Che materia stai cercando?

Anteprima

ESTRATTO DOCUMENTO

i s

The gamma-ray energy a b s o r p t i o n build-up f a c t o r d e f i n e d s i m i l a r l y t o t h e

dose build-up f a c t o r

- a t

t o t a l energy a b s o r p t i o n r a t e d e t e c t o r p o i n t F

- (3)

a t

u n c o l l i d e d energy a b s o r p t i o n r a t e d e t e c t o r p o i n t

BE F

and m a t e r i a l equiva-

(or

as

are

and t h e s e d a t a l i k e w i s e given f u n c t i o n s of b , EO)

l e n t atomic number, Z ) . i n s h i e l d i n g c a l c u l a t i o n s

are

These gamma-ray build-up f a c t o r s important

s h i e l d d e s i g n e r engineer t o o b t a i n c o l l i d e d dose r a t e s

or

s i n c e t h e y permit t h e r a t e s u s i n g t h e s t r a i g h t f o r w a r d p o i n t k e r n e l t e c h n i q u e ,

and energy a b s o r p t i o n

1 r The p o i n t k e r n e l e q u a t i o n may be w r i t t e n

which assumes e x p o n e n t i a l a t t e n u a t i o n .

(S) h a s c o o r d i n a t e s and s t r e n g t h and t h e f i e l d

where t h e source p o i n t S

0 )

-+ i s f l u x

$un($) t h e u n c o l l i d e d

F r . a t

p o i n t d e t e c t o r p o i n t has c o o r d i n a t e s

or

-+ - + - +

- ,

=

d Ir r'l and b d e f i n e d by Equation

i s ( 2 ) .

at

r from t h e s o u r c e S

0 i s

The t o t a l dose r a t e t h e n given by

% t h e dose build-up f a c t o r .

i s

i s

where flux-to-dose conversion f a c t o r and

a B

D

S i m i l a r l y , t h e t o t a l energy a b s o r p t i o n r a t e given by

i s

i s B

where k an energy a b s o r p t i o n c o e f f i c i e n t , and t h e energy a b s o r p t i o n

i s

E

ea

build-up f a c t o r . BUILD-UP

OF GAMMA-RAY

I1 PARAMETRIC REPRESENTATION FACTORS

( 6 )

( h ) , ( 5 ) , and may be i n t e g r a t e d

The p o i n t k e r n e l given by Equations )

( E

t h e energy and e q u i v a l e n t

If

numerically over a r b i t r a r y source volumes. 0

atomic number a r e known, build-up f a c t o r may b e found corresponding t o each

( Z ) a One technique t h a t may be

v a l u e of b c a l c u l a t e d d u r i n g t h e i n t e g r a t i o n p r o c e s s . and t o

used t o f i n d t h e build-up f a c t o r s simply t o look i n e x i s t i n g t a b l e s ,

i s

s o t h a t build-up f a c t o r s not e x p l i c i t l y given

s p e c i f y some i n t e r p o l a t i o n scheme

This technique used i n t h e SPAN-4 program

i s

i n t h e t a b l e s may b e found.

7 ) , (as

a

(Reference which has of build-up f a c t o r dat'a given i n Refer-

l i b r a r y

as of SPAN-4 uses l i n e a r i n t e r -

an

1) s t o r e d i n t e g r a l p a r t t h e program.

ence Eo, Two of t h e reasons

i s r e q u i r e d .

p o l a t i o n whenever i n t e r p o l a t i m on b , or Z 3

it

are ( a )

used i n SPAN-4 provides b e t t e r accuracy t h a n t h a t which

t h i s method i s of t h e p a r a m e t r i c r e p r e s e n t a t i o n s a v a i l a b l e t h e

could be achieved by any one a t

i s

w r i t t e n , it new

time w a s materials,

SPAN-4 and ( b ) easy t o i n p u t d a t a f o r s i n c e

p a r a m e t r i c c o e f f i c i e n t s need n o t b e d e r i v e d .

widely used t o f i n d build-up f a c t o r s r e q u i r e s

Another technique t h a t i s I n a given prublem

t h a t t h e build-up f a c t o r s be r e p r e s e n t e d p a r a m e t r i c a l l y . i s

i n t e r p o l a t i o n with r e s p e c t t o energy and atomic number done only once,

( E ) ( Z )

i s

b u t i n t e r p o l a t i o n w i t h r e s p e c t t o o p t i c a l d i s t a n o e ( b ) done r e p e t i t i v e l y ; v

as t h e parameter have beep proposed

t h e r e f o r e , many r e p r e s e n t a t i o n s with b

8 ) .

(Reference are

Such p a r a m e t r i c r e p r e s e n t a t i o n s convenient f o r many hand c a l c u l a t i o n s ;

fewer

are

t h e y a l s o u s e f u l i n computer programs s i n c e d a t a need t o be i n p u t and

a

manipulated, and c a l c u l a t i n g build-up f a c t o r p a r a m e t r i c a l l y may be simpler

or i n t e r p o l a t i n g available tabulated information. However, u n l e s s

than searching

t h e parametric c o e f f i c i e n t s a r e c a r e f u l l y d e r i v e d , t h e build-up f a c t o r s c a l -

f i t a material

new

and t h e use of build-up f a c t o r s f o r

a c c u r a t e ,

c u l a t e d may not be f i r s t .

requires t h a t parametric c o e f f i c i e n t s be derived

f i t

convenient and widely used p a r a m e t r i c r e p r e s e n t a t i o n of build-up f a c t o r s

A 8 , 9 , 11,

(References and which

1 2 )

given by Taylor e x p o n e n t i a l 1 0 ,

f i t

i s t h e

uses t h r e e parameters b -a2b

-a i

% -

+

= Ae A ) e

(1

where % = BD(b,Eo,Z)

A(E~,z)

=

A ,z

1

= al(Eo

1

a ,Z)

= ( E

a

a 2 2 0

( 5 )

Equation t h e n becomes +

+ a l ) b a 2 ) b

-(1 -(1

So(:*)% - 1

+ ( 8

A ) e

(1

=

D,,,(f) 4n d 2 {Ae i n

i s a l s o

i s

convenient i n many hand c a l c u l a t i o n s and a d a p t a b l e f o r use

which

computer programs. Since t h r e e c o e f f i c i e n t s cover t h e complete range of v a l u e s ,

b

fewer i t e m s

d a t a need t o be i n p u t and/or s t o r e d t o d e s c r i b e t h e build-up f a c t o r s

i s

Also, no e x p l i c i t i n t e r p o l a t i o n on b

a material

f o r given and energy.

