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Carlo DTS: A Monte Carlo code for the dual thin scintillator neutron detector
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CARLO DTS" A MONTE CARLO CODE FOR THE DUAL THIN SCINTILLATOR NEUTRON DETECTOR M.~,uRo S. DIAS a n d RONALD G. JOHNSON* Instituto de Pesquisas Energ6ticas e Nucleares, CNEN/SP, Caixa Postal 11049, CEP 05499. S8o Paulo, SP, Brazil *National Institute of Standards and Technolog,,, Gaithersburg, MD 20899, U.S.A.
A Monte Carlo code called C A R L O DTS, developed for the e f f i c i e n c y a n d p r o t o n r e c o i l s p e c t r a c a l c u l a t i o n of the Dual T h i n S c i n t i l l a t o r (DTS) n e u t r o n d e t e c t o r is d e s c r i b e d . The c o d e C A R L O DTS c o v e r s the n e u t r o n e n e r g y r a n g e b e t w e e n 1 and 20 MeV. The c r o s s s e c t i o n s a n d a n g u l a r distributions were t a k e n f r o m the E N D F / B - V d a t a file for the n u c l e a r reactions involved: H(n.n)H, C(n,n)C and inelastic scattering, (n,~), (n,n')3a reactions on carbon-12. The theoretical c a l c u l a t i o n s are c o m p a r e d to experimental results at two n e u t r o n e n e r g i e s , n a m e l y : 2 . 4 4 6 a n d 14.04 MeV, obtained by m e a n s of the T i m e C o r r e l a t e d A s s o c i a t e d P a r t i c l e T e c h n i q u e .
INTRODUCTION
The M o n t e C a r l o code C A R L O DTS, d e v e l o p e d for the e f f i c i e n c y &nd p r o t o n r e c o i l s p e c t r a c a l c u l a t i o n of the D U A L T H I N S C I N T I L L A T O R (DTS) n e u t r o n d e t e c t o r is d e s c r i b e d . C o m p l e t e d e t a i l s a b o u t the DTS c h a r a c t e r i s t i c s and performance have b e e n p u b l i s h e d (Dias et al., 1984, D i a s et al., 1985 and Dias, 1988). B a s i c a l l y , T h e DTS n e u t r o n d e t e c t o r c o n s i s t s of two thin c y l i n d r i c a l p i e c e s of plastic scintillators, 0.254 cm thick, 4.70 and 4.90 c m in diameter, r e s p e c t i v e l y , p l a c e d c o a x i a l in f r o n t of each other ( f i g u r e i). Each s c i n t i l l a t o r w a s c o u p l e d to a p a i r of p h o t o t u b e s , by m e a n s of a p e r s p e x light guide, in a h e a d - o n g e o m e t r y . A d e t a i l e d d e s c r i p t i o n of the c o d e CARLO DTS will be p u b l i s h e d e l s e w h e r e (Dias and J o h n s o n , 1990). In the p r e s e n t paper, only the main aspects are emphasized. T h e c o d e C A R L O D T S c o v e r s the n e u t r o n e n e r g y r a n g e between 1 and 20 MeV. The d e t e c t o r p a r a m e t e r s a n d the c o o r d i n a t e s y s t e m orientation are s h o w n in F i g u r e I. T h e d e t e c t o r is c o n s i d e r e d as a c y l i n d e r of h e i g h t H T and r a d i u s R, f i l l e d w i t h s c i n t i l l a t o r c o n t a i n i n g h y d r o g e n and c a r b o n of c o n c e n t r a t i o n s NH and N C, r e s p e c t i v e l y . T h e n e u t r o n beam, w i t h a r a d i u s R N, is a s s u m e d to be homogeneous and normally incident to the d e t e c t o r frontface. Nonhomogeneity or o t h e r i n c i d e n c e a n g l e s m a y be i n t r o d u c e d by changing subroutine SOURCE
* Formely
National
Bureau
of S t a n d a r d s . 295
296
M . S . DI.~,s and R. O. JoHxso'~
according to the case of interest.
Z,W
Zone 3 Zone 2 (Scintillator 2)
z, HT
I ~ o-''~--'-~ . ~
, • HI __ _
/ Zone 1 (Scintillator 11
~
I.°-'-
y,v
I 5 <.I
~eutron Beam (Radius R N )
Fig.
i:
C o o r d i n a t e system. scintillators.
ZONE 3 is the region
outside the
The cylindrical regions where the scintillators 1 and 2 are iocatedare called ZONES 1 and 2, respectively. ZONE 3 is located outside the scintillators. The c o n t r i b u t i o n of the perspex light guide in the detector response is not considered. It has been e s t i m a t e d to be negligible for neutron beam diameters much smaller than the detector diameter (Dias, 1984). Easy m o d i f i c a t i o n s can be introduced in the code to calculate the response for neutron beams comparable or larger than the scintillators. Because the scintillators are thin, a neutron with energy in the range of 1 to 15 MeV will have, on the average, only one collision inside the detector. The m a x i m u m number of collisions is b e l o w nine and the m a j o r i t y of neutrons escape the detector before being absorbed. To achieve a statistical u n c e r t a i n t y around 0.4% about 105 histories are necessary, applying the forced c o l l i s i o n technique. Good pulse height distributions are o b t a i n e d with about 4 x 105 histories.
NEUTRON KINEMATICS Table 1 shows the reactions which c o n t r i b u t e to the DTS detector response, including the Q value and the first and second reaction thresholds. The reaction cross sections were c o n s i d e r e d to be zero below the second reaction threshold. All cross section values were taken from the E N D F / B - V evaluation (ENDF/B-V, 1979). Intermediate values to those c o n t a i n e d in the cross section tables are obtained by linear interpolation, for all reactions involved. The
CARLO
t a b l e s c o n t a i n m e s h p o i n t s appropriate m i n i m i z e i n t e r p o l a t i o n errors, m a i n l y
Table
i:
DTS
29"7,
to the c r o s s s e c t i o n s t r u c t u r e near the c a r b o n ~ e s o n a n c e s .
Reactions which contribute to the S c i n t i l l a t o r (DTS) d e t e c t o r r e s p o n s e .
