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On the use of a NaI(Tl) crystal detector for neutron capture cross section measurements
NUCLEAR
INSTRUMENTS
A N D M E T H O D S 98 ( I 9 7 2 ) I 7 5 - I 7 7 ;
© NORTH-HOLLAND
PUBLISHING
CO.
ON T H E USE OF A NaI(TI) CRYSTAL D E T E C T O R FOR NEUTRON CAPTURE CROSS SECTION MEASUREMENTS H. VAN HALEM*, A. D. T U R R I A N and L. M. CASPERS
Interuniversitair Reactor Instituut, Delft, The Netherlands Received 21 July 1971
For a NaI(TI) crystal an electronic weighting function has been calculated with which cascade independent measurements of the absorption cross section aa can be made. The function appears to be approximately proportional to the energy.
1. Introduction
Since for most isotopes the possible gamma cascades following neutron capture are known incompletely any detector for determining (n#) cross sections should be cascade independent. As is well known this may be achieved by using: (1) detectors with 100% efficiency') for any capture event, or (2) detectors with an efficiency proportional to the photon energy. The proportionality may be obtained in "hardware", such as in Moxon-Rae type detectors 2- s) or by means of "electronic pulse weighting" as has been applied by, amongst others, Macklin and Gibbons6'7). They determined suitable weighting functions for detectors based on a plastic and a liquid scintillator. The pulse weighting technique may in principle be applied to any detector, provided its electronic response as a function of gamma energy is known. For NaI (TI) crystals this response has been tabulated and, moreover, may for various sample/detector geometries be calculated numerically with e.g. the E F N A I program 8) available from the E N E A Library. Since NaI(T1) detectors have (for the same volume) a higher efficiency than plastic scintillators it seemed worthwhile to determine the appropriate weighting function. We based our study on the geometry indicated in fig:. 1 which we intend to use in future experiments.
where B n is the binding energy of the neutron. The summed response S of the detector to N captures, leading to the same decay mode is:
s = N Z
i=l
where F(Er,) is the detector response to a photon with energy E w When F(Er,)=kEr, it follows: S = c o n s t . (E,+Bn) , hence S has become decay-independent. We separate F(E~) into two factors:
F(Er)= P(E~)"G(E~),
P(E~) is the gamma interaction probability and G(Er) is an "electronic" response function. Define P(Er, r, f2)drdf2 as the probability that a
where
gamma photon with energy Er, leaving the sample from area dr around position r (see fig. 1) in solid angle dr2 around direction f2 has an interaction in the crystal. P(E~) follows from
P(E~) = f dr~P(Er, r, f2)df2. * Present address: Comprimo N.V., Amsterdam, The Netherlands. ~)=
90 m m
photo
crystal
I"
~/)0
d
__i - ~(~--.-Tff0m m
-
multiplier
2. Discussion
Consider a particular decay mode, consisting of rn photons with energy Ei, following the capture of a neutron with energy En. Then
~
Er~ =
B. + En,
.~__ Collimated
760
mm
~v
neutron beam
Fig. 1. Sample/detector geometry; d = distance between centre of cylindrical sample and detector front face, O = angle between
sample normal and detector axis.
i=l
175
176
H. V A N H A L E M et al.
Define also N(E~,Ee)dEe as the probability that a g a m m a interaction in the crystal gives an electric pulse with a voltage between Ee and Eo + dEe. We use normalised spectra, so
f l ~"N(E~,Ee)dE~ =
250 W(Ee)
I
1.
200
Legend
The electronic response function
150
S? []
8 =~/2, d:Scm 8 =77"/2, d=lOcm
0
0 =1.75° (rod),d=8cm
J~7
equals unity if no pulse weighting is applied. In that case F(E~)=P(E~), otherwise
F(E,) = P(E,)"
N(E.,,E~)W(Ee)dE¢.