.

es

nec a r y

s

4 The t a b l e of

was

This technique used i n t h e SPAN-3 program (Reference 11).

f i t i s

Taylor e x p o n e n t i a l c o e f f i c i e n t s used by SPAN-3 given i n Reference 11

( 6 ) )

(b), ( 5 ) , a

i s

When t h e p o i n t k e r n e l (Equations and i n t e g r a t e d over

volumetric source r e g i o n i n any of t h e geometric s i t u a t i o n s t h a t may be t r e a t e d

When

a n a l y t i c a l l y , t h e build-up f a c t o r should be included i n t h e i n t e g r a n d .

Taylor c o e f f i c i e n t s a v a i l a b l e , requirement may be immediately s a t i s -

are

f i t t h i s

( 8 ) as t h e i n t e g r a n d , s i n c e t h i s r e p l a c e s an i n t e g r a l

f i e d by u s i n g Equation 9 ,

(See Reference p

similar 412

i n t e g r a l s .

z o n t a i n i n g an e x p o n e n t i a l w i t h two f f . )

SPAN-4

When build-up f a c t o r r e p r e s e n t a t i o n f o r t h e program being inves-

w a s

made t o improve t h e Taylor e x p o n e n t i a l c o e f f i c i e n t s

an e f f o r t w a s

t i g a t e d , f i t

8

of Buscaglioni and Manzini small computer programs,

S e v e r a l

(References and 1 2 ) .

endeavor,.were used t o e v a l u a t e and improve c o e f f i c i e n t s

w r i t t e n t o a i d i n t h i s

f o r many m a t e r i a l s .

w a s

It found t h e Taylor e x p o n e n t i a l not s u f f i c i e n t l y a c c u r a t e

w a s

t h a t f i t

f o r t h o s e c a s e s having simultaneously low e n e r g i e s and low atomic numbers ( s e e

it

Appendix). Another p a r a m e t r i c r e p r e s e n t a t i o n need f o r t h e s e c a s e s , and

w a s

r e q u i r e d t o be uncomplicated,

w a s polynomial r e p r e s e n t a t i o n w a s chosen f o r

A c u b i c polynomial r e q u i r i n g o n l y

s i m p l i c i t y and e a s e of use. I n most c a s e s , a

three coefficients sufficient. few extreme c a s e s r e q u i r e q u a r t i c

is a

A

representation.

The cubic and q u a r t i c polynomial r e p r e s e n t a t i o n s a r e

2 3

% +

+

+

= (9)

Ab b

1 . 0 a a2b

1

and +

+ +

+ 4

1 . 0 Ab alb2 a2b3 a3b (10)

BD or a

f i t E

t h e polynomial f o r some s p e c i f i c and such t h a t nega-

i s i s

Z a

If 2 3

0

should not be used f o r b

t i v e , t h a t f i t 20.

> 1 4 )

13) a l s o

(Reference and Capo (Reference have p u b l i s h e d e x t e n s i v e

Tobias f i t s o f , b u i l d - u p f a c t o r c o e f f i c i e n t s .

t a b l e s o f polynomial IV, ( a )

t h e r e f o r e , g i v e Taylor e x p o n e n t i a l f i t

The t a b l e s given i n S e c t i o n

are

t h e y reasonably a c c u r a t e r e p r e s e n t a t i o n s of t h e corresponding

c o e f f i c i e n t s i f o r q u a r t i c polynomial f i t s f o r t h o s e c a s e s

build-up f a c t o r d a t a and ( b ) cubic

5 5 2.2 are

where Taylor e x p o n e n t i a l f i t s not s a t i s f a c t o r y .

E

1 3 ,

(Z MeV)

0 5

I n g e n e r a l , t h e accuracy requirement e s t a b l i s h e d f o r t h e s e t a b l e s t h a t

i s

build-up f a c t o r c a l c u l a t e d build-up f a c t o r

s

from p a r a m e t r i c c o e f f i c i e n t s from t a b l e 5

.-5% I x 10%

100

build-up f a c t o r from t a b l e s 7 . 0 ,

f o r each of t h e seven s t a n d a r d b v a l u e s 4.0,

( 1 . 0 , 2 . 0 , 1 5 . 0 , and

1 0 . 0 ,

are

mfp) f o r which build-up f a c t o r d a t a u s u a l l y t a b u l a t e d .

20.0

111. SOURCES DATA

OF

Reference ( G o l d s t e i n and W i l k i n s ) been t h e primary source o f build-up

1 has

it w a s p u b l i s h e d i n . 1 9 5 4 .

f a c t o r d a t a s i n c e The t a b l e s given h e r e f o r water,

aluminum, i r o n , t i n , t u n g s t e n , l e a d , and uranium a r e based on d a t a from

Reference except t h a t d a t a f o r water 0 . 5 and Mev drawn from t h e

a t 1 . 0 i s

1, 1 6 ) .

15) and Morris and C h i l t o n (Reference

newer work 'of Berger (Reference

B u i l d - u p - f a c t o r d a t a f o r o r d i n a r y c o n c r e t e have been p u b l i s h e d by C h i l t o n

17) 18).

(Reference and Clarke and Trubey (Reference Their r e s u l t s agree

6 )

w e l l .

reasonably Engholm (Reference a l s o calculated r e l a t e d concrete build-

and and C h i l t o n .

up f a c t o r s and o b t a i n e d good agreement w i t h w i t h

C l a r k e Trubey

Clarke and Trubey a l s o o b t a i n e d build-up f a c t o r s f o r magnetic and b a r y t e s con-

for o r d i n a r y , m a g n e t i t e , and b a r y t e s c o n c r e t e s

cretes. The t a b l e s given h e r e

18.

based on Reference

are a t

Engholm has a l s o c a l c u l a t e d build-up, f a c t o r s f o r b e r y l l i u m and carbon t

low e n e r g i e s , and has checked some of G o l d s t e i n ' s r e s u l t s u s i n g gamma t r a n s p o r t

a

a l l

I n results

c a s e s Engholm's a g r e e r e a s o n a b l y w e l l w i t h G o l d s t e i n ' s

program. 6) log-log p l o t s of dose build-up f a c t o r s v e r s u s

Fhgholm a l s o g i v e s ( i n Reference c u r v e s , which he

atomic number. These p l o t s g i v e smooth and r e l a t i v e l y f l a t

recommends f o r f i n d i n g build-up f a c t o r s f o r i n t e r m e d i a t e atomic numbers. The

t a b l e s o f d a t a f o r b e r y l l i u m and carbon come from t h e log-log p l o t s of Refer-

