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Depth dose and depth dose equivalent data for neutrons with energy from thermal up to several TeV
Nuclear Instruments and Methods 199 (1982) 563-572 North-Holland Publishing Company
563
DEPTH DOSE AND DEPTH DOSE EQUIVALENT DATA FOR NEUTRONS WITH ENERGY FROM THERMAL UP TO SEVERAL TeV
E.A. BELOGORLOV, V.T. GOLOVACHIK, V.N. LEBEDEV and E.L. P O T J O M K I N Institute for High Energy Physics, Serpukhov, Moscow region, U.S.S.R. 142284 Received 23 February 1981 and in revised form 20 October 1981
Depth distribution of adsorbed dose and dose equivalent is presented in this paper. The energy range of incident neutrons considered is from thermal up to several TeV. The irradiation geometry is an infinite slab of 30 g/cm 2 thickness irradiated by a broad, normal incident beam. The data is the result of compilation and further fitting of the known calculation results. For neutrons with energy up to 12 MeV we present the results of a compilation made by K.B. Shaw and co-workers. The data presented in tables and on graphs are convenient for practical use.
The bulk of the data of the International and National Recommendations concerning the depth dose and dose equivalent data on radiation is not sufficient for practical requirements. For instance the International Comission on Radiological protection [1] and NRB-76 in the Soviet U n i o n [2] provide only recommendations for the values of the maximum dose equivalent in phantom and an average quality factor in the same depth of the phantom. The handbook of the depth dose characteristics [3] contains insufficient information about depth dose and dose equivalent data for neutrons. The systematization of depth dose and dose equivalent data for neutrons, carried out by K.B. Shaw and co-workers [4] is the most convenient for practical appli-
cation when solving the problems of radiation safety and for radiation research. However at present when the energy of modern accelerators is hundreds of GeV, and that of planned, future accelerators will be several TeV such a compilation (up to 20 GeV) is not up to date. During the last decade calculations and experimental investigations, e.g. refs. 5 and 6, have been carried out. This work helped to clarify the values and to extend greatly the energy range of depth dose and depth dose equivalent data for neutrons. The purpose of the present work is to obtain compilations in as a convenient form for practical application as the compilations of ref. 4 but for a greater neutron energy range.
-7-~
egD
~gH
_,o\//
_
1
-11 ~
-
-2
~.gE(MeV)
_i _6- U
-8
Fig. 1. Dose equivalent as a function of neutron energy and phantom depth. 0167-5087/82/0000-0000/$02.75
© 1982 North-Holland
Fig. 2. Absorbed dose as a function of neutron energy and phantom depth.
564
E.A. Belogorlov et al. / Depth dose for neutrons
Table 1 Dose equivalent per unit neutron fluence, rem/(neutron, cm 2), as a function of neutron energy at given depths. Energy
0.5 MeV 2 MeV 10 MeV 18 MeV 30 MeV 60 MeV 60 MeV 60 MeV 100 MeV 180 MeV 200 MeV 300 MeV 400 MeV 400 MeV 500 MeV 525 MeV 600 MeV 600 MeV 700 MeV 800 MeV 900 MeV l GeV l GeV 1 GeV 1.5 GeV 2 GeV 3 GeV 3.5 GeV 10 GeV 30 GeV 30 GeV 100 GeV 100 GeV 300 GeV 1 TeV 1 TeV 3 TeV 10 TeV
Depth'(cm)
Ref.
0.5
5
10
15
20
25
30
2.5E--08 a 5.7E--08 3.4E--08 5.6E-08 8.0E-08 5 . 0 E - 08 3.6E--08 2.9E - 08 3 . 4 E - 08 2.8E-08 3.0E-08 3.3E-08 3.8E-08 2.5E--08 4.8E-08 4.6E--08 4.8E-08 5.1E-08 5.5E-08 5.8E-08 6.2E--08 6.5E-08 6.0E-08 5 . 7 E - 08 9.7E-08 8.8E-08 I.IE-07 1.5E-07 2 . 0 E - 07 1.3E-07 4.0E-07 1.4E-07 6 . 2 E - 07 1.5E-07 1.6E-07 2.3E--06 1.7E-07 1.7E-07
1.1E-08 4.5E--08 3.3E-- 08 5.9E-- 08 6.7E--08 4.6E--08 3 . 6 E - 08 3.7E - 08 4.6E-08 4.0E-08 4 . 3 E - 08 4.3E-08 4 . 6 E - 08 4.7E--08 6.8E--08 7.0E-08 6.5E-08 7.4E--08 8.0E-08 8.7E-08 9.3E--08 1 . 0 E - 07 8.1E--08 7.3E--08 1.5E-07 1.3E-07 1.4E-07 1.7E-07 1 . 9 E - 07 2.2E-07 4 . 0 E - 07 2.4E-07 5.0E--07 2 . 7 E - 07 2 . 9 E - 07 1.0E--06 3.1E-07 3.3E-07
2.1E--09 2.5E-08 3 . 0 E - 08 4.6E--08 5.0E-08 6 . 9 E - 08 4.6E--08 3.9E -- 08 5 . 2 E - 08 4.5E-08 5.1E-08 5.0E-08 5.2E-08 6 . 8 E - 08 7.4E-08 7.2E-08 7.2E-08 8.1E-08 9.0E--08 9 . 8 E - 08 l.lE-07 1.2E-07 9.1E--08 1.4E-07 1 . 2 E - 07 1 . 4 E - 07 1.8E--07 1.9E-07 3.4E-07 2 . 9 E - 07 4.0E-07 3.3E-07 5.1E-07 3.7E-07 4.1E-07 1.4E-06 4 . 5 E - 07 4 . 8 E - 07
5.1E-- 10 8.8E-09 2.6E--08 4.5E--08 5.4E-08 6.0E-08 4.5E-08 4.0E - 08 5.5E-08 4.7E-08 5.5E-08 5.3E-08 5.6E--08 5.7E-08 7 . 6 E - 08 7.0E--08 7.6E-08 8 . 4 E - 08 9.3E--08 1.0E-07 1.1E--07 1.2E--07 1.0E-07 1.1E-07 1.4E-07 1.5E-07 1.8E-07 2.1E-07 2.7E--07 3.3E-07 5.8E-07 3.9E-07 7 . 3 E - 07 4.5E-07 5.0E-07 2 . 2 E - 06 5.5E--07 5.9E-07
2 . 5 E - 10 4.4E--09 1.8E-08 3.2E-08 4.8E--08 5.5E--08 3.3E--08 4.0E -- 08 5.6E--08 4 . 8 E - 08 5 . 7 E - 08 5.6E-08 6.0E-08 7.8E-08 7.7E-08 7.6E--08 8.2E--08 8.5E--08 9.5E-08 1 . 0 E - 07 1.1E-07 1.2E-07 l.lE-07 1.2E--07 1.5E-07 1.6E-07 1.9E-07 1.7E--07 3.6E--07 3.8E-07. 5 . 0 E - 07 4.6E--07 8 . 4 E - 07 5.3E-07 6.1E--07 2 . 0 E - 06 6 . 7 E - 07 7.3E-07
1 . 6 E - 10 1.7E--09 1.2E--08 2.5E-08 4.2E-08 5.0E-08 4.0E-08 3.9E - 08 5.4E-08 4.8E-- 08 5.8E-08 5.7E--08 6.2E-08 6.1E-08 7.8E--08 7.4E 08 9 . 0 E - 08 8.8E--08 9.9E--08 l.lE--07 1.2E--07 1.3E-07 1.2E-07 I.IE-07 1.6E-07 1.7E-07 2 . 0 E - 07 1.9E-07 3.3E-07 4.4E-07 5 . 4 E - 07 5.5E-07 7.0E-07 6.4E-07 7.4E--07 1.9E-06 8.2E-07 8.9E-07
1 . 2 E - 10 I.IE--09 7 . 0 E - 09 1.8E-08 2.6E 08 5.1E-08 3.5E-08 3.6E - 08 5.8E-08 4.2E-08 5.8E-08 5 . 7 E - 08 6.2E-08 6.8E--08 7.2E-08 8.0E-08 9.5E--08 8.0E-08 9 . 0 E - 08 1 . 0 E - 07 l.lE--07 1.2E-07 1.3E 07 1.2E-07 1.7E-07 1.8E-07 1.7E-07 1.8E-07 3.8E-07 4.4E-07 4.0E-07 5.5E 07 7 . 9 E - 07 6 . 7 E - 07 7.8E-07 2.1E-06 8 . 7 E - 07 9 . 4 E - 07
[8] [8] [8] [8] [8] [8] [5] [7] [7] [5] [7] [7] [7] [5] [6] [5 l [9] [6] [6] [6] [6] [6] [9] [5] [5] [9] [5] [10] [10] [6] [10] [6] [10] [6] [6] [10] [6] [6]
a 2.5 x 10-8.
F o r n e u t r o n s w i t h e n e r g y b e l o w 12 M e V t h e [4] compilation data are taken without any changes. For h i g h e r e n e r g i e s we u s e d t h e d a t a o f refs. 5 - 9 p r e s e n t e d in t a b l e s 1 a n d 2. T h e d a t a of c a l c u l a t i o n s [10] for e n e r g i e s h i g h e r t h a n 10 G e V w e r e n o t u s e d as t h e s e r e s u l t s w e r e n o t s u f f i c i e n t l y well f o u n d e d [6]. All t h e d a t a u s e d a n d t h e r e s u l t s o b t a i n e d are r e l a t e d to t h e c a s e o f a b r o a d , n o r m a l i n c i d e n t b e a m of m o n o e n e r g e t i c n e u t r o n s o n o n e side o f a n i n f i n i t e t i s s u e - e q u i v a l e n t slab o f 30 c m t h i c k n e s s a n d o f d e n s i t y 1 g / c m 3.
T h e c o m p i l a t i o n p r o c e d u r e w a s as follows. (1) T h e d a t a f r o m refs. 5 - 9 were t a b u l a t e d a n d a d d e d to t h e d a t a f r o m ref. 4. (2) T h e d o s e a n d d o s e e q u i i v a l e n t e n e r g y d e p e n d e n c e s w e r e s m o o t h e d in t h e e n e r g y r a n g e a b o v e 12 M e V for e a c h d e p t h value. T h e r e s u l t a n t c u r v e s were tabulated. (3) T h e t w o - d i m e n s i o n a l m a t r i x of d a t a , t h u s o b tained, was smoothed by fitting a second order surface, taking into account (by weighting) the different errors
E.A. Belogorlov et al. / Depth dose for neutrons
565
Table 2 Absorbed dose per unit neutron fluence, r a d / ( n e u t r o n . c m - 2 ) , as a function of neutron energy at given depths. Energy
0.5 MeV 2 MeV 10 MeV 18 MeV 30 MeV 60 MeV 60 MeV 60 MeV 100 MeV 180 MeV 200 MeV 300 MeV 400 MeV 400 MeV 500 MeV 525 MeV 600 MeV 600 MeV 700 MeV 800 MeV 900 MeV 1 GeV 1 GeV 1 GeV 1.5 GeV 2 GeV 3 GeV 3 GeV 3.5 GeV 10 GeV 10 GeV 30 GeV 30 GeV 100 GeV 100 GeV 300 GeV 1 TeV 1 TeV 3 TeV 10 TeV
Depth (cm)
Refs.
