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A fast neutron spectrometric technique
NUCLEAR INSTRUMENTS AND METHODS 40 (I966) 235-237; © NORTH-HOLLAND PUBLISHING CO.
A FAST NEUTRON
SPECTROMETRIC
TECHNIQUE
D R. KOEHLER and J. T. GRISSOM
Army Mlssde Command, Redstone Arsenal, Alabama Received 30 September 1965 A new fast neutron spectromemc techmque is described which incorporates the proton recoil distribution as a measure of the responsible neutron energy spectrum The protons are present in a scintillator material and therefore the proton energy dlstrlbutmn
is observed through a hght detectmn system Subsequent analysis of the hght spectrum unfolds the neutron distribution in excellent agreement w~th the original neutron spectrum.
Neutron spectrometry is handicapped by the paucity of neutron interactions to utilize in a spectrometric techmque. Consequently, the state-of-the-art in directional flux spectrometry is represented for example by time-of-flight techniques and in non-directional flux spectrometry by foil activation techniques. The present work describes the development of a neutron spectrometric technique for utlhzatlon in unqualified neutron environments. The system is not limited to pure neutron fluxes but can be used, through incorporation of standard gamma-ray discrimination techniques, in a mixed neutron, gamma-ray environment. The technique uses the proton energy distribution, resulting from recoils w~th incident neutrons, as a measure of the neutron energy distribution. The theory of neutron scattering from hydrogen (protons) is well understood and documented in many textbooks. When neutrons, of energy En, scatter through interaction with protons, the resultant scattering is isotroplc for lab. energies up to ~ 14 MeV and leads to an energy distribution of the recoiling protons which is flat~). That as, the number of protons in the energy interval from Ep to Ep+dEp is
tion technique employs the fact that the light pulses from protons have a different decay time than the light pulses from electrons produced by gamma rays and therefore one can electronically discriminate against the gammas. Due to the non-linearlty of light production as a function of proton energy the actual "output light spectrum" is
Nn(En)
Np(Ep) dEp = C O~
dEp,
NL(P ) = dEp fEn(max)CI°'(E,,) Nn(E.) dEn,
dP~p
En
where
dEp/dP = { 1 + kB(dEp/dx) } is the non-linear response function of the scintillator as given by Blrks 2' 3). Up to this point nothing new has been stated. The technique of this work involves utilizing this integral output light spectrum to unfold the neutron energy spectrum Nn(E.). By dividing the light spectrum by
dEp/dP = F(Ep) and differentiating, we obtain
(1)
d
up to a maximum E,, where Co is a constant, Nn(E,) is the number of neutrons and E n is the energy of these monoenergetic neutrons. For the case of a non-monoenergetic neutron source
{
fen()
NL(Ep) t
F(ep) J =
.... C I ~ p~ ,a(E.)N.(En)~ [ K ] dE.
a{En(max)}Nn{En(max)} dEn(max) + Ci
E~(max)
Np(Ep)dEp =
dEp
fEn(maX)CltYn(En)~ .
N.(E.)
dEn, (2)
_
,d Ep
where now Nn(E~,) is the incident neutron energy distribution and o(E,) is the scattering cross section at energy E.. The spectrometric technique under discussion utilizes the proton scatterer in the form of a plastic or hydrogenous scintillator. Consequently, the recoiling protons will generate light pulses. The gamma-ray discrimina-
dEp
_ Cla(Ep ) Nn(Ep) dEp Ep
.
(3)
dEp
a(Ep)N.(Ep) C1"
(4)
Ep Finally then we "solve" for N.(Ep) by multiplying our differentiated spectrum by - Ep/{o(Ep)C,
).
All steps of this technique were readily performed on the IBM 7094 computer. 235
236
D. R. K O E H L E R A N D J. T. G R I S S O M
For this part of the calculation, the response function given by Birks, that is,
3oo
d P / d E = { 1 + k B ( d E / d x ) }- t wxth k B = 0.0120 m g / c m 2" keV, was approximated by d P / d E = 0.253 E ° 445. This approximation in no way causes a loss of generality to the techmque and for that matter a light response function in experimental tabular form could be used m an actual application.
~00
104
I/
~'
o
:~
I
i
i
6
~
,o
ENERGY
,~
IN MeV
Fig. 1 I n p u t neutron d~stnbution.
c
~, 103
To demonstrate the technique, a neutron spectrum was fabricated in the f o r m o
3
N.(E.) = Z
Amexp[-(En-Em) 2/2¢7z]
~ro~ o g
m=t
g
which IS displayed m fig. 1. The resulting proton recoil spectrum, eq. (2), is shown in fig. 2 where 4) o'(En) :
F3/(E n+4.30)+
F-
IOI y
1/(E.+0.08)] x X
Np
N[
"---
j
Nn
1.3l(10) -24 cm 2.
This proton recoil spectrum is further modified by the light response function to yield the final light spectrum.
300
too
t°'l /
~
z o t
0 ~: zoo l,-¢/) £3
I00
i
I
4.
i
[
l
I
L
i
i
6 8 I0 ENERGY IN MEV
I
12
l
i
14
Fig 3 Distributions: Nn = neutron spectrum; Np = proton recoil spectrum; N L = hght spectrum.
_J z o I--
2
Np)
Q.
ENERGY
IN MeV
Fig. 2. Recod proton and generated light spectra.
