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Calculated efficiency of a 4π detector of BGO or BaF2 for monoenergetic gamma rays and gamma cascades following neutron capture
Nuclear Instruments and Methods in Physics Research 221 (1984) 385-392 North-Holland, Amsterdam
385
CALCULATED EFFICIENCY O F A 4qr D E T E C T O R OF BGO OR BaF 2 FOR MONOENERGETIC GAMMA RAYS AND GAMMA CASCADES FOLLOWING NEUTRON CAPTURE K. WISSHAK,
F. K A P P E L E R
a n d (3. S C H A T Z
Kernforschungszentrum Karlsruhe, lnstitut fur Kernphysik HI, P.O.B. 3640, D.7500 Karlsruhe, Fed. Rep. Germany Received 24 August 1983
The applicability of a spherical shell of BGO or BaF2 as a 4~" detector for high precision measurements of neutron capture cross sections was investigated. First the efficiency of both scintillator materials for monoenergetic gamma rays was calculated in the energy range from 0.5 to 10 MeV. Configurations with different thicknesses and inner radii were considered. Second, neutron capture cascades were calculated for several isotopes with widely different capture gamma ray spectra according to the statistical model. This information allowed to determine the efficiency of an actual detector for neutron capture events in dependence of the threshold energy. A thickness of 10 cm BGO or 17.5 cm BaF2 proved to be sufficient to register more than 95% of all capture events above a threshold energy of 3 MeV. This reduces the systematic uncertainty due to the detector efficiency in an absolute cross section measurement to less than 1% and in a relative measurement using a gold standard to less than 0.5%.
1. Introduction Recently a proposal was m a d e [1] to build a 4~r detector for high precision m e a s u r e m e n t s of n e u t r o n capture cross sections in the keV range. The justification of such a n i n s t r u m e n t can be f o u n d mainly in two fields: (1) In nuclear astrophysics the investigation of nucleosynthesis requires detailed knowledge of nuclear reaction rates. Especially, the p r o d u c t i o n of heavy elem e n t s in the so called s-process (slow n e u t r o n capture process) calls for very accurate m e a s u r e m e n t s of neut r o n capture cross sections [1]. If a precision of 0.5-1% can be reached it will be possible to d e t e r m i n e the s-process age as well as its physical conditions such as temperature, n e u t r o n density, etc. T h e answer to these questions has a general impact on models of stellar a n d galactic evolution. (2) M a n y requests still exist in c o n n e c t i o n with reactor design, fuel reprocessing a n d storage. There, a n accuracy up to - 1% is needed for the most i m p o r t a n t cross sections like n e u t r o n capture in 23SU. T h e present experimental techniques for n e u t r o n capture m e a s u r e m e n t s are restricted to a n accuracy of - 4 - 5 % (ref. 1) which is not sufficient to meet the r e q u i r e m e n t s formulated above. It was therefore proposed to use instead a 4~r detector with good energy resolution a n d near-100% efficiency for g a m m a - r a y energies up to 10 MeV. This idea can b e realized using b i s m u t h g e r m a n a t e as detector material. Scintillation crystals of b i s m u t h germanate, Bi4Ge3012 ( B G O ) are of rapidly increasing 0 1 6 7 - 5 0 8 7 / 8 4 / $ 0 3 . 0 0 O Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
i m p o r t a n c e as g a m m a detectors in nuclear physics [2,3] or as shower detectors in particle physics [4,5]. W i t h the availability of large size crystals n u m e r o u s proposals have been m a d e for 4~r detector systems [6-8] in order to measure as completely as possible the energy a n d angular distribution of g a m m a cascades p o p u l a t e d in (HI, x n ) reactions. B G O offers the a d v a n t a g e of a very high density ( p = 7.13 g c m - 3 ) . This allows to reduce the active volume b y a factor of - 10 c o m p a r e d to a N a I detector with equal efficiency, resulting in a less complicated set-up a n d c o m p e n s a t i n g for the higher price of BGO. Even more i m p o r t a n t for an application in n e u t r o n capture work, it also ensures a significantly lower sensitivity for capture of slow n e u t r o n s which are the m a i n source of b a c k g r o u n d in this type of experiments. The m a i n disadvantage is the low light o u t p u t of B G O which restricts energy a n d time resolution to values which are a factor of 2 - 3 lower t h a n for NaI. As in m e a s u r e m e n t s of n e u t r o n capture cross sections the n e u t r o n energy is d e t e r m i n e d by the time of flight ( T O F ) technique, the energy resolution is restricted. This can b e c o m p e n s a t e d only b y a n increase of the flight p a t h which causes a strong reduction of the neut r o n flux at the sample position. In this respect B a F 2 offers ideal conditions as the fast ultraviolet c o m p o n e n t in light emission at 220 n m allows for a s u b - n a n o s e c o n d timing [9]. T h e density of B a F 2 is 4.88 g / c m 3 a n d thus its specific efficiency is between t h a t of N a I a n d BGO. T h e small n e u t r o n capture cross section of b a r i u m restricts the sensitivity to 4ow energetic n e u t r o n s to a b o u t the same level as ,for B G O even if one takes into account that a detector with
386
K. Wlsshak ct a/
Effhwnt) ula 4~r BGO or Bat:, dt'te~mr
tile same efficiency has a much larger volume. A further advantage is the low price of BaF 2 crystals which are widely used as windows in UV-spectroscopy. The aim of the present paper is to evaluate the optimum thickness of a spherical shell of BGO and BaF 2 with respect to the following requirements: 1) The systematic uncertainty caused by the detector efficiency should be less than 1% in an absolute measurement of neutron capture cross sections. 2) The systematic uncertainty caused by the detector efficiency should be less than 0.5% in a relative measurement of two neutron capture cross sections. 3) Capture events should be detected only above a threshold energy of 2 - 3 MeV, which is necessary to suppress low energy background. 4) The inner radius of the shell should be 8-10 cm, to allow for time of flight discrimination of scattered neutrons (see ref. 1). 5) The detector should be composed of as few individual parts as possible to avoid efficiency losses at the borders and to allow for optimum light collection (32..-42 elements). 6) The individual detector element should be machined from a cylindrical crystal not larger than 10 cm in diameter in case of BGO and 15 cm diameter in case of BaF 2, which seem to be the maximum sizes presently available. Our calculations were carried out in four steps: 1) The efficiency of a spherical shell of the respective scintillator material (inner radius R i and outer radius R o ) to monoenergetic gamma-rays in the energy range from 0 to 10 MeV was calculated analytically. 2) Capture cascades of several isotopes with widely differing binding energies and level densities were calculated in the framework of the statistical model. 3) The efficiency for a single capture cascade was evaluated as a function of the threshold energy. Finally, the overall efficiency was determined by weighting the results for the individual cascades with their respective probabilities. 4) The results obtained for a fixed threshold energy but with different assumptions for the geometry (step 1) and with widely different capture gamma-ray spectra (step 2) led to a realistic estimate of the systematic uncertainty caused by the detector efficiency in an actual measurement. We do not discuss here the sensitivity of such a detector to scattered neutrons which may be another important source of uncertainty and give only some qualitative arguments at the end of the paper. This problem has already been discussed in ref. 1 and will be covered on a more quantitative basis in future calculations. A fully documented Kernforschungszentrum Karlsruhe (KfK) report [10] has been published on the present work and should be consulted for more details. Especially all numerical results calculated for a variety of detector configurations are tabulated in this report.