6. l o w

ence A t e n e r g i e s t h e v a l u e s p l o t t e d were a c t u a l l y c a l c u l a t e d , and a t

h i g h e r e n e r g i e s Mev) t h e y were t h e r e s u l t e x t r a p o l a t i o n ( l o g - l o g ) of

( > 2 of

Goldstein's data. l9),

Clarke

Data f o r sand, and wood come from t h e work o f (Reference

a i r ,

and t h e dose build-up f a c t o r t a b l e s f o r hydride given h e r e were published

l i t h i u m

Kam Clarke

by i n Reference

and 20. expcnenzial

The s t a r t i n g p o i n t f o r t h e c a l c u l a t i o n of t h e Taylor f i t coef-

w a s e x c e l l e n t s e t of d a t a published by Buscaglioni and

f i c i e n t s given h e r e t h e

Manzini i n Reference Without t h e s e d a t a , t h e t a s k of o b t a i n i n g t h e r e s u l t s

1 2 .

s e t f o r t h i n t h i s r e p o r t would have been much more d i f f i c u l t .

6 Build-up f a c t o r daT-a a r e o r d i n a r i l y t a b u l a t e d f o r e i g h t s t a n d a r d energy

6.0, 8.0,

3 . 0 ,

values ( 0 . 5 , 4.0, and Mev); b u t , f o r t h e

2 . 0 ,

1 . 0 , 1 0 . 0

u s e r s ' convenience, t h e t a b u l a t e d d a t a f o r b e r y l l i u m , carbon, aluminum, i r o n ,

t i n , t u n g s t e n , l e a d , uranium, water, and c o n c r e t e were e x t r a p o l a t e d and l i n e a r l y

31 energy l e v e l s i n t h e range t o MeV.

i n t e r p o l a t e d t o g i v e v a l u e s a t 0.25 1 0 . 0

are water

(Build-up f a c t o r s a t Mev given only f o r i n t h e l i t e r a t u r e ; t h e r e -

0 . 2 5 for

aware here

factors

t h a t t h e o t h e r

f o r e , t h e u s e r should be build-up given )

m a t e r i a l s Mev are not based on independent c a l c u l a t i o n s o r experiment.

a t 0 . 2 5 a l l

Parametric c o e f f i c i e n t s were energy l e v e l s . Linear i n t e r p o l a t i o n

derived for

i t s

of it

used because s i m p l i c i t y and because g i v e s reasonably

on energy w a s

a c c u r a t e i n t e r m e d i a t e v a l u e s f o r most c a s e s of i n t e r e s t i n s h i e l d i n g c a l c u l a t i o n s .

P l o t s , t a b l e s , and much a d d i t i o n a l u s e f u l i n f o r m a t i o n c a n . b e found i n most

6 , 1 5 ,

8, 9 , 19.

of t h e r e f e r e n c e s a l r e a d y c i t e d , e s p e c i a l l y References and

1,

are

I n a d d i t i o n much information and t h e o r y summarized i n Reference 21.

AND

OF BUILD-UP COEFFICIENTS

IV. TABLES DOSE ENERGY ABSORPTION FACTORS AND

TABLE 1 A . GAMMA-RAY DOSE BUILD-UP FACTORS FOR BERYLLIUM 5%

Error Magnitudes Greater than

Energy b(mfp) Paired with Corresponding values

o

- - - - - ( %

)

. 1.00 2.00 4.00 7.00 10.00 15.00 20.00 ALPHA2 ALPHA3 Type* E r r o r , b(mfp))

(Nev A A&HA~

25

050

060

070

080

090

i

.oo

1.25

1.50

1.75

2.00

2.20

2.50

2.75

3.06

3.50

4.00

4.50

5.00

5.50

6.00

6.30

6.50

7. 00

7.50

7.65

8.00

8.50

9.00

9.50

10.00 c o e f f i c i e n t s

*T s i g n i f i e s Taylor exponential f i t

= ) + )

Build-up f a c t o r A*exp(-alphale (1-A )*exp(-alpha2q

s i g n i f i e s cubic polynomial f i t c o e f f i c i e n t s

C + + +

=

Build-up f a c t o r 1 . 0 A*b alphal*b**2 alpha2*b**3

Q s ; g n i f i e s q u a r t i c polynomial f i t c o e f f i c i e n t s

+ + +

+

=

Build-up f a c t o r 1.0 A*b alphal*bY*2 alpha2*b**3 alpha3*b**4

TABLE GAMMA-RAY..ENEFiGY

ABSORPTION BUILD-UP FACTORS FOR

1B. BERYUIUM 5%

E r r o r Magnitudes G r e a t e r t h a n

Energy b(rnfa) P a i r e d 'Corresponding b v a l u e s

w i t h

-

) (% Error, b(mfp))

(i4ev) ALPHA2

ALF'HAl

A.

s i g n i f i e s Taylor e x p o n e n t i a l f i t C o e f f i c i e n t s

*T = A*exp(-alphal*b) (1-A)*exp(-alpha2*b)

Build-up f a c t o r +

s i e i f i e s cubic polynomial f i t c o e f f i c i e n t s

C = +

+ +

f a c t o r 1 . 0 A*b alphal*bi*2 alpha2*b**3

Build-up BUILD-UP FACTORS FOR CARBON (GRAPHITE)

GAMMA-RAY DOSE

TABLE 2A. 5%

Error Magnitudes Greater than

Paired with Corresponding b values

Energy b(mfp)

------- Type* ( % Error, b(mfp))

A ALPHAl ALPHA2

(Mev) 0. 1.00 2.00 4.00 7.00 10.00 15.00 20.00

W signifies Taylor exponential fit coefficients

+

= Alexp(-alphal*b) (1-A)*exp(-alpha2*b)

Build-up factor

C signifies cubic polynomial fit coefficients

+ + +

=

Build-up factor 1.0 A*b alphal*b**2 alphaZ*b**3

.