Reaction
Q (MeV)
iH(n,n)iH 12C(n,n)12 C 12C(n,n'~)12C 12C(n,~)9Be 12C(n,n')12*C * 8Be + ~ 3~
-4.433 -5.704 -7.656 +0.289 +0.102
i st T h r e s h o l d (MeV) _ _ 4.805 6.183 8.299 -
Dual
in o r d e r %o
Thin
2 nd T h r e s h o l d (MeV)
5.840 6.428 8.359
The a n g u l a r d i s t r i b u t i o n for the e l a s t i c s c a t t e r i n g on hydrogen, H(n,n)H, was o b t a i n e d f r o m H o p k i n s a n d B r e i t (1971). T h e a n g u l a r d i s t r i b u t i o n d a t a for the e l a s t i c s c a t t e r i n g on c a r b o n , C ( n , n ) C , has b e e n o b t a i n e d f r o m ENDF/B-V (1979). Since the coefficients for the e x p a n s i o n in L e g e n d r e p o l y n o m i n a l s are g i v e n for the c e n t e r - o f - m a s s system, it was n e c e s s a r y a t r a n s f o r m a t i o n to the laboratory s y s t e m in o r d e r to be c o m p a t i b l e w i t h the M o n t e C a r l o code. For the C ( n , n ' Y ) C r e a c t i o n the a n i s o t r o p y in the a n g u l a r distribution of s c a t t e r e d n e u t r o n s has b e e n c o n s i d e r e d . T h e L e g e n d r e c o e f f i c i e n t s w e r e t a k e n f r o m G l a s g o w et al. (1976) for the e n e r g y r a n g e b e t w e e n 8970 and 1 4 9 3 0 KeY. For the r e m a i n i n g e n e r g y r a n g e ( b e t w e e n 4812 a n d 2 0 0 0 0 keV) the c o e f f i c i e n t s were t a k e n f r o m the E N D F / B - V (1979). The d e t e c t i o n of g a m m a - r a y s f r o m 1 2 C ( n , n ' y ) 1 2 C reaction has been c a l c u l a t e d s e p a r a t e l y by m e a n s of a s i m p l i f i e d M o n t e C a r l o c o d e as d e s c r i b e d b y Dias (1988). T h e c o r r e c t i o n f a c t o r due to this e f f e c t is less t h a n 0.4% for a n e u t r o n b e a m i n c i d e n t on the d e t e c t o r axis. For f i n i t e b e a m s i z e s the c o r r e c t i o n t e n d s to be lower. T h e a n g u l a r d i s t r i b u t i o n of a l p h a s f r o m the 1 2 C ( n , a ) 9 B e reaction has b e e n c o n s i d e r e d as i s o t r o p i c in the l a b o r a t o r y system. T h i s s i m p l i f i c a t i o n has v e r y l i t t l e e f f e c t on the r e s u l t s s i n c e the discrimination level of the proton-recoil s p e c t r u m can a l w a y s be c h o s e n a b o v e the c h a n n e l c o r r e s p o n d i n g to the maximum e n e r g y of the a l p h a p a r t i c l e s p r o d u c e d b y this r e a c t i o n . The a n g u l a r d i s t r i b u t i o n of a l p h a s f r o m the 1 2 C ( n , n ' ) 3 a r e a c t i o n has b e e n c o n s i d e r e d as i s o t r o p i c in the l a b o r a t o r y system. The Q value for t h ~ react/on has b e e n d e t e r m i n e d c o n s i d e r i n g all the e x c i t a t i o n e n e r g y levels, real or virtual c o n t a i n e d in the E N D F / B - V (1979). For e a c h n e u t r o n e n e r g y a set of excitation p r o b a b i l i t i e s v a l u e s , Pi, h a s b e e n g e n e r a t e d for the c o m p o u n d n u c l e u s states. T h i s p r o b a b i l i t y is the r a t i o b e t w e e n the p a r t i a l c r o s s s e c t i o n for a given e x c i t a t i o n s t a t e and the t o t a l c r o s s s e c t i o n for the ~hat n e u t r o n e n e r g y . T h e s e c r o s s s e c t i o n v a l u e s w e r e a l s o o b t a i n e d f r o m E N D F / B - V (1979). APPLICATION
OF THE
FORCED
FIRST
COLLISION
TECHNIQUE
T h i s t e c h n i q u e a l l o w s a r e d u c t i o n in the n u m b e r of h i s t o r i e s followed by the M o n t e C a r l o code, w i t h o u t s i g n i f i c a n t loss in the s t a t i s t i c a l accuracy a c h i e v e d . It was u s e d to define the point w h e r e the first neutron collosion will occc~c or
298
M . S . DIAs and R. G. JoH~SO'~
to make the neutron collide p r e f e r e n t i a l l y
with
F o r c e d first c o l l i s i o n
the h y d r o g e n atoms in r/he scintillator.
inside
the d e t e c t o r
The DTS d e t e c t o r has high t r a n s m i s s i o n for M e V n e u t r o n s , and consequently a low detection efficiency. T h e r e f o r e a g r e a t n u m b e r of incident n e u t r o n s should be n e c e s s a r y to get a low s t a t i s t i c a l u n c e r t a i n t y , d e m a n d i n g a long p r o c e s s ~ g tune. T h i s p r o b l e m has b e e n s o l v e d by c o n f i n i n g the n e u t r o n first collision inside the d e t e c t o r (Cashwell and Everett, 1959). T h i s p r o c e d u r e r e s u l t s in a 100% detection e f f i c i e n c y . T h e r e d u c t i o n in the p r o c e s s i n g time r e a c h e s a f a c t o r a r o u n d 20 at 15 MeV. To the c a l c u l a t e d e f f i c i e n c y an a p p r o p r i a t e f a c t o r is applied. The d i s t a n c e to s u b s e q u e n t collisions are c a l c u l a t e d in the u s u a l way. F o r c e d first c o l l i s i o n on h y d r o g e n and ZONE 1 T a b l e 2 s h o w s the p e r c e n t a g e c o n t r i b u t i o n in the DTS detector e f f i c i e n c y f r o m e v e n t s o r i g i n a t e s b y n e u t r o n f i r s t c o l l i s i o n on h y d r o g e n and c a r b o n for d i f f e r e n t n e u t r o n e n e r g i e s . B e t w e e n 8 9 - 9 6 % c o n t r i b u t i o n c o m e s f r o m events w h e r e the f i r s t n e u t r o n c o l l i s i o n w a s on h y d r o g e n . Table
2:
C o n t r i b u t i o n to the DTS d e t e c t i o n efficiency of e v e n t s o r i g i n a t e d by n e u t r o n f i r s t c o l l i s i o n on h i d r o g e n , c a r b o n a n d Z O N E S 1 a n d 2 (in p e r c e n t ) .
Neutron Energy (MeV) 1.0 2.4 14.0
Contribution Hydrogen 89.0 93.8 96.4
to the E f f i c i e n c y
Carbon
ZONE
ii.0 6.2 3.6
95.6 96.7 98.6
1
(%) ZONE
2
4.4 3.3 1.4
S i n c e the r a t i o b e t w e e n the t o t a l c r o s s s e c t i o n s of h y d r o g e n and carbon are in the r a n g e of 0.5 to 3, for 1 to 15 M e V n e u t r o n s , the fraction of n e u t r o n s w h i c h h a v e f i r s t c o l l i s i o n on h y d r o g e n is b e t w e e n 30 a n d 77%. Therefore it b e c o m e s c o n v e n i e n t to f o r c e the f i r s t c o l l i s i o n on h y d r o g e n in o r d e r to r e d u c e the p r o c e s s i n g t i m e b y a f a c t o r up to a b o u t 3. A f r a c t i o n fH of the i n c i d e n t n e u t r o n s is f o r c e d to c o l l i d e against h y d r o g e n a n d (i - fH ) c o l l i d e a g a i n s t c a r b o n atoms. T h e n u m b e r of c o u n t s in the p r o t o n - r e c o i l s p e c t r u m b e c o m e s r e a l numbers. The n u m b e r o f p r o c e s s e d neutrons, N s, g i v e s r i s e to a l a r g e r n u m b e r of c o u n t s in the p r o t o n - r e c o i l s p e c t r u m , N' s. T h e p r o c e s s i n g t i m e is r e d u c e d b y the f a c t o r N ' s / N s. At 14 M e V and using fH = 0.9, t h i s f a c t o r is e q u a l to 2.4. As s h o w n in t a b l e 2, b e t w e e n 95 to 99% of the c o u n t s w h i c h c o n t r i b u t e to the e f f i c i e n c y are o r i g i n a t e d b y a n e u t r o n first collision in the first scintillator (ZONE1). B e c a u s e of the h i g h t r a n s m i s s i o n t h r o u g h the detector for 1 to 15 M e V n e u t r o n s , a b o u t h a l f of the n e u t r o n s a r e i n c i d e n t in ZONE 1 and h a l f are i n c i d e n t in ZONE 2. T h e r e f o r e a p p l y i n g the f o r c e d f i r s t c o l l i s i o n in the f i r s t s c i n t i l l a t o r (ZONE I) it is p o s s i b l e to r e d u c e the p r o c e s s i n g time b y a f a c t o r of 2. A f r a c t i o n f of t h e i n c i d e n t n e u t r o n s is f o r c e d to c o l l i d e in ZONE 1 s a n d (i - fs ) c o l l i d e in ZONE 2. T h e n u m b e r of p r o c e s s e d n e u t r o n s N' s g i v e s rise to a l a r g e r n u m b e r of c o u n t s , N" s. T h e p r o c e s s i n g t i m e is r e d u c e d b y the factor N"s/N' s. T h e t o t a l r e d u c t i o n , i n c l u d i n g the f o r c e d collision on hydrogen b e c o m e s N " s / N s. At 14 M e V a n d u s i n g fs = fH = 0.9, the t o t a l r e d u c t i o n is 4.3.