2. Calculation of the efficienc~ gamma-rays
for nmnoenergetic
The efficiency of a spherical shell of BG() and hlaF'~ to monoenergetic gamma-rays was calculated analytically considering up to three subsequent interactions. This code is described in detail in ref. l l and therefore we restrict ourselves to enumerate the individual processes considered: P(O): probability that no interaction occurs: P(C): probability for Compton scattering: P(F): probability for photoabsorption; P(P): probability for pair production. These interactions are composed of the following parts: P(C) = P ( C O ) Compton scattering without interaction of the scattered gamma-ray. + P(CC) Twofold Compton scattering. + P(CF) Compton scattering followed by photoabsorption of the scattered gamma-ray. + P(CP) Compton scattering and pair production of the scattered gammaray. P(P) = P(P2F) Pair production and photoabsorption of both annihilation quanta. + P(P2C) Pair production and Compton scattering of both annihilation quanta. + P ( P F C ) Pair production and photoabsorption of one, Compton scattering of the other annihilation quantum. + P ( P E F ) Pair production and photoabsorption of one annihilation quantum while the other escapes. + P(PEC) Pair production and Compton scattering of one annihilation quantum while the other escapes. Finally, P(CC) is the sum of the following interactions: P ( C C ) = P ( C C O ) Escape of the gamma-ray remaining after twofold C o m p t o n scattering. + P(CCF)Photoabsorption of the gammaray remaining after twofold Compton scattering. + P(CCC)Threefold Compton scattering. + P(CCP)Pair production after twofold Compton scattering. The probability that the total energy of the gamma-ray is absorbed in the scintillator is given by: P(FTOT) = P(F) + ?(CF) + P(P2F) + P(CCF). The efficiency for monoenergetic gamma-rays was calculated in steps of 1 MeV up to 10 MeV. The thickness of the spherical shell was chosen between 8
K. Wisshak et aL / Efficiency o f a 4~r B G O or B a F 2 detector
s t a n t resolution of - 1 0 % a n d divided each g a m m a energy Ev into ten equal parts. T h e g a m m a intensity is then given by the difference in SW between the lower a n d u p p e r energy of the respective bin. The results for six B G O a n d four B a F 2 configurations (see table 1) are t a b u l a t e d in ref. 10. As a n example, fig. 1 shows the spectra for monoenergetic gamma-rays calculated for the B G O configuration I ( R i = 10 cm, R o = 20 cm) with the conservative lower limit for the detector probability, S W ( M I N ) . The full energy peak contains 6 0 - 9 0 % of the efficiency for energies between 2 MeV a n d 10 MeV. In cases where the peak efficiency is low most of the r e m a i n i n g intensity is found in the n e i g h b o r i n g bins. T h e first bin is d o m i n a t e d by the p r o b a b i l i t y that the g a m m a - r a y escapes without interaction. The respective p r o b a b i l i t y is - 6% for this configuration. The intensity in the intermediate bins 2 to 6 is generally below 1%. The full energy peak [always assuming S W ( M I N ) ] increases to 70-95% for energies between 2 and 10 MeV if the thickness of the B G O crystal shell is increased from 10 to 12 cm. In that case only 3 - 4 % of the g a m m a - r a y s escape without interaction. R e d u c i n g the thickness to 8 cm decreases the peak efficiency to 5 0 - 8 5 % while the losses increase to 9-11%. Generally, the differences between configurations of equal thickness but different radii are small. The respective calculations for the BaF 2 scintillator showed that a spherical shell with 17.5 cm thickness has a b o u t the same efficiency as 10 cm BGO.
Table 1 Different geometrical configurations of a spherical shell used in the present efficiency calculations Configuration
Ri [cm]
Ro [cm]
d [cm]
10 8 9 8 10 8
20 18 21 20 18 16
10 10 12 12 8 8
10 10 10 10
22.5 25 27.5 30
12.5 15 17.5 20
B G O scintillator:
I II I11 IV V VI B a F 2 scintillator:
1 I1 III 1V
cm a n d 12 c m for B G O a n d between 12.5 cm a n d 20 cm for BaF 2 with R i a n d R o as compiled in table 1. These d i m e n s i o n s are a c o m p r o m i s e between detector volume a n d an optimal time-of-flight discrimination of scattered n e u t r o n s [1]. T h e code calculates the probability SW to detect a g a m m a - r a y with energy Ey above a threshold energy E~. Simplifying a s s u m p t i o n s were m a d e for some of the interactions which are described in detail in ref. 11. In order to avoid biasing, these assumptions were m a d e in a n optimistic a n d a pessimistic way with respect to the efficiency. Consequently, the results are given as S W ( M A X ) a n d S W ( M I N ) which represent an u p p e r a n d lower limit for the true detection probability. The g a m m a spectrum recorded by a detector is given by the derivative of SW folded with the respective energy resolution. To simulate this we assumed a con100% -
P 50%
]-~~Ri
=lOcm
387
3. Efficiency for gamma cascades following neutron capture To calculate the efficiency of a spherical shell of B G O or BaF 2 for n e u t r o n capture events we chose three
BGO Ro =20cm
IIIn
o*~
M I-1N o
0.'5
E/El
I.o
Fig. 1. Calculated detection probability p for monoenergetic gamma rays with energy E, in a spherical shell of BGO ( R i = 10 cm, R o = 20 cm). Each gamma energy E, is divided artificially into 10 bins to simulate an energy resolution of 10%.
388
K. Wisshak et al. / £~fficiency o] a 4~r BGO or BaFe detector
examples which represent typical capture gamma-ray spectra: capture in 241Am, 197Au and 56Fe. The high level density in the 242Am compound nucleus leads to capture cascades with a high gamma-ray multiplicity and consequently to a soft gamma-ray spectrum. Contrarily, the low level density in 57Fe yields a low multiplicity and therefore the spectrum is dominated by a hard component from direct transitions to the ground state. Neutron capture in gold can be regarded as an intermediate case. For these three isotopes individual capture cascades have been calculated in the framework of the statistical model as described in detail in refs. 12-14. In these calculations which were performed for a neutron energy of 30 keV, up to - 20000 cascades were determined for each isotope, together with the respective partial cross sections. For the purpose of the present efficiency calculations we selected the cascades with the highest partial cross section. As shown in table 2 the binding energy and consequently the energy of the capture cascade varies between 5.6 and 7.7 MeV for the three examples. The average multiplicity of the capture cascades changes between 3 and 5. A total number of 1000 cascades was sufficient to cover more than 75% of the total capture cross section in case of 24~Am and 197Au while for 56Fe only 300 cascades accounted for more than 96%. Fig. 2 demonstrates that the total capture gamma-ray spectra for all isotopes are significantly different in shape. The energy spectrum which will be measured using a spherical shell of BGO or BaF 2 for a fixed capture cascade emitted from the center, was calculated in the following way: the energy of each gamma-ray in the cascade with multiplicity K was divided into ten equal energy bins, E, (i = 1 . . . 10) according to the representation in fig. 1. The detection probability of each bin, P ( E , ) was obtained by a linear interpolation between the respective values for neighboring monoenergetic gamma-rays. The energy spectrum for a particular cascade was then obtained by combining the detection probabilities for the individual gamma-rays considering
all possible combinations of all energy bins: 10
P(Ez.)=
Nucleus
24LAm 197Au 56Fe
Binding energy [MeV]
Average multiplicity of capture cascade
Number of cascades used in efficiency calculation
Covered percentage of total capture cross section
5.5 6.5 7.6
4.8 4.1 3.0
1000 1000 300
75.0 80.2 96.2
P,( E,).P2( E,)...
Px(l:
).
~ :-1
i,/-.-
where the index 1 , 2 . - . K enumerates the various cascade gamma-rays, K being the multiplicity. For each combination, the detected gamma-ray energy is the sum of the respective bin energies: E,.=E,+E
+ ... +E,
(i,j...
x=l
...
10).
All these pairs P ( E z ) , E s are then sorted to give the final energy spectrum of the cascade. Finally, the results for the individual cascades were summed up and weighted with the corresponding partial capture cross section in order to get the spectrum which can be expected in an actual measurement. In table 3 the final results of the efficiency of a spherical shell of BGO for capture in 197Au are compiled. The respective tables for capture in 241Am and S6Fe as well as the results for BaF z are given in ref. 10. The results obtained for the optimistic and pessimistic view of the detector probability for monoenergetic gamma-rays are quoted separately. The numbers given
2/,1Am 15
En = 30 keY
1C O5 2>
\
OC
~
/.
