V N U . J O U R N A L O F S C IE N C E , M a th e m a tic s - P h y s ic s , T.xx, N 02, 2 0 0 4
S U R V E Y I N G T H E H P G e G A M M A D E T E C T O R A B S O L U T E E F F I C I E N C Y
T r a n T ri V ie n , D o a n Q u a n g T u y e n , T r a n V i e t N h a n H a o , D o a n T h a n h S o n , N g u y e n T r u n g T i n h
College o f Science, V N U
A b s tra c t. In many nuclear experiments, the energy efficiency of detector is a param eter without negligibility. In this paper, the absolute efficiency of HPGe detector is surveyed and mearsured at different distances from detector and different gamma energies.
1. I n t r o d u c t i o n
I n m an y n u c le a r e x p e r im e n ta l m e a s u r e m e n ts , t h e d e te r m in e d re s u lts d e p e n d on e x p e r im e n ta l p a r a m e t e r s , one of th e s e p a r a m e t e r s is a b so lu te detector efficiency. B u t u n f o r t u n a t e l y th e efficiency of n u c le a r d e te c to r is n o t co n stan t, it d e p e n d on th e e n erg y of m e a s u r e m e n ta l ra d ia tio n . So t h a t , m ak in g efficiency c a lib ra tio n of d e te c to r is n e c e ssa ry . I n th is p a p e r, t h e a b s o lu te efficiency c alib ratio n of H P G e g a m m a d e te c to r is su rvey ed .
A b s o l u t e e f f i c i e n c y o f d e t e c t o r TỊabs a t a e n e r g y v a l u e i s d e t e r m i n e d t h r o u g h ,
p h o to p e a k a re a , s , by e q u a tio n below:
s
ị Vn = — —
labs A .I.t(1)
w here: A -activity of ra d io a c tiv ity source I - ra d io a c tiv ity e m iss io n p ro b ab ility t. - m e a s u r e m e n ta l tim e
As e q u a tio n (1), t h e e rr o r of efficiency d e p e n d on t h e p h o to p e a k a rea (S). In o rd er to d e c re a se s tro n g ly th e e rro r of efficiency. T h e m e a s u r e m e n ta l a re a of p h o to p ea k sh o u ld d e te r m in e w ith h ig h precision. To reso lv e t h is problem, some d e te r m in a tio n p h o to p e a k a r e a stu d ie d :
- T h e to ta l p e a k a r e a a p p ro x im a tio n - T h e Covell m e th o d
- T h e W a sso n m e th o d
Beside, th e s u p e rp o sitio n , d e a d tim e, t h e effect a r e co nsided.
In th is p a p e r , th e g a m m a H P G e d etecto r efficiency is d e te r m in e d th ro u g h th e p h o to p e a k a r e a of s t a n d a r d sources, th e d e te r m i n a ti o n of d e te cto r efficiency is able to be p e rfo rm e d by c a lc u la tio n . B u t w ith t h is m e th o d , th e d etecto r geometry
44
Surveying the HPGe g a m m a d e t e c t o r a b so l u te efficiency 45 h as to be known. So, in e x p e rim e n t, th e efficiency c a lib r a tio n m e th o d is com bined w ith se m i-em p irial r e la tio n be come m o st reliab le.
In order to re je c t t h e in flu en ce of th e d is to r tio n of p h o to p e a k s h a p e d ue to th e high activity a n d by th e c o u n tin g loss d ue to th e pile-up effects, th e sa m p le sh o u ld be p u t at place w ith d ifferen t d ista n c e s to detector.