,oo
N(E~, E¢) and P(ET)have -
for the geometry outlined in fig. 1 - been computed with the E F N A I programme for E 7 varying from 350 keV to l l.2 MeV in steps of 350 keY. The purpose of introducing W(E~) is, of course, to obtain the desired proportionality between F(E~) and E r Hence W(Ee) should fulfil the following relation:
P(ET).f~TN(Ev, Ee) W(Ee)dEe=kE7,
(1)
which in discretised form reads i
Z N(ETi,Eej)W(gej) = kETi/P(ETi) (i= 1 t o n), (2) j=l where the fixed step in Ee, AE~, has been absorbed into the constant k. The values W(E~j), j = 1 to n, follow
5O
0
1
2
3
4
5
6
7 8 ~- Ee (MeV)
9
Fig. 2. Weighting function for various sample-detector geometries (cf. fig. 1). The results have not been corrected for detector resolution. For clarity of presentation not all measured points are shown and the energy region above 9 M e V has been left out.
Ee(E~) = f~N(Er, E~)EedEe
from solving this set of equations. 3. Results Fig. 2 shows weighting functions calculated for 32 energy points in steps of 350 keV for a 3" x 3" NaI(T1) crystal and the source-crystal geometry shown in fig. 1 for three cases, i.e. (a) d = 8 cm, 0 = zr/2; (b) d = 10 cm, 0 = n/2; (c) d = 8 cm, 0 = 1.750 rad. The relatively large energy steps have been chosen to save analyzer memory. We note that the weighting function is proportional to the electron energy within about 5%. This "linearity" is rather fortunate, because a) it makes corrections for multiple detection of photons resulting from the same capture event unnecessary as has been pointed out by Czirr 9) and b) on-line linear weighting can be easily realized in hardware. Investigations of the E F N A I results show P(E~) to be approximately constant between 1 and 10 MeV. Moreover, the average electronic energy
shows to be proportional with E r Considering these facts one may expect that the solution of eq. (2) yields a linear W(Ee) function. For other (smaller) crystals non-linear weighting functions may, however, still be possible. Although the above results look promising, we must make the following observations: 1. The E F N A I program assumes an isotropic source distribution of the emitted g a m m a photons. Anisotropy in the g a m m a production will affect the weighting function. 2. The E F N A I program only treats the bare NaI(T1) crystal. Possible backscattering effects due to shielding are still to be evaluated. The same holds for further background effects. 3. Neutrons scattered by the sample into the NaI(T1) crystal give capture g a m m a rays and activate both Na and I. Since for many isotopes a(n,n) is much
NaI(TI) CRYSTAL DETECTOR larger t h a n a(n,y) the crystal should be shielded against n e u t r o n s (e.g. with borated paraffin). This will p r o b a b l y limit the use of N a l (T1) for a , measurements to low energy n e u t r o n s ( < 2 - 3 keV). The above points still need further theoretical and experimental verification.
References 1) j. H. Gibbons, R. L. Macklin, P. D. Miller and J. H. Neiler, Phys. Rev. 122, no. 1 (1961) 182. 2) M. C. Moxon and E. R. Rae, in Neutron time-of-flight methods (ed. J. Spaepen; EURATOM, Brussels, 1961).
177
a) M. C. Moxon and E. R. Rae, Nucl. Instr. and Meth. 24 (1963) 445. a) H. Weigmann, G. Carraro and K. H. B6ckhoff, Nucl. Instr. and Meth. 50 (1967) 265. 5) R. L. Macklin, J. H. Gibbons and T. Inada, Nucl, Phys. 43 (1963) 353. 6) R. L. Macklin and J. H. Gibbons, WASH-1053 (1964) p. 57. 7) R. L. Macklin and J. H. Gibbons, Phys. Rev. 159, no. 4 (1967) 1007. s) M. Giannini, P. R. Oliva and M. C. Ramoniro, CNEN Report RT/Fi (1969) p. 15. 9) j. B. Czirr, Nucl. Instr. and Meth. 72 (1969) 23.