C A R L O DTS
LOST
COINCIDENCES
2t)~
EFFECT
For M e V n e u t r o n s , t h e r e is a l a r g e e f f e c t due to the e s c a p e of p r o t o n s from the forward face of the f i r s t s c i n t i l l a t o r in the DTS d e t e c t o r . However, the c o r r e s p o n d i n g d i s t o r t i o n in the p r o t o n r e c o i l spectrum is eliminated e x p e r i m e n t a l l y by d e t e c t i n g t h e s e e s c a p e d p r o t o n s at the s e c o n d scintillator, p l a c e d b e h i n d the f i r s t one. S i n c e t h i s p r o c e d u r e r e q u i r e s a coincidence signal, t h e r e is a l o w e r limit for the first scintillator pulse amplitude to be detectable. The s u m - c o i n c i d e n c e p u l s e s o r i g i n a t e d f r o m p u l s e s in the first scintillator b e l o w this limit w i l l be lost. S o m e of t h e s e lost s u m - c o i n c i d e n c e pulses can have an a m p l i t u d e a b o v e the d i s c r i m i n a t i o n l e v e l a d o p t e d for the detec=ion e f f i c i e n c y c a l c u l a t i o n ( u s u a l l y 30% of the m a x i m u m p r o t o n e n e r g y ) . T h e r e f o r ~ a c o r r e c t i o n for t h e s e lost c o i n c i d e n c e s is r e q u i r e d . At low neutron energies t h e r e are s u m - c o i n c i d e n c e p u l s e s a l s o due to n e u t r o n m u l t i p l e scattering inside the s c i n t i l l a t o r s . T h e loss of s u c h e v e n t s m u s t be t a k e n into a c c o u n t . The lost c o i n c i d e n c e s e f f e c t c a u s e d b y the e s c a p e of p r o t o n s has b e e n i n c o r p o t a t e d in the C A R L O DTS code, by c a l c u l a t i n g the p r o t o n e n e r g y fraction d e p o s i t e d i n s i d e e a c h s c i n t i l l a t o r . T h e total l i g h t p r o d u c e d by a g i v e n n e u t r o n in the M o n t e C a r l o c o d e has b e e n d i v i d e d into two parts: the first one c o r r e s p o n d s to the t o t a l l i g h t p r o d u c e d in the f i r s t s c i n t i l l a t o r (ZONE i) and the s e c o n d one c o r r e s p o n d s to the t o t a l l i g h t p r o d u c e d in the second s c i n t i l l a t o r (ZONE 2). T h e e v e n t s w h i c h p r o d u c e a l i g h t y i e l d b e l o w a g i v e n t h r e s h o l d are r e j e c t e d . In this way, the loss of c o i n c i d e n c e s c a u s e d by m u l t i p l e scattering are a l s o i n c l u d e d . T h e c o r r e c t i o n for lost c o i n c i d e n c e s are s h o w n in fig. 2 as a f u n c t i o n of the f r a c t i o n a l d i s c r i m i n a t o r l o w e r l e v e l (ratio b e t w e e n the c h a n n e l at the d i s c r i m i n a t o r l o w e r l e v e l a n d the c h a n n e l at the e n d of the spectrum), for several e n e r g i e s of the i n c i d e n t n e u t r o n , in t h i s figure, the discrimination level adopted for the c a l c u l a t e d e f f i c i e n c y c o r r e s p o n d s to 30% of the m a x i m u m p r o t o n e n e r g y .
too
~ "~t
I
/
1.0 M eV
z
o
r'r
0.90
n.-
"~!~14.0
MeV
I 0.10 DLL
1 0.15
O (j
0.85
I 0.05 FRACTIONAL
Fig.
2:
L o s t c o i n c i d e n c e s c o r r e c t i o n as a f u n c t i o n f r a c t i o n a l l o w e r d i s c r i m i n a t i o n level.
of
the
300
M . S . DIAS and R. G. J o H s s o ~
VARIATION
IN L I G H T C O L L E C T I O N
The v a r i a t i o n in the l i g h t c o l l e c t i o n e f f i c i e n c y at d i f f e r e n t points in the s c i n t i l l a t o r has b e e n t a k e n i n t o account by assuming a quadratic d e p e n d e n c e of the a v e r a g e l i g h t r e s p o n s e as a f u n c t i o n of the d i s t a n c e f r o m the c e n t e r of the s c i n t i l l a t o r . T h e c o e f f i c i e n t s w e r e o b t a i n e d b y a l e a s t square fit to e x p e r i m e n t a l l i g h t r e s p o n s e v a l u e s (Dias et al., 1984).
RESULTS
OF
THE
CALCULATIONS
T h e b e h a v i o r of t h e c a l c u l a t e d b i a s e d ( t h e w o r d b i a s e d m e a n i n g a b o v e a g i v e n d i s c r i m i n a t o r l e v e l ) e f f i c i e n c y w i t h n e u t r o n e n e r g y is s h o w n in fig. 3 t o g e t h e r w i t h t w o e x p e r i m e n t a l p o i n t s o b t a i n e d at 2 . 4 4 6 a n d 1 4 . 0 4 M e V (Dias et al., 1984). The curve follows essentially the H(n,n)H cross section. Contributions from C(n,n)C and 12C(n,n'y)12C cross section cause some small i r r e g u l a r i t i e s in the e f f i c i e n c y c u r v e , m a i n l y in the regions of carbon r e s o n a n c e s . For this curve, the bias e n e r g y w a s l o c a t e d at 30% of the maximum energy.
-- TIIEORT-CARLO D T S
N
%-
EXpElqimmT~d ( 4 )
I
UJ
/
2078.05
key
1.10
~
\
1.05
2t
1.0O
0.95 t 1
10
20 Ic ( i t ~ v !
Fig.
3:
D T S e f f i c i e n c y c u r v e for 1 to M e V n e u t r o n s . S p e c t r u m d i s c r i m i n a t o r at 30% of the m a x i m u m energy. The points at 2.446 and 14.04 M e V were obtained e x p e r i m e n t a l l y . T h e s o l i d line is the Monte Carlo calculation.