TABU 2B. FACTORS FOR

GAMMA-RAY ENERGY ABSORPTION BUILD-Up CARBON (GRAPHITE) 55

E r r o r Magnitudes G r e a t e r than

C o r r e s p o n d n g values

Paired

Lnera with b

b(mfp)

- - Type' Error, b(mfp))

15.00 (%

ALPHA2

4.00 7.00

(Nev) 2.00 10.00 A

1.00 ALPHA1

0. 20.00 .49776 .01032 C

295.00 .820

71.30 163.00

4.73 35.60

12.80

2.39

0.50 1.00 -

2.08 3.73 8.45 18.90 31.80 59.60 93.50 .9010 .0050

1.00 C

1.00 .280 (11.44,1),

.03326 (7.04,2),

1.0283

31.30 0. (11.41,20)

1.85 5.56 10.30 15.10 C

23.50

2.98

1.00

2.00

*T s i g n i f i e s Taylor exponential f i t c o e f f i c i e n t s

= +

A*exp(-alphal'b! (l-A)*exp(-alph&*b)

Build-up f a c t o r

s i g n i f i e s cubic polynomial f i t c o e f f i c i e n t s

C = +

Build-up f a c t o r A*b alphal*b**2 alpha2*b**3

1 . 0 +

+ GAMMA-RAY

TABLE DOSE FACTORS

3A. BUILD-UP ALUMINUM

FOR 5%

- Error Magnitudes Greater than

- -

.

Energy Paired with Corresponding b values

- - - - -

- 20.00

10.00

1.00 A ALPHA2

ALPHAl

2.00 15.00 ( % Error, b(mfD))

(MeV 0. 63.99

2.72

25 5.21 150.89

1.00 290.44 1.171 C

4.24

2.3y 38.90

1.00 141.00

.SO 80.80 0,976 C

2630 35.36 72.22

I.00 124.50

060 4,05 0.983 C

2.23 31.82

3.87 lO8.00

1 . 0 0

70 63.64 0.990 C

..oo 2.16 28.28

3.68 91.50

080 55.04 0.99R C

1.00 2.09 3.50 24.74 75.00

.90 C

46.4A 1 .ooq

*oQ

1 2 1

3.31

2.02 37.9n

a20 58 050

1.00 1.313 C

18.87

1.25 1.00 1.95 .

45

50

3.13 330 0.961

1 0 C

1.88 2.96

1.00 16.55 $2.60 C

1.50 28 30 0.910

a

1.82

j.00

1.75 2-76 n.nSa

. C

14.22 35

34

23.50 16.6*1

1.75 2.61 11

1.00

2.00 0 9 0 26.30 (5.0,l)

T

18.70 15.430

2.20 1.00 2.55 .11

1.73 25 T

17.56 58

24 (5.4.11, (5.2,20

1.76

2.50 1.00 13,61?

2.46 10.27 (5.1.1)

22.00 T

15.85

2.75 12.99~

1.67 2.39

1.00 9.46 T

19.85

16.42 10.583 T

1.64 8.65

3.00 2.32

i.00 17.70

13.00

1.59 T

7.76

3.50 1 . 0 0 15.55

11.55

2.?0 9 055

5 000 7.526

6.88 T

1.53

4.00 2.08 13.40

10.10

1 7.077

1 e 5 6 1

6.53

2.02

4.50 12.65

9.57

.OQ h.620

la48

l a 0 0

5.00 6.19

1.97 T

11.90

9.03

1.00

5.50 1.65 5.84 T

11.15 6.166

1.91 8.50

1.42 5.49 5.717 I

1.00 1.85 7.97 10.60

6.00 i 5,567

6.30 5.35

000 f

1.82

1.45 10.12

7.76

'

1.40

6.50 1.00 1.81 5.26 9.93 T

5.464

7.6%

1.00

7.00 1.77

1.38 5.03 9.66 5.214 1

7.26

1

1.36 m72 8.99

4.81

1.00

7.50 T

6.91 6-96?

j.00 1 e71

1.35 4.14 8.85

7.65 T

4,@9n

b.81

1.40 1.34 1.68 4.58

8.00 8.52

6.56 4.716 1

8.22

1.00 1.65

8.50 4042 .577

1.31 6.33 T

Q

j.00

9.00 1.61 4.27 4.357

7.92

6.09

1.31 1

1.00 1.30

9.50 4.11

1.58 7.62 b.17R

5.86 T

000

1 1.55 7.32

3.96

1.28

10.00 3.999

5.63 1

*T signifies Taylor exponential fit coefficients

+

= A*exp(-alphalQ) (l-A)*exp(-alphQ*b)

Build-up factor

C signifies cubic polynomial fit coefficients

+ +

+

= A*b alphal*b**2 alpha2*b**3

Build-up factor 1.0 GAMMA-RAY ENERGY

TABLE 3B. ABSORPTION BUILD-UP FACTORS FOR ALUMINUM 5;

E r r o r Magnitudes Z r e a t e r than

P a i r e d with Ccrresgonding b v a l u e s

- Type' ( %

ALPHA2 E r r o r , b(mfu))

o.ilr4

0.

C

I).

I).

I.

0.

0.

0.

0 4 128

- n o

-o.nlui

-3.(r060

-0.0027

0.n047

0.nniv

9.0934

o.no4o

no44

1)

Q.flP4R

n.ig52

0.nn*9

rl.nO4R

o.n')44

().noun

0-ri03q

o.nn37

7.nn36

0.0036

n.nn35

9.nn35

*T s i g n i f i e s Taylor e x p o n e n t i a l f i t c o e f f i c i e n t s

+

=

Build-up f a c t o r A*exp(-alphal*b) (1-A )*exp(-alpha2*b)

s i g n i f i e s c u b i c polynomial f i t c o e f f i c i e n t s

C +

= + +

1 . 0 A*b alphal*bs*2 alpha2*bi*3

Build-up f a c t o r 4A.

TABLE GAMMA-RAY DOSE FACTORS FOR IRON

BUILD-UP

Energy bimfu) -

- - 9 1

(:lev) A 4

4.00 25ul

7.30

1.00

0. 15.30 20.x T

25 12.85 59-22

42-17

21.73

2.06

eo0 48.63800 -.07LLO -.U5130 T

11070 55.60

-50 1.9R 19-20 35.4r)

e00 40.43700 -.U3940

-.06410 T

53 02

11 18-60

e60 33.94

-40

1.96

000 -.

38.04OUO -.063u0 3603

U T

50.44

.70 11.10 32.56

18.00

1.99

-00 35.64300 -.U3410

06 180 T

67.86

1.91

.80 10.80

*OF 31.14

17.40 33.246UU -.U3140

-.06070 T

45-28

1.89

.96 10.50

.OC 16.80 29.72 30.84800 -.32880

-e05960 T

-.

1.00 1.87

.OC 42.70

10.20 16.20 28.30 28,45100 05840 -e02610 T

1.25 39-30

9.46 14-87 u

1.84

-00 25,6? 2 100

-e05540

25.80500 T

1.50 -00 8.72

i.8i 13.55 33-90

22-95 -.05230

23.16000 -.U1580 T

1.75 7.99 29-50

12.22

1.79 20.27 2

-00 0.5 1 4 0 0 -e04920 -.dl060

-. 1

2.00 -00 7.25

1.76 25.10

10.90 17.97400

7.60 -e04630 -.00570

.