INSTRUMENTS
A N D M E T H O D S 98 ( I 9 7 2 ) I 7 5 - I 7 7 ;
© NORTH-HOLLAND
PUBLISHING
CO.
ON T H E USE OF A NaI(TI) CRYSTAL D E T E C T O R FOR NEUTRON CAPTURE CROSS SECTION MEASUREMENTS H. VAN HALEM*, A. D. T U R R I A N and L. M. CASPERS
Interuniversitair Reactor Instituut, Delft, The Netherlands Received 21 July 1971
For a NaI(TI) crystal an electronic weighting function has been calculated with which cascade independent measurements of the absorption cross section aa can be made. The function appears to be approximately proportional to the energy.
1. Introduction
Since for most isotopes the possible gamma cascades following neutron capture are known incompletely any detector for determining (n#) cross sections should be cascade independent. As is well known this may be achieved by using: (1) detectors with 100% efficiency') for any capture event, or (2) detectors with an efficiency proportional to the photon energy. The proportionality may be obtained in "hardware", such as in Moxon-Rae type detectors 2- s) or by means of "electronic pulse weighting" as has been applied by, amongst others, Macklin and Gibbons6'7). They determined suitable weighting functions for detectors based on a plastic and a liquid scintillator. The pulse weighting technique may in principle be applied to any detector, provided its electronic response as a function of gamma energy is known. For NaI (TI) crystals this response has been tabulated and, moreover, may for various sample/detector geometries be calculated numerically with e.g. the E F N A I program 8) available from the E N E A Library. Since NaI(T1) detectors have (for the same volume) a higher efficiency than plastic scintillators it seemed worthwhile to determine the appropriate weighting function. We based our study on the geometry indicated in fig:. 1 which we intend to use in future experiments.
where B n is the binding energy of the neutron. The summed response S of the detector to N captures, leading to the same decay mode is:
s = N Z
i=l
where F(Er,) is the detector response to a photon with energy E w When F(Er,)=kEr, it follows: S = c o n s t . (E,+Bn) , hence S has become decay-independent. We separate F(E~) into two factors:
F(Er)= P(E~)"G(E~),
P(E~) is the gamma interaction probability and G(Er) is an "electronic" response function. Define P(Er, r, f2)drdf2 as the probability that a
where
gamma photon with energy Er, leaving the sample from area dr around position r (see fig. 1) in solid angle dr2 around direction f2 has an interaction in the crystal. P(E~) follows from
P(E~) = f dr~P(Er, r, f2)df2. * Present address: Comprimo N.V., Amsterdam, The Netherlands. ~)=
90 m m
photo
crystal
I"
~/)0
d
__i - ~(~--.-Tff0m m
-
multiplier
2. Discussion
Consider a particular decay mode, consisting of rn photons with energy Ei, following the capture of a neutron with energy En. Then
~
Er~ =
B. + En,
.~__ Collimated
760
mm
~v
neutron beam
Fig. 1. Sample/detector geometry; d = distance between centre of cylindrical sample and detector front face, O = angle between
sample normal and detector axis.
i=l
175
176
H. V A N H A L E M et al.
Define also N(E~,Ee)dEe as the probability that a g a m m a interaction in the crystal gives an electric pulse with a voltage between Ee and Eo + dEe. We use normalised spectra, so
f l ~"N(E~,Ee)dE~ =
250 W(Ee)
I
1.
200
Legend
The electronic response function
150
S? []
8 =~/2, d:Scm 8 =77"/2, d=lOcm
0
0 =1.75° (rod),d=8cm
J~7
equals unity if no pulse weighting is applied. In that case F(E~)=P(E~), otherwise
F(E,) = P(E,)"
N(E.,,E~)W(Ee)dE¢.