C A R L O DTS
5~![
A clear c o r r e l a t i o n between the b~ased efficiency and the carbon hydrogen cross section has been observed. Particularly, good accuracy in interpolation of the e f f i c i e n c y for various neutron energies was achieved following formula: ~B/~H
and the by
= a I + a2: C + a3~ H
where ~B oC oH al,a2,a 3
is the b i a s e d efficiency, is the carbon elastic plus inelastic is the H ( n , n ) H cross sections, are constants.
scattering
cross
sections,
The values of a I, a 2 and a 3 were o b t a i n e d by least squares fit between the b i a s e d e f f i c i e n c y and the cross sections. The e f f i c i e n c y has been calculated at several s e l e c t e d neutron energies, at points where the carbon cross sec%ion shows the largest variations. Updated results of the fits are p r e s e n t e d in table 3 for three fractional bias energies, namely: 0.30, 0.35 and 0.40 of the m a x i m u m energy. These e f f i c i e n c i e s were c a l c u l a t e d at zero d i s c r i m i n a t i o n Lower level. The average a c c u r a c y o b t a i n e d in the interpolation goes from 0.8 to 1.8% at the fractional biases of 0.30 and 0.40, respectively.
Table
3:
Fractional Bias Energy 0.30 0.35 0.40
C o e f f i c i e n t s of the i n t e r p o l a t i o n to the DTS biased efficiency.
formula
aI
a2
a3
(x 10-3b -I )
(x 10-4b -2 )
(x 10-4b -2)
9.474 8.798 8.134
1.901 1.664 1.522
1.576 1.710 1.719
applicable
Reduced Chi Square 1.04 1.19 i.i0
Figure 4 shows the u n c e r t a i n t i e s involved in the c a l c u l a t e d efficiency. The u n c e r t a i n t y indicated for the H(n,n)H cross section has been taken from ENDF/B-VI (0.3%). The p r e d o m i n a n t c o n t r i b u t i o n s to the total u n c e r t a i n t y are from the h y d r o g e n areal density and statistics in the calculation, except near the carbon resonance at 2078 keV were the m u l t i p l e scattering u n c e r t a i n t y is predominant. The u n c e r t a i n t y in the c o r r e c t i o n for lost coincidences has not been included in fig. 4 since it depends on the d i s c r i m i n a t i o n level used. This u n c e r t a i n t y is e s t i m a t e d to be around 10% of the correction (i.e. 0.4%) and has little c o n t r i b u t i o n in the total uncertainty. The total u n c e r t a i n t y is between 0.8 to 1.0% except near the carbon resonance at 2078 keV, where it reaches the m a x i m u m value of 1.2% The c o m p a r i s o n between the results of proton recoil spectra calculated by the code CARLO DTS, in c o m p a r i s o n to e x p e r i m e n t a l spectra o b t a i n e d at 2.446 and 14.04 MeV, is shown in figures 5 and 6. The fitting between the calculated and the e x p e r i m e n t a l spectra was p e r f o r m e d using a revised version of a code written by Meier (1984), which takes into account the Poisson statistics in the number of p h o t o e l e c t r o n s detected. The agreement between the calculated and the e x p e r i m e n t a l s p e c t r u m shapes is excellent, indicating little s e n s i t i v i t y with respect to the s e l e c te d bias energy.
3tC
M.S.
Dl.~s and R. G. J¢ H>,SO',
|
/
Total
........ ..--~'- .
.................
//
H a~eal
density z
%
?(n,.)H
.u.
- ....................
~" I
~
,
-
]
.- /
-- ~
Oiscciminat~on
level
~/~ I
~ I
T
I0 N :UTRON
4:
. "
+ C(n,.Ic . -
/
. .
"
/ /I
-/~ ....
C(n,n)C
"
Fig.
StatistLcs
ENERGY
l
I
15
(MeV)
Uncertainties in t h e C A R L O D T S The indicated error corresponds standard deviation.
efficiency to the
calculation relative
E. : 2.44 MeV 2000 Z Z
z
1000
8
00'|
'
I
I
I
I
10
20
30
40
50
~
'
60
CHANNEL
Fig.
5:
Comparison between experimental(dots) and calculated proton-recoil spectra ( s o l i d line) at 2.446 MeV n e u t r o n energy.
C A R L O DTS
5~(
En= 140 MeV Spectrum A
Spectrum 8
== o ()
~ •
0
Spectrum C iOS at 30% of max enerc3y
I
I
10
20
30
I
I
I
I
40
50
60
70
~"~ 80
90
Channel
Fig.
6:
Comparison between e x p e r i m e n t a l (dots) and calculated proton-recoil spectra (solid line) at 14.04 MeV neutron energy. In this figure s p e c t r u m A corresponds to singles from the first scintillator; spectrum B are coincidences between the two scintillators and spectrum C is the sum s p e c t r u m which approximates the ideal thin scintillator response.
~0-~
NI. S. Dl.~s and R. O. Jo~Nso~.
REFERENCES
i. C A S H W E E L E.D. Carlos m e t h o d
and EVERETT for random
C.J. (1959) A practical manual walk problems. Pergamon, NY.
on
the
Monte
2. DIAS M.S. (1988) D e v e l o p m e n t and a p p l i c a t i o n of a detector for the absolute m e a s u r e m e n t of the neutron fluence rate in the MeV energy region PhD Thesis (Instituto de Pesquisas E n e r g e t i c a s e Nucleares University of Sao Paulo, Brazil, in portuguese). 3. DIAS M.S., JOHNSON R.G. R e s p o n s e c a l c u l a t i o n of the Dual Thin Scintillator (DTS) neutron detector by the Monte Carlo method. To be published. 4. DIAS M.S.; JOHNSON R.G. and WASSON O.A. (1984) Design and c a l i b r a t i o n of an absolute flux detector for 1-15 MeV neutrons. Nuclear Instrum. and Meth. in Phys. Research, 224, 532. 5. DIAS M.S.; C A R L S O N A.D.; JOHNSON R.G. and W A S S O N O.A. (1985) A p p l i c a t i o n of the Dual Thin S c i n t i l l a t o r neutron flux monitor in a 235U(n,f) cross section measurement. P r o c e e d i n g s of an A d v i s o r y Group Meeting on Nuclear S t a n d a r d R e f e r e n c e Data, p. 467. Geel, 12-16 November 1984: IAEA-TECDOC-335. 6. E N D F / B - V (1979), Data file for 12C (MAT 1306), e v a l u a t i o n by FU C.Y. and PEREY F.G. (ORNL), B N L - N C S - 1 7 5 4 1 (ENDF-201), ed., KINSEY R., available from the National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY. 7. E N D F / B - V (1979), Data file for IH (MAT 1301), evaluation by STEWART L.; LABAUVE R.J. and YOUNG P.G. (LANL), B N L - N C S - 1 7 5 4 1 (ENDF-201) ed., KINSEY R.. A v a i l a b l e from the National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY. 8.
D.W.; PURSER BOYCE J.R.; EPPERSON BILPUCH E.G.; NEWSON inelastic scattering Eng., 61, 521. GLASCOW
F.O.; HOGUE H.; C L E M E N T E J.C.; STELZER K.; MACK G.; D.H.; BUCCINO S.G.; LISOWSKI P.W.; GLENDINNING S.G.; H.W. and GOULD C.R. (1976) D i f f e r e n c i a l elastic and of 9 to 15 MeV neutrons from carbon. Nucl. Sci.