06
6 197Au E n =30 keV
OZ. Z
z 0.2 .< ~E ~E <~ ~9
Table 2 Important parameters of the calculations of capture cascades
II
O0
2
L
6 56Fe
g
E n = 30 key
0.02 1 001
0
2
/6 8 GAMMA RAY ENERGY(MeV)
Fig. 2. Capture gamma ray spectra for neutron capture in :41Am, ~97Auand 56Fe as calculated according to the statistical model.
389
K. Wisshak et aL / Efficiency of a 4~r BGO or B a F2 detector
100,
~.
~°,K 146 MeV
10s-
77 r7 I t -j
k ~ k
il
10a.
A
lo
.i
S 2 , r
i
_ !2.61 MeV \~k./'~10xl0cm
/
BG0
unshielded
r- - J _ 2 - _ S -
z z
lo3.
5cm of lead W
r-_-.A
o._ 10~.
>_ 1
g
zD 8
_o U_ UW
.__i
i
--'--
10
2t'lAm
! 01 2.o,..oo7] 1
I
2
I
i
~
3 /5 GAMMA RAY ENERGY(MeV)
L
| - -
6
7
Fig. 3. Calculated pulse height spectrum of a spherical shell of BGO (R i =10 cm, R o = 20 cm) for neutron capture in 56Fe, 197Au and 241Am.
are the probabilities in % to detect a capture event above the threshold energy E s. The pulse height spectra as expected for a spherical shell of B G O with 10 cm thickness and R~ = 10, R o = 20 cm are plotted in fig. 3. It has to be noted that the resolution of the full energy peak is mainly determined by the number of gamma-rays escaping from the crystal and not by the energy resolution. It depends therefore on the thickness of the detector and deteriorates rapidly if this falls below 10 cm. It was mentioned above that an electronic threshold has to be set in an actual measurement of capture events in order to suppress low energy background. Fig. 4 shows a background spectrum taken with a cylindrical 10 cm × 10 cm B G O detector in a measuring time of 24 h. The background is dominated by the gamma-ray lines from the decay of 4°K (1.4 MeV) and from the day of 212 Po and 2°8T1 (2.6 MeV). At higher energies the background drops by two orders of magnitude. This suggests the choice of a threshold energy around 3 MeV. In that case the following conclusions can be drawn from the present calculations: (1) The differences in efficiency between SW(MIN) and SW(MAX) are on the average 0.4%, 0.7% and 1.2% for B G O crystals with 12 cm, 10 cm and 8 cm thickness, respectively. The corresponding values range between 0.7% and 1.9% for BaF 2 crystals with thicknesses between 20 cm and 12.5 cm. This indicates that the systematic uncertainty in the efficiency calculation due to the approximations in the code is less than 0.5% if a thickness of at least 10 cm B G O or 17 cm BaF 2 is chosen.
o
£o
~o
o60
o~o
1ooo
CHANNEL
Fig. 4. Gamma-ray background measured with a cylindrical BGO detector (10 cm diameter, 10 cm thickness).
(2) The absolute detection efficiency is - 95% for a 10 cm thick B G O detector. It increases to 97% for 12 cm, but decreases to 91% for 8 cm thickness. A BaF 2 detector of 17.5 cm thickness is comparable to a B G O crystal of 10 cm thickness. (3) The difference in efficiency for neutron capture cascades from nuclei with widely different binding energies, gamma-ray multiplicities and capture gamma-ray spectra is - 1 % for a 10 cm thick B G O detector. It decreases to 0.5% for 12 cm and increases to 1.5% for 8 cm thickness. Thus the systematic uncertainty caused by the calculation of capture cascades is certainly less than 0.3% if a thickness of at least 10 cm is chosen. (4) The efficiency is insensitive to a change of the inner radius by 2 cm. F r o m the above points one may conclude that the absolute efficiency can be determined with an accuracy of better than 1%. However, a spherical shell of at least 10 cm B G O or 17 cm BaF 2 thickness should be used for the final design. In absolute measurements of capture cross sections the neutron flux has to be determined with the same accuracy as the capture rate. As this may be problematic in most applications, relative measurements are preferable. In these cases many systematic uncertainties like e.g. gamma-ray self-absorption in the sample or multiple scattering are strongly reduced or cancel out, and the flux determination is avoided. Especially in investigations for nuclear astrophysics most of the interesting questions can be solved by very accurate measurements of cross section ratios (ref. 1).
8/18
10 /2 0
99.81 98.87 98.54 97.73 96.49 94.44 92.26 88.97 85.42 81.27 73.31 44.68
Ri/Ro (cm):
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
99.89 99.40 99.22 98.77 98.05 96.82 95.48 93.37 90.95 87.70 80.36 50.06
9/21
Il l
99.64 99.40 99.22 98.77 98.05 96.82 95.48 93.36 90.94 87.68 80.33 50.04
8/20
IV
99.64 97.76 97.10 95.60 93.44 90.04 86.55 81.54 76.42 70.99 62.19 36.34
10/18
V
99.64 97.76 97.10 95.59 93.43 90.03 86.53 81.52 76.42 70.92 62.09 36.22
8/16
VI
99.82 98.88 98.64 97.94 96.90 94.95 93.28 90.18 86.71 83.87 81.47 73.75
10/20
I
99.82 98.88 98.64 97.94 96.90 94.94 93.27 90.17 86.69 83.84 81.42 73.68
8/18
II
99.90 99.41 99.28 98.89 98.30 97.12 96.12 94.18 92.01 90.26 88.73 81.72
9/ 21
Ill
99.90 99.41 99.28 98.89 98.30 97.13 96.12 94.18 92.01 90.24 88.69 81.68
8/20
IV
99.66 97.79 97.28 95.95 94.13 90.88 88.17 83.37 78.10 73.74 70.23 61.85
10/18
V
Results obtained assuming SW(MAX) for monoenergetic g amma rays
99.66 97.78 97.27 95.95 94.12 90.88 88.15 83.37 78.08 73.71 70.16 61.76
8/16
VI
0.97 1.19 1.02 - 0.60
1.19 - 0.81 0.15 1.17
%( 24XAm)/o~(I97Au) 2.0 0.97 2.5 1.19 3.0 1.02 3.5 - 0.58
ov ( 56F e ) / % (19VAu) 2.0 -- 1.19 2.5 0.80 3.0 0.15 3.5 1.17
10/20
-0.70 0.48 0.08 0.70
0.56 0.71 0.65 0.34
9/ 21
-0.70 - 0.48 0.08 0.70
0.56 0.71 0.64 - 0.35
8/20
- 1.99 - 1.27 0.36 2.02
1.70 1.93 1.47 1.19
10/18
- 1,99 - 1.26 0.36 2.03
1.71 1.93 1.47 - 1.20
8/16
- 1.26 - 0.92 - 0.03 0.64
0.91 1.39 1.82 0.32
10/20
-- 1.26 - 0.92 - 0.02 0.65
0.91 1.39 1.83 0.32
8/18
I!
-- 0.73 -- 0.55 - 0.02 0.37
0.52 0.82 1.13 0.26
9/21
Il l
0.73 -- 0.55 0.02 0.37
0.52 0.82 1.13 0.26
8/20
IV
~ 2.10 1.46 0.07 1.20
1.62 2.28 2.76 0.20
10/18
V
8/18
Vl
I
V
R ~/R o (cm):
IV
II
Configuration: 1
III
Results obtained assuming SW(MAX) for monoenergetic gamma rays
E (MeV) Results obtained assuming SW(MtN) for monoenergetic gamma rays
the threshold energy E. (All values are given in percent.)
