i s produced by n o n e l a s t i c n u c l e a r c o l l i s i o n s .
Numerical a n a l y s i s has to be based on the n u c l e a r cross s e c t i o n s i n each
p a r t i c u l a r case. The p r o b a b i l i t y that an event produced i n a c a v i t y by
a V-shaped t r a c k i s a double event i s given by the formula:
p
'K
<5>
where L i s the combined length o f the two arms o f the t r a c k and c i s the
d i s t a n c e o f the two t e r m i n a l p o i n t s (see r e f . ( 7 ) ) .
The V - e f f e c t i s s m a l l
f o r neutrons below 10 MeV, and f o r heavy charged p a r t i c l e s o f considerably
h i g h e r energy.
3.2
E l e c t r o n s , x Rays, and y Rays
E l e c t r o n s have a much s m a l l e r 6 ray t r a c k length per u n i t l e n g t h
of primary t r a c k than heavy charged p a r t i c l e s . Between 10 kV and 1 MeV
the value 0.06 i s never exceeded.
Between 100 and 300 keV the value i s
near 0.03 (see ( 7 ) ) .
The 6 ray e f f e c t i s t h e r e f o r e small f o r e l e c t r o n s ,
x rays and y r a y s .
IAEA-SM-145/6
51
Approximately 20% of a l l events i n a c o n v e n t i o n a l counter are,
however, double events due to the b a c k s c a t t e r i n g of the primary e l e c t r o n .
This f o l l o w s from the f a c t that the Albedo, R, p r o p e r l y averaged over a l l
angles, l i e s between .25 and .20 f o r e l e c t r o n s from 2 keV to 1 MeV (11).
One
bracketed
can a l s o show that the f r a c t i o n of r e t u r n i n g e l e c t r o n s i s
by the f o l l o w i n g equation:
2 r
(6)
r
where r i s the i n t e g r a t e d ränge of the e l e c t r o n without 5 rays and r
i s the d i s t a n c e between the s t a r t i n g p o i n t and the end p o i n t of the
t r a c k ( 7 ) . T h i s r e l a t i o n agrees with the c a l c u l a t e d Albedo v a l u e s ,
and confirms that the re-entry e f f e c t i s dominant f o r e l e c t r o n s .
Q
P a i r production can f u r t h e r c o n t r i b u t e to the w a l l e f f e c t s .
Due
to t h e i r curved t r a c k s the two e l e c t r o n s can siraultaneously t r a v e r s e the
c a v i t y i n s p i t e of the f a c t that they S t a r t out d i a m e t r i c a l l y .
3.3
Requirements f o r W a l l - l e s s
Configurations
W a l l - l e s s p r o p o r t i o n a l counters work on the p r i n c i p l e that the
s e n s i t i v e region U i of diameter d-^ i s p o s i t i o n e d i n the center of a
c a v i t y U2 of l a r g e r diameter, d?.
In such a c o n f i g u r a t i o n only 6 rays
of ränge exceeding (d2-di)/2 c a n b e i n v o l v e d in w a l l e f f e c t s . H o w e v e r
simultaneous events can s t i l l occur due to long ränge 6 r a y s , due to
e l e c t r o n r e - e n t r y , and due to the V - e f f e c t . The f o l l o w i n g r e l a t i o n i s
u s e f u l f o r an estimate of the extant e f f e c t s .
I f a convex body, U^, of s u r f a c e Sj^ i s s i t u a t e d i n s i d e a convex
body,
of s u r f a c e S2 then the f r a c t i o n S1/S2
of a l l random chords
traversing
pass through U^.
This can be shown on the b a s i s of
formulae on the random t r a v e r s a l of convex bodies (10) .
The r e l a t i o n i m p l i e s that the extent of the w a l l e f f e c t s decreases
by the f a c t o r ( d 2 / d i ) ^ f o r a l l those double events i n which the angle of
entrance of simultaneous segments i s u n c o r r e l a t e d .
For e l e c t r o n b a c k s c a t t e r t h i s i s a c o n s e r v a t i v e estimate because
re-entry i s most l i k e l y f o r those e l e c t r o n s which leave the s u r f a c e of
U2 under a small angle, and most of the r e - e n t e r i n g e l e c t r o n s r e - e n t e r
under a small angle. A r a t i o , 6 . 2 / d i , of 4 w i l l t h e r e f o r e decrease the
percentage of simultaneous events due to e l e c t r o n r e - e n t r y to w e l l below
1%.
On the other band i t must be assumed that the most e n e r g e t i c 6 rays
run n e a r l y p a r a l l e l to the primary track at l e a s t i n the i n i t i a l parts of
t h e i r t r a c k . The p r o b a b i l i t y of simultaneous events due to these 6 rays
w i l l then decrease by l e s s than the f a c t o r (d2/d^)2 #
R e l a t i v i s t i c heavy n u c l e i can produce s p a l l a t i o n showers which
are s h a r p l y bundled forward. In t h i s case one would have to have a
r a t i o d^/d2
much s m a l l e r than the angle between the n u c l e a r fragments
i n the bündle i f simultaneous events were to be suppressed. T h i s may
l e a d t o p r o h i b i t i v e values of d2/di»
KELLERER
52
ACKNOWLEDGEMENTS
The author i s g r e a t l y indebted to Dr. H.H. Rossi and Dr. W. Gross
f o r frequent d i s c u s s i o n s and f o r many v a l u a b l e suggestions.
REFERENCES
[1]
[2]
ROSSI, H.H. M i c r o s c o p i c energy d i s t r i b u t i o n i n i r r a d i a t e d matter.
In R a d i a t i o n Dosimetry, V o l . I , 43-92, A t t i x and Roesch e d i t o r s ,
Academic P r e s s , New York (1968).