9. HOPKINS J.C. and BREIT G. (1971) IH(n.n)iH scattering r e q u i r e d for high p r e c i s i o n f a s t - n e u t r o n measurements. A9, 137. i0. M E I E R M.M. (1984) Data reduction programs for Harris Bureau of Standards Internal Report, (February 1978, 1984)
observables Nucl.Data Tables,
computer. National revised September
b~.~)
,11 i ~ i q - i l , ' " ) ~I)q~) (" i')')[ P,.r:Liin~)u P r c ~
~ll
pk
CARLO DTS" A MONTE CARLO CODE FOR THE DUAL THIN SCINTILLATOR NEUTRON DETECTOR M.~,uRo S. DIAS a n d RONALD G. JOHNSON* Instituto de Pesquisas Energ6ticas e Nucleares, CNEN/SP, Caixa Postal 11049, CEP 05499. S8o Paulo, SP, Brazil *National Institute of Standards and Technolog,,, Gaithersburg, MD 20899, U.S.A.
A Monte Carlo code called C A R L O DTS, developed for the e f f i c i e n c y a n d p r o t o n r e c o i l s p e c t r a c a l c u l a t i o n of the Dual T h i n S c i n t i l l a t o r (DTS) n e u t r o n d e t e c t o r is d e s c r i b e d . The c o d e C A R L O DTS c o v e r s the n e u t r o n e n e r g y r a n g e b e t w e e n 1 and 20 MeV. The c r o s s s e c t i o n s a n d a n g u l a r distributions were t a k e n f r o m the E N D F / B - V d a t a file for the n u c l e a r reactions involved: H(n.n)H, C(n,n)C and inelastic scattering, (n,~), (n,n')3a reactions on carbon-12. The theoretical c a l c u l a t i o n s are c o m p a r e d to experimental results at two n e u t r o n e n e r g i e s , n a m e l y : 2 . 4 4 6 a n d 14.04 MeV, obtained by m e a n s of the T i m e C o r r e l a t e d A s s o c i a t e d P a r t i c l e T e c h n i q u e .
INTRODUCTION
The M o n t e C a r l o code C A R L O DTS, d e v e l o p e d for the e f f i c i e n c y &nd p r o t o n r e c o i l s p e c t r a c a l c u l a t i o n of the D U A L T H I N S C I N T I L L A T O R (DTS) n e u t r o n d e t e c t o r is d e s c r i b e d . C o m p l e t e d e t a i l s a b o u t the DTS c h a r a c t e r i s t i c s and performance have b e e n p u b l i s h e d (Dias et al., 1984, D i a s et al., 1985 and Dias, 1988). B a s i c a l l y , T h e DTS n e u t r o n d e t e c t o r c o n s i s t s of two thin c y l i n d r i c a l p i e c e s of plastic scintillators, 0.254 cm thick, 4.70 and 4.90 c m in diameter, r e s p e c t i v e l y , p l a c e d c o a x i a l in f r o n t of each other ( f i g u r e i). Each s c i n t i l l a t o r w a s c o u p l e d to a p a i r of p h o t o t u b e s , by m e a n s of a p e r s p e x light guide, in a h e a d - o n g e o m e t r y . A d e t a i l e d d e s c r i p t i o n of the c o d e CARLO DTS will be p u b l i s h e d e l s e w h e r e (Dias and J o h n s o n , 1990). In the p r e s e n t paper, only the main aspects are emphasized. T h e c o d e C A R L O D T S c o v e r s the n e u t r o n e n e r g y r a n g e between 1 and 20 MeV. The d e t e c t o r p a r a m e t e r s a n d the c o o r d i n a t e s y s t e m orientation are s h o w n in F i g u r e I. T h e d e t e c t o r is c o n s i d e r e d as a c y l i n d e r of h e i g h t H T and r a d i u s R, f i l l e d w i t h s c i n t i l l a t o r c o n t a i n i n g h y d r o g e n and c a r b o n of c o n c e n t r a t i o n s NH and N C, r e s p e c t i v e l y . T h e n e u t r o n beam, w i t h a r a d i u s R N, is a s s u m e d to be homogeneous and normally incident to the d e t e c t o r frontface. Nonhomogeneity or o t h e r i n c i d e n c e a n g l e s m a y be i n t r o d u c e d by changing subroutine SOURCE
* Formely
National
Bureau
of S t a n d a r d s . 295
296
M . S . DI.~,s and R. O. JoHxso'~
according to the case of interest.
Z,W
Zone 3 Zone 2 (Scintillator 2)
z, HT
I ~ o-''~--'-~ . ~
, • HI __ _
/ Zone 1 (Scintillator 11
~
I.°-'-
y,v
I 5 <.I
~eutron Beam (Radius R N )
Fig.
i:
C o o r d i n a t e system. scintillators.
ZONE 3 is the region
outside the
The cylindrical regions where the scintillators 1 and 2 are iocatedare called ZONES 1 and 2, respectively. ZONE 3 is located outside the scintillators. The c o n t r i b u t i o n of the perspex light guide in the detector response is not considered. It has been e s t i m a t e d to be negligible for neutron beam diameters much smaller than the detector diameter (Dias, 1984). Easy m o d i f i c a t i o n s can be introduced in the code to calculate the response for neutron beams comparable or larger than the scintillators. Because the scintillators are thin, a neutron with energy in the range of 1 to 15 MeV will have, on the average, only one collision inside the detector. The m a x i m u m number of collisions is b e l o w nine and the m a j o r i t y of neutrons escape the detector before being absorbed. To achieve a statistical u n c e r t a i n t y around 0.4% about 105 histories are necessary, applying the forced c o l l i s i o n technique. Good pulse height distributions are o b t a i n e d with about 4 x 105 histories.
NEUTRON KINEMATICS Table 1 shows the reactions which c o n t r i b u t e to the DTS detector response, including the Q value and the first and second reaction thresholds. The reaction cross sections were c o n s i d e r e d to be zero below the second reaction threshold. All cross section values were taken from the E N D F / B - V evaluation (ENDF/B-V, 1979). Intermediate values to those c o n t a i n e d in the cross section tables are obtained by linear interpolation, for all reactions involved. The
CARLO
t a b l e s c o n t a i n m e s h p o i n t s appropriate m i n i m i z e i n t e r p o l a t i o n errors, m a i n l y
Table
i:
DTS
29"7,
to the c r o s s s e c t i o n s t r u c t u r e near the c a r b o n ~ e s o n a n c e s .
Reactions which contribute to the S c i n t i l l a t o r (DTS) d e t e c t o r r e s p o n s e .