2.20 6-97

-00 1.72 23-90 T ,

6.7R

l(r.42 045YL) -.UO470

1 7 . 0 2 3 0 0 - T

u

2.56 6.55 22.10

5.55

1.67 9.70

-00 5 3d

15.596Ui) -.u0330

4

-. T

2.75 -00 1.60 2 0

6.20 60 -.u021u

14.4U70U

6.52 -.044U0

9.11 T

3-06 5-85

e00 1.55 19-10

8.51 044343

3.50 -.UOOY0

13.2 11100

.on T

3.50 1.50 17.55

5.38 2-35

7.81 -.04>bd

11.421OU .UOO4U T

4.00 1 6 ~ 0 0

4-91

1.45 1.20

a00 1.11 -.047UO .UOl80

9.62400 -

-on T

4.72

1.42

4.50 15.67

0.87

6.84 - 0 5 060 .U0080

8.68500 -. T

000 1.40

5.00 15-35

4.52 6.56 0.54 -.05149 -.00006

8.13225 T

1.37 4.33

5.50 15-02

6.29 0*2?

eo? 05 790 -.uo100

6.80600 T

6-00 1.34 14.70

4.16 9.89

6.02

eo0 -e06150 -.U0190

5.867OO -. T

6.30 *OO 1.33 14-44

4.04 5.88 9.68 -.06330 .U0160

5.47300 T

1.32 3.98 14.27

-00

6-56 5.78 9.54 4.95045 0

064Y -00546 T

13.85

3.81

1-30

7.00 a00 5.54 9-19 -e06820 .U1018

4.32725 -. T

13.42

e00 1.29

7.50 3-65 5.31 -.0716U

3.89900 U0930

8.85 T

3-60 13.30

7.65 1.24

-06 8.74

5.24 0 162 3

3.33180 .U1978 T

3.49 13.00

1.27

8.00 e00 5.07 3.2430u

8.56 -.075u0 .JLlLO

-. T

3.36

8.50 12.85

6.89 8.26

1.25 -.085U5

2.58210 .U3087

eo0 -. T

3.24 12-70

9.00 8.07

4.71 OA7UO

L.370L5

1.23 -02622

e00 T

9.50 12-55

7.74

3.11

1.22 4.53 093UO

2.12100

-00 .U3?00 1

1.20

10.00 12.40

2.99 7.54

roo. -.09900

1.74700

4-35 eU6630

s i g n i f i e s e - q o n e n t i a i f i t c o e f f i c i e n t s

T a y l o r

*? +

=

f a c t o r (l-A)*eq(-algna2%1

Build-up A*exp(-al?hal*o)

4 ~ . GAMMA-RAY ENERGY ABSORPTION BUILD-UP FACTORS FOR IRON

TABLE 5%

Error Magnitudes Greater than

Paired with Corresponding values

b

Energy

- ( % Error, b(mfp))

(Mev)

*T signifies Taylor exponential fit coefficients

= +

Build-up factor A*exp(-alphal*b) (1-A)*exp(-alpha2*b) BUILD-UP

DOSE

TABLE 5 A . GAMMA-RAY FACTORS FOR T I N 5%

Error Magnitudes Greater than

Paired with Corresponding b values

( % Error, b(mfp))

*T s i g n i f i e s Taylor exponential c o e f f i c i e n t s

f i t +

= A*exp(-alphal*b) (1-A)*exp(-alpha2*b)

Build-up f a c t o r 5B.

TABLE GAMMA-RAY ENERGY ABSORPTION BUILD-UP FACTORS FOR TIN

Energy

(MeV) SSP

1 9.1

.25

.so -0, J G l 4 l 0 R

9.1

1 6 9 1 1i.n.(79

-0.

60 - 6 . ,774 1.6467

a70 -u.u431 0.0735

-80 -0. " 7 5 9 1.n229

.90 - U . ~ G O J f3*02J1

'

1.00

1.25 - 3 l . n l 73

-0. ,627 n.c~*h

1.50

1.75 1

-n. , 6 + 3 1.n l A

, 6 5 3 -~.nqil

2.00 -0.

2.26 -i.u~43 0.nnl6

2.50 ,472 -0.00 79

- 0 .

2.75 -0. ,774 -d.n7~0

3 00 -n.n2*5

-0.J773

-n.,15lj4 -Q.*?52

3.50 - 0 . ~ 6 2 3 -0.q319

@WOO ~ 7 1 3 - 0 . n 4 l h

-0.

4.50 - ~ . ~ , o o 7 -Q.n7r3

5.00 -0.1,+eg -1."?79

5.50 n , 7 , -0.n1 ~h

6.00 -0.1737 -o.n1,+0

6.30 1 7 6 9 1 7 0

-n.n

6.50 -q.

-!,ioca -n.nq>3

7.00

. -n,lq27 -n.nn25

7.50 -n.1550 -n.n?19

65

7 -0.16 16 1.

8.00 -0.1636 16

8.50 1 a 0 1

9.00

9.50

10.00

*T s i g n i f i e s Taylor exponential f i t c o e f f i c i e n t s

= ) (

+ )

)*exp

~ * e x p ( - a l p h a l c b (-alpha2*b

Build-up f a c t o r 1-A

6A.

TABLE FOR

BUILD-UP FACTORS

GAMMA-'RAY DOSE TUNGSTEN 5%

Error Greater than

Magnitudes

Jbergy with b

Corresponding values

b(mfp) Paired

7.00

00.