0.5
5
10
15
20
25
30
2.4E--09 a 4.1E--09 7.0E-09 8.1E-09 9 . 4 E - 09 7.8E--09 6.5E-09 6.4E--09 5.5E-- 09 4 . 2 E - 09 4.4E--09 5.0E--09 6.0E-- 09 4 . 4 E - 09 8.7E--09 7.5E--09 5 . 0 E - 09 9.4E-- 09 1.0E-08 I.IE--08 1.2E-08 1.2E-08 6.0E-09 1.3E--08 1.8E-08 7 . 0 E - 09 2.3E--08 2.1E-08 3.5E--08 2.3E--08 4.8E--08 2.5E--08 6 . 0 E - 08 2 . 8 E - 08 8 . 0 E - 08 3.0E - 08 3.2E-08 1.3E--07 3.4E-- 08 3.6E--08
1.3E--09 3.0E--09 6.2E--09 8 . 4 E - 09 9.1E--09 7.5E--09 9.0E-09 8.5E--09 9.5E--09 9.8E--09 9.5E--09 9.5E--09 1.0E--08 1.2E--08 1.9E--08 1.6E--08 1.8E-08 2 . 0 E - 08 2.2E-08 2.3E--08 2.5E-08 2.6E-08 2.3E-08 2.0E--08 3.5E-08 3.0E - 08 4.5E--08 4.4E-08 5.0E-08 5.1E--08 5.2E-- 08 5.9E--08 7.1E-08 6.7E-08 9.0E-08 7.4E - 08 8.2E-08 1.4E--07 9.0E-- 08 9.5E--08
6.5E-- 10 1.9E-09 5.7E-09 7 . 4 E - 09 7 . 7 E - 09 1.0E--08 1.2E-08 8.9E--09 1.1E-08 1.4E--08 1.3E--08 1.3E-08 1.3E--08 1.7E--08 2.4E-- 08 2.0E--08 2.6E - 0 8 2.6E - 08 2.8E-08 3.0E--08 3.2E-08 3.5E-08 3.0E-08 3.2E--08 4 . 0 E - 08 4.4E - 08 6.0E-- 08 5.9E--08 5.5E-08 7.2E--08 6.3E-08 8.6E-08 7.7E-08 1.0E-07 1.2E-07 1.1E - 07 1.3E-07 1.7E-- 07 1.5E-- 07 1.5E-07
3.6E-- 10 9 . 3 E - 10 4.8E-09 6.1E-09 7.6E--09 8.8E-09 1.0E-08 8.5E--09 I.IE-08 1.6E--08 1.5E--08 1.5E-08 1.6E-08 1.8E--08 2.7E-- 08 2.2E--08 3.2E-08 2.9E - 08 3.2E-08 3.5E-- 08 3.8E-08 4.1E-08 3.8E--08 3.3E--08 4.5E-08 5.4E - 08 6.3E--08 7.3E--08 6.2E-08 9.2E--08 7.3E--08 I.IE-07 1 . 2 E - 07 1.4E-07 1.4E-07 1.6E - 07 1.8E-07 2.6E--07 2.1 E - - 07 2.2E--07
2.4E-- 10 5 . 7 E - 10 3.1E-09 4.9E-09 6 . 6 E - 09 8.5E-09 9.0E-09 8.0E--09 1.1E--08 1.7E--08 1.5E-08 1.6E-08 1.8E--08 2.0E--08 2.9E-08 2.4E--08 3.6E-08 3.2E - 08 3.6E--08 3.9E--08 4.2E-08 4.6E-08 4.4E-08 3.7E--08 5.0E-08 6.2E - 08 7 . 4 E - 08 8.6E-08 6.0E-08 1.1E--07 8.5E--08 1.4E-07 1.1E-07 1.8E-07 1 . 6 E - 07 2.1E - 07 2 . 4 E - 07 2.7E--07 2.7E-- 07 2.9E-07
1,7E-- 10 3 . 3 E - 10 2.3E-09 3 . 7 E - 09 6.2E--09 7 . 2 E - 09 9.2E-09 7.2E--09 1.0E-- 08 1.7E--08 1.5E--08 1.8E--08 1.9E--08 2.0E--08 3.1E--08 2.5E--08 3 . 9 E - 08 3.4E - 08 3.8E--08 4 . 2 E - 08 4.6E-08 5.1E-08 4.8E--08 4.0E--08 5.2E-08 7.0E -- 08 8.0E--08 1.0E-07 6.2E--08 1.3E--07 8.5E--08 1.7E-07 1.2E--07 2.2E--07 1.7E-07 2.6E - 07 3.0E-07 3.0E--07 3.4E-- 07 3.7E--07
1.3E-- 10 2 . 4 E - 10 1.5E-09 2 . 9 E - 09 3 . 9 E - 09 7.1E-09 7.0E-09 6.6E--09 9.0E--09 1.5E--08 1.4E--08 1.8E--08 2 . 0 E - 08 2.2E--08 2.8E--08 2.7E-08 4.0E-08 3.2E - 08 3.6E--08 4.0E-08 4 . 4 E - 08 4 . 8 E - 08 5.0E--08 3.8E--08 5.2E-08 7.5E - 08 7 . 0 E - 08 9.7E-08 6.0E-08 1 . 4 E - 07 8.5E-08 1.8E-07 1.0E-07 2 . 3 E - 07 1.8E-07 2.8 E - 07 3.3E--07 3.7E-07 3 . 8 E - 07 4.1E--07
[8] [8] [8] [8] [8] [8] [5] [7] [7] [5] [7] [7] [7] [5] [6] [5] [9] [6] [6] [6] [6] [6] [9] [5] [5] [9] [5] [6] [10] [6] [10] [6] [10] [6] [10] [6] [6] [10] [6] [6]
a 2 . 4 x 10 -9.
for t h e s e p a r a t e p a r t s o f t h e d a t a . I n t h e e n e r g y r a n g e f r o m 12 u p to 10 3 M e V t h e d a t a w a s a s s i g n e d a 5% error, a n d f o r h i g h e r e n e r g i e s t h e e r r o r w a s 15%, w h e n b e i n g s m o o t h e d t h e v a l u e s o f t h e f u n c t i o n a n d its first derivative were matched. This procedure provided us with a system of d e p t h - e n e r g y d e p e n d e n c e s for d o s e a n d d o s e e q u i v a l e n t in t h e d e p t h r a n g e o f 0 - 3 0 g / c m 2 w i t h a 5 g / c m 2 s t e p a n d o v e r a n e n e r g y r a n g e f r o m t h e t h e r m a l u p to 8 T e V
w i t h a 0.2 l o g a r i t h m i c step. T h e d a t a a r e g i v e n in t a b l e s 3 a n d 4 a n d in t h e figures. T w o - d i m e n s i o n a l g r a p h s (for the dependences of dose and dose equivalent on energy a n d d e p t h ) a r e g i v e n in figs. 1 a n d 2. Figs. 3 - 9 i l l u s t r a t e the dependences of the dose and dose equivalent on e n e r g y for t h e i n d i c a t e d d e p t h values. T h e c u r v e s in t h e figures are a result of our approximation procedure. The p o i n t s a r e t h e o r i g i n a l r e s u l t s o f refs. 5 - 9 . I n t h e last t w o f i g u r e s t h e r e s u l t s a r e c o m p a r e d w i t h
,- - - ' I
- --'-i
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- - ~
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- --'-i
- -~-~
- -'-3
- -"-I
- --'-~
- ~
• "-'I
"--"1
- --~,
,)
o ,) o o
L,= d>
o
RE~Z~TEUTRO7. CI,!- 2
° o
o o
REI,V (?IEUTRON , CL-2
R,~ RAD/(!:NUT:~OT. CE - 2 -
~c n** *
DEPFH, 10 DEPrH,
/
oo+,-
o - IRV67 o+-
RLSTO ZER65 NEU69 , - COL75 o - RRM72
• -
, -
0-
10 .7 l0 "~ 10 .5 10 "~ 10 -m 10 .2 ~0"t 10 -~ l0 -~ t0 -~ 10 -~ 10 .3 t0 -2 10 -L
1
|0
10 2
10 ~
10 ~
CM
.SCM
~0 ~
l0 ~
10
10 2
t0 ]
10 4
10 5
10 ~
10 7
ENERGY. MEV
lO ~
ENERGY. MEV
1
[RV67 RLS70 ZER65 NEU69 COL?5 ARM72
Fig. 5. Absorbed dose and dose equivalent per unit neutron
Fig. 3. A b s o r b e d dose and d o s e equivalent per unit neutron fluence as a function of energy at a depth of 0.5 cm.
fluence as a function of energy at a depth of 10 cm.
o
o
r
o
b
oO
$°'*
:
L~
REH/('~TELF£RO!i.CM- 2 )
>
2EE/(:TEUTRO?!. C~."-2 )
L~
BAD/( N g LFi'20]:. C~[-2-,)
g
RAD/(LEU~ROI:. Cr,1-2 )
DEPFH,
oa÷,. -
~-
10- 7
10- '5 10- 5
1O-4 10" I
10- ~
10"
I
10
10 2
10 2
5
DEPFH, 15
CM
o=-
IRV67 RLSTO ZER65 . NEU6g ¢ - COL75 ¢- RRM72
IRV67 RL570 ZER65 NEU69 GOL75 RRM72
10'
l0 S
CM
. -
10 ~
10 7
10 -7
tO -t
I0 -s
10 ~4
10 -I
I0 -~
Fig. 4. A b s o r b e d dose and d o s e equivalent per unit neutron fluence as a function of energy at a depth of 5 cm.
10 -t
I
lO
iO ~
tO ~
10 4
10 ~
I0 t
ENERGY, MEV
ENERGY. MEV Fig.
6.
fluence
Absorbed
dose
as a function
and of
dose
energy
equivalent at a depth
per of
unit
15 cm.
neutron
I0'
~~o o o+
RZ"/(-~:~::~O-~:.c~,:- ~ )
o
o-FF z REM/(NEUTROtT.
>
CtC 2 )
RAD/(t]EUTROIT. C M -2 RAD/(VEUTROF,
CM_2) o
DEP[H,
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20
CM
OEPFH, 30 CM y
o - IRV6? a - RLSTO + - ZER65 - NEUSg • - 00L75
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10 -~
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i
10
i0 =
10'
$0 4
t0 5
l0 ~
10 ~
~
oo+,-
IRVB7 BLS?O ZER65 NEU69
•-
COL?5 ARM?2
o-
tO "~ 10 .5 tO "~ lO"
{0'i 10 .2 ~0 -L
1
[0
tO"
I0 j
~O 4
10-
~0 ~
,0 ~
ENERGY. MEV
ENERGY. MEV
Fig. 7. A b s o r b e d dose and dose equivalent per unit neutron fluence as a function of energy at a depth of 20 cm.
Fig. 9. A b s o r b e d dose and dose equivalent per unit neutron fluence as a function of energy at a depth of 30 cm.
~-
I ERpI-2i - ~ 7 6
//°
% REL:/(V~UTR0::. C H -2 )
o
w
g~ >
o . o b ci:
R A D / ( Y E U T : : O : ~. C H - 2 )
A
OEPrH, 25
oa+ •
o-
104
tO -G tO -5 10 -4 I0 ") 10 -2 I0 -L
I
10
tO ~
I0 ~
','M
IRV67 RLSTO ZERG5 NEUG9 00L75 RRM72
~04
I0 S
~o-* I0 s
I0 ~
ENERGY. MFV
Fig. 8. A b s o r b e d dose and dose equivalent per unit neutron fluence as a function of energy at a depth of 25 cm.
;o -~
to ~
to -~
to-'
to - I
to -~
~o- I
1
to
lo~
1oI
1o4
1o ~
lo*
ENERGY.NEV
Fig. 10. D o s e equivalent per unit neutron fluence as a function of energy and depth in p h a n t o m and r e c o m m e n d a t i o n s of refs. 1 and 2.