Reaction
Q (MeV)
iH(n,n)iH 12C(n,n)12 C 12C(n,n'~)12C 12C(n,~)9Be 12C(n,n')12*C * 8Be + ~ 3~
-4.433 -5.704 -7.656 +0.289 +0.102
i st T h r e s h o l d (MeV) _ _ 4.805 6.183 8.299 -
Dual
in o r d e r %o
Thin
2 nd T h r e s h o l d (MeV)
5.840 6.428 8.359
The a n g u l a r d i s t r i b u t i o n for the e l a s t i c s c a t t e r i n g on hydrogen, H(n,n)H, was o b t a i n e d f r o m H o p k i n s a n d B r e i t (1971). T h e a n g u l a r d i s t r i b u t i o n d a t a for the e l a s t i c s c a t t e r i n g on c a r b o n , C ( n , n ) C , has b e e n o b t a i n e d f r o m ENDF/B-V (1979). Since the coefficients for the e x p a n s i o n in L e g e n d r e p o l y n o m i n a l s are g i v e n for the c e n t e r - o f - m a s s system, it was n e c e s s a r y a t r a n s f o r m a t i o n to the laboratory s y s t e m in o r d e r to be c o m p a t i b l e w i t h the M o n t e C a r l o code. For the C ( n , n ' Y ) C r e a c t i o n the a n i s o t r o p y in the a n g u l a r distribution of s c a t t e r e d n e u t r o n s has b e e n c o n s i d e r e d . T h e L e g e n d r e c o e f f i c i e n t s w e r e t a k e n f r o m G l a s g o w et al. (1976) for the e n e r g y r a n g e b e t w e e n 8970 and 1 4 9 3 0 KeY. For the r e m a i n i n g e n e r g y r a n g e ( b e t w e e n 4812 a n d 2 0 0 0 0 keV) the c o e f f i c i e n t s were t a k e n f r o m the E N D F / B - V (1979). The d e t e c t i o n of g a m m a - r a y s f r o m 1 2 C ( n , n ' y ) 1 2 C reaction has been c a l c u l a t e d s e p a r a t e l y by m e a n s of a s i m p l i f i e d M o n t e C a r l o c o d e as d e s c r i b e d b y Dias (1988). T h e c o r r e c t i o n f a c t o r due to this e f f e c t is less t h a n 0.4% for a n e u t r o n b e a m i n c i d e n t on the d e t e c t o r axis. For f i n i t e b e a m s i z e s the c o r r e c t i o n t e n d s to be lower. T h e a n g u l a r d i s t r i b u t i o n of a l p h a s f r o m the 1 2 C ( n , a ) 9 B e reaction has b e e n c o n s i d e r e d as i s o t r o p i c in the l a b o r a t o r y system. T h i s s i m p l i f i c a t i o n has v e r y l i t t l e e f f e c t on the r e s u l t s s i n c e the discrimination level of the proton-recoil s p e c t r u m can a l w a y s be c h o s e n a b o v e the c h a n n e l c o r r e s p o n d i n g to the maximum e n e r g y of the a l p h a p a r t i c l e s p r o d u c e d b y this r e a c t i o n . The a n g u l a r d i s t r i b u t i o n of a l p h a s f r o m the 1 2 C ( n , n ' ) 3 a r e a c t i o n has b e e n c o n s i d e r e d as i s o t r o p i c in the l a b o r a t o r y system. The Q value for t h ~ react/on has b e e n d e t e r m i n e d c o n s i d e r i n g all the e x c i t a t i o n e n e r g y levels, real or virtual c o n t a i n e d in the E N D F / B - V (1979). For e a c h n e u t r o n e n e r g y a set of excitation p r o b a b i l i t i e s v a l u e s , Pi, h a s b e e n g e n e r a t e d for the c o m p o u n d n u c l e u s states. T h i s p r o b a b i l i t y is the r a t i o b e t w e e n the p a r t i a l c r o s s s e c t i o n for a given e x c i t a t i o n s t a t e and the t o t a l c r o s s s e c t i o n for the ~hat n e u t r o n e n e r g y . T h e s e c r o s s s e c t i o n v a l u e s w e r e a l s o o b t a i n e d f r o m E N D F / B - V (1979). APPLICATION
OF THE
FORCED
FIRST
COLLISION
TECHNIQUE
T h i s t e c h n i q u e a l l o w s a r e d u c t i o n in the n u m b e r of h i s t o r i e s followed by the M o n t e C a r l o code, w i t h o u t s i g n i f i c a n t loss in the s t a t i s t i c a l accuracy a c h i e v e d . It was u s e d to define the point w h e r e the first neutron collosion will occc~c or
298
M . S . DIAs and R. G. JoH~SO'~
to make the neutron collide p r e f e r e n t i a l l y
with
F o r c e d first c o l l i s i o n
the h y d r o g e n atoms in r/he scintillator.
inside
the d e t e c t o r
The DTS d e t e c t o r has high t r a n s m i s s i o n for M e V n e u t r o n s , and consequently a low detection efficiency. T h e r e f o r e a g r e a t n u m b e r of incident n e u t r o n s should be n e c e s s a r y to get a low s t a t i s t i c a l u n c e r t a i n t y , d e m a n d i n g a long p r o c e s s ~ g tune. T h i s p r o b l e m has b e e n s o l v e d by c o n f i n i n g the n e u t r o n first collision inside the d e t e c t o r (Cashwell and Everett, 1959). T h i s p r o c e d u r e r e s u l t s in a 100% detection e f f i c i e n c y . T h e r e d u c t i o n in the p r o c e s s i n g time r e a c h e s a f a c t o r a r o u n d 20 at 15 MeV. To the c a l c u l a t e d e f f i c i e n c y an a p p r o p r i a t e f a c t o r is applied. The d i s t a n c e to s u b s e q u e n t collisions are c a l c u l a t e d in the u s u a l way. F o r c e d first c o l l i s i o n on h y d r o g e n and ZONE 1 T a b l e 2 s h o w s the p e r c e n t a g e c o n t r i b u t i o n in the DTS detector e f f i c i e n c y f r o m e v e n t s o r i g i n a t e s b y n e u t r o n f i r s t c o l l i s i o n on h y d r o g e n and c a r b o n for d i f f e r e n t n e u t r o n e n e r g i e s . B e t w e e n 8 9 - 9 6 % c o n t r i b u t i o n c o m e s f r o m events w h e r e the f i r s t n e u t r o n c o l l i s i o n w a s on h y d r o g e n . Table
2:
C o n t r i b u t i o n to the DTS d e t e c t i o n efficiency of e v e n t s o r i g i n a t e d by n e u t r o n f i r s t c o l l i s i o n on h i d r o g e n , c a r b o n a n d Z O N E S 1 a n d 2 (in p e r c e n t ) .
Neutron Energy (MeV) 1.0 2.4 14.0
Contribution Hydrogen 89.0 93.8 96.4
to the E f f i c i e n c y
Carbon
ZONE
ii.0 6.2 3.6
95.6 96.7 98.6
1
(%) ZONE
2
4.4 3.3 1.4
S i n c e the r a t i o b e t w e e n the t o t a l c r o s s s e c t i o n s of h y d r o g e n and carbon are in the r a n g e of 0.5 to 3, for 1 to 15 M e V n e u t r o n s , the fraction of n e u t r o n s w h i c h h a v e f i r s t c o l l i s i o n on h y d r o g e n is b e t w e e n 30 a n d 77%. Therefore it b e c o m e s c o n v e n i e n t to f o r c e the f i r s t c o l l i s i o n on h y d r o g e n in o r d e r to r e d u c e the p r o c e s s i n g t i m e b y a f a c t o r up to a b o u t 3. A f r a c t i o n fH of the i n c i d e n t n e u t r o n s is f o r c e d to c o l l i d e against h y d r o g e n a n d (i - fH ) c o l l i d e a g a i n s t c a r b o n atoms. T h e n u m b e r of c o u n t s in the p r o t o n - r e c o i l s p e c t r u m b e c o m e s r e a l numbers. The n u m b e r o f p r o c e s s e d neutrons, N s, g i v e s r i s e to a l a r g e r n u m b e r of c o u n t s in the p r o t o n - r e c o i l s p e c t r u m , N' s. T h e p r o c e s s i n g t i m e is r e d u c e d b y the f a c t o r N ' s / N s. At 14 M e V and using fH = 0.9, t h i s f a c t o r is e q u a l to 2.4. As s h o w n in t a b l e 2, b e t w e e n 95 to 99% of the c o u n t s w h i c h c o n t r i b u t e to the e f f i c i e n c y are o r i g i n a t e d b y a n e u t r o n first collision in the first scintillator (ZONE1). B e c a u s e of the h i g h t r a n s m i s s i o n t h r o u g h the detector for 1 to 15 M e V n e u t r o n s , a b o u t h a l f of the n e u t r o n s a r e i n c i d e n t in ZONE 1 and h a l f are i n c i d e n t in ZONE 2. T h e r e f o r e a p p l y i n g the f o r c e d f i r s t c o l l i s i o n in the f i r s t s c i n t i l l a t o r (ZONE I) it is p o s s i b l e to r e d u c e the p r o c e s s i n g time b y a f a c t o r of 2. A f r a c t i o n f of t h e i n c i d e n t n e u t r o n s is f o r c e d to c o l l i d e in ZONE 1 s a n d (i - fs ) c o l l i d e in ZONE 2. T h e n u m b e r of p r o c e s s e d n e u t r o n s N' s g i v e s rise to a l a r g e r n u m b e r of c o u n t s , N" s. T h e p r o c e s s i n g t i m e is r e d u c e d b y the factor N"s/N' s. T h e t o t a l r e d u c t i o n , i n c l u d i n g the f o r c e d collision on hydrogen b e c o m e s N " s / N s. At 14 M e V a n d u s i n g fs = fH = 0.9, the t o t a l r e d u c t i o n is 4.3.