For fittin g th e e x p e r im e n ta l d etecto r efficiency d a t a w i t h th e o ric a l fuction. In th is paper, two th e o ric a l fu n ctio n s d escrib in g th e d e p e n d e n c e of efficiency on energy are used, such as:
r| = y H.lnte) 1 1 = 1 ( 1 , ^ '
2. E x p e r i m e n t a l a b s o l u t e e f f i c i e n c y c a l i b r a t i o n
For g e ttin g e x p e r im e n ta l efficiency v a lu e . T h e so u rc es w ith d ifferen t g a m m a ray energies a re u s e d in o u r e x p e rim e n t: E u 152, C s 137 a n d A m 241. T h e so u rces w ith sh ap of disk w ith 1 Cm r a d i u s a re su p p lie d by IAEA w ith p a r a m e t e r s as following:
S o u r c e : E u 152
Half-life: 12.7 Y ear
D a te of produce: A u g u s t l 8t 2002 A ctiv ity in itia l: 3672.62 Bq S o u r c e : A m 241
Half-life: 433 Y ear
D a te of produce: J u l y 15th 2002 A ctivity in itial: 3759.2 Bq S o u r c e : C s 137
lf-life: 30.1 Y ear
D a te of produce: D ecem ber l 8t 1994 A ctiv ity in itia l: 36445 Bq
For efficiency c a lib r a tio n of d etecto r, in o u r e x p e r im e n t we h a v e to know th e activity of source a t th e e x p e r im e n ta l tim e. T h is w o rk is n o t difficult by u sin g equation:
A=A0e Xt
T he p a r a m e t e r s of e x p e r im e n t w ith H P G e g a m m a v is io n s p e c tro m e try are given in tab le 1 a n d plot of e x p e r im e n ta l efficiency c a lib r a tio n i n fig .l.
46 T r a n Tri Vien, D o a n Q u a n g Tuyen, T r a n Viet N h a n Hao...
T a b l e l . The efficiency of detector depend on energies a t 2 cm from detector Order
Number
Energy
(KeV) It
(%)
Count Count pel' second
Activity of source
Detection efficiency
1 121.7793 30.6788 14020 46.7350 1057.0718 0.0442±2%
9 344.31 97 9 6977 23.2591 937.2056 0.0248±2.3%
3 411.13 2.2848 544 1.8189 78.7253 0.0230±9%
4 778.91 12.7187 1517 5.05667 438.2368 0.0115±4%
5 964.05 14.3344 1633 5.44500 493.9075 0.0110*4%
6 1085.81 10.0966 1072 3.57367 347.8895 0.0103±3%
7 1112.08 13.4042 1244 4.14667 461.8565 0.0090±4%
8 1408.08 20.7264 1562 5.20667 714.1509 0.0073±4%
9 (Am) 59.739 35.75 5983 9.97200 1341.13114 0.0074±1.7%
10 (Cs)661.38 85.05 37674 418.5944 25278.6461 0.0166±6%
After fittin g th e e x p eim e n tal d a ta with th e theorical fun ctio n :
’1 =
a n d r| = Ỵ a M E ) 1
th e absolute efficiency function of H PG e gam m avision sp e c tro m e try is as following:
11, (E) = 11.5436 E '1- 1110.34 E '2 + 60344.9 E 3 -2008730 E 1 rj2(B) =-3.09414(lnE) 1+73.7661(lnE )'2-68 7 .0 9 8 (ln E )'3+ 2 9 6 7 .1 l( ln E ) 4-4814.21(lnE)'5 (3)
Absolute efficiency
0.04
0 .0 3
0.02
0 .01
200 400 600 800 1000 1200 1400 Energy
Fig. 1 The dependence of efficiency of detector on e n erg ies a t 2 cm from detector
Surveying the HPGc g a m m a dete cto r absolute efficiency 47 T a b le 2 . The efficiency of detector depend on energies a t 5 cm from detector Order
Number
Energy
(KeV) Iy
(%)
Count Count per
second
Activity of source
Detection efficiency
1 121.7793 30.6788 37400 10.3889 1057.0718 0.0098±1.72%
9 244.6927 7.7193 5740 1.5944 265.9770 0.0060±2.71%
3 295.96 0.4324 269 0.0747 14.8988 0.0050±1.16%
4 344.32 97 9 15500 4.3056 937.2059 0.0046±2.01%
5 444.03 2.8832 1320 0.3667 99.3438 0.0037±4.82%
6 688.62 0.8514 220 0.0611 29.3359 0.0021±13.6%
7 778.91 12.7187 3310 0.9194 438.2368 0.0021±3.16%
8 867.39 4.0963 852 0.2367 141.1425 0.0017±6.36%
9 964.05 14.3344 2990 0.8306 493.9075 0.0017±3.17%
10 1005.06 0.6364 134 0.0372 21.9306 0.0017±16.81%
11 1085.81 10.0966 1960 0.5444 347.8895 0.0016±3.6%
12 1089.73 1.8115 356 0.0989 62.4172 0.0016±1.16%
13 1112.08 13.4042 2560 0.0711 461.8565 0.0015±3.02%
14 1212.94 1.496 230 0.0639 51.5463 0.0012±11.24%
15 1299.2 1.74624 246 0.0683 60.1686 0.0011±1.16%
16 1408.08 20.7264 3140 0.8722 714.1509 0.0012±2.81%
A b s o l u t e e f f i c i e n c y
200 400 600 800 1000 1200 1400
Fig.2. The d e p en d en ce of detector efficiency on th e energies a t 5cm from detector After fiting th e e x p e im e n ta l d a ta with th e theorical function:
and TỊ = ^ a-ln(i?)_l
48 T r a n T ri Vien, D o a n Q u a n g Tuy en, T r a n Viet N h a n Hao..
th e a b so lu te efficiency fu n c tio n of H P G e g a m m a v isio n sp e c tr o m e tr y is as following:
6l(E) = 1.65095 E 1 - 30.281 E '2 - 3103.08 E 3
e2(E) = 0 .3 6 0 4 5 8 ( ln E ) 1-7.62022 (InE)-2 + 4 3 .9 9 1 6 (ln E )'3 -8 4 .6 5 7 1 (ln E )4 (4)
F i g .3. T h e d e p e n d e n c e of a b s o lu te efficiency of d e te cto r on e n e rg ie s of HPG e gam m a G a m m a v is io n sp e ctro m etry .
Absolute efficienc
Fig.4. The d e p e n d e n c e of a b so lu te efficiency of d e te cto r o n e n e rg ie s of HPG e gam m a G e n n ie 2000 s p e c tro m e try
Su rv eyi ng the HPGc g a m m a d e te c t o r a bs o lu te efficiency 49
In order to d e te r m in e th e d e p en d e n ce of a b so lu te d e te c to r efficiency on g a m m a en erg ies a t d iffe re n t d ista n c e s from d e te cto r to source. G a m m a sources are p laced a t d ifferen t d is ta n c e s from detecto r surface. In o u r e x p e rim e n t, g a m m a sources are placed a t po sitio n from 2 cm to 16 cm to su rfa c e of d etecto r.
The a b so lu te efficiency of H P G e g a m m a G a m m a v is io n sp e c tro m e try are show n in fig.3.
The a b so lu te efficiency of H P G e g a m m a G e n n ie 2000 s p e c tr o m e tr y a re show n in fig.4.
3. R e s u lt s a n d d i s c u s s i o n
F ittin g th e e x p e r im e n t d a t a for d e te rm in in g a b s o lu te efficiency of detector w ith theorical fu n ctio n s is c a r r i e d out.
In order to select th e m o st s u ita b le th eo rica l fu n c tio n for fittin g w ith e x p e rim e n ta l d a ta . T h e fittin g p a r a m e t e r s of e x p e r im e n ta l d a t a wich th eo rical functions:
T! = £ a,:l n ( E ) ' ( 5 )
a n d n = x > £ ‘ (6)
a re com pared.
In g en eral, th e fittin g d ia g ra m s of th e s e two fu n c tio n s a r e closing to e x p e rim e n ta l points. H ow ever, th e fu n ctio n (2) is m ore s u i t a b l e to h ig h en erg en tic
r a d i a t i o n s b e c a u s e B c o e f f i c i e n t s h a v e s m a l l e r f a i l u r e s , t h e r e f o r e , e r r o r a r e s m a l l .
A c k n o w l e d g e m e n t s : T h e V ie tn a m N a tio n a l U n iv e rs ity , H a n o i su p p o r ts th is w ork th ro u g h th e su b je ct QG-04-02.
R e f e r e n c e s
1. Boston M., E r d u r a n M .N .,S irin M. a n d S u b a s t M., Isom eric cro ss-sectio n ra tio for th e (n,2n) r e a c tio n on Sc from 13.6 to 14.9 MeV , Phys. R e v , New York, V.
56, No 2(1997), pp 918-921.
2. w . M a a h a r t a n d H. Vonach, T h e g a m m a -ra y a b s o r p tio n coefficients for Nal(Tl), Nucl.Instr. Meth. E lsev ier, V.134, No 4(1976), pp 347-351 .
3. Kolev D., S tu d ies of som e Isom eric Yield R atio s P ro d u c e d w ith B r e m s s tr a h lu n g , Appl. R a d ia t i . h o t , G r e a t B rita in , V.49, No. 8(1998), p p .989-995.
4. Seuyng-Gy Ro,..., A b so lu te dection efficienies of c y lin d ric a l N al(T l) c ry s ta l for point source g a m m a -ra y s , J .K o r. A ss o .R ad ia t. Prot, K orea, V. 8, No 3(2002), pp 235-241.