E.A. Belogorlov et al. / Depth dose for neutrons
568
Table 3 Dose equivalent (rem cm2/neutron) as a function of neutron energy and depth. Energy (MeV
Depth (cm) 0.5
5
10
15
20
25
30
1.26E-08 a 2.00E--08 3,16E--08 5.01E--08 7.94E--08
9.10E9.05E-9.00E-8.95E8.90E--
10 10 10 10 10
1.66E1.91E-2.13E-2.38E-2.68E--
10 10 10 10 10
8.45E9.60E-1.05E-1.18E-1.32E--
11 11 10 10 10
5.45E6.10E-6.80E-7.50E-8.15E--
11 11 11 11 11
4.00E4.50E5.00E5.50E6.10E-
11 11 11 11 11
2.96E3.30E3.70E4.12E4.55E-
11 11 11 11 11
2.24E-2.60E-3.05E-3.65E-4.05E-
11 11 11 11 11
1.26E--07 2.00E--07 3.16E-07 5.01E-07 7.94E-07
8.85E-8.78E-8.70E-8.62E-8.55E--
10 10 10 10 10
2.96E-3.30E-3.65E-4.05E-4.48E--
10 10 10 10 10
1.47E-1.62E-1.78E1.95E2.12E-
10 10 10 10 10
9.00E-9.80E-1.06E-1.15E-1.24E--
11 11 10 10 10
6.70E7.35E8.00E-8.70E-9.30E--
I1 11 11 11 11
5.00E-5.50E-6.00E-6.55E-7,00E--
11 11 11 11 11
4.65E 5.30E5.90E 6.50E7.20E-
11 11 11 11 11
1.26E-06 2.00E-06 3.16E-06 5.01E-06 7.94E-06
8.50E8.50E-8.50E-8.50E-8.45E--
10 10 10 10 10
4.95E-5.45E-5.90E-6.50E-7.05E--
10 10 10 10 10
2.30E2.48E2.67E2.85E-3.08E-
10 10 10 10 10
1.34E-1.44E-1.53E-1.63E-1.72E--
10 10 10 10 10
1.00E1.06E-1.12E1.19E-1.24E-
10 10 10 10 10
7.60E-8.20E-8.80E-9.40E-9.90E--
11 11 11 11 11
7.80E8.20E8.70E-9.10E9.20E--
11 11 11 11 11
1.26E-05 2.00E-05 3,16E-05 5.01E-05 7.94E--05
8.45E8.50E8.50E8.55E-8.55E--
10 10 10 10 10
7.55E-8.10E8.65E9.20E-9.60E--
10 10 10 10 10
3.23E3.42E3.60E3.80E-3.95E--
10 10 10 10 10
1.82E-1.90E1.97E2.02E-2.06E
10 10 10 10 10
1.3 IE 1.37E1.42E1.48E-1.53E
10 10 10 10 10
1.03E-1.08E1.10E1.12E-1.12E--
10 10 10 10 10
9.30E-9.30E9.10E8.80E8.50E
11 11 11 11 11
1.26E--04 2.00E-04 3.16E--04 5.01E-04 7.94E--04
8.55E8.55E8.60E8.70E-8.95E--
10 10 10 10 10
1.01E-09 1.03E-09 1.05E-09 1.07E--09 1.08E--09
4.07E-4.19E-4.25E-4.30E-4.38E--
10 10 10 10 10
2.09E2.10E-2.11E2.11E2.10E-
10 10 10 10 10
1.59E1.60E-1.58E-1.59E1.57E-
10 10 10 10 10
I. 11E-1.08E-1.05E-1.03E1.02E-
10 10 10 10 10
8.20E-7.90E-7.60E-7.40E7.20E
11 11 11 11 11
1.26E--03 2.00E--03 3.16E-03 5.01E-03 7.94E-03
9.40E-- 10 1.01E--09 1.08E--09 1.21E--09 1.44E--09
1.08E--09 1.06E--09 1.03E--09 1.01E--09 9.85E-- 10
4.42E-- 10 4.46E-- 10 4.50E-- 10 4.51E--10 4.52E-- 10
2 . 1 0 E - 10 2 . 1 0 E - 10 2 . 1 1 E - 10 2.13E--10 2 . 1 7 E - 10
1.53E1.51E1.50E1,49E 1.48E-
10 10 10 10 10
9.80E-9.60E-9.50E 9.40E 9.50E
11 11 11 11 11
7 . 1 0 E - 11 7.00E 11 6 . 9 5 E - 11 7.00E-I1 7 . 1 0 E - 11
1.26E-02 2.00E-02 3.16E-02 5.01E-02 7.94E-02
1.82E--09 2.48E--09 3.45E--09 4.90E--09 7.00E--09
9.70E-- 10 9.80E-- 10 1,04E--09 1.17E--09 1.35E-09
4.53E-4.58E-4.70E-4.80E-5.00E--
10 10 10 10 10
2.23E-2.31E2.40E2.55E2.70E-
10 10 10 10 10
1.48E-1.49E1.51E1.56E1.61E
10 10 10 10 10
9.70E-9.90E-1.02E1.08E1.12E-
11 11 10 10 10
7.30E7.40E 7.60E 7.80E 8.00E--
11 11 11 11 11
1.26E-01 2.00E--01 3.16E--01 5.01E--01 7.94E--01
9.95E--09 1,34E--08 1.78E--08 2.27E--08 2,67E-08
1.72E-09 2.47E-09 3.70E--09 6.95E-09 1.19E-08
5.45E-- 10 6 . 5 0 E - 10 8.40E-- 10 1.25E--09 2.15E--09
2.92E3.20E 3.61E4.20E5.40E
10 10 10 10 10
1.66E1.74E1.88E-2.07E-2.40E-
10 10 10 10 10
1.17E1.25E1.33E 1.43E 1.65E-
10 10 10 10 10
8.20E8.50E 9.10E1.02E1.27E--
11 11 11 10 10
1.26E 2.00E 3.16E 5.01E 7.94E
00 00 00 00 00
3,08E--08 3.47E--08 3.79E--08 4.01E--08 4.12E--08
1.77E-08 2.44E--08 3.17E-08 3.61E-08 4.00E-- 08
5,30E--09 1.30E--08 1.96E--08 2.65E--08 3,12E--08
1.30E-09 5.10E--09 1.13E-08 1 . 6 7 E - 08 2.34E--08
3 . 7 0 E - 10 1.35E-09 5 . 4 0 E - 09 1 . 0 3 E - 08 1 . 7 5 E - 08
2.05E 7.50E2.05E4.70E9.40E-
10 10 09 09 09
1.78E-- 10 5.30E-- 10 1.37E--09 3.10E--09 6.10E--09
1.26E 2.00E 3.16E 5.01E 7.94E
01 01 01 01 01
4.10E--08 4,36E--08 4.34E-- 08 4.11E-08 3.85E-08
4.06E-08 4.53E-08 4.75E-08 4.65E--08 4.52E-08
3.69E--08 4.34E--08 4.77E-- 08 4.87E--08 4.90E-- 08
3.09E--08 3.81E-08 4.41E-08 4.72E--08 4.93E--08
2 . 3 7 E - 08 3 . 0 8 E - 08 3.75E--08 4.24E--08 4.59E--08
1.68E-08 2 . 2 9 E - 08 2.92E--08 3.52E--08 3.95E--08
1.19E--08 1.69E--08 2.25E--08 2.87E--08 3.32E--08
E.A. Belogorlov et al. / Depth dose for neutrons
569
Table 3 (continued) Energy (MeV
Depth (cm) 0.5
5
10
15
20
25
30
1.26E 2.00E 3.16E 5.01E 7.94E
02 02 02 02 02
3.57E--08 3.27E-08 3.50E--08 4.44E-- 08 5.89E--08
4 . 3 4 E - 08 4.12E-08 4.43E-- 08 5.69E--08 7.68E--08
4.89E--08 4.81E-08 5.23E--08 6.79E--08 9.33E--08
5.09E-08 5.20E-08 5.73E--08 7.54E--08 1.05E--07
4.91E--08 5.21E-08 5.83E--08 7.80E--08 1.11E--07
4.39E-08 4.82E-- 08 5.52E--08 7.51E--08 1.09E-07
3.79E-08 4.29E-- 08 5.02E-- 08 6.93E--08 1.02E--07
1.26E 2.00E 3.16E 5.01E 7.94E
03 03 03 03 03
7.37E--08 8.68E--08 9.91E--08 1.10E--07 1.16E--07
9.78E--08 1.17E--07 1.36E--07 1.53E--07 1.66E-07
1.21E--07 1.48E--07 1.74E--07 1.98E--07 2 . 2 0 E - 07
1.39E--07 1.73E--07 2.06E-- 07 2 . 3 8 E - 07 2.69E-07
1.49E--07 1.89E--07 2.27E--07 2.66E--07 3 . 0 4 E - 07
1.49E- 07 1.92E--07 2.33E--07 2.76E--07 3.18E-07
1.41E--07 1.85E--07 2.25E--07 2.70E-- 07 3.11E-07
1.26E 2.00E 3.16E 5.01E 7.94E
04 04 04 04 04
1.24E--07 1.31E--07 1.37E--07 1.43E--07 1.48E--07
1.79E-- 07 1.91E--07 2.03E--07 2.13E--07 2.23E-07
2.39E--07 2.58E--07 2.77E--07 2 . 9 4 E - 07 3.10E-07
2.96E--07 3.22E--07 3.49E--07 3.75E-07 3.99E-07
3.38E--07 3.72E--07 4.06E-- 07 4 . 4 1 E - 07 4 . 7 4 E - 07
3.56E--07 3.96E--07 4.37E--07 4.79E-07 5.21E--07
3.52E--07 3.94E-- 07 4.38E--07 4.84E--07 5.31E--07
1.26E 2.00E 3.16E 5.01E 7.94E
05 05 05 05 05
1.51 E-- 07 1.56E--07 1.61E--07 1.65E--07 1.69E--07
2.32E-- 07 2.41E--07 2.50E--07 2.58E--07 2.66E--07
3.27E-- 07 3.42E--07 3.57E--07 3.71E--07 3.85E--07
4.26E-- 07 4.48E-- 07 4.70E-- 07 4.91E--07 5.13E--07
5.09E-- 07 5.39E--07 5.69E--07 5.99E--07 6.29E--07
5.61 E-- 07 5.98E--07 6.35E--07 6.72E-- 07 7.10E--07
5.71 E-- 07 6.11E--07 6.53E--07 6.95E--07 7.37E-- 07
1.26E 2.00E 3.16E 5.01E 7.94E
06 06 06 06 06
1.72E--07 1.75E--07 1.78E--07 1.80E--07 1.82E--07
2.73E--07 2.79E-- 07 2.85E--07 2.90E--07 2.95E--07
3.97E--07 4.10E--07 4.21E--07 4.31E--07 4.40E-- 07
5.33E--07 5.53E--07 5.71E--07 5.88E--07 6.05E--07
6.58E-07 6.86E--07 7.14E--07 7.40E-- 07 7.65E--07
7.47E--07 7.85E--07 8.21E--07 8.57E--07 8.91E--07
7.80E--07 8.23E--07 8.65E--07 9.07E-- 07 9.49E-- 07
15
20
25
30
a 1.26 X 10-8.