-

-

4

.oo rype*

A Error, b(mfp))

( %

ALPHAl

1.00 15.00 ALPHA2

2.00 10.00 20.00

1.71 T

1.65

1.55 1 e60 1.574

1.33

1.20 .so 3.59 T

2.24 2.61 3.12 2.575

1

1.28 4.34

2.52 T

3.02 3.75

1.3i 2.746

1 .57 5.09 1

3.42 4.37

2.79 2.916

1 063

1.34 5.85 T

3.07 3.83 5.00 3.087

1 e70

1.3~ 6.60 T

3.34 4.23 3.25A

5.62

1 e76

1.41 r

7.35

4.64

3.62 6.25 3.42a

1.83

1.44 T

8.16

4.80

3.74 6.70 3.553

1.43 1 a 8 3 8.97 T

3.86 7.16 3.679

4.95

1 a43 1 .A4 9.79 1

3.97 5.11

1.42 7.61

1 3.004

a 8 4 T

10.60

8.07

4.09 5.27 3.924

1 .85

1.4? T

11.30

4.07 5.40 8.39

1-61 4.084

1 e83 12.35 T

5.59

4.04 8.86 4.323

1.39 1 .RO 13.22 1

5.76 9.26

4.02

1.77

1.38 4.523

14.10 1

5.92

4.00 9.66 4.727

1.74

,1.36 17.50 T

6.09 10.83

1 .68 4.01

1.32 5.121

2 0 90 T

12.00

4.03 6.27

1.29 1.62 5.52n

24.75 T

3.92 12.92

6.28

e57

1

1.27 0.0244

28.60 T

6.28

3-01

1.52

1.24 13.05 1.69RS

32.45

3.71 T

14.77

6.28 1.

1 .48 R6Pn

1*23 36.30

6.29 T

3.60

1.43

1.20 15.70 1 e273

37.14 1

3.52 (5.3,4),(6.4,7), (5.8,10), (7.9,20)

1.41 6.16

1.19 15.62 1.182

.

37.70 T

3.46 6.07

1.19 15.57

1 e40 1 .OUR9

39.10 T

5.84 15.45

3.32

1.17 1-36 ,8712

50 T

40

5.62

3.19 15.32 .7346

e35

1.16 1 1, 1

T

4 0 92 (6.5,7), (5.4,20

(7.0,lO

15-29

5.56

3.15 0.771

1.15 1 .34 41.90 T

3.05 0.66h

5.40

1.14 15.20

1.32 1

41.25

2.94 0.625

1.13 14.90

5.21

1 e30 T

40.60

2.83 5.02

1.28 14.60 0.687

1.13 1

39.95 0.549

4.84 16.30

2.73

1 .27

1.13 T

39.30 0.509

2.62 4.65

1.11 14.00

1.25

signifies Taylor exponential fit coefficients

VT +

factor A*exp(-alphal*b) (l-A)*exp(-alpha2*b)

=

Build-up 7A. DOSE BUILD-UP

TABLE GAMMA-RAY FACTORS FOR LEAD none

*T s i g n i f i e s Taylor exponential f i t c o e f f i c i e n t s

= +

) exp

Build-up f a c t o r ~ " e x (-alphal*b

p (1-A)* (-alpha2'b )

TABLE 7B. GAMMA-RAY ENERGY ABSORPTION BUILD-UP FACTORS FOR LEAD

N

0 5 %

E r r o r Magnitudes Greater than

Energy b (mfp) Paired with Corresponding values

b

- - - - - - - - -

(Mev) 0. 1.00 2.00 4.00 7.00 10.00 15.00 20.00 (% Error, b(mfp))

Type'

T

1.644 O.unZ4 T

2.030 -0.;37u

2.467 -0. J7H4 T

14,

2.75~ -0.3615

-n. T

3. l e i 2 4 7 5 T

3.76n -0.~615 T

4-19? -0.~426 T

4,775 1A.4413 T

4*55q -0.3640

-;. T

4.456 -n.uo3f

6.507 T

J775 T

6.640 -i.u79b T

6,RbQ -0. J b 7 7 T

7.02i -0.~454 T

7.194 -0.1~480 T

4-13? -0.~694 T

2.520 -0.~909 T

1-67? -0.llq2 T

1.237 -:.I348 T

.029 -0.1072

1 T

0.777 -6.1660 T

0.713 -001716 T

0.676 -0.1754 T

0.576 -?.la47 T

0.470 -n. 1 9 4 1 T

0.449 -0.1O6Q T

0.381 -0.2035 T

0.320 -0.21 1 3 T

0.276 -n.2192 T

0.729 -n.2?71 T

0.171 -0.d35D

s i g n i f i e s Taylor e x p o n e n t i a l f i t c o e f f i c i e n t s

= +

) )

A*exp(-alphal'b (1-A)*exp(-alpha2*b

Build-up f a c t o r TABLE URANIUM

8A. GAMMA-RAY FACTORS FOR

BUILD-UP

DOSE 5%

E r r o r Magnitudes G r e a t e r t h a n

b(-)

Energy - - - P a i r e d w i t h Corresponiinq v a l u e s

b

a.oo

- 7.00

1.00 h.oq ( R

A

15.00 20.00 rype.

10.00

0.

(MeV) E r r o r . b(mfD))

T

moo (7.?,20)

1

l*UO 1.30

e26

1.17 1.28

1.29 1.13n

1

25 T

1.444

1.85 2-36

1.17 1.30 1 a67

j.00 2eOR

.

e50 .e*

1 moo T

2.79

1 1

1.26 1.35 .S?l

2107 2.40

a60 T

3.21 1

1.23 1.40 2.72

2.00 .hQQ

2130

1.00

79 I

moo 1.426

3.64

3.03

1.25 1.46 2.17

I 2.52

.EO i T

2.75 1.955

3.35 6.06

1.29 1.51 2.33

.90 *OQ

moo

.oo T

4.49

2.97 3.67

1 2.50 2.081

1 1.31. 1.56 T

4.99

2-65 4.09

1.25 1.58

1.31 2.45t

3.21

1.00

m oo T

5.48

1.32 1.60 3.46

2.79 4.51

1

1 2.821

a 5 0 T

5.98

2.94

1.32 1.62 3.70 6.94

i.00 3,194

1.75 1

6.46

3.95 5.36

3.09

1 1.33 1.64

2.00 .o9 3.S5n T

7.16

5.6n

3-13

1.33 1.63

2.20 1 4.06 3.P17

.00 8.18

6.16

4.23 T

1.31 1.61

2.50 1-18 4.216

l.09 9.03

6.57

1.30 1.59 3.22 4.37 1

2.75 1 4.9517

.06 9108

3.27 6.97 T

1.29 1.58 4.51

3.00 1 .OO 4.AA3

11.29

7.49 T

3.24

1.27 1.54 4.58

3.50 j.00 3.441

m o o T

12.70

3.21

1.24 4.66 8.01

1.50

1

4.00 2.8qn

j.oo T

15.27

4.69

3.15 8.71

1.22 1.46 1

4.56 ,RO? t

17.85

1.63 3.08 4.73 9.40 1.369

1.20

1.00

5.00 1

4.76 20162

10.10 1.0913

1 3.02

1.18 1.39

5.50 * O Q T

23.00 0.979

10.80 .