2.tt.~ t.46 0.06 t .2 l
1.62 2.28 2.75 0.20
8/16
VI
Table 4 Difference in efficiency c(sample) - ¢(reference sample) as expected in a relative measurement of capture cross section using a BGO detector and a gold standard in dependence of
99.81 98.87 98.54 97.73 96.49 94.44 92.26 88.96 85.39 81.23 73.25 44.62
II
Configuration: 1
E (MeV) Results obtained assuming SW(MIN) for monoenergetie ga mma rays
Table 3 Efficiency of a spherical shell of BGO for neutron capture cascades emitted in the 197Au + FI reaction in dependence of the threshold energy E. (All values are given in percent.}
~e
391
K. Wisshak et al. / Efficiency of a 4~r BGO or BaF, detector
Table 5 Difference in efficiency c(sample)- ~(reference sample) as' expected in a relative measurement of capture cross section using a BaF2 detector and a gold standard in dependence of the threshold energy E. (All values are given in percent.) Results obtained assuming SW(MAX) for monoenergetic gamma rays
Results obtained assuming SW(MIN) for monoenergetic gamma rays Configuration:
I
!I
IIl
IV
I
II
III
IV
10/22.5
10/25
10/27.5
10/30
10/22.5
10/25
10/27.5
10/30
% ( 241Am)/ov ( 197Au) 2.0 1.99 2.5 1.62 3.0 0.41 3.5 - 2.65
1.36 1.23 0.51 - 1.63
0.92 0.88 0.46 - 1.07
0.62 0.62 0.35 - 0.76
1.99 2.62 3.06 0.26
% ( 56Fe)/% ( 197Au) 2.0 - 2.43 2.5 - 1.60 3.0 0.23 3.5 2.29
- 1.71 - 1.20 0.02 1.48
- 1.18 -0.85 - 0.03 0.98
- 0.80 -0.58 - 0.04 0.65
- 2.67 - 1.97 - 0.24 1.02
ERi/Ro
(cm):
With gold as a s t a n d a r d we illustrate the situation with the example of a relative m e a s u r e m e n t % ( 5 6 F e ) / %(~97Au) a n d ov(2alAm)/o'y(197Au). In tables 4 a n d 5 the difference of the efficiency for sample a n d reference sample is given as a function of the threshold energy E s for all configurations considered here. It is found that this difference is of the order of 1% or even less if a B G O detector thickness of a least 10 cm or a BaF 2 detector thickness of 17 cm is chosen. The results differ in general by less than 0.5% between the two assumptions S W ( M I N ) a n d S W ( M A X ) . Keeping in m i n d that the present examples represent cases with extreme differences in the capture g a m m a - r a y spectra, b i n d i n g energies a n d cascade multiplicities, one may conclude that the systematic uncertainty in a relative m e a s u r e m e n t due to the difference in efficiency can be reduced to less t h a n 0.5% for most practical applications. This holds especially for the suggested m e a s u r e m e n t s in nuclear astrophysics [1] where cross section ratios of neighboring nuclei have to be determined.
4. Conclusions A spherical shell of B G O with - 10 cm thickness or BaF 2 with - 1 7 cm thickness a n d a n inner radius of 8 - 1 0 cm offers a n efficiency for g a m m a - r a y cascades following n e u t r o n capture which is high enough to reduce the correlated systematic u n c e r t a i n t y to less t h a n 1% in absolute m e a s u r e m e n t s a n d less than 0.5% in relative measurements. This holds even for isotopes with widely different b i n d i n g energies, capture g a m m a - r a y spectra a n d cascade multiplicities. It holds the more in case of an actual detector because then the theoretical
-
1.32 1.87 2.40 0.57
0.87 1.29 1.75 0.56
0.58 0.88 1.24 0.47
- 1.87
- 1.28 1.03 -0.27 0.27
-0.86 -0.71 -0.21 0.14
1.45
-0.31 0.52
-
calculation of the detection probability SW a n d the capture g a m m a - r a y spectra can be replaced by direct measurements. Such a detector which can be realised with presently available crystals by subdivision into 32 or 42 elements [1] will be able to increase the accuracy of present day techniques for capture cross section m e a s u r e m e n t s at least by a factor of 5. It will be able to meet the accuracy of nuclear data requirements for nuclear astrophysics as well as for reactor design. The present p a p e r concentrates on the detector efficiency but as the aspect of n e u t r o n sensitivity is also very important, we finally add some qualitative argum e n t s showing that this will not severely affect the accuracy of the measurements. 1) A t low energies (in the eV range) n e u t r o n s scattered from the sample m a y be shielded effectively by a thin layer of 6Li or l°B inside the spherical shell. 2) At higher energies ( 1 0 - 1 0 0 keV) time-of-flight discrimination of scattered neutrons is applicable if p r i m a r y flight p a t h s of 5 0 - 1 0 0 cm are used as it is possible at Van de G r a a f f accelerators. Moreover, in the keV range the ratio of scattering to capture in b o t h scintillator materials is of the order of 20-100; therefore scattered n e u t r o n s have a high p r o b a b i l i t y to escape from the detector before being c a p t u r e d because the scattering length is of the order of 2 cm. But if n e u t r o n s are captured after 5 - 1 0 scattering events the respective g a m m a - r a y s are also already delayed in time a n d can thus be discriminated from primary events. The arguments, however, will be p u t on a more quantitative basis in a forthcoming publication. We would like to t h a n k F. F a b b r i and G. Reffo for m a k i n g available the individual capture cascades needed
392
K. Wisshak et al. / Efficiency oj a 4+r B G O or B a F , detector
for the present calculations. We appreciate very much the help of J. Oehlschl~ger in handling the code to calculate the efficiency for monoenergetic gamma-rays.
References [1] F. K~tppeler, G. Schatz, and K. Wisshak, KfK 3472, Kernforschungszentrum Karlsruhe (1983). [2] M. Moszynski, C. Gresset, J. Vacher and R. Odru, Nucl. Instr. and Meth. 188 (1981) 403. [3] D.M. Drake, L.R. Nilsson, and J. Faucett Nucl. Instr. and Meth. 188 (1981) 313. [4] M. Kobayashi, S.I. Kurokawa, S. Sugimoto, Y. Yoshimura, M. Chiba, H. Yoshida, M. Ishii, S. Akiyama and H. Ishibashi, Nucl. Instr. and Meth. 189 (1981) 629. [5] P. Pavlopoulos, M. Hasinoff, J. Repond+ L. Tauscher, D. Tr6ster, M. Rousseau, K. Fransson, T. Alberis and K. Zioutas, Nucl. Instr. and Meth. 197 (1982) 331. [6] R.M. Diamond and F.S. Stephens, The high resolution ball, unpublished proposal.
17] M.A. Lone+ O. H~usser+ T.K. Alexander+ J. Ga~,c~;n and 1+++ Hageberg, BGO Conf., Princeton. and private communications. [8] J.X. Saladin, C. Baktash, I.Y. Lee+ R. Blue, R. Ronningen and R.A. Sorensen+ Progress Report+ Michigan State Lniversity (1982). [9] M+ Laval, M. Moszynski, R. Allemand, E. Cormoreche, P. Guinet, R. Ordu and J. Vacher. Nuct. Instr. and Meth. 206 (1983) 169. [10] K. Wisshak, F. K~.ppeler and G. Schatz, KfK 3580 Kernforschungszentrum Karlsruhe (1983). [11] G. Schatz and J. Oehlschl~.ger+ KfK 3710, Kernforschungszentrum Karlsruhe (1984). [12] G. Reffo, F. Fabbri, K. Wisshak and F. K~ippeler. Nucl. Sci. Eng. 80 (1982) 630. [13] K. Wisshak, J. Wickenhauser+ F. K~ippeler+ G. Reffo and F. Fabbri, Nucl. Sci. Eng 81 (1982) 396. [14] K. Wisshak, F. K~tppeler, G. Reffo and F. Fabbri, KfK 3515, Kernforschungszentrum Karlsruhe (1983).