Table 4 Absorbed dose (tad cm2/neutron) as a function of neutron energy and depth Energy (MeV)
Depth (cm) 0.5
5
10
1.26E-08 a 2.00E-08 3.16E--08 5.01E--08 7.94E--08
2.90E3.08E2L28E-3.44E-3.60E--
10 10 10 10 10
1.25E- 10 1.47E- 10 1.66E-- 10 1.89E-- 10 2.11E--10
8.45E9.50E-1.05E-1.14E-1.24E--
11 11 10 10 10
5 . 4 5 E - 11 6 . 1 0 E - 11 6.80E-- 11 7.50E-- 11 8.15E--11
4.00E4.50E5.00E-5.50E-6.10E--
11 11 11 11 11
2.96E3.30E3.70E-4.12E-4.55E--
11 11 11 11 11
2.24E2.60E3.05E-3.65E-4.05E--
11 11 11 11 11
1.26E-- 07 2.00E--07 3.16E--07 5.01E--07 7.94E-- 07
3.76E-3.90E-4.07E-4.21E-4.35E--
10 10 10 10 10
2.36E-2.62E-2.93E-3.26E-3.58E--
10 10 l0 10 10
1.34E-1.46E-1.58E-1.72E-1.85E--
10 10 l0 10 10
9.00E-9.80E-1.06E-1.15E-1.24E--
11 I1 l0 10 10
6.70E-7.35E-8.00E-8.70E-9.30E--
11 11 11 11 11
5.00E-5.50E-6.00E-6.55E-7.00E--
11 11 11 11 11
4.65E-5.30E-5.90E-6.50E-7.20E--
11 11 1l II l1
1.26E-- 06 2.00E-- 06 3.16E--06 5.01E--06 7.94E-- 06
4.48E-4.58E-4.70E-4.80E-4.88E--
10 10 10 10 10
3.92E-4.26E-4.53E-4.85E-5.15E--
10 10 10 10 10
1.98E-2.13E-2.28E-2.41E-2.56E--
10 10 10 10 l0
1.34E-1.44E-1.53E-1.63E-1.72E--
10 10 10 10 10
1.00E-1.06E-I. 12E-1.19E-1.24E--
10 10 l0 10 l0
7.60E-8.20E-8.80E-9.40E-9.90E--
11 11 11 11 11
7.80E-8.20E-8.70E-9.10E-9.20E--
11 1l 11 11 11
E.A. Belogorlov et al. / Depth dose for neutrons
570 Table 4 (continued) Energy (MeV)
Depth (cm) 0.5
5
10
15
20
25
30
1.26E-05 2.00E-05 3.16E-05 5.01E-05 7.94E-05
4.95E4.98E-5.00E-5.00E-5.00E-
10 10 10 10 10
5.40E5.65E5.90E-6.05E6.10E-
10 10 10 10 10
2.70E-2.83E2.98E3.10E3.06E-
10 10 10 10 10
1.81E1.90E-1.97E-2.02E2.06E-
10 10 10 10 10
1.31E1.37E1.42E1.48E1.52E
10 10 10 10 10
1.03E1.08E1.10E1.12E1.12E-
10 10 10 10 10
9.30E 9.30E9.10E-8.80E8.50E-
11 11 11 11 11
1.26E-04 2.00E-04 3.16E-04 5.01E-04 7.94E-04
4.98E4.92E-4.80E-4.70E-4.60E-
10 10 10 10 10
6.10E6.05E6.00E-5.95E-5.85E-
10 10 10 10 10
3.20E3.25E3.32E-3.40E3.45E--
10 10 10 10 10
2.09E2.10E2.11E 2.11 E 2.10E-
10 10 10 10 10
1.59E1.60E1.59E1.58E1.57E-
10 10 10 10 10
1.11 E 1.08E1.05E1.03E1.01E-
10 10 10 10 10
8.20E7.90E7.60E7.40E7.20E-
11 11 11 11 11
1.26E-03 2.00E 03 3.16E-03 5.01E-03 7.94E--03
4.50E-10 4.42E--10 4 . 3 7 E - 10 4.32E-10 4 . 4 5 E - 10
5.70E-10 5.60E-10 5.45E-- 10 5.35E-10 5.25E-- 10
3.50E--10 3.55E-10 3 . 5 5 E - 10 3.55E--10 3 . 5 5 E - 10
2.10E-10 2.10E-10 2.11E 10 2.13E--10 2 . 1 5 E - 10
1.53E 1.51E 1.50E1.49E 1.48E-
10 10 10 10 10
9.80E-11 9.60E-11 9 . 5 0 E - 11 9.40E--11 9.50E 11
7.10E I1 7.00E 11 6 . 9 5 E - 11 7.00E-II 7.10E-- 11
1.26E-02 2.00E-02 3.16E-02 5.01E-02 7.94E-02
4.70E--10 5.05E-- 10 5 . 7 5 E - 10 7.20E-I0 9.30E--10
5.30E-10 5 . 3 0 E - 10 5 . 3 5 E - 10 5.45E-10 5.60E-10
3.52E-10 3 . 5 0 E - 10 3 . 5 0 E - 10 3.50E-10 3.55E--10
2.18E--10 2 . 2 0 E - 10 2 . 2 2 E - 10 2.27E 10 2.38E-10
1.49E-10 1 . 4 9 E - 10 1.51 E - 10 1.56E--10 1.61E-10
9.70E 9.90E 1.02E1.08E 1.12E
7.30E 7.40E 7.60E7.80E 8.00E
1.2 6E-0 1 2 . 0 0 E - 01 3.16E-01 5.01E-01 7.94E-01
1.21E--09 1.57E--09 1.96E-09 2.38E-09 2.88E-09
6.10E--10 7 . 2 5 E - 10 9.10E-10 1.12E-09 1.44E-09
3.70E-10 4.00E-- 10 4.50E 10 5.15E 10 6.90E 10
2.50E-10 2.67E-- 10 2.90E--10 3.25E-10 4 . 0 0 E - 10
1.66E 10 1.74E-- 10 1.88E--10 2.07E-10 2 . 4 0 E - 10
1.17E-10 1 . 2 5 E - 10 1.33E-10 1.43E-10 1 . 6 5 E - 10
8.20E-11 8 . 4 0 E - 11 8.75E 11 9.30E-I1 1 . 0 3 E - 10
1.26E 2.00E 3.16E 5.01E 7.94E
00 00 00 00 00
3.47E-09 4.25E-09 4.80E-09 5.60E-09 6.35E--09
1.89E--09 2.60E-09 3.55E-09 4.75E--09 5.85E--09
1.05E-09 1.64E-09 2.40E-09 3.45E-09 4.80E-09
5 . 4 0 E - 10 8 . 9 5 E - 10 1.55E--09 2.36E-09 3.60E--09
3 . 2 0 E - 10 5 . 6 0 E - 10 1.01E-09 1.71E-09 2.70E-09
2 . 0 5 E - 10 3 . 1 5 E - 10 5 . 7 5 E - 10 9.60E-- 10 1.63E-09
1.27E1.85E3.00E 5.35E-9.70E-
1.26E 2.00E 3.16E 5.01E 7.94E
01 01 01 01 01
7.35E-09 8.10E--09 8.55E--09 8 . 0 0 E - 09 6 . 3 0 E - 09
7 . 0 5 E - 09 8 . 0 0 E - 09 8.55E-09 9.00E-- 09 9 . 2 5 E - 09
6 . 0 0 E - 09 7.05E--09 8.10E-09 9.20E-- 09 1.03E--08
4 . 8 5 E - 09 6 . 0 0 E - 09 7.10E-09 8 . 4 0 E - 09 1.00E-08
3.95E-09 5.35E-09 6.75E-09 8.20E - 09 1.00E-08
2 . 9 2 E - 09 4 . 0 8 E - 09 5.40E-- 09 7.00E - 09 9.10E-09
1.70E--09 2.60E--09 3.75E-09 5 . 5 0 E - 09 6 . 7 0 E - 09
1.26E 2.00E 3.16E 5.01E 7.94E
02 02 02 02 02
5.00E-09 4.60E-09 5.00E-- 09 8.59E--09 1.24E-08
9.45E-09 9.70E-09 1.03E--08 1.38E--08 2.00E--08
1.18E-08 1.28E 08 1.40E-08 1.97E-08 2.87E--08
1.26E-08 1.48E-08 1.62E-08 2.51E--08 3.69E--08
1.20E--08 1.43E--08 1.80E-08 2 . 8 6 E - 08 4 . 2 3 E - 08
1.22E-08 1.54E-08 1.80E--08 2.91E--08 4 . 3 3 E - 08
1.02E 08 1.33E 08 1.70E--08 2.71E-08 4.07E-08
1.26E 2.00E 3.16E 5.01E 7.94E
03 03 03 03 03
1.60E 08 1.92E--08 2.21E--08 2.47E--08 2.67E--08
2.60E--08 3.13E--08 3.64E--08 4.12E--08 4.52E-08
3.76E--08 4.56E--08 5.38E--08 6.16E-08 6.85E-08
4.87E 08 5.96E--08 7.12E--08 8.25E--08 9.28E-08
5.62E 08 6.97E-08 8.43E-08 9 . 8 8 E - 08 1.12E--07
5.80E 08 7.30E--08 8.93E--08 1.06E-07 1 . 2 2 E - 07
5.47E-08 6.99E--08 8.63E--08 1.03E--07 1.20E--07
1.26E 2.00E 3.16E 5.01E 7.94E
04 04 04 04 04
2.81E--08 2.87E-- 08 2.98E-08 3.09E--08 3.21E--08
4 . 8 2 E - 08 5.04E-- 08 5.29E-08 5.56E--08 5.83E--08
7.38E--08 7.88E - 08 8.37E--08 8.90E--08 9 . 4 5 E - 08
1.01E-07 1 . 1 0 E - 07 1.18E-07 1.27E-07 1 . 3 6 E - 07
1.24E-07 1.36E - 07 1.48E--07 1.61E-07 1.75E-07
1.36E-07 1.51E - 07 1.66E-07 1.83E-07 2.01E--07
1.36E--07 1 . 5 0 E - 07 1 . 6 7 E - 07 1.86E--07 2 . 0 6 E - 07
11 11 10 10 10
11 11 11 11 11
10 10 10 10 10
571
E.A. Belogorlov et al. / Depth dose for neutrons
Table 4 (continued) Energy (MeV)
Depth (cm) 0.5
5
10
15
20
25
30
1.26E 2.00E 3.16E 5.01E 7.94E
05 05 05 05 05
3.33E-08 3.42E-08 3.52E-08 3.57E--08 3.64E--08
6.12E-08 6.42E-08 6.67E-08 6.87E- 08 7.05E- 08
1.00E-07 1.07E-07 1.12E-07 1.17E--07 1.21E--07
1.47E-07 1.58E-07 1.67E-07 1.76E--07 1.83E--07
1.91E-07 2.07E- 07 2.21E-07 2.35E--07 2.46E--07
2.21E-07 2.41E-07 2.60E-07 2.77E--07 2.93E--07
2.29E-07 2.50E-07 2.72E-07 2.90E--07 3.09E-07
1.26E 2.00E 3.16E 5.01E 7.94E
06 06 06 06 06
3.71E-08 3.77E-08 3.83E--08 3.89E-- 08 3.94E--08
7.23E-08 7.41E--08 7.58E- 08 7.74E--08 7.90E-- 08
1.25E- 07 1.29E-- 07 1.33E--07 1.37E-07 1.41E--07
1.91E-07 1.98E--07 2.06E-07 2.14E-07 2.21E-07
2.58E-07 2.70E--07 2.83E--07 2.95E--07 3.08E--07
3.10E-07 3.26E- 07 3.44E- 07 3.62E- 07 3.80E- 07
3.28E-07 3.48E--07 3.68E-07 3.90E- 07 4.12E-07
a 1.26× 10 -s.
the m a x i m u m dose a n d m a x i m u m dose equivalent values r e c o m m e n d e d b y refs. 1 a n d 2. The data for the a b s o r b e d dose for r e c o m m e n d a t i o n s [1,2] are t a k e n as the ratio of the dose equivalent to the quality factors.
~,~_ ~.- I£RP-~l ,NRB -75
As is seen the data o b t a i n e d in this work is in good agreement with the m a x i m u m dose equivalent recomm e n d e d by ref. 1. Ref. 2 r e c o m m e n d a t i o n s are somew h a t higher for the energy range from 10 - 6 up to 1 MeV. This follows from comparison of ref. 1 recomm e n d a t i o n s , the d a t a presented in the chart [3] a n d works [11] with those from [12]. Ref. 2 r e c o m m e n d a tions seems to be quite reasonable w h e n one deals with p r o b l e m s concerning radiation safety in cases where i n f o r m a t i o n a b o u t the n e u t r o n energy spectrum is poor, e.g., only the average energy of the spectrum is known. W h e n i n f o r m a t i o n a b o u t the spectrum is quite sufficient, application of the d e p t h - e n e r g y dependences q u o t e d in this work would provide physically more correct estimates for n e u t r o n dose.
References ff 8
/
10 4
10 )
10 -~
10 -s
10 -q
10 -1
10 "~
10 :L
1
tO
10 ~
101
10 4
10 s
10 s
[.NERF~Y ,MEV
Fig. 11. Absorbed dose per unit neutron fluence as a function of energy and depth in phantom and recommendations of refs. 1 and 2.
[1] ICRP Publication 21 (Pergamon Press, Oxford, 1973). [2] The Radiation Safety Standards NRB-76 (Moscow, Atomizdat, 1978). [3] Atlas of dose characteristics of external ionizing radiation (Handbook) ed., E.E. Kovalev (Moscow, Atomizdat, 1978). [4] K.B. Shaw, G.R. Stevenson and R.H. Thomas, preprint RHEL/MI49, Chilton (1968). [5] R.G. Alsmiller, T.W. Armstrong and W.A. Coleman, preprint ORNL-TM-2924, Oak Ridge (1970). [6] V.T. Golovachik, E.L. Potjomkin, V.N. Lebedev and V.V. Frolov, Proc. of IVth Union Conf. on Charged Particle Accelerators, vol. 2 (Moscow, "Nauka", 1975) pp. 212214; Preprint IHEP 74-58, Serpukhov (1974). [7] C.D. Zerby and W.E. Kinney, Nucl. Instr. and Meth. 36 (1965) 125-140. [8] D.C. Irving, R.G. Alsmiller and H.S. Moran, preprint ORNL-4032 UC-41, Oak Ridge (1967). [9] J. Neufeld, W.S. Snyder, J.E. Turner et al., Health Physics, 17 (1969) 449-457.
572
E.A. Belogorlov et al. / Depth dose for neutrons
[10] T.W. Armstrong and K.C. Chandler, preprint ORNL-TM3758, Oak Ridge (1972). [11] V.G. Zolotukhin, I.B. Keyrim-Markus, O.A. Kochetkov et al., Neutron Tissue Dose in Human Body (Moscow, Atomizdat, 1972).