C A R L O DTS
LOST
COINCIDENCES
2t)~
EFFECT
For M e V n e u t r o n s , t h e r e is a l a r g e e f f e c t due to the e s c a p e of p r o t o n s from the forward face of the f i r s t s c i n t i l l a t o r in the DTS d e t e c t o r . However, the c o r r e s p o n d i n g d i s t o r t i o n in the p r o t o n r e c o i l spectrum is eliminated e x p e r i m e n t a l l y by d e t e c t i n g t h e s e e s c a p e d p r o t o n s at the s e c o n d scintillator, p l a c e d b e h i n d the f i r s t one. S i n c e t h i s p r o c e d u r e r e q u i r e s a coincidence signal, t h e r e is a l o w e r limit for the first scintillator pulse amplitude to be detectable. The s u m - c o i n c i d e n c e p u l s e s o r i g i n a t e d f r o m p u l s e s in the first scintillator b e l o w this limit w i l l be lost. S o m e of t h e s e lost s u m - c o i n c i d e n c e pulses can have an a m p l i t u d e a b o v e the d i s c r i m i n a t i o n l e v e l a d o p t e d for the detec=ion e f f i c i e n c y c a l c u l a t i o n ( u s u a l l y 30% of the m a x i m u m p r o t o n e n e r g y ) . T h e r e f o r ~ a c o r r e c t i o n for t h e s e lost c o i n c i d e n c e s is r e q u i r e d . At low neutron energies t h e r e are s u m - c o i n c i d e n c e p u l s e s a l s o due to n e u t r o n m u l t i p l e scattering inside the s c i n t i l l a t o r s . T h e loss of s u c h e v e n t s m u s t be t a k e n into a c c o u n t . The lost c o i n c i d e n c e s e f f e c t c a u s e d b y the e s c a p e of p r o t o n s has b e e n i n c o r p o t a t e d in the C A R L O DTS code, by c a l c u l a t i n g the p r o t o n e n e r g y fraction d e p o s i t e d i n s i d e e a c h s c i n t i l l a t o r . T h e total l i g h t p r o d u c e d by a g i v e n n e u t r o n in the M o n t e C a r l o c o d e has b e e n d i v i d e d into two parts: the first one c o r r e s p o n d s to the t o t a l l i g h t p r o d u c e d in the f i r s t s c i n t i l l a t o r (ZONE i) and the s e c o n d one c o r r e s p o n d s to the t o t a l l i g h t p r o d u c e d in the second s c i n t i l l a t o r (ZONE 2). T h e e v e n t s w h i c h p r o d u c e a l i g h t y i e l d b e l o w a g i v e n t h r e s h o l d are r e j e c t e d . In this way, the loss of c o i n c i d e n c e s c a u s e d by m u l t i p l e scattering are a l s o i n c l u d e d . T h e c o r r e c t i o n for lost c o i n c i d e n c e s are s h o w n in fig. 2 as a f u n c t i o n of the f r a c t i o n a l d i s c r i m i n a t o r l o w e r l e v e l (ratio b e t w e e n the c h a n n e l at the d i s c r i m i n a t o r l o w e r l e v e l a n d the c h a n n e l at the e n d of the spectrum), for several e n e r g i e s of the i n c i d e n t n e u t r o n , in t h i s figure, the discrimination level adopted for the c a l c u l a t e d e f f i c i e n c y c o r r e s p o n d s to 30% of the m a x i m u m p r o t o n e n e r g y .
too
~ "~t
I
/
1.0 M eV
z
o
r'r
0.90
n.-
"~!~14.0
MeV
I 0.10 DLL
1 0.15
O (j
0.85
I 0.05 FRACTIONAL
Fig.
2:
L o s t c o i n c i d e n c e s c o r r e c t i o n as a f u n c t i o n f r a c t i o n a l l o w e r d i s c r i m i n a t i o n level.
of
the
300
M . S . DIAS and R. G. J o H s s o ~
VARIATION
IN L I G H T C O L L E C T I O N
The v a r i a t i o n in the l i g h t c o l l e c t i o n e f f i c i e n c y at d i f f e r e n t points in the s c i n t i l l a t o r has b e e n t a k e n i n t o account by assuming a quadratic d e p e n d e n c e of the a v e r a g e l i g h t r e s p o n s e as a f u n c t i o n of the d i s t a n c e f r o m the c e n t e r of the s c i n t i l l a t o r . T h e c o e f f i c i e n t s w e r e o b t a i n e d b y a l e a s t square fit to e x p e r i m e n t a l l i g h t r e s p o n s e v a l u e s (Dias et al., 1984).
RESULTS
OF
THE
CALCULATIONS
T h e b e h a v i o r of t h e c a l c u l a t e d b i a s e d ( t h e w o r d b i a s e d m e a n i n g a b o v e a g i v e n d i s c r i m i n a t o r l e v e l ) e f f i c i e n c y w i t h n e u t r o n e n e r g y is s h o w n in fig. 3 t o g e t h e r w i t h t w o e x p e r i m e n t a l p o i n t s o b t a i n e d at 2 . 4 4 6 a n d 1 4 . 0 4 M e V (Dias et al., 1984). The curve follows essentially the H(n,n)H cross section. Contributions from C(n,n)C and 12C(n,n'y)12C cross section cause some small i r r e g u l a r i t i e s in the e f f i c i e n c y c u r v e , m a i n l y in the regions of carbon r e s o n a n c e s . For this curve, the bias e n e r g y w a s l o c a t e d at 30% of the maximum energy.
-- TIIEORT-CARLO D T S
N
%-
EXpElqimmT~d ( 4 )
I
UJ
/
2078.05
key
1.10
~
\
1.05
2t
1.0O
0.95 t 1
10
20 Ic ( i t ~ v !
Fig.
3:
D T S e f f i c i e n c y c u r v e for 1 to M e V n e u t r o n s . S p e c t r u m d i s c r i m i n a t o r at 30% of the m a x i m u m energy. The points at 2.446 and 14.04 M e V were obtained e x p e r i m e n t a l l y . T h e s o l i d line is the Monte Carlo calculation.