ROSSI, H.H. Energy D i s t r i b u t i o n i n the Absorption of R a d i a t i o n ,
chapter from 'Advances i n B i o l o g i c a l and Medical P h y s i c s , V o l .
11, 27-85, Academic Press (1967).
BIAVATI, B.J. e t a l .
W a l l - l e s s p r o p o r t i o n a l counters.
USAEC-NY0-2740-5, p. 61-68 (1968).
GROSS, W. Microdosimetry o f d i r e c t l y i o n i z i n g p a r t i c l e s w i t h
w a l l - l e s s p r o p o r t i o n a l counters, 249-263, i n Proceedings Second
Symposium on Microdosimetry, S t r e s a , H.G. Ebert, e d i t o r , Euratom,
Brüssels (1969).
GLASS, W.A. and BRABY, L.A. A w a l l - l e s s detector f o r measuring
energy d e p o s i t i o n s p e c t r a . Radiat. Res. 39, 230-240 (1969).
WILSON, K.S.J. P r e l i m i n a r y measurements with a c y l i n d r i c a l
w a l l - l e s s counter, 235-246, i n Proceedings Second Symposium
on Microdosimetry, S t r e s a , H.G. E b e r t , e d i t o r , Euratom,
Brüssels (1969).
KELLERER, A.M. Event s i m u l t a n e i t y i n c a v i t i e s , to be p u b l i s h e d .
KELLERER, A.M. Assessment o f w a l l e f f e c t s i n m i c r o d o s i m e t r i c
measurements. To be p u b l i s h e d .
FANO, U. Note on the Bragg-Gray c a v i t y p r i n c i p l e f o r measuring
energy d i s s i p a t i o n , R a d i a t . Res. 3L, 237-240, (1954).
KELLERER, A.M. C o n s i d e r a t i o n s on the random t r a v e r s a l o f convex
bodies and S o l u t i o n f o r general c y l i n d e r s . To be p u b l i s h e d .
BERGER, M. P r i v a t e communication.
1
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
DISCUSSION
V . I. I V A N O V : B o t h y o u r s e l f a n d M r . K a t z ( i n p a p e r I A E A - S M - 1 4 5 / 9 )
m e n t i o n e d d o s e d i s t r i b u t i o n i n t h e t r a c k . W h a t does " d o s e " signify in
this case?
A. M. K E L L E R E R : A b s o r b e d d o s e i s a l w a y s an e x p e c t a t i o n value.
I would therefore b e hesitant to speak about absorbed dose in a track.
M i c r o d o s i m e t r y d i s t i n g u i s h e s b e t w e e n t h e s t o c h a s t i c q u a n t i t y of s p e c i f i c
e n e r g y a n d t h e n o n - s t o c h a s t i c q u a n t i t y of a b s o r b e d d o s e . T h e a b s o r b e d
d o s e , D , c a n b e d e f i n e d a s t h e e x p e c t a t i o n v a l u e of t h e s p e c i f i c e n e r g y ,
Z . In t h i s s e n s e o n e m a y t a l k a b o u t a d o s e p r o f i l e a r o u n d a t r a c k ; i t i s
an idealized profile, obtained when t h e p a r t i c l e p a s s a g e is r e p e a t e d v e r y
often.
These Proceedings.
1
IAEA-SM-145/6
53
F o r a r i g o r o u s d e f i n i t i o n g i v e n , f o r e x a m p l e , i n t h e I C R U r e p o r t on
Quantities and Units, one m u s t include a limit p r o c e s s by r e d u c i n g to
z e r o t h e v o l u m e V in w h i c h Z i s m e a s u r e d :
D = lim Z
V^O
H. H. E I S E N L O H R : I w o n d e r h o w g e n e r a l t h e g e n e r a l i z e d C a u c h y
t h e o r e m i s ? Is t h e r e , f o r i n s t a n c e , a n y r e s t r i c t i o n i m p o s e d on t h e
angle by which the p a r t i c l e is bent inside the v o l u m e ?
A . M . K E L L E R E R : T h e t h e o r e m i s v a l i d f o r a r b i t r a r y s h a p e s of
the t r a c k and for regions which need not b e convex. T h e sole condition
is that the p a r t i c l e fluence is uniform and isotropic.
R. K A T Z : What a r e y o u r future plans for g e n e r a t i n g s u r v i v a l c u r v e s
from microdosimetric theory?
A . M . K E L L E R E R : We f e e l t h a t g e n e r a t i n g s u r v i v a l c u r v e s a n d c u r v e
f i t t i n g t e c h n i q u e s a r e l i m i t e d b y t h e f a c t t h a t s u r v i v a l c u r v e s a r e in
g e n e r a l t h e c o m p l e x r e s u l t of s e v e r a l d i f f e r e n t s t o c h a s t i c f a c t o r s . T h e
s t a t i s t i c s of e n e r g y d e p o s i t i o n i s o n l y o n e of t h e s e f a c t o r s . O n e c a n n o t
t h e r e f o r e e x p e c t t h a t e q u a t i o n s b a s e d on t h i s S i n g l e f a c t o r w i l l l e a d t o
v a l i d c o n c l u s i o n s on t h e p r i m a r y m e c h a n i s m s of r a d i a t i o n a c t i o n . W e
t r y to apply m i c r o d o s i m e t r i c r e a s o n i n g in a g e n e r a l way in o r d e r to obtain
n u m b e r s of i n t e r a c t i n g a b s o r p t i o n e v e n t s a n d t h e i r i n t e r a c t i o n d i s t a n c e s .
In a n o t h e r p a p e r ( I A E A - S M - 1 4 5 / 1 0 ) 2 M r . R o s s i w i l l präsent d e t a i l s a n d
results.
2
These Proceedings.