385
CALCULATED EFFICIENCY O F A 4qr D E T E C T O R OF BGO OR BaF 2 FOR MONOENERGETIC GAMMA RAYS AND GAMMA CASCADES FOLLOWING NEUTRON CAPTURE K. WISSHAK,
F. K A P P E L E R
a n d (3. S C H A T Z
Kernforschungszentrum Karlsruhe, lnstitut fur Kernphysik HI, P.O.B. 3640, D.7500 Karlsruhe, Fed. Rep. Germany Received 24 August 1983
The applicability of a spherical shell of BGO or BaF2 as a 4~" detector for high precision measurements of neutron capture cross sections was investigated. First the efficiency of both scintillator materials for monoenergetic gamma rays was calculated in the energy range from 0.5 to 10 MeV. Configurations with different thicknesses and inner radii were considered. Second, neutron capture cascades were calculated for several isotopes with widely different capture gamma ray spectra according to the statistical model. This information allowed to determine the efficiency of an actual detector for neutron capture events in dependence of the threshold energy. A thickness of 10 cm BGO or 17.5 cm BaF2 proved to be sufficient to register more than 95% of all capture events above a threshold energy of 3 MeV. This reduces the systematic uncertainty due to the detector efficiency in an absolute cross section measurement to less than 1% and in a relative measurement using a gold standard to less than 0.5%.
1. Introduction Recently a proposal was m a d e [1] to build a 4~r detector for high precision m e a s u r e m e n t s of n e u t r o n capture cross sections in the keV range. The justification of such a n i n s t r u m e n t can be f o u n d mainly in two fields: (1) In nuclear astrophysics the investigation of nucleosynthesis requires detailed knowledge of nuclear reaction rates. Especially, the p r o d u c t i o n of heavy elem e n t s in the so called s-process (slow n e u t r o n capture process) calls for very accurate m e a s u r e m e n t s of neut r o n capture cross sections [1]. If a precision of 0.5-1% can be reached it will be possible to d e t e r m i n e the s-process age as well as its physical conditions such as temperature, n e u t r o n density, etc. T h e answer to these questions has a general impact on models of stellar a n d galactic evolution. (2) M a n y requests still exist in c o n n e c t i o n with reactor design, fuel reprocessing a n d storage. There, a n accuracy up to - 1% is needed for the most i m p o r t a n t cross sections like n e u t r o n capture in 23SU. T h e present experimental techniques for n e u t r o n capture m e a s u r e m e n t s are restricted to a n accuracy of - 4 - 5 % (ref. 1) which is not sufficient to meet the r e q u i r e m e n t s formulated above. It was therefore proposed to use instead a 4~r detector with good energy resolution a n d near-100% efficiency for g a m m a - r a y energies up to 10 MeV. This idea can b e realized using b i s m u t h g e r m a n a t e as detector material. Scintillation crystals of b i s m u t h germanate, Bi4Ge3012 ( B G O ) are of rapidly increasing 0 1 6 7 - 5 0 8 7 / 8 4 / $ 0 3 . 0 0 O Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
i m p o r t a n c e as g a m m a detectors in nuclear physics [2,3] or as shower detectors in particle physics [4,5]. W i t h the availability of large size crystals n u m e r o u s proposals have been m a d e for 4~r detector systems [6-8] in order to measure as completely as possible the energy a n d angular distribution of g a m m a cascades p o p u l a t e d in (HI, x n ) reactions. B G O offers the a d v a n t a g e of a very high density ( p = 7.13 g c m - 3 ) . This allows to reduce the active volume b y a factor of - 10 c o m p a r e d to a N a I detector with equal efficiency, resulting in a less complicated set-up a n d c o m p e n s a t i n g for the higher price of BGO. Even more i m p o r t a n t for an application in n e u t r o n capture work, it also ensures a significantly lower sensitivity for capture of slow n e u t r o n s which are the m a i n source of b a c k g r o u n d in this type of experiments. The m a i n disadvantage is the low light o u t p u t of B G O which restricts energy a n d time resolution to values which are a factor of 2 - 3 lower t h a n for NaI. As in m e a s u r e m e n t s of n e u t r o n capture cross sections the n e u t r o n energy is d e t e r m i n e d by the time of flight ( T O F ) technique, the energy resolution is restricted. This can b e c o m p e n s a t e d only b y a n increase of the flight p a t h which causes a strong reduction of the neut r o n flux at the sample position. In this respect B a F 2 offers ideal conditions as the fast ultraviolet c o m p o n e n t in light emission at 220 n m allows for a s u b - n a n o s e c o n d timing [9]. T h e density of B a F 2 is 4.88 g / c m 3 a n d thus its specific efficiency is between t h a t of N a I a n d BGO. T h e small n e u t r o n capture cross section of b a r i u m restricts the sensitivity to 4ow energetic n e u t r o n s to a b o u t the same level as ,for B G O even if one takes into account that a detector with
386
K. Wlsshak ct a/
Effhwnt) ula 4~r BGO or Bat:, dt'te~mr
tile same efficiency has a much larger volume. A further advantage is the low price of BaF 2 crystals which are widely used as windows in UV-spectroscopy. The aim of the present paper is to evaluate the optimum thickness of a spherical shell of BGO and BaF 2 with respect to the following requirements: 1) The systematic uncertainty caused by the detector efficiency should be less than 1% in an absolute measurement of neutron capture cross sections. 2) The systematic uncertainty caused by the detector efficiency should be less than 0.5% in a relative measurement of two neutron capture cross sections. 3) Capture events should be detected only above a threshold energy of 2 - 3 MeV, which is necessary to suppress low energy background. 4) The inner radius of the shell should be 8-10 cm, to allow for time of flight discrimination of scattered neutrons (see ref. 1). 5) The detector should be composed of as few individual parts as possible to avoid efficiency losses at the borders and to allow for optimum light collection (32..-42 elements). 6) The individual detector element should be machined from a cylindrical crystal not larger than 10 cm in diameter in case of BGO and 15 cm diameter in case of BaF 2, which seem to be the maximum sizes presently available. Our calculations were carried out in four steps: 1) The efficiency of a spherical shell of the respective scintillator material (inner radius R i and outer radius R o ) to monoenergetic gamma-rays in the energy range from 0 to 10 MeV was calculated analytically. 2) Capture cascades of several isotopes with widely differing binding energies and level densities were calculated in the framework of the statistical model. 3) The efficiency for a single capture cascade was evaluated as a function of the threshold energy. Finally, the overall efficiency was determined by weighting the results for the individual cascades with their respective probabilities. 4) The results obtained for a fixed threshold energy but with different assumptions for the geometry (step 1) and with widely different capture gamma-ray spectra (step 2) led to a realistic estimate of the systematic uncertainty caused by the detector efficiency in an actual measurement. We do not discuss here the sensitivity of such a detector to scattered neutrons which may be another important source of uncertainty and give only some qualitative arguments at the end of the paper. This problem has already been discussed in ref. 1 and will be covered on a more quantitative basis in future calculations. A fully documented Kernforschungszentrum Karlsruhe (KfK) report [10] has been published on the present work and should be consulted for more details. Especially all numerical results calculated for a variety of detector configurations are tabulated in this report.