[12] W.S. Snyder, NBS Handbook 63 (1957); NCRP Report No. 20, (Washington D.C., NCRP, 1957) pp. 39-66. [13] T.A. Gabriel et al., preprint ORNL-4542, Oak Ridge (1970).
563
DEPTH DOSE AND DEPTH DOSE EQUIVALENT DATA FOR NEUTRONS WITH ENERGY FROM THERMAL UP TO SEVERAL TeV
E.A. BELOGORLOV, V.T. GOLOVACHIK, V.N. LEBEDEV and E.L. P O T J O M K I N Institute for High Energy Physics, Serpukhov, Moscow region, U.S.S.R. 142284 Received 23 February 1981 and in revised form 20 October 1981
Depth distribution of adsorbed dose and dose equivalent is presented in this paper. The energy range of incident neutrons considered is from thermal up to several TeV. The irradiation geometry is an infinite slab of 30 g/cm 2 thickness irradiated by a broad, normal incident beam. The data is the result of compilation and further fitting of the known calculation results. For neutrons with energy up to 12 MeV we present the results of a compilation made by K.B. Shaw and co-workers. The data presented in tables and on graphs are convenient for practical use.
The bulk of the data of the International and National Recommendations concerning the depth dose and dose equivalent data on radiation is not sufficient for practical requirements. For instance the International Comission on Radiological protection [1] and NRB-76 in the Soviet U n i o n [2] provide only recommendations for the values of the maximum dose equivalent in phantom and an average quality factor in the same depth of the phantom. The handbook of the depth dose characteristics [3] contains insufficient information about depth dose and dose equivalent data for neutrons. The systematization of depth dose and dose equivalent data for neutrons, carried out by K.B. Shaw and co-workers [4] is the most convenient for practical appli-
cation when solving the problems of radiation safety and for radiation research. However at present when the energy of modern accelerators is hundreds of GeV, and that of planned, future accelerators will be several TeV such a compilation (up to 20 GeV) is not up to date. During the last decade calculations and experimental investigations, e.g. refs. 5 and 6, have been carried out. This work helped to clarify the values and to extend greatly the energy range of depth dose and depth dose equivalent data for neutrons. The purpose of the present work is to obtain compilations in as a convenient form for practical application as the compilations of ref. 4 but for a greater neutron energy range.
-7-~
egD
~gH
_,o\//
_
1
-11 ~
-
-2
~.gE(MeV)
_i _6- U
-8
Fig. 1. Dose equivalent as a function of neutron energy and phantom depth. 0167-5087/82/0000-0000/$02.75
© 1982 North-Holland
Fig. 2. Absorbed dose as a function of neutron energy and phantom depth.
564
E.A. Belogorlov et al. / Depth dose for neutrons
Table 1 Dose equivalent per unit neutron fluence, rem/(neutron, cm 2), as a function of neutron energy at given depths. Energy
0.5 MeV 2 MeV 10 MeV 18 MeV 30 MeV 60 MeV 60 MeV 60 MeV 100 MeV 180 MeV 200 MeV 300 MeV 400 MeV 400 MeV 500 MeV 525 MeV 600 MeV 600 MeV 700 MeV 800 MeV 900 MeV l GeV l GeV 1 GeV 1.5 GeV 2 GeV 3 GeV 3.5 GeV 10 GeV 30 GeV 30 GeV 100 GeV 100 GeV 300 GeV 1 TeV 1 TeV 3 TeV 10 TeV
Depth'(cm)
Ref.
0.5
5
10
15
20
25
30
2.5E--08 a 5.7E--08 3.4E--08 5.6E-08 8.0E-08 5 . 0 E - 08 3.6E--08 2.9E - 08 3 . 4 E - 08 2.8E-08 3.0E-08 3.3E-08 3.8E-08 2.5E--08 4.8E-08 4.6E--08 4.8E-08 5.1E-08 5.5E-08 5.8E-08 6.2E--08 6.5E-08 6.0E-08 5 . 7 E - 08 9.7E-08 8.8E-08 I.IE-07 1.5E-07 2 . 0 E - 07 1.3E-07 4.0E-07 1.4E-07 6 . 2 E - 07 1.5E-07 1.6E-07 2.3E--06 1.7E-07 1.7E-07
1.1E-08 4.5E--08 3.3E-- 08 5.9E-- 08 6.7E--08 4.6E--08 3 . 6 E - 08 3.7E - 08 4.6E-08 4.0E-08 4 . 3 E - 08 4.3E-08 4 . 6 E - 08 4.7E--08 6.8E--08 7.0E-08 6.5E-08 7.4E--08 8.0E-08 8.7E-08 9.3E--08 1 . 0 E - 07 8.1E--08 7.3E--08 1.5E-07 1.3E-07 1.4E-07 1.7E-07 1 . 9 E - 07 2.2E-07 4 . 0 E - 07 2.4E-07 5.0E--07 2 . 7 E - 07 2 . 9 E - 07 1.0E--06 3.1E-07 3.3E-07
2.1E--09 2.5E-08 3 . 0 E - 08 4.6E--08 5.0E-08 6 . 9 E - 08 4.6E--08 3.9E -- 08 5 . 2 E - 08 4.5E-08 5.1E-08 5.0E-08 5.2E-08 6 . 8 E - 08 7.4E-08 7.2E-08 7.2E-08 8.1E-08 9.0E--08 9 . 8 E - 08 l.lE-07 1.2E-07 9.1E--08 1.4E-07 1 . 2 E - 07 1 . 4 E - 07 1.8E--07 1.9E-07 3.4E-07 2 . 9 E - 07 4.0E-07 3.3E-07 5.1E-07 3.7E-07 4.1E-07 1.4E-06 4 . 5 E - 07 4 . 8 E - 07
5.1E-- 10 8.8E-09 2.6E--08 4.5E--08 5.4E-08 6.0E-08 4.5E-08 4.0E - 08 5.5E-08 4.7E-08 5.5E-08 5.3E-08 5.6E--08 5.7E-08 7 . 6 E - 08 7.0E--08 7.6E-08 8 . 4 E - 08 9.3E--08 1.0E-07 1.1E--07 1.2E--07 1.0E-07 1.1E-07 1.4E-07 1.5E-07 1.8E-07 2.1E-07 2.7E--07 3.3E-07 5.8E-07 3.9E-07 7 . 3 E - 07 4.5E-07 5.0E-07 2 . 2 E - 06 5.5E--07 5.9E-07
2 . 5 E - 10 4.4E--09 1.8E-08 3.2E-08 4.8E--08 5.5E--08 3.3E--08 4.0E -- 08 5.6E--08 4 . 8 E - 08 5 . 7 E - 08 5.6E-08 6.0E-08 7.8E-08 7.7E-08 7.6E--08 8.2E--08 8.5E--08 9.5E-08 1 . 0 E - 07 1.1E-07 1.2E-07 l.lE-07 1.2E--07 1.5E-07 1.6E-07 1.9E-07 1.7E--07 3.6E--07 3.8E-07. 5 . 0 E - 07 4.6E--07 8 . 4 E - 07 5.3E-07 6.1E--07 2 . 0 E - 06 6 . 7 E - 07 7.3E-07
1 . 6 E - 10 1.7E--09 1.2E--08 2.5E-08 4.2E-08 5.0E-08 4.0E-08 3.9E - 08 5.4E-08 4.8E-- 08 5.8E-08 5.7E--08 6.2E-08 6.1E-08 7.8E--08 7.4E 08 9 . 0 E - 08 8.8E--08 9.9E--08 l.lE--07 1.2E--07 1.3E-07 1.2E-07 I.IE-07 1.6E-07 1.7E-07 2 . 0 E - 07 1.9E-07 3.3E-07 4.4E-07 5 . 4 E - 07 5.5E-07 7.0E-07 6.4E-07 7.4E--07 1.9E-06 8.2E-07 8.9E-07
1 . 2 E - 10 I.IE--09 7 . 0 E - 09 1.8E-08 2.6E 08 5.1E-08 3.5E-08 3.6E - 08 5.8E-08 4.2E-08 5.8E-08 5 . 7 E - 08 6.2E-08 6.8E--08 7.2E-08 8.0E-08 9.5E--08 8.0E-08 9 . 0 E - 08 1 . 0 E - 07 l.lE--07 1.2E-07 1.3E 07 1.2E-07 1.7E-07 1.8E-07 1.7E-07 1.8E-07 3.8E-07 4.4E-07 4.0E-07 5.5E 07 7 . 9 E - 07 6 . 7 E - 07 7.8E-07 2.1E-06 8 . 7 E - 07 9 . 4 E - 07
[8] [8] [8] [8] [8] [8] [5] [7] [7] [5] [7] [7] [7] [5] [6] [5 l [9] [6] [6] [6] [6] [6] [9] [5] [5] [9] [5] [10] [10] [6] [10] [6] [10] [6] [6] [10] [6] [6]
a 2.5 x 10-8.
F o r n e u t r o n s w i t h e n e r g y b e l o w 12 M e V t h e [4] compilation data are taken without any changes. For h i g h e r e n e r g i e s we u s e d t h e d a t a o f refs. 5 - 9 p r e s e n t e d in t a b l e s 1 a n d 2. T h e d a t a of c a l c u l a t i o n s [10] for e n e r g i e s h i g h e r t h a n 10 G e V w e r e n o t u s e d as t h e s e r e s u l t s w e r e n o t s u f f i c i e n t l y well f o u n d e d [6]. All t h e d a t a u s e d a n d t h e r e s u l t s o b t a i n e d are r e l a t e d to t h e c a s e o f a b r o a d , n o r m a l i n c i d e n t b e a m of m o n o e n e r g e t i c n e u t r o n s o n o n e side o f a n i n f i n i t e t i s s u e - e q u i v a l e n t slab o f 30 c m t h i c k n e s s a n d o f d e n s i t y 1 g / c m 3.
T h e c o m p i l a t i o n p r o c e d u r e w a s as follows. (1) T h e d a t a f r o m refs. 5 - 9 were t a b u l a t e d a n d a d d e d to t h e d a t a f r o m ref. 4. (2) T h e d o s e a n d d o s e e q u i i v a l e n t e n e r g y d e p e n d e n c e s w e r e s m o o t h e d in t h e e n e r g y r a n g e a b o v e 12 M e V for e a c h d e p t h value. T h e r e s u l t a n t c u r v e s were tabulated. (3) T h e t w o - d i m e n s i o n a l m a t r i x of d a t a , t h u s o b tained, was smoothed by fitting a second order surface, taking into account (by weighting) the different errors
E.A. Belogorlov et al. / Depth dose for neutrons
565
Table 2 Absorbed dose per unit neutron fluence, r a d / ( n e u t r o n . c m - 2 ) , as a function of neutron energy at given depths. Energy
0.5 MeV 2 MeV 10 MeV 18 MeV 30 MeV 60 MeV 60 MeV 60 MeV 100 MeV 180 MeV 200 MeV 300 MeV 400 MeV 400 MeV 500 MeV 525 MeV 600 MeV 600 MeV 700 MeV 800 MeV 900 MeV 1 GeV 1 GeV 1 GeV 1.5 GeV 2 GeV 3 GeV 3 GeV 3.5 GeV 10 GeV 10 GeV 30 GeV 30 GeV 100 GeV 100 GeV 300 GeV 1 TeV 1 TeV 3 TeV 10 TeV
Depth (cm)
Refs.