,oo
N(E~, E¢) and P(ET)have -
for the geometry outlined in fig. 1 - been computed with the E F N A I programme for E 7 varying from 350 keV to l l.2 MeV in steps of 350 keY. The purpose of introducing W(E~) is, of course, to obtain the desired proportionality between F(E~) and E r Hence W(Ee) should fulfil the following relation:
P(ET).f~TN(Ev, Ee) W(Ee)dEe=kE7,
(1)
which in discretised form reads i
Z N(ETi,Eej)W(gej) = kETi/P(ETi) (i= 1 t o n), (2) j=l where the fixed step in Ee, AE~, has been absorbed into the constant k. The values W(E~j), j = 1 to n, follow
5O
0
1
2
3
4
5
6
7 8 ~- Ee (MeV)
9
Fig. 2. Weighting function for various sample-detector geometries (cf. fig. 1). The results have not been corrected for detector resolution. For clarity of presentation not all measured points are shown and the energy region above 9 M e V has been left out.
Ee(E~) = f~N(Er, E~)EedEe
from solving this set of equations. 3. Results Fig. 2 shows weighting functions calculated for 32 energy points in steps of 350 keV for a 3" x 3" NaI(T1) crystal and the source-crystal geometry shown in fig. 1 for three cases, i.e. (a) d = 8 cm, 0 = zr/2; (b) d = 10 cm, 0 = n/2; (c) d = 8 cm, 0 = 1.750 rad. The relatively large energy steps have been chosen to save analyzer memory. We note that the weighting function is proportional to the electron energy within about 5%. This "linearity" is rather fortunate, because a) it makes corrections for multiple detection of photons resulting from the same capture event unnecessary as has been pointed out by Czirr 9) and b) on-line linear weighting can be easily realized in hardware. Investigations of the E F N A I results show P(E~) to be approximately constant between 1 and 10 MeV. Moreover, the average electronic energy
shows to be proportional with E r Considering these facts one may expect that the solution of eq. (2) yields a linear W(Ee) function. For other (smaller) crystals non-linear weighting functions may, however, still be possible. Although the above results look promising, we must make the following observations: 1. The E F N A I program assumes an isotropic source distribution of the emitted g a m m a photons. Anisotropy in the g a m m a production will affect the weighting function. 2. The E F N A I program only treats the bare NaI(T1) crystal. Possible backscattering effects due to shielding are still to be evaluated. The same holds for further background effects. 3. Neutrons scattered by the sample into the NaI(T1) crystal give capture g a m m a rays and activate both Na and I. Since for many isotopes a(n,n) is much
NaI(TI) CRYSTAL DETECTOR larger t h a n a(n,y) the crystal should be shielded against n e u t r o n s (e.g. with borated paraffin). This will p r o b a b l y limit the use of N a l (T1) for a , measurements to low energy n e u t r o n s ( < 2 - 3 keV). The above points still need further theoretical and experimental verification.
References 1) j. H. Gibbons, R. L. Macklin, P. D. Miller and J. H. Neiler, Phys. Rev. 122, no. 1 (1961) 182. 2) M. C. Moxon and E. R. Rae, in Neutron time-of-flight methods (ed. J. Spaepen; EURATOM, Brussels, 1961).
177
a) M. C. Moxon and E. R. Rae, Nucl. Instr. and Meth. 24 (1963) 445. a) H. Weigmann, G. Carraro and K. H. B6ckhoff, Nucl. Instr. and Meth. 50 (1967) 265. 5) R. L. Macklin, J. H. Gibbons and T. Inada, Nucl, Phys. 43 (1963) 353. 6) R. L. Macklin and J. H. Gibbons, WASH-1053 (1964) p. 57. 7) R. L. Macklin and J. H. Gibbons, Phys. Rev. 159, no. 4 (1967) 1007. s) M. Giannini, P. R. Oliva and M. C. Ramoniro, CNEN Report RT/Fi (1969) p. 15. 9) j. B. Czirr, Nucl. Instr. and Meth. 72 (1969) 23.