2. Calculation of the efficienc~ gamma-rays
for nmnoenergetic
The efficiency of a spherical shell of BG() and hlaF'~ to monoenergetic gamma-rays was calculated analytically considering up to three subsequent interactions. This code is described in detail in ref. l l and therefore we restrict ourselves to enumerate the individual processes considered: P(O): probability that no interaction occurs: P(C): probability for Compton scattering: P(F): probability for photoabsorption; P(P): probability for pair production. These interactions are composed of the following parts: P(C) = P ( C O ) Compton scattering without interaction of the scattered gamma-ray. + P(CC) Twofold Compton scattering. + P(CF) Compton scattering followed by photoabsorption of the scattered gamma-ray. + P(CP) Compton scattering and pair production of the scattered gammaray. P(P) = P(P2F) Pair production and photoabsorption of both annihilation quanta. + P(P2C) Pair production and Compton scattering of both annihilation quanta. + P ( P F C ) Pair production and photoabsorption of one, Compton scattering of the other annihilation quantum. + P ( P E F ) Pair production and photoabsorption of one annihilation quantum while the other escapes. + P(PEC) Pair production and Compton scattering of one annihilation quantum while the other escapes. Finally, P(CC) is the sum of the following interactions: P ( C C ) = P ( C C O ) Escape of the gamma-ray remaining after twofold C o m p t o n scattering. + P(CCF)Photoabsorption of the gammaray remaining after twofold Compton scattering. + P(CCC)Threefold Compton scattering. + P(CCP)Pair production after twofold Compton scattering. The probability that the total energy of the gamma-ray is absorbed in the scintillator is given by: P(FTOT) = P(F) + ?(CF) + P(P2F) + P(CCF). The efficiency for monoenergetic gamma-rays was calculated in steps of 1 MeV up to 10 MeV. The thickness of the spherical shell was chosen between 8
K. Wisshak et aL / Efficiency o f a 4~r B G O or B a F 2 detector
s t a n t resolution of - 1 0 % a n d divided each g a m m a energy Ev into ten equal parts. T h e g a m m a intensity is then given by the difference in SW between the lower a n d u p p e r energy of the respective bin. The results for six B G O a n d four B a F 2 configurations (see table 1) are t a b u l a t e d in ref. 10. As a n example, fig. 1 shows the spectra for monoenergetic gamma-rays calculated for the B G O configuration I ( R i = 10 cm, R o = 20 cm) with the conservative lower limit for the detector probability, S W ( M I N ) . The full energy peak contains 6 0 - 9 0 % of the efficiency for energies between 2 MeV a n d 10 MeV. In cases where the peak efficiency is low most of the r e m a i n i n g intensity is found in the n e i g h b o r i n g bins. T h e first bin is d o m i n a t e d by the p r o b a b i l i t y that the g a m m a - r a y escapes without interaction. The respective p r o b a b i l i t y is - 6% for this configuration. The intensity in the intermediate bins 2 to 6 is generally below 1%. The full energy peak [always assuming S W ( M I N ) ] increases to 70-95% for energies between 2 and 10 MeV if the thickness of the B G O crystal shell is increased from 10 to 12 cm. In that case only 3 - 4 % of the g a m m a - r a y s escape without interaction. R e d u c i n g the thickness to 8 cm decreases the peak efficiency to 5 0 - 8 5 % while the losses increase to 9-11%. Generally, the differences between configurations of equal thickness but different radii are small. The respective calculations for the BaF 2 scintillator showed that a spherical shell with 17.5 cm thickness has a b o u t the same efficiency as 10 cm BGO.
Table 1 Different geometrical configurations of a spherical shell used in the present efficiency calculations Configuration
Ri [cm]
Ro [cm]
d [cm]
10 8 9 8 10 8
20 18 21 20 18 16
10 10 12 12 8 8
10 10 10 10
22.5 25 27.5 30
12.5 15 17.5 20
B G O scintillator:
I II I11 IV V VI B a F 2 scintillator:
1 I1 III 1V
cm a n d 12 c m for B G O a n d between 12.5 cm a n d 20 cm for BaF 2 with R i a n d R o as compiled in table 1. These d i m e n s i o n s are a c o m p r o m i s e between detector volume a n d an optimal time-of-flight discrimination of scattered n e u t r o n s [1]. T h e code calculates the probability SW to detect a g a m m a - r a y with energy Ey above a threshold energy E~. Simplifying a s s u m p t i o n s were m a d e for some of the interactions which are described in detail in ref. 11. In order to avoid biasing, these assumptions were m a d e in a n optimistic a n d a pessimistic way with respect to the efficiency. Consequently, the results are given as S W ( M A X ) a n d S W ( M I N ) which represent an u p p e r a n d lower limit for the true detection probability. The g a m m a spectrum recorded by a detector is given by the derivative of SW folded with the respective energy resolution. To simulate this we assumed a con100% -
P 50%
]-~~Ri
=lOcm
387
3. Efficiency for gamma cascades following neutron capture To calculate the efficiency of a spherical shell of B G O or BaF 2 for n e u t r o n capture events we chose three
BGO Ro =20cm
IIIn
o*~
M I-1N o
0.'5
E/El
I.o
Fig. 1. Calculated detection probability p for monoenergetic gamma rays with energy E, in a spherical shell of BGO ( R i = 10 cm, R o = 20 cm). Each gamma energy E, is divided artificially into 10 bins to simulate an energy resolution of 10%.
388
K. Wisshak et al. / £~fficiency o] a 4~r BGO or BaFe detector
examples which represent typical capture gamma-ray spectra: capture in 241Am, 197Au and 56Fe. The high level density in the 242Am compound nucleus leads to capture cascades with a high gamma-ray multiplicity and consequently to a soft gamma-ray spectrum. Contrarily, the low level density in 57Fe yields a low multiplicity and therefore the spectrum is dominated by a hard component from direct transitions to the ground state. Neutron capture in gold can be regarded as an intermediate case. For these three isotopes individual capture cascades have been calculated in the framework of the statistical model as described in detail in refs. 12-14. In these calculations which were performed for a neutron energy of 30 keV, up to - 20000 cascades were determined for each isotope, together with the respective partial cross sections. For the purpose of the present efficiency calculations we selected the cascades with the highest partial cross section. As shown in table 2 the binding energy and consequently the energy of the capture cascade varies between 5.6 and 7.7 MeV for the three examples. The average multiplicity of the capture cascades changes between 3 and 5. A total number of 1000 cascades was sufficient to cover more than 75% of the total capture cross section in case of 24~Am and 197Au while for 56Fe only 300 cascades accounted for more than 96%. Fig. 2 demonstrates that the total capture gamma-ray spectra for all isotopes are significantly different in shape. The energy spectrum which will be measured using a spherical shell of BGO or BaF 2 for a fixed capture cascade emitted from the center, was calculated in the following way: the energy of each gamma-ray in the cascade with multiplicity K was divided into ten equal energy bins, E, (i = 1 . . . 10) according to the representation in fig. 1. The detection probability of each bin, P ( E , ) was obtained by a linear interpolation between the respective values for neighboring monoenergetic gamma-rays. The energy spectrum for a particular cascade was then obtained by combining the detection probabilities for the individual gamma-rays considering
all possible combinations of all energy bins: 10
P(Ez.)=
Nucleus
24LAm 197Au 56Fe
Binding energy [MeV]
Average multiplicity of capture cascade
Number of cascades used in efficiency calculation
Covered percentage of total capture cross section
5.5 6.5 7.6
4.8 4.1 3.0
1000 1000 300
75.0 80.2 96.2
P,( E,).P2( E,)...
Px(l:
).
~ :-1
i,/-.-
where the index 1 , 2 . - . K enumerates the various cascade gamma-rays, K being the multiplicity. For each combination, the detected gamma-ray energy is the sum of the respective bin energies: E,.=E,+E
+ ... +E,
(i,j...
x=l
...
10).
All these pairs P ( E z ) , E s are then sorted to give the final energy spectrum of the cascade. Finally, the results for the individual cascades were summed up and weighted with the corresponding partial capture cross section in order to get the spectrum which can be expected in an actual measurement. In table 3 the final results of the efficiency of a spherical shell of BGO for capture in 197Au are compiled. The respective tables for capture in 241Am and S6Fe as well as the results for BaF z are given in ref. 10. The results obtained for the optimistic and pessimistic view of the detector probability for monoenergetic gamma-rays are quoted separately. The numbers given
2/,1Am 15
En = 30 keY
1C O5 2>
\
OC
~
/.