0.5
5
10
15
20
25
30
2.4E--09 a 4.1E--09 7.0E-09 8.1E-09 9 . 4 E - 09 7.8E--09 6.5E-09 6.4E--09 5.5E-- 09 4 . 2 E - 09 4.4E--09 5.0E--09 6.0E-- 09 4 . 4 E - 09 8.7E--09 7.5E--09 5 . 0 E - 09 9.4E-- 09 1.0E-08 I.IE--08 1.2E-08 1.2E-08 6.0E-09 1.3E--08 1.8E-08 7 . 0 E - 09 2.3E--08 2.1E-08 3.5E--08 2.3E--08 4.8E--08 2.5E--08 6 . 0 E - 08 2 . 8 E - 08 8 . 0 E - 08 3.0E - 08 3.2E-08 1.3E--07 3.4E-- 08 3.6E--08
1.3E--09 3.0E--09 6.2E--09 8 . 4 E - 09 9.1E--09 7.5E--09 9.0E-09 8.5E--09 9.5E--09 9.8E--09 9.5E--09 9.5E--09 1.0E--08 1.2E--08 1.9E--08 1.6E--08 1.8E-08 2 . 0 E - 08 2.2E-08 2.3E--08 2.5E-08 2.6E-08 2.3E-08 2.0E--08 3.5E-08 3.0E - 08 4.5E--08 4.4E-08 5.0E-08 5.1E--08 5.2E-- 08 5.9E--08 7.1E-08 6.7E-08 9.0E-08 7.4E - 08 8.2E-08 1.4E--07 9.0E-- 08 9.5E--08
6.5E-- 10 1.9E-09 5.7E-09 7 . 4 E - 09 7 . 7 E - 09 1.0E--08 1.2E-08 8.9E--09 1.1E-08 1.4E--08 1.3E--08 1.3E-08 1.3E--08 1.7E--08 2.4E-- 08 2.0E--08 2.6E - 0 8 2.6E - 08 2.8E-08 3.0E--08 3.2E-08 3.5E-08 3.0E-08 3.2E--08 4 . 0 E - 08 4.4E - 08 6.0E-- 08 5.9E--08 5.5E-08 7.2E--08 6.3E-08 8.6E-08 7.7E-08 1.0E-07 1.2E-07 1.1E - 07 1.3E-07 1.7E-- 07 1.5E-- 07 1.5E-07
3.6E-- 10 9 . 3 E - 10 4.8E-09 6.1E-09 7.6E--09 8.8E-09 1.0E-08 8.5E--09 I.IE-08 1.6E--08 1.5E--08 1.5E-08 1.6E-08 1.8E--08 2.7E-- 08 2.2E--08 3.2E-08 2.9E - 08 3.2E-08 3.5E-- 08 3.8E-08 4.1E-08 3.8E--08 3.3E--08 4.5E-08 5.4E - 08 6.3E--08 7.3E--08 6.2E-08 9.2E--08 7.3E--08 I.IE-07 1 . 2 E - 07 1.4E-07 1.4E-07 1.6E - 07 1.8E-07 2.6E--07 2.1 E - - 07 2.2E--07
2.4E-- 10 5 . 7 E - 10 3.1E-09 4.9E-09 6 . 6 E - 09 8.5E-09 9.0E-09 8.0E--09 1.1E--08 1.7E--08 1.5E-08 1.6E-08 1.8E--08 2.0E--08 2.9E-08 2.4E--08 3.6E-08 3.2E - 08 3.6E--08 3.9E--08 4.2E-08 4.6E-08 4.4E-08 3.7E--08 5.0E-08 6.2E - 08 7 . 4 E - 08 8.6E-08 6.0E-08 1.1E--07 8.5E--08 1.4E-07 1.1E-07 1.8E-07 1 . 6 E - 07 2.1E - 07 2 . 4 E - 07 2.7E--07 2.7E-- 07 2.9E-07
1,7E-- 10 3 . 3 E - 10 2.3E-09 3 . 7 E - 09 6.2E--09 7 . 2 E - 09 9.2E-09 7.2E--09 1.0E-- 08 1.7E--08 1.5E--08 1.8E--08 1.9E--08 2.0E--08 3.1E--08 2.5E--08 3 . 9 E - 08 3.4E - 08 3.8E--08 4 . 2 E - 08 4.6E-08 5.1E-08 4.8E--08 4.0E--08 5.2E-08 7.0E -- 08 8.0E--08 1.0E-07 6.2E--08 1.3E--07 8.5E--08 1.7E-07 1.2E--07 2.2E--07 1.7E-07 2.6E - 07 3.0E-07 3.0E--07 3.4E-- 07 3.7E--07
1.3E-- 10 2 . 4 E - 10 1.5E-09 2 . 9 E - 09 3 . 9 E - 09 7.1E-09 7.0E-09 6.6E--09 9.0E--09 1.5E--08 1.4E--08 1.8E--08 2 . 0 E - 08 2.2E--08 2.8E--08 2.7E-08 4.0E-08 3.2E - 08 3.6E--08 4.0E-08 4 . 4 E - 08 4 . 8 E - 08 5.0E--08 3.8E--08 5.2E-08 7.5E - 08 7 . 0 E - 08 9.7E-08 6.0E-08 1 . 4 E - 07 8.5E-08 1.8E-07 1.0E-07 2 . 3 E - 07 1.8E-07 2.8 E - 07 3.3E--07 3.7E-07 3 . 8 E - 07 4.1E--07
[8] [8] [8] [8] [8] [8] [5] [7] [7] [5] [7] [7] [7] [5] [6] [5] [9] [6] [6] [6] [6] [6] [9] [5] [5] [9] [5] [6] [10] [6] [10] [6] [10] [6] [10] [6] [6] [10] [6] [6]
a 2 . 4 x 10 -9.
for t h e s e p a r a t e p a r t s o f t h e d a t a . I n t h e e n e r g y r a n g e f r o m 12 u p to 10 3 M e V t h e d a t a w a s a s s i g n e d a 5% error, a n d f o r h i g h e r e n e r g i e s t h e e r r o r w a s 15%, w h e n b e i n g s m o o t h e d t h e v a l u e s o f t h e f u n c t i o n a n d its first derivative were matched. This procedure provided us with a system of d e p t h - e n e r g y d e p e n d e n c e s for d o s e a n d d o s e e q u i v a l e n t in t h e d e p t h r a n g e o f 0 - 3 0 g / c m 2 w i t h a 5 g / c m 2 s t e p a n d o v e r a n e n e r g y r a n g e f r o m t h e t h e r m a l u p to 8 T e V
w i t h a 0.2 l o g a r i t h m i c step. T h e d a t a a r e g i v e n in t a b l e s 3 a n d 4 a n d in t h e figures. T w o - d i m e n s i o n a l g r a p h s (for the dependences of dose and dose equivalent on energy a n d d e p t h ) a r e g i v e n in figs. 1 a n d 2. Figs. 3 - 9 i l l u s t r a t e the dependences of the dose and dose equivalent on e n e r g y for t h e i n d i c a t e d d e p t h values. T h e c u r v e s in t h e figures are a result of our approximation procedure. The p o i n t s a r e t h e o r i g i n a l r e s u l t s o f refs. 5 - 9 . I n t h e last t w o f i g u r e s t h e r e s u l t s a r e c o m p a r e d w i t h
,- - - ' I
- --'-i
- ~
- - ~
- ---I
- --~
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- -~-~
- -'-3
- -"-I
- --'-~
- ~
• "-'I
"--"1
- --~,
,)
o ,) o o
L,= d>
o
RE~Z~TEUTRO7. CI,!- 2
° o
o o
REI,V (?IEUTRON , CL-2
R,~ RAD/(!:NUT:~OT. CE - 2 -
~c n** *
DEPFH, 10 DEPrH,
/
oo+,-
o - IRV67 o+-
RLSTO ZER65 NEU69 , - COL75 o - RRM72
• -
, -
0-
10 .7 l0 "~ 10 .5 10 "~ 10 -m 10 .2 ~0"t 10 -~ l0 -~ t0 -~ 10 -~ 10 .3 t0 -2 10 -L
1
|0
10 2
10 ~
10 ~
CM
.SCM
~0 ~
l0 ~
10
10 2
t0 ]
10 4
10 5
10 ~
10 7
ENERGY. MEV
lO ~
ENERGY. MEV
1
[RV67 RLS70 ZER65 NEU69 COL?5 ARM72
Fig. 5. Absorbed dose and dose equivalent per unit neutron
Fig. 3. A b s o r b e d dose and d o s e equivalent per unit neutron fluence as a function of energy at a depth of 0.5 cm.
fluence as a function of energy at a depth of 10 cm.
o
o
r
o
b
oO
$°'*
:
L~
REH/('~TELF£RO!i.CM- 2 )
>
2EE/(:TEUTRO?!. C~."-2 )
L~
BAD/( N g LFi'20]:. C~[-2-,)
g
RAD/(LEU~ROI:. Cr,1-2 )
DEPFH,
oa÷,. -
~-
10- 7
10- '5 10- 5
1O-4 10" I
10- ~
10"
I
10
10 2
10 2
5
DEPFH, 15
CM
o=-
IRV67 RLSTO ZER65 . NEU6g ¢ - COL75 ¢- RRM72
IRV67 RL570 ZER65 NEU69 GOL75 RRM72
10'
l0 S
CM
. -
10 ~
10 7
10 -7
tO -t
I0 -s
10 ~4
10 -I
I0 -~
Fig. 4. A b s o r b e d dose and d o s e equivalent per unit neutron fluence as a function of energy at a depth of 5 cm.
10 -t
I
lO
iO ~
tO ~
10 4
10 ~
I0 t
ENERGY, MEV
ENERGY. MEV Fig.
6.
fluence
Absorbed
dose
as a function
and of
dose
energy
equivalent at a depth
per of
unit
15 cm.
neutron
I0'
~~o o o+
RZ"/(-~:~::~O-~:.c~,:- ~ )
o
o-FF z REM/(NEUTROtT.
>
CtC 2 )
RAD/(t]EUTROIT. C M -2 RAD/(VEUTROF,
CM_2) o
DEP[H,
-~
20
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10 -~
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i
10
i0 =
10'
$0 4
t0 5
l0 ~
10 ~
~
oo+,-
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•-
COL?5 ARM?2
o-
tO "~ 10 .5 tO "~ lO"
{0'i 10 .2 ~0 -L
1
[0
tO"
I0 j
~O 4
10-
~0 ~
,0 ~
ENERGY. MEV
ENERGY. MEV
Fig. 7. A b s o r b e d dose and dose equivalent per unit neutron fluence as a function of energy at a depth of 20 cm.
Fig. 9. A b s o r b e d dose and dose equivalent per unit neutron fluence as a function of energy at a depth of 30 cm.
~-
I ERpI-2i - ~ 7 6
//°
% REL:/(V~UTR0::. C H -2 )
o
w
g~ >
o . o b ci:
R A D / ( Y E U T : : O : ~. C H - 2 )
A
OEPrH, 25
oa+ •
o-
104
tO -G tO -5 10 -4 I0 ") 10 -2 I0 -L
I
10
tO ~
I0 ~
','M
IRV67 RLSTO ZERG5 NEUG9 00L75 RRM72
~04
I0 S
~o-* I0 s
I0 ~
ENERGY. MFV
Fig. 8. A b s o r b e d dose and dose equivalent per unit neutron fluence as a function of energy at a depth of 25 cm.
;o -~
to ~
to -~
to-'
to - I
to -~
~o- I
1
to
lo~
1oI
1o4
1o ~
lo*
ENERGY.NEV
Fig. 10. D o s e equivalent per unit neutron fluence as a function of energy and depth in p h a n t o m and r e c o m m e n d a t i o n s of refs. 1 and 2.