C A R L O DTS
5~![
A clear c o r r e l a t i o n between the b~ased efficiency and the carbon hydrogen cross section has been observed. Particularly, good accuracy in interpolation of the e f f i c i e n c y for various neutron energies was achieved following formula: ~B/~H
and the by
= a I + a2: C + a3~ H
where ~B oC oH al,a2,a 3
is the b i a s e d efficiency, is the carbon elastic plus inelastic is the H ( n , n ) H cross sections, are constants.
scattering
cross
sections,
The values of a I, a 2 and a 3 were o b t a i n e d by least squares fit between the b i a s e d e f f i c i e n c y and the cross sections. The e f f i c i e n c y has been calculated at several s e l e c t e d neutron energies, at points where the carbon cross sec%ion shows the largest variations. Updated results of the fits are p r e s e n t e d in table 3 for three fractional bias energies, namely: 0.30, 0.35 and 0.40 of the m a x i m u m energy. These e f f i c i e n c i e s were c a l c u l a t e d at zero d i s c r i m i n a t i o n Lower level. The average a c c u r a c y o b t a i n e d in the interpolation goes from 0.8 to 1.8% at the fractional biases of 0.30 and 0.40, respectively.
Table
3:
Fractional Bias Energy 0.30 0.35 0.40
C o e f f i c i e n t s of the i n t e r p o l a t i o n to the DTS biased efficiency.
formula
aI
a2
a3
(x 10-3b -I )
(x 10-4b -2 )
(x 10-4b -2)
9.474 8.798 8.134
1.901 1.664 1.522
1.576 1.710 1.719
applicable
Reduced Chi Square 1.04 1.19 i.i0
Figure 4 shows the u n c e r t a i n t i e s involved in the c a l c u l a t e d efficiency. The u n c e r t a i n t y indicated for the H(n,n)H cross section has been taken from ENDF/B-VI (0.3%). The p r e d o m i n a n t c o n t r i b u t i o n s to the total u n c e r t a i n t y are from the h y d r o g e n areal density and statistics in the calculation, except near the carbon resonance at 2078 keV were the m u l t i p l e scattering u n c e r t a i n t y is predominant. The u n c e r t a i n t y in the c o r r e c t i o n for lost coincidences has not been included in fig. 4 since it depends on the d i s c r i m i n a t i o n level used. This u n c e r t a i n t y is e s t i m a t e d to be around 10% of the correction (i.e. 0.4%) and has little c o n t r i b u t i o n in the total uncertainty. The total u n c e r t a i n t y is between 0.8 to 1.0% except near the carbon resonance at 2078 keV, where it reaches the m a x i m u m value of 1.2% The c o m p a r i s o n between the results of proton recoil spectra calculated by the code CARLO DTS, in c o m p a r i s o n to e x p e r i m e n t a l spectra o b t a i n e d at 2.446 and 14.04 MeV, is shown in figures 5 and 6. The fitting between the calculated and the e x p e r i m e n t a l spectra was p e r f o r m e d using a revised version of a code written by Meier (1984), which takes into account the Poisson statistics in the number of p h o t o e l e c t r o n s detected. The agreement between the calculated and the e x p e r i m e n t a l s p e c t r u m shapes is excellent, indicating little s e n s i t i v i t y with respect to the s e l e c te d bias energy.
3tC
M.S.
Dl.~s and R. G. J¢ H>,SO',
|
/
Total
........ ..--~'- .
.................
//
H a~eal
density z
%
?(n,.)H
.u.
- ....................
~" I
~
,
-
]
.- /
-- ~
Oiscciminat~on
level
~/~ I
~ I
T
I0 N :UTRON
4:
. "
+ C(n,.Ic . -
/
. .
"
/ /I
-/~ ....
C(n,n)C
"
Fig.
StatistLcs
ENERGY
l
I
15
(MeV)
Uncertainties in t h e C A R L O D T S The indicated error corresponds standard deviation.
efficiency to the
calculation relative
E. : 2.44 MeV 2000 Z Z
z
1000
8
00'|
'
I
I
I
I
10
20
30
40
50
~
'
60
CHANNEL
Fig.
5:
Comparison between experimental(dots) and calculated proton-recoil spectra ( s o l i d line) at 2.446 MeV n e u t r o n energy.
C A R L O DTS
5~(
En= 140 MeV Spectrum A
Spectrum 8
== o ()
~ •
0
Spectrum C iOS at 30% of max enerc3y
I
I
10
20
30
I
I
I
I
40
50
60
70
~"~ 80
90
Channel
Fig.
6:
Comparison between e x p e r i m e n t a l (dots) and calculated proton-recoil spectra (solid line) at 14.04 MeV neutron energy. In this figure s p e c t r u m A corresponds to singles from the first scintillator; spectrum B are coincidences between the two scintillators and spectrum C is the sum s p e c t r u m which approximates the ideal thin scintillator response.
~0-~
NI. S. Dl.~s and R. O. Jo~Nso~.
REFERENCES
i. C A S H W E E L E.D. Carlos m e t h o d
and EVERETT for random
C.J. (1959) A practical manual walk problems. Pergamon, NY.
on
the
Monte
2. DIAS M.S. (1988) D e v e l o p m e n t and a p p l i c a t i o n of a detector for the absolute m e a s u r e m e n t of the neutron fluence rate in the MeV energy region PhD Thesis (Instituto de Pesquisas E n e r g e t i c a s e Nucleares University of Sao Paulo, Brazil, in portuguese). 3. DIAS M.S., JOHNSON R.G. R e s p o n s e c a l c u l a t i o n of the Dual Thin Scintillator (DTS) neutron detector by the Monte Carlo method. To be published. 4. DIAS M.S.; JOHNSON R.G. and WASSON O.A. (1984) Design and c a l i b r a t i o n of an absolute flux detector for 1-15 MeV neutrons. Nuclear Instrum. and Meth. in Phys. Research, 224, 532. 5. DIAS M.S.; C A R L S O N A.D.; JOHNSON R.G. and W A S S O N O.A. (1985) A p p l i c a t i o n of the Dual Thin S c i n t i l l a t o r neutron flux monitor in a 235U(n,f) cross section measurement. P r o c e e d i n g s of an A d v i s o r y Group Meeting on Nuclear S t a n d a r d R e f e r e n c e Data, p. 467. Geel, 12-16 November 1984: IAEA-TECDOC-335. 6. E N D F / B - V (1979), Data file for 12C (MAT 1306), e v a l u a t i o n by FU C.Y. and PEREY F.G. (ORNL), B N L - N C S - 1 7 5 4 1 (ENDF-201), ed., KINSEY R., available from the National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY. 7. E N D F / B - V (1979), Data file for IH (MAT 1301), evaluation by STEWART L.; LABAUVE R.J. and YOUNG P.G. (LANL), B N L - N C S - 1 7 5 4 1 (ENDF-201) ed., KINSEY R.. A v a i l a b l e from the National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY. 8.
D.W.; PURSER BOYCE J.R.; EPPERSON BILPUCH E.G.; NEWSON inelastic scattering Eng., 61, 521. GLASCOW
F.O.; HOGUE H.; C L E M E N T E J.C.; STELZER K.; MACK G.; D.H.; BUCCINO S.G.; LISOWSKI P.W.; GLENDINNING S.G.; H.W. and GOULD C.R. (1976) D i f f e r e n c i a l elastic and of 9 to 15 MeV neutrons from carbon. Nucl. Sci.
9. HOPKINS J.C. and BREIT G. (1971) IH(n.n)iH scattering r e q u i r e d for high p r e c i s i o n f a s t - n e u t r o n measurements. A9, 137. i0. M E I E R M.M. (1984) Data reduction programs for Harris Bureau of Standards Internal Report, (February 1978, 1984)
observables Nucl.Data Tables,
computer. National revised September