06
6 197Au E n =30 keV
OZ. Z
z 0.2 .< ~E ~E <~ ~9
Table 2 Important parameters of the calculations of capture cascades
II
O0
2
L
6 56Fe
g
E n = 30 key
0.02 1 001
0
2
/6 8 GAMMA RAY ENERGY(MeV)
Fig. 2. Capture gamma ray spectra for neutron capture in :41Am, ~97Auand 56Fe as calculated according to the statistical model.
389
K. Wisshak et aL / Efficiency of a 4~r BGO or B a F2 detector
100,
~.
~°,K 146 MeV
10s-
77 r7 I t -j
k ~ k
il
10a.
A
lo
.i
S 2 , r
i
_ !2.61 MeV \~k./'~10xl0cm
/
BG0
unshielded
r- - J _ 2 - _ S -
z z
lo3.
5cm of lead W
r-_-.A
o._ 10~.
>_ 1
g
zD 8
_o U_ UW
.__i
i
--'--
10
2t'lAm
! 01 2.o,..oo7] 1
I
2
I
i
~
3 /5 GAMMA RAY ENERGY(MeV)
L
| - -
6
7
Fig. 3. Calculated pulse height spectrum of a spherical shell of BGO (R i =10 cm, R o = 20 cm) for neutron capture in 56Fe, 197Au and 241Am.
are the probabilities in % to detect a capture event above the threshold energy E s. The pulse height spectra as expected for a spherical shell of B G O with 10 cm thickness and R~ = 10, R o = 20 cm are plotted in fig. 3. It has to be noted that the resolution of the full energy peak is mainly determined by the number of gamma-rays escaping from the crystal and not by the energy resolution. It depends therefore on the thickness of the detector and deteriorates rapidly if this falls below 10 cm. It was mentioned above that an electronic threshold has to be set in an actual measurement of capture events in order to suppress low energy background. Fig. 4 shows a background spectrum taken with a cylindrical 10 cm × 10 cm B G O detector in a measuring time of 24 h. The background is dominated by the gamma-ray lines from the decay of 4°K (1.4 MeV) and from the day of 212 Po and 2°8T1 (2.6 MeV). At higher energies the background drops by two orders of magnitude. This suggests the choice of a threshold energy around 3 MeV. In that case the following conclusions can be drawn from the present calculations: (1) The differences in efficiency between SW(MIN) and SW(MAX) are on the average 0.4%, 0.7% and 1.2% for B G O crystals with 12 cm, 10 cm and 8 cm thickness, respectively. The corresponding values range between 0.7% and 1.9% for BaF 2 crystals with thicknesses between 20 cm and 12.5 cm. This indicates that the systematic uncertainty in the efficiency calculation due to the approximations in the code is less than 0.5% if a thickness of at least 10 cm B G O or 17 cm BaF 2 is chosen.
o
£o
~o
o60
o~o
1ooo
CHANNEL
Fig. 4. Gamma-ray background measured with a cylindrical BGO detector (10 cm diameter, 10 cm thickness).
(2) The absolute detection efficiency is - 95% for a 10 cm thick B G O detector. It increases to 97% for 12 cm, but decreases to 91% for 8 cm thickness. A BaF 2 detector of 17.5 cm thickness is comparable to a B G O crystal of 10 cm thickness. (3) The difference in efficiency for neutron capture cascades from nuclei with widely different binding energies, gamma-ray multiplicities and capture gamma-ray spectra is - 1 % for a 10 cm thick B G O detector. It decreases to 0.5% for 12 cm and increases to 1.5% for 8 cm thickness. Thus the systematic uncertainty caused by the calculation of capture cascades is certainly less than 0.3% if a thickness of at least 10 cm is chosen. (4) The efficiency is insensitive to a change of the inner radius by 2 cm. F r o m the above points one may conclude that the absolute efficiency can be determined with an accuracy of better than 1%. However, a spherical shell of at least 10 cm B G O or 17 cm BaF 2 thickness should be used for the final design. In absolute measurements of capture cross sections the neutron flux has to be determined with the same accuracy as the capture rate. As this may be problematic in most applications, relative measurements are preferable. In these cases many systematic uncertainties like e.g. gamma-ray self-absorption in the sample or multiple scattering are strongly reduced or cancel out, and the flux determination is avoided. Especially in investigations for nuclear astrophysics most of the interesting questions can be solved by very accurate measurements of cross section ratios (ref. 1).
8/18
10 /2 0
99.81 98.87 98.54 97.73 96.49 94.44 92.26 88.97 85.42 81.27 73.31 44.68
Ri/Ro (cm):
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
99.89 99.40 99.22 98.77 98.05 96.82 95.48 93.37 90.95 87.70 80.36 50.06
9/21
Il l
99.64 99.40 99.22 98.77 98.05 96.82 95.48 93.36 90.94 87.68 80.33 50.04
8/20
IV
99.64 97.76 97.10 95.60 93.44 90.04 86.55 81.54 76.42 70.99 62.19 36.34
10/18
V
99.64 97.76 97.10 95.59 93.43 90.03 86.53 81.52 76.42 70.92 62.09 36.22
8/16
VI
99.82 98.88 98.64 97.94 96.90 94.95 93.28 90.18 86.71 83.87 81.47 73.75
10/20
I
99.82 98.88 98.64 97.94 96.90 94.94 93.27 90.17 86.69 83.84 81.42 73.68
8/18
II
99.90 99.41 99.28 98.89 98.30 97.12 96.12 94.18 92.01 90.26 88.73 81.72
9/ 21
Ill
99.90 99.41 99.28 98.89 98.30 97.13 96.12 94.18 92.01 90.24 88.69 81.68
8/20
IV
99.66 97.79 97.28 95.95 94.13 90.88 88.17 83.37 78.10 73.74 70.23 61.85
10/18
V
Results obtained assuming SW(MAX) for monoenergetic g amma rays
99.66 97.78 97.27 95.95 94.12 90.88 88.15 83.37 78.08 73.71 70.16 61.76
8/16
VI
0.97 1.19 1.02 - 0.60
1.19 - 0.81 0.15 1.17
%( 24XAm)/o~(I97Au) 2.0 0.97 2.5 1.19 3.0 1.02 3.5 - 0.58
ov ( 56F e ) / % (19VAu) 2.0 -- 1.19 2.5 0.80 3.0 0.15 3.5 1.17
10/20
-0.70 0.48 0.08 0.70
0.56 0.71 0.65 0.34
9/ 21
-0.70 - 0.48 0.08 0.70
0.56 0.71 0.64 - 0.35
8/20
- 1.99 - 1.27 0.36 2.02
1.70 1.93 1.47 1.19
10/18
- 1,99 - 1.26 0.36 2.03
1.71 1.93 1.47 - 1.20
8/16
- 1.26 - 0.92 - 0.03 0.64
0.91 1.39 1.82 0.32
10/20
-- 1.26 - 0.92 - 0.02 0.65
0.91 1.39 1.83 0.32
8/18
I!
-- 0.73 -- 0.55 - 0.02 0.37
0.52 0.82 1.13 0.26
9/21
Il l
0.73 -- 0.55 0.02 0.37
0.52 0.82 1.13 0.26
8/20
IV
~ 2.10 1.46 0.07 1.20
1.62 2.28 2.76 0.20
10/18
V
8/18
Vl
I
V
R ~/R o (cm):
IV
II
Configuration: 1
III
Results obtained assuming SW(MAX) for monoenergetic gamma rays
E (MeV) Results obtained assuming SW(MtN) for monoenergetic gamma rays
the threshold energy E. (All values are given in percent.)