E.A. Belogorlov et al. / Depth dose for neutrons
568
Table 3 Dose equivalent (rem cm2/neutron) as a function of neutron energy and depth. Energy (MeV
Depth (cm) 0.5
5
10
15
20
25
30
1.26E-08 a 2.00E--08 3,16E--08 5.01E--08 7.94E--08
9.10E9.05E-9.00E-8.95E8.90E--
10 10 10 10 10
1.66E1.91E-2.13E-2.38E-2.68E--
10 10 10 10 10
8.45E9.60E-1.05E-1.18E-1.32E--
11 11 10 10 10
5.45E6.10E-6.80E-7.50E-8.15E--
11 11 11 11 11
4.00E4.50E5.00E5.50E6.10E-
11 11 11 11 11
2.96E3.30E3.70E4.12E4.55E-
11 11 11 11 11
2.24E-2.60E-3.05E-3.65E-4.05E-
11 11 11 11 11
1.26E--07 2.00E--07 3.16E-07 5.01E-07 7.94E-07
8.85E-8.78E-8.70E-8.62E-8.55E--
10 10 10 10 10
2.96E-3.30E-3.65E-4.05E-4.48E--
10 10 10 10 10
1.47E-1.62E-1.78E1.95E2.12E-
10 10 10 10 10
9.00E-9.80E-1.06E-1.15E-1.24E--
11 11 10 10 10
6.70E7.35E8.00E-8.70E-9.30E--
I1 11 11 11 11
5.00E-5.50E-6.00E-6.55E-7,00E--
11 11 11 11 11
4.65E 5.30E5.90E 6.50E7.20E-
11 11 11 11 11
1.26E-06 2.00E-06 3.16E-06 5.01E-06 7.94E-06
8.50E8.50E-8.50E-8.50E-8.45E--
10 10 10 10 10
4.95E-5.45E-5.90E-6.50E-7.05E--
10 10 10 10 10
2.30E2.48E2.67E2.85E-3.08E-
10 10 10 10 10
1.34E-1.44E-1.53E-1.63E-1.72E--
10 10 10 10 10
1.00E1.06E-1.12E1.19E-1.24E-
10 10 10 10 10
7.60E-8.20E-8.80E-9.40E-9.90E--
11 11 11 11 11
7.80E8.20E8.70E-9.10E9.20E--
11 11 11 11 11
1.26E-05 2.00E-05 3,16E-05 5.01E-05 7.94E--05
8.45E8.50E8.50E8.55E-8.55E--
10 10 10 10 10
7.55E-8.10E8.65E9.20E-9.60E--
10 10 10 10 10
3.23E3.42E3.60E3.80E-3.95E--
10 10 10 10 10
1.82E-1.90E1.97E2.02E-2.06E
10 10 10 10 10
1.3 IE 1.37E1.42E1.48E-1.53E
10 10 10 10 10
1.03E-1.08E1.10E1.12E-1.12E--
10 10 10 10 10
9.30E-9.30E9.10E8.80E8.50E
11 11 11 11 11
1.26E--04 2.00E-04 3.16E--04 5.01E-04 7.94E--04
8.55E8.55E8.60E8.70E-8.95E--
10 10 10 10 10
1.01E-09 1.03E-09 1.05E-09 1.07E--09 1.08E--09
4.07E-4.19E-4.25E-4.30E-4.38E--
10 10 10 10 10
2.09E2.10E-2.11E2.11E2.10E-
10 10 10 10 10
1.59E1.60E-1.58E-1.59E1.57E-
10 10 10 10 10
I. 11E-1.08E-1.05E-1.03E1.02E-
10 10 10 10 10
8.20E-7.90E-7.60E-7.40E7.20E
11 11 11 11 11
1.26E--03 2.00E--03 3.16E-03 5.01E-03 7.94E-03
9.40E-- 10 1.01E--09 1.08E--09 1.21E--09 1.44E--09
1.08E--09 1.06E--09 1.03E--09 1.01E--09 9.85E-- 10
4.42E-- 10 4.46E-- 10 4.50E-- 10 4.51E--10 4.52E-- 10
2 . 1 0 E - 10 2 . 1 0 E - 10 2 . 1 1 E - 10 2.13E--10 2 . 1 7 E - 10
1.53E1.51E1.50E1,49E 1.48E-
10 10 10 10 10
9.80E-9.60E-9.50E 9.40E 9.50E
11 11 11 11 11
7 . 1 0 E - 11 7.00E 11 6 . 9 5 E - 11 7.00E-I1 7 . 1 0 E - 11
1.26E-02 2.00E-02 3.16E-02 5.01E-02 7.94E-02
1.82E--09 2.48E--09 3.45E--09 4.90E--09 7.00E--09
9.70E-- 10 9.80E-- 10 1,04E--09 1.17E--09 1.35E-09
4.53E-4.58E-4.70E-4.80E-5.00E--
10 10 10 10 10
2.23E-2.31E2.40E2.55E2.70E-
10 10 10 10 10
1.48E-1.49E1.51E1.56E1.61E
10 10 10 10 10
9.70E-9.90E-1.02E1.08E1.12E-
11 11 10 10 10
7.30E7.40E 7.60E 7.80E 8.00E--
11 11 11 11 11
1.26E-01 2.00E--01 3.16E--01 5.01E--01 7.94E--01
9.95E--09 1,34E--08 1.78E--08 2.27E--08 2,67E-08
1.72E-09 2.47E-09 3.70E--09 6.95E-09 1.19E-08
5.45E-- 10 6 . 5 0 E - 10 8.40E-- 10 1.25E--09 2.15E--09
2.92E3.20E 3.61E4.20E5.40E
10 10 10 10 10
1.66E1.74E1.88E-2.07E-2.40E-
10 10 10 10 10
1.17E1.25E1.33E 1.43E 1.65E-
10 10 10 10 10
8.20E8.50E 9.10E1.02E1.27E--
11 11 11 10 10
1.26E 2.00E 3.16E 5.01E 7.94E
00 00 00 00 00
3,08E--08 3.47E--08 3.79E--08 4.01E--08 4.12E--08
1.77E-08 2.44E--08 3.17E-08 3.61E-08 4.00E-- 08
5,30E--09 1.30E--08 1.96E--08 2.65E--08 3,12E--08
1.30E-09 5.10E--09 1.13E-08 1 . 6 7 E - 08 2.34E--08
3 . 7 0 E - 10 1.35E-09 5 . 4 0 E - 09 1 . 0 3 E - 08 1 . 7 5 E - 08
2.05E 7.50E2.05E4.70E9.40E-
10 10 09 09 09
1.78E-- 10 5.30E-- 10 1.37E--09 3.10E--09 6.10E--09
1.26E 2.00E 3.16E 5.01E 7.94E
01 01 01 01 01
4.10E--08 4,36E--08 4.34E-- 08 4.11E-08 3.85E-08
4.06E-08 4.53E-08 4.75E-08 4.65E--08 4.52E-08
3.69E--08 4.34E--08 4.77E-- 08 4.87E--08 4.90E-- 08
3.09E--08 3.81E-08 4.41E-08 4.72E--08 4.93E--08
2 . 3 7 E - 08 3 . 0 8 E - 08 3.75E--08 4.24E--08 4.59E--08
1.68E-08 2 . 2 9 E - 08 2.92E--08 3.52E--08 3.95E--08
1.19E--08 1.69E--08 2.25E--08 2.87E--08 3.32E--08
E.A. Belogorlov et al. / Depth dose for neutrons
569
Table 3 (continued) Energy (MeV
Depth (cm) 0.5
5
10
15
20
25
30
1.26E 2.00E 3.16E 5.01E 7.94E
02 02 02 02 02
3.57E--08 3.27E-08 3.50E--08 4.44E-- 08 5.89E--08
4 . 3 4 E - 08 4.12E-08 4.43E-- 08 5.69E--08 7.68E--08
4.89E--08 4.81E-08 5.23E--08 6.79E--08 9.33E--08
5.09E-08 5.20E-08 5.73E--08 7.54E--08 1.05E--07
4.91E--08 5.21E-08 5.83E--08 7.80E--08 1.11E--07
4.39E-08 4.82E-- 08 5.52E--08 7.51E--08 1.09E-07
3.79E-08 4.29E-- 08 5.02E-- 08 6.93E--08 1.02E--07
1.26E 2.00E 3.16E 5.01E 7.94E
03 03 03 03 03
7.37E--08 8.68E--08 9.91E--08 1.10E--07 1.16E--07
9.78E--08 1.17E--07 1.36E--07 1.53E--07 1.66E-07
1.21E--07 1.48E--07 1.74E--07 1.98E--07 2 . 2 0 E - 07
1.39E--07 1.73E--07 2.06E-- 07 2 . 3 8 E - 07 2.69E-07
1.49E--07 1.89E--07 2.27E--07 2.66E--07 3 . 0 4 E - 07
1.49E- 07 1.92E--07 2.33E--07 2.76E--07 3.18E-07
1.41E--07 1.85E--07 2.25E--07 2.70E-- 07 3.11E-07
1.26E 2.00E 3.16E 5.01E 7.94E
04 04 04 04 04
1.24E--07 1.31E--07 1.37E--07 1.43E--07 1.48E--07
1.79E-- 07 1.91E--07 2.03E--07 2.13E--07 2.23E-07
2.39E--07 2.58E--07 2.77E--07 2 . 9 4 E - 07 3.10E-07
2.96E--07 3.22E--07 3.49E--07 3.75E-07 3.99E-07
3.38E--07 3.72E--07 4.06E-- 07 4 . 4 1 E - 07 4 . 7 4 E - 07
3.56E--07 3.96E--07 4.37E--07 4.79E-07 5.21E--07
3.52E--07 3.94E-- 07 4.38E--07 4.84E--07 5.31E--07
1.26E 2.00E 3.16E 5.01E 7.94E
05 05 05 05 05
1.51 E-- 07 1.56E--07 1.61E--07 1.65E--07 1.69E--07
2.32E-- 07 2.41E--07 2.50E--07 2.58E--07 2.66E--07
3.27E-- 07 3.42E--07 3.57E--07 3.71E--07 3.85E--07
4.26E-- 07 4.48E-- 07 4.70E-- 07 4.91E--07 5.13E--07
5.09E-- 07 5.39E--07 5.69E--07 5.99E--07 6.29E--07
5.61 E-- 07 5.98E--07 6.35E--07 6.72E-- 07 7.10E--07
5.71 E-- 07 6.11E--07 6.53E--07 6.95E--07 7.37E-- 07
1.26E 2.00E 3.16E 5.01E 7.94E
06 06 06 06 06
1.72E--07 1.75E--07 1.78E--07 1.80E--07 1.82E--07
2.73E--07 2.79E-- 07 2.85E--07 2.90E--07 2.95E--07
3.97E--07 4.10E--07 4.21E--07 4.31E--07 4.40E-- 07
5.33E--07 5.53E--07 5.71E--07 5.88E--07 6.05E--07
6.58E-07 6.86E--07 7.14E--07 7.40E-- 07 7.65E--07
7.47E--07 7.85E--07 8.21E--07 8.57E--07 8.91E--07
7.80E--07 8.23E--07 8.65E--07 9.07E-- 07 9.49E-- 07
15
20
25
30
a 1.26 X 10-8.