2.96 4mRO

I 1.16 1.36

6.00 rOO T

23.75

10.86

2.91

j.00 1.35 4.73 0.910

6.30 1.15 T

24 25

.09

I 10.90

2.87

1.34

1.15

6.50 4.69 0.983 T

25.50

4.58 6.7AR

11.00

2.78

1.31

7-00 j.00 le14 T

4.47 26-75

11.10

1.13 1.29

7.50 2.70

!.OO 0,695 T

27.12

4.44

1.29 11.13

7.65 2.67 0.667

1.13

I r o o T

28.00

1.12 11.20

4.36

2.61

8.00 IWOO 1.27 0.607

28.12 T

2.52 4.21

1.11 Il.02

1.25

8.50 1.00 0.551 T

28.25

10.85

4.07

1 2.43

1.16 1.23

9.00 .OO 0.500 T

28.37

10.67

1.22 2.35 3.92

1.10 0.45n

9.50 1.00 r

28.50

10.50

2.26

10.00 1.09 1.20 3.78

1.00 0.399

f i t

*T Taylor

s i g n i f i e s e x p o n e n t i a l c o e f f i c i e n t s

= +

A*exp(-alphalab) (l-A)*exp(-alph&*b)

Build-up f a c t o r BUILD-UP

TABLE g A . GAMMA-RAY DOSE FACTORS FOR WATER

N

N 5 %

Error Magnitudes G r e a t e r t h a n

Ehergy b(mfp) ? a i r e d w i t h Corresponding b v a l u e s

- - - - -

(Nev) 4.00

0. 1.00 7.00

2.00 TvpeY-

10.00 15.00 ( 5

A

20.00 ’.LPFAl AL?€iA2 E r r o r , b(nfo))

-

. ,

, , C

0

335 6924

3 0

i.00 0 8 3 5

.cq 1

25 166.00 9~2.00 C

1.09 63.10 0,4805

0,98S

2. i 6 0

.SO 252.09 0052

e

o

55.9r1 C

2.3Y 0,993 0,4195

1.00

60 H,O*

21 ,004a

, ,

.oo 0 C

3386

2.73 4b.70 1,001

1 0

lR4.09 0036

a70 e

1 . E O 0,2845

1.00 2 .?6

.BO 1,004 0,0021

4 150.1? e

39.50

2-20

1.00 0,2215

1,002

116.16 0,001~

.90 C

1 0,1575

048

2 7 . 1 ~

1.00 1.00 0,oo

n2.20

2.13 e

.ze; moo 23.62 C

2,’5

1 0.1241

1,007

68.57 0,o

.sa C

1 1.00 19.75 0,966 0,0907

54.95

i.qa 0,o

, c

,

.oo ,o

0

1.75 0 5 7 4

1-40

1 61.32 rl

10.07 920 G

1 .oo T

3 6 9 -0,0521

13

2.00 12*4’J 77.70 0,0166

1 .?3 e

1 11.65

2.20 .0o 1 T

75.56

,afl -0,0488

12,917 0,0197

,

ld.51 T

- 0

1.74 72.35 O43R

12,230

1.00 0,0243

2.50 , T

9.57

1.72 675

11 -0,3397

1 19.67 0,0282

r o o

2.75 ,

.oo ,

* O

B.63 I

1 1.69 0 3 5 5

3.00 11 0

,110

17,017 0321

,

1 T

I -0

3.50 e 0 0 .78 11,137

.c3 0305 0 0312

1 14.95

4.94

!.OO T

4.00 1 ,0254

11,163

12.90 0,0303

.kd w o ,

,

*cs ,

.On T

- 0

1 0234

0.50

4-50 4 6 9

10

1 0 0331

11.69 ,

.OQ

1 .‘2

5.00 T

I 9 -0,0218

7 7 4

0.~6 10.P7 0,0359

,

1.00

5.50 5.62 I

9,070

1 .u9 0200

9.P6 0 0388

e

YO

,

1.00

6.00 T

-b,5182

8 385

5.18 0

1,Cb 0416

9,P5 e

, ,

1.00

6.30 9.56 T

5.c4 -0,3194

7 822

1.45 C 0460

1 * a

6.56 T

7,447

r o o 4.95 ,0202

1 0.0490

a.37

. C *

1 ,

7.00 .OO I

v.71

1-42 -0.0223

6,510

7.9r 0 0 5 6 2

,

, ,

- 0

.Of T

1 : 5 7 2

S O Z 4 S 0

I 4.48

7.50 0636

7.42

.‘4

.oo I

1

7.65 -0,0249

4.41 0.0658

1.a’) 7.79 T

000

8.00 4.25

1.36 90,0263

6.95 0;071Q

,

1.00 T

- 0

8.50 0272 0,0750

4.11

1.37 6.71

.OO

1

9.00 I

3.98

1.3s -0,0261

6.46 0,0791

5 , ,

.Oo T

- 0

3,PS

9.50 0290 0

4.7? 0831

1.34 , T

00

1 .OO 0299

5.99

3.72

10.00 0,0872

1.33

YT s i g n i f i e s T a y l o r e x p o n e n t i a l f i t c o e f f i c i e n t s

+

= A * e x p ( - a l p h a l * b ) ( l - A ) * e x p ( - a l p h a 2 * b )

Build-up f a c t o r f i t

C s i g n i f i e s cubic polynomial c o e f f i c i e n t s

+ +

= 1.0 +

Build-up f a c t o r alphal*b**2 alpha2*b**3

A*b

TABLE 9 B . GAMMA-RAY ENERGY ABSORPTION BUILD-UP FACTORS FOR WATER Error Magnitudes Greater t h a a j%

)

Ehergy Paired .with Corresponding -ralues

b

b (mfp

- - - - - - - - - - - Type'

(Mev) 0. 1.00 2.00 4.00 7.00 10.00 15.00 20.00 ALPHA1 .%FHA2

A ( % Error, b ( n f p ) )

None

*T s i g n i f i e s Taylor exponential f i t c o e f f i c i e n t s

= +

)

A*exp (-alphal*b )*exp (-alpha2*b)

Build-up f a c t o r (1-A

s i g n i f i e s cubic polynomial f i t c o e f f i c i e n t s

C = +

+

Build-up f a c t o r 1 . 0 A*b alphal*b**2 alpha2*b**3

+

TABLE 1 0 A . GAMMA-RAY DOSE BUILD-UP FACTORS FOR ORDINARY CONCRETE

IU

C 5%

Error Magnitudes Greater than

Paired with Corresponding b values

( % Error, b(mfp))

"T s i g n i f i e s Taylor exponential f i t c o e f f i c i e n t s

= +

) )

A*exp (-alphal*b (LA

)*exp (-alpha2*b

Build-up factor

s i g n i f i e s cubic polynomial. f i t c o e f f i c i e n t s

C +

= + +

A*b

Build-up factor alphal*b**2 alpha2*b**3

1.0

10B.