2.tt.~ t.46 0.06 t .2 l
1.62 2.28 2.75 0.20
8/16
VI
Table 4 Difference in efficiency c(sample) - ¢(reference sample) as expected in a relative measurement of capture cross section using a BGO detector and a gold standard in dependence of
99.81 98.87 98.54 97.73 96.49 94.44 92.26 88.96 85.39 81.23 73.25 44.62
II
Configuration: 1
E (MeV) Results obtained assuming SW(MIN) for monoenergetie ga mma rays
Table 3 Efficiency of a spherical shell of BGO for neutron capture cascades emitted in the 197Au + FI reaction in dependence of the threshold energy E. (All values are given in percent.}
~e
391
K. Wisshak et al. / Efficiency of a 4~r BGO or BaF, detector
Table 5 Difference in efficiency c(sample)- ~(reference sample) as' expected in a relative measurement of capture cross section using a BaF2 detector and a gold standard in dependence of the threshold energy E. (All values are given in percent.) Results obtained assuming SW(MAX) for monoenergetic gamma rays
Results obtained assuming SW(MIN) for monoenergetic gamma rays Configuration:
I
!I
IIl
IV
I
II
III
IV
10/22.5
10/25
10/27.5
10/30
10/22.5
10/25
10/27.5
10/30
% ( 241Am)/ov ( 197Au) 2.0 1.99 2.5 1.62 3.0 0.41 3.5 - 2.65
1.36 1.23 0.51 - 1.63
0.92 0.88 0.46 - 1.07
0.62 0.62 0.35 - 0.76
1.99 2.62 3.06 0.26
% ( 56Fe)/% ( 197Au) 2.0 - 2.43 2.5 - 1.60 3.0 0.23 3.5 2.29
- 1.71 - 1.20 0.02 1.48
- 1.18 -0.85 - 0.03 0.98
- 0.80 -0.58 - 0.04 0.65
- 2.67 - 1.97 - 0.24 1.02
ERi/Ro
(cm):
With gold as a s t a n d a r d we illustrate the situation with the example of a relative m e a s u r e m e n t % ( 5 6 F e ) / %(~97Au) a n d ov(2alAm)/o'y(197Au). In tables 4 a n d 5 the difference of the efficiency for sample a n d reference sample is given as a function of the threshold energy E s for all configurations considered here. It is found that this difference is of the order of 1% or even less if a B G O detector thickness of a least 10 cm or a BaF 2 detector thickness of 17 cm is chosen. The results differ in general by less than 0.5% between the two assumptions S W ( M I N ) a n d S W ( M A X ) . Keeping in m i n d that the present examples represent cases with extreme differences in the capture g a m m a - r a y spectra, b i n d i n g energies a n d cascade multiplicities, one may conclude that the systematic uncertainty in a relative m e a s u r e m e n t due to the difference in efficiency can be reduced to less t h a n 0.5% for most practical applications. This holds especially for the suggested m e a s u r e m e n t s in nuclear astrophysics [1] where cross section ratios of neighboring nuclei have to be determined.
4. Conclusions A spherical shell of B G O with - 10 cm thickness or BaF 2 with - 1 7 cm thickness a n d a n inner radius of 8 - 1 0 cm offers a n efficiency for g a m m a - r a y cascades following n e u t r o n capture which is high enough to reduce the correlated systematic u n c e r t a i n t y to less t h a n 1% in absolute m e a s u r e m e n t s a n d less than 0.5% in relative measurements. This holds even for isotopes with widely different b i n d i n g energies, capture g a m m a - r a y spectra a n d cascade multiplicities. It holds the more in case of an actual detector because then the theoretical
-
1.32 1.87 2.40 0.57
0.87 1.29 1.75 0.56
0.58 0.88 1.24 0.47
- 1.87
- 1.28 1.03 -0.27 0.27
-0.86 -0.71 -0.21 0.14
1.45
-0.31 0.52
-
calculation of the detection probability SW a n d the capture g a m m a - r a y spectra can be replaced by direct measurements. Such a detector which can be realised with presently available crystals by subdivision into 32 or 42 elements [1] will be able to increase the accuracy of present day techniques for capture cross section m e a s u r e m e n t s at least by a factor of 5. It will be able to meet the accuracy of nuclear data requirements for nuclear astrophysics as well as for reactor design. The present p a p e r concentrates on the detector efficiency but as the aspect of n e u t r o n sensitivity is also very important, we finally add some qualitative argum e n t s showing that this will not severely affect the accuracy of the measurements. 1) A t low energies (in the eV range) n e u t r o n s scattered from the sample m a y be shielded effectively by a thin layer of 6Li or l°B inside the spherical shell. 2) At higher energies ( 1 0 - 1 0 0 keV) time-of-flight discrimination of scattered neutrons is applicable if p r i m a r y flight p a t h s of 5 0 - 1 0 0 cm are used as it is possible at Van de G r a a f f accelerators. Moreover, in the keV range the ratio of scattering to capture in b o t h scintillator materials is of the order of 20-100; therefore scattered n e u t r o n s have a high p r o b a b i l i t y to escape from the detector before being c a p t u r e d because the scattering length is of the order of 2 cm. But if n e u t r o n s are captured after 5 - 1 0 scattering events the respective g a m m a - r a y s are also already delayed in time a n d can thus be discriminated from primary events. The arguments, however, will be p u t on a more quantitative basis in a forthcoming publication. We would like to t h a n k F. F a b b r i and G. Reffo for m a k i n g available the individual capture cascades needed
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K. Wisshak et al. / Efficiency oj a 4+r B G O or B a F , detector
for the present calculations. We appreciate very much the help of J. Oehlschl~ger in handling the code to calculate the efficiency for monoenergetic gamma-rays.
References [1] F. K~tppeler, G. Schatz, and K. Wisshak, KfK 3472, Kernforschungszentrum Karlsruhe (1983). [2] M. Moszynski, C. Gresset, J. Vacher and R. Odru, Nucl. Instr. and Meth. 188 (1981) 403. [3] D.M. Drake, L.R. Nilsson, and J. Faucett Nucl. Instr. and Meth. 188 (1981) 313. [4] M. Kobayashi, S.I. Kurokawa, S. Sugimoto, Y. Yoshimura, M. Chiba, H. Yoshida, M. Ishii, S. Akiyama and H. Ishibashi, Nucl. Instr. and Meth. 189 (1981) 629. [5] P. Pavlopoulos, M. Hasinoff, J. Repond+ L. Tauscher, D. Tr6ster, M. Rousseau, K. Fransson, T. Alberis and K. Zioutas, Nucl. Instr. and Meth. 197 (1982) 331. [6] R.M. Diamond and F.S. Stephens, The high resolution ball, unpublished proposal.
17] M.A. Lone+ O. H~usser+ T.K. Alexander+ J. Ga~,c~;n and 1+++ Hageberg, BGO Conf., Princeton. and private communications. [8] J.X. Saladin, C. Baktash, I.Y. Lee+ R. Blue, R. Ronningen and R.A. Sorensen+ Progress Report+ Michigan State Lniversity (1982). [9] M+ Laval, M. Moszynski, R. Allemand, E. Cormoreche, P. Guinet, R. Ordu and J. Vacher. Nuct. Instr. and Meth. 206 (1983) 169. [10] K. Wisshak, F. K~.ppeler and G. Schatz, KfK 3580 Kernforschungszentrum Karlsruhe (1983). [11] G. Schatz and J. Oehlschl~.ger+ KfK 3710, Kernforschungszentrum Karlsruhe (1984). [12] G. Reffo, F. Fabbri, K. Wisshak and F. K~ippeler. Nucl. Sci. Eng. 80 (1982) 630. [13] K. Wisshak, J. Wickenhauser+ F. K~ippeler+ G. Reffo and F. Fabbri, Nucl. Sci. Eng 81 (1982) 396. [14] K. Wisshak, F. K~tppeler, G. Reffo and F. Fabbri, KfK 3515, Kernforschungszentrum Karlsruhe (1983).