Table 4 Absorbed dose (tad cm2/neutron) as a function of neutron energy and depth Energy (MeV)
Depth (cm) 0.5
5
10
1.26E-08 a 2.00E-08 3.16E--08 5.01E--08 7.94E--08
2.90E3.08E2L28E-3.44E-3.60E--
10 10 10 10 10
1.25E- 10 1.47E- 10 1.66E-- 10 1.89E-- 10 2.11E--10
8.45E9.50E-1.05E-1.14E-1.24E--
11 11 10 10 10
5 . 4 5 E - 11 6 . 1 0 E - 11 6.80E-- 11 7.50E-- 11 8.15E--11
4.00E4.50E5.00E-5.50E-6.10E--
11 11 11 11 11
2.96E3.30E3.70E-4.12E-4.55E--
11 11 11 11 11
2.24E2.60E3.05E-3.65E-4.05E--
11 11 11 11 11
1.26E-- 07 2.00E--07 3.16E--07 5.01E--07 7.94E-- 07
3.76E-3.90E-4.07E-4.21E-4.35E--
10 10 10 10 10
2.36E-2.62E-2.93E-3.26E-3.58E--
10 10 l0 10 10
1.34E-1.46E-1.58E-1.72E-1.85E--
10 10 l0 10 10
9.00E-9.80E-1.06E-1.15E-1.24E--
11 I1 l0 10 10
6.70E-7.35E-8.00E-8.70E-9.30E--
11 11 11 11 11
5.00E-5.50E-6.00E-6.55E-7.00E--
11 11 11 11 11
4.65E-5.30E-5.90E-6.50E-7.20E--
11 11 1l II l1
1.26E-- 06 2.00E-- 06 3.16E--06 5.01E--06 7.94E-- 06
4.48E-4.58E-4.70E-4.80E-4.88E--
10 10 10 10 10
3.92E-4.26E-4.53E-4.85E-5.15E--
10 10 10 10 10
1.98E-2.13E-2.28E-2.41E-2.56E--
10 10 10 10 l0
1.34E-1.44E-1.53E-1.63E-1.72E--
10 10 10 10 10
1.00E-1.06E-I. 12E-1.19E-1.24E--
10 10 l0 10 l0
7.60E-8.20E-8.80E-9.40E-9.90E--
11 11 11 11 11
7.80E-8.20E-8.70E-9.10E-9.20E--
11 1l 11 11 11
E.A. Belogorlov et al. / Depth dose for neutrons
570 Table 4 (continued) Energy (MeV)
Depth (cm) 0.5
5
10
15
20
25
30
1.26E-05 2.00E-05 3.16E-05 5.01E-05 7.94E-05
4.95E4.98E-5.00E-5.00E-5.00E-
10 10 10 10 10
5.40E5.65E5.90E-6.05E6.10E-
10 10 10 10 10
2.70E-2.83E2.98E3.10E3.06E-
10 10 10 10 10
1.81E1.90E-1.97E-2.02E2.06E-
10 10 10 10 10
1.31E1.37E1.42E1.48E1.52E
10 10 10 10 10
1.03E1.08E1.10E1.12E1.12E-
10 10 10 10 10
9.30E 9.30E9.10E-8.80E8.50E-
11 11 11 11 11
1.26E-04 2.00E-04 3.16E-04 5.01E-04 7.94E-04
4.98E4.92E-4.80E-4.70E-4.60E-
10 10 10 10 10
6.10E6.05E6.00E-5.95E-5.85E-
10 10 10 10 10
3.20E3.25E3.32E-3.40E3.45E--
10 10 10 10 10
2.09E2.10E2.11E 2.11 E 2.10E-
10 10 10 10 10
1.59E1.60E1.59E1.58E1.57E-
10 10 10 10 10
1.11 E 1.08E1.05E1.03E1.01E-
10 10 10 10 10
8.20E7.90E7.60E7.40E7.20E-
11 11 11 11 11
1.26E-03 2.00E 03 3.16E-03 5.01E-03 7.94E--03
4.50E-10 4.42E--10 4 . 3 7 E - 10 4.32E-10 4 . 4 5 E - 10
5.70E-10 5.60E-10 5.45E-- 10 5.35E-10 5.25E-- 10
3.50E--10 3.55E-10 3 . 5 5 E - 10 3.55E--10 3 . 5 5 E - 10
2.10E-10 2.10E-10 2.11E 10 2.13E--10 2 . 1 5 E - 10
1.53E 1.51E 1.50E1.49E 1.48E-
10 10 10 10 10
9.80E-11 9.60E-11 9 . 5 0 E - 11 9.40E--11 9.50E 11
7.10E I1 7.00E 11 6 . 9 5 E - 11 7.00E-II 7.10E-- 11
1.26E-02 2.00E-02 3.16E-02 5.01E-02 7.94E-02
4.70E--10 5.05E-- 10 5 . 7 5 E - 10 7.20E-I0 9.30E--10
5.30E-10 5 . 3 0 E - 10 5 . 3 5 E - 10 5.45E-10 5.60E-10
3.52E-10 3 . 5 0 E - 10 3 . 5 0 E - 10 3.50E-10 3.55E--10
2.18E--10 2 . 2 0 E - 10 2 . 2 2 E - 10 2.27E 10 2.38E-10
1.49E-10 1 . 4 9 E - 10 1.51 E - 10 1.56E--10 1.61E-10
9.70E 9.90E 1.02E1.08E 1.12E
7.30E 7.40E 7.60E7.80E 8.00E
1.2 6E-0 1 2 . 0 0 E - 01 3.16E-01 5.01E-01 7.94E-01
1.21E--09 1.57E--09 1.96E-09 2.38E-09 2.88E-09
6.10E--10 7 . 2 5 E - 10 9.10E-10 1.12E-09 1.44E-09
3.70E-10 4.00E-- 10 4.50E 10 5.15E 10 6.90E 10
2.50E-10 2.67E-- 10 2.90E--10 3.25E-10 4 . 0 0 E - 10
1.66E 10 1.74E-- 10 1.88E--10 2.07E-10 2 . 4 0 E - 10
1.17E-10 1 . 2 5 E - 10 1.33E-10 1.43E-10 1 . 6 5 E - 10
8.20E-11 8 . 4 0 E - 11 8.75E 11 9.30E-I1 1 . 0 3 E - 10
1.26E 2.00E 3.16E 5.01E 7.94E
00 00 00 00 00
3.47E-09 4.25E-09 4.80E-09 5.60E-09 6.35E--09
1.89E--09 2.60E-09 3.55E-09 4.75E--09 5.85E--09
1.05E-09 1.64E-09 2.40E-09 3.45E-09 4.80E-09
5 . 4 0 E - 10 8 . 9 5 E - 10 1.55E--09 2.36E-09 3.60E--09
3 . 2 0 E - 10 5 . 6 0 E - 10 1.01E-09 1.71E-09 2.70E-09
2 . 0 5 E - 10 3 . 1 5 E - 10 5 . 7 5 E - 10 9.60E-- 10 1.63E-09
1.27E1.85E3.00E 5.35E-9.70E-
1.26E 2.00E 3.16E 5.01E 7.94E
01 01 01 01 01
7.35E-09 8.10E--09 8.55E--09 8 . 0 0 E - 09 6 . 3 0 E - 09
7 . 0 5 E - 09 8 . 0 0 E - 09 8.55E-09 9.00E-- 09 9 . 2 5 E - 09
6 . 0 0 E - 09 7.05E--09 8.10E-09 9.20E-- 09 1.03E--08
4 . 8 5 E - 09 6 . 0 0 E - 09 7.10E-09 8 . 4 0 E - 09 1.00E-08
3.95E-09 5.35E-09 6.75E-09 8.20E - 09 1.00E-08
2 . 9 2 E - 09 4 . 0 8 E - 09 5.40E-- 09 7.00E - 09 9.10E-09
1.70E--09 2.60E--09 3.75E-09 5 . 5 0 E - 09 6 . 7 0 E - 09
1.26E 2.00E 3.16E 5.01E 7.94E
02 02 02 02 02
5.00E-09 4.60E-09 5.00E-- 09 8.59E--09 1.24E-08
9.45E-09 9.70E-09 1.03E--08 1.38E--08 2.00E--08
1.18E-08 1.28E 08 1.40E-08 1.97E-08 2.87E--08
1.26E-08 1.48E-08 1.62E-08 2.51E--08 3.69E--08
1.20E--08 1.43E--08 1.80E-08 2 . 8 6 E - 08 4 . 2 3 E - 08
1.22E-08 1.54E-08 1.80E--08 2.91E--08 4 . 3 3 E - 08
1.02E 08 1.33E 08 1.70E--08 2.71E-08 4.07E-08
1.26E 2.00E 3.16E 5.01E 7.94E
03 03 03 03 03
1.60E 08 1.92E--08 2.21E--08 2.47E--08 2.67E--08
2.60E--08 3.13E--08 3.64E--08 4.12E--08 4.52E-08
3.76E--08 4.56E--08 5.38E--08 6.16E-08 6.85E-08
4.87E 08 5.96E--08 7.12E--08 8.25E--08 9.28E-08
5.62E 08 6.97E-08 8.43E-08 9 . 8 8 E - 08 1.12E--07
5.80E 08 7.30E--08 8.93E--08 1.06E-07 1 . 2 2 E - 07
5.47E-08 6.99E--08 8.63E--08 1.03E--07 1.20E--07
1.26E 2.00E 3.16E 5.01E 7.94E
04 04 04 04 04
2.81E--08 2.87E-- 08 2.98E-08 3.09E--08 3.21E--08
4 . 8 2 E - 08 5.04E-- 08 5.29E-08 5.56E--08 5.83E--08
7.38E--08 7.88E - 08 8.37E--08 8.90E--08 9 . 4 5 E - 08
1.01E-07 1 . 1 0 E - 07 1.18E-07 1.27E-07 1 . 3 6 E - 07
1.24E-07 1.36E - 07 1.48E--07 1.61E-07 1.75E-07
1.36E-07 1.51E - 07 1.66E-07 1.83E-07 2.01E--07
1.36E--07 1 . 5 0 E - 07 1 . 6 7 E - 07 1.86E--07 2 . 0 6 E - 07
11 11 10 10 10
11 11 11 11 11
10 10 10 10 10
571
E.A. Belogorlov et al. / Depth dose for neutrons
Table 4 (continued) Energy (MeV)
Depth (cm) 0.5
5
10
15
20
25
30
1.26E 2.00E 3.16E 5.01E 7.94E
05 05 05 05 05
3.33E-08 3.42E-08 3.52E-08 3.57E--08 3.64E--08
6.12E-08 6.42E-08 6.67E-08 6.87E- 08 7.05E- 08
1.00E-07 1.07E-07 1.12E-07 1.17E--07 1.21E--07
1.47E-07 1.58E-07 1.67E-07 1.76E--07 1.83E--07
1.91E-07 2.07E- 07 2.21E-07 2.35E--07 2.46E--07
2.21E-07 2.41E-07 2.60E-07 2.77E--07 2.93E--07
2.29E-07 2.50E-07 2.72E-07 2.90E--07 3.09E-07
1.26E 2.00E 3.16E 5.01E 7.94E
06 06 06 06 06
3.71E-08 3.77E-08 3.83E--08 3.89E-- 08 3.94E--08
7.23E-08 7.41E--08 7.58E- 08 7.74E--08 7.90E-- 08
1.25E- 07 1.29E-- 07 1.33E--07 1.37E-07 1.41E--07
1.91E-07 1.98E--07 2.06E-07 2.14E-07 2.21E-07
2.58E-07 2.70E--07 2.83E--07 2.95E--07 3.08E--07
3.10E-07 3.26E- 07 3.44E- 07 3.62E- 07 3.80E- 07
3.28E-07 3.48E--07 3.68E-07 3.90E- 07 4.12E-07
a 1.26× 10 -s.
the m a x i m u m dose a n d m a x i m u m dose equivalent values r e c o m m e n d e d b y refs. 1 a n d 2. The data for the a b s o r b e d dose for r e c o m m e n d a t i o n s [1,2] are t a k e n as the ratio of the dose equivalent to the quality factors.
~,~_ ~.- I£RP-~l ,NRB -75
As is seen the data o b t a i n e d in this work is in good agreement with the m a x i m u m dose equivalent recomm e n d e d by ref. 1. Ref. 2 r e c o m m e n d a t i o n s are somew h a t higher for the energy range from 10 - 6 up to 1 MeV. This follows from comparison of ref. 1 recomm e n d a t i o n s , the d a t a presented in the chart [3] a n d works [11] with those from [12]. Ref. 2 r e c o m m e n d a tions seems to be quite reasonable w h e n one deals with p r o b l e m s concerning radiation safety in cases where i n f o r m a t i o n a b o u t the n e u t r o n energy spectrum is poor, e.g., only the average energy of the spectrum is known. W h e n i n f o r m a t i o n a b o u t the spectrum is quite sufficient, application of the d e p t h - e n e r g y dependences q u o t e d in this work would provide physically more correct estimates for n e u t r o n dose.
References ff 8
/
10 4
10 )
10 -~
10 -s
10 -q
10 -1
10 "~
10 :L
1
tO
10 ~
101
10 4
10 s
10 s
[.NERF~Y ,MEV
Fig. 11. Absorbed dose per unit neutron fluence as a function of energy and depth in phantom and recommendations of refs. 1 and 2.
[1] ICRP Publication 21 (Pergamon Press, Oxford, 1973). [2] The Radiation Safety Standards NRB-76 (Moscow, Atomizdat, 1978). [3] Atlas of dose characteristics of external ionizing radiation (Handbook) ed., E.E. Kovalev (Moscow, Atomizdat, 1978). [4] K.B. Shaw, G.R. Stevenson and R.H. Thomas, preprint RHEL/MI49, Chilton (1968). [5] R.G. Alsmiller, T.W. Armstrong and W.A. Coleman, preprint ORNL-TM-2924, Oak Ridge (1970). [6] V.T. Golovachik, E.L. Potjomkin, V.N. Lebedev and V.V. Frolov, Proc. of IVth Union Conf. on Charged Particle Accelerators, vol. 2 (Moscow, "Nauka", 1975) pp. 212214; Preprint IHEP 74-58, Serpukhov (1974). [7] C.D. Zerby and W.E. Kinney, Nucl. Instr. and Meth. 36 (1965) 125-140. [8] D.C. Irving, R.G. Alsmiller and H.S. Moran, preprint ORNL-4032 UC-41, Oak Ridge (1967). [9] J. Neufeld, W.S. Snyder, J.E. Turner et al., Health Physics, 17 (1969) 449-457.
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[10] T.W. Armstrong and K.C. Chandler, preprint ORNL-TM3758, Oak Ridge (1972). [11] V.G. Zolotukhin, I.B. Keyrim-Markus, O.A. Kochetkov et al., Neutron Tissue Dose in Human Body (Moscow, Atomizdat, 1972).
[12] W.S. Snyder, NBS Handbook 63 (1957); NCRP Report No. 20, (Washington D.C., NCRP, 1957) pp. 39-66. [13] T.A. Gabriel et al., preprint ORNL-4542, Oak Ridge (1970).