TABLE GAMMA-RAY ENERGY ABSORPTION BUILD-UP FACTORS FOR ORDINARY CONCRETE 5 -

E r r o r Magnitudes Sreattr t z a r

-. - -

b(nfp) P a i r e d w i t h Correspon6;q r l , e -

;

-. -

- - - - - - - ( %

A

7.00 15.00 20.00 ALPHA1 ALPHA2 TypeY Error,

1.33 2.00 4.00 10.00 S ' ~ , f o ) ,

-- . 656

j

fi

I.

.

P .

"

I.

1.

".

'l.

- 'l.

- .C)'+72

- .OB?~T

*r)O150

- .coz93

.0@07t:

.

.ao.?76

.

n 7.46~

CU94C'

.

oQhle

r ?hap

. r7p

. Y O

"riR&

@

.

.p~rh72

.

p.~572

ot~sbc

CC487

i)t'499

c504

.(

I

5968

G

CPY9C

*oouqc

*- -r2ifies Taylor exponential f i t c o e f f i c i e n t s

zL +

= ) )

(1-A

Euild-up f a c t o r ~ * e x p ( - a l p h a l * b )*exp (-alpha2*b

s i g n i f i e s c u b i c polynomial f i t c o e f f i c i e n t s

C + + +

=

Build-up f a c t o r 1.0 A*b alphelYb**2 alpha2*b**3

TABLE 11A. GAMMA-RAY DOSE BUILD-UP FACTORS FOR MAGNETITE CONCRETE

N

c

n 50,

Error Magnitudes Greater than

Energy Paired with Corresponding values

b

b(mfp)

-- - - - - - - ( 5

A Type*

(Mev) 0. 1.00 2.00 4.00 7.00 10.00 15.00 20.00 ALPHA1. ALPHA2 Error, b(mfp))

*T s i g n i f i e s Taylor e x p o n e n t i a l f i t c o e f f i c i e n t s

+

= )

Build-up f a c t o r A*exp(-alphal*h (1-A)*exp(-alpha2"h) I

TABLE 1 1 B . GAMMA-RAY ENERGY ABSORPTION BUILD-UP FACTORS FOR MAGNETITE CONCRETE 5%

Error Magnitudes than

Greater

Energy Paired with Corresponding values

b

b(rnfp)

-- - - - - - -

(MeV) 2.00 20.00 ALPM2

ALPFA ( %

7.00 15.00 E r r o r ,

4.00 10.00

1.00 A

0. b(!nfDj)

-

. -

213.96

55 56 T

61.9615

25 30.38 -

so 118.00 T

36.10 37.5751

20.90 -

106.06 T

33.18 81.h937

19.38

60 -

94.12 T

30.26 44,2056

70 17.86 82.18 T

41.5unl -

27.34

16.34

080 -

70.24 T

24.42 51.5673

.90 14.02 58.30 - T

21.50 33.nln2

1.00 13.30 -

50 T

52 3 n . 8 ~ ~ ~

19.15

1.2s 12.01 -

42.75 27.P869 T

1.50 16.80

10.72 34.97

14.45 T

24.977n

1.75 -

9.44 -

27020 T

2.00 27.9076

12.10

8.15 -

25.46 T

11045

2.20 27.66~3

7.76 -

22085

2.50 10.49 T

24.73R7

7.17 -

2 0 67

9.68 T

2.75 72.20q4

6.69 -

18.50

8.87 T

3.00 1R.7572

6.20 -

16055

8.06

3.50 1

15.867@

5.68 -

14060 15,0859 T

7.24

4.00 5.17 -

13.62

6.82 T

4.50 4.90 13.64p7 -

12.65 T

6.41

5.00 ll,P976

4.63 (6.0.20)

-

11.67 T

5.99

5-90 8.A9R6

4.36 5.57 10.70 T

6.00 4.09 8.3079 -

5.46 10.46 T

6.30 8.3079

4.01 *

-

5.38 10.31 T

6.50 8.3079

3.97 -

9.91

5.20 8.67517

7.00 1

3.84 -

9.52 1

7.50 5.01

3.72 8.1711 -

9.40 T

7.65 4.96 8.1711

3.68 -

9.13

4.83 T

8.00 7.7171

3.59 -

8090

8.50 4.72 T

7,9657

3.51 8.67 -

4.60

9.00 7.5465 T

3.44 -

8.45

4.49 T

9.50 3.36 7.2632

8.22

4.38 1

10.00 3.28 6.8092

s i g n i f i e s Taylor exponential c o e f f i c i e n t s

f i t

*T +

Build-up factor A*exp(-alphal*b) (l-A)*exp(-alphaZ*b)

=

rU TABLE 1 2 A . BUILD-UP

GAMMA-RAY DOSE FACTORS FOR BARYTES CONCRETE

03 5;

Error Magnitudes Greater tnsc

Energy Paired with Corresponding v a l ~ e s

b

- ( %

)

(:,!ev Error, b(mfp))

T

T

1

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

1

T

r

T

T

T

T

T

T

T

YT signifies Taylor exponential fit coefficients

= +

A*exp(-alphal*b) (1-A)*exp(-alpha2*b)

Build-up factor

TABLE 1 2 B . GAMMA-RAY ENERGY ABSORPTION BUILD-UP FACTORS FOR BARYTES CONCRETE

P r o r Yagni~udes

ires-.-r ::.A? 1;

Energy b(mfp) Paired Zcrrespondrng *rslses

with 3

------- Type'

0. 1.00 2.00 4.00 7.00 10.00 15.00 20.00 AUHA2

(Mev) .A ,

ALDHA1 ( % E r r x b(n:> ) I

*T s i g n i f i e s Taylor exponential f i t c o e f f i c i e n t s

+

= *exp

) ( ( )

l - A )

Build-up factor A*exp(-alphal*b -alpha2*b


PAGINE

60

PESO

2.29 MB

AUTORE

Atreyu

PUBBLICATO

+1 anno fa


DETTAGLI
Corso di laurea: Corso di laurea in ingegneria energetica
SSD:
Università: Bologna - Unibo
A.A.: 2009-2010

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Atreyu di informazioni apprese con la frequenza delle lezioni di Protezione dalla radiazioni e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Bologna - Unibo o del prof Mostacci Domiziano.

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