The resultant light spectrum is also shown in fig. 2 The p r o t o n recoil dxstribution and output light dtstrlbution are displayed again in fig. 3 on a semi-logarithmic plot where the input neutron distribution is also shown for reference purposes The dramatic lack o f structure in the light spectrum incurred through the original p r o t o n recoiling process and the subsequent light production process, seen in these figures is to be contrasted with the structured neutron distribution
A FAST N E U T R O N S P E C T R O M E T R I C T E C H N I Q U E
300
~200
I00
2
4
6
ENERCY
8
IN NleV
I0
12
Fig. 4 Unfolded neutron energy spectrum.
After applying the described data analysis technique a reconstructed neutron spectrum, the upper curve of fig. 4, was generated. This curve has been displaced along the positive ordinate axis in order to facilitate comparison with the initial input neutron spectrum which is the lower curve of this figure. For no part of the distrlbut'on was there more than a 2 ~ difference
237
and for the major portion the agreement was better than 1 ~ . We have not considered in the present work corrections for crystal end and side effects, carbon recoil effects, multiple scattering nor experimental resolution effects~); however, the crystal size effects and multiple scattering can be minimized through proper design of the scintillator. A program to unfold the experimental smearing is underway and preliminary results indicate that the techniques proposed in that area will be fruitful. In summary, the presently described work offers a spectrometric technique which should prove useful to neutron spectroscopists. This neutron spectrometer is merely a hydrogenous scintillator plus photomultlplier tube, with the associated electronics for gamma-ray discrimination and multichannel analysis. The spectroscopic information is generated from the light output spectrum through a computer oriented data analysis program and, as has been shown, this data analysis is the heart of the spectrometer system. References
1) C. D Swartz and G. E. Owen, in Fast Neutron Phystcs 1 (ed J B Marion and J. L. Fowler, Intersclence, New York, 1960) Ch II B. 2) j 8. Birks, Proc. Phys. Soc. (London) 64A (1951) 874. 3) J B. Birks, Phys. Rev. 84 (1951) 364. 4) H A. Bethe and R. F Bacher, Rev. Mod. Phys. 8 (1936) 117.
A FAST NEUTRON
SPECTROMETRIC
TECHNIQUE
D R. KOEHLER and J. T. GRISSOM
Army Mlssde Command, Redstone Arsenal, Alabama Received 30 September 1965 A new fast neutron spectromemc techmque is described which incorporates the proton recoil distribution as a measure of the responsible neutron energy spectrum The protons are present in a scintillator material and therefore the proton energy dlstrlbutmn
is observed through a hght detectmn system Subsequent analysis of the hght spectrum unfolds the neutron distribution in excellent agreement w~th the original neutron spectrum.
Neutron spectrometry is handicapped by the paucity of neutron interactions to utilize in a spectrometric techmque. Consequently, the state-of-the-art in directional flux spectrometry is represented for example by time-of-flight techniques and in non-directional flux spectrometry by foil activation techniques. The present work describes the development of a neutron spectrometric technique for utlhzatlon in unqualified neutron environments. The system is not limited to pure neutron fluxes but can be used, through incorporation of standard gamma-ray discrimination techniques, in a mixed neutron, gamma-ray environment. The technique uses the proton energy distribution, resulting from recoils w~th incident neutrons, as a measure of the neutron energy distribution. The theory of neutron scattering from hydrogen (protons) is well understood and documented in many textbooks. When neutrons, of energy En, scatter through interaction with protons, the resultant scattering is isotroplc for lab. energies up to ~ 14 MeV and leads to an energy distribution of the recoiling protons which is flat~). That as, the number of protons in the energy interval from Ep to Ep+dEp is
tion technique employs the fact that the light pulses from protons have a different decay time than the light pulses from electrons produced by gamma rays and therefore one can electronically discriminate against the gammas. Due to the non-linearlty of light production as a function of proton energy the actual "output light spectrum" is
Nn(En)
Np(Ep) dEp = C O~
dEp,
NL(P ) = dEp fEn(max)CI°'(E,,) Nn(E.) dEn,
dP~p
En
where
dEp/dP = { 1 + kB(dEp/dx) } is the non-linear response function of the scintillator as given by Blrks 2' 3). Up to this point nothing new has been stated. The technique of this work involves utilizing this integral output light spectrum to unfold the neutron energy spectrum Nn(E.). By dividing the light spectrum by
dEp/dP = F(Ep) and differentiating, we obtain
(1)
d
up to a maximum E,, where Co is a constant, Nn(E,) is the number of neutrons and E n is the energy of these monoenergetic neutrons. For the case of a non-monoenergetic neutron source
{
fen()
NL(Ep) t
F(ep) J =
.... C I ~ p~ ,a(E.)N.(En)~ [ K ] dE.
a{En(max)}Nn{En(max)} dEn(max) + Ci
E~(max)
Np(Ep)dEp =
dEp
fEn(maX)CltYn(En)~ .
N.(E.)
dEn, (2)
_
,d Ep
where now Nn(E~,) is the incident neutron energy distribution and o(E,) is the scattering cross section at energy E.. The spectrometric technique under discussion utilizes the proton scatterer in the form of a plastic or hydrogenous scintillator. Consequently, the recoiling protons will generate light pulses. The gamma-ray discrimina-
dEp
_ Cla(Ep ) Nn(Ep) dEp Ep
.
(3)
dEp
a(Ep)N.(Ep) C1"
(4)
Ep Finally then we "solve" for N.(Ep) by multiplying our differentiated spectrum by - Ep/{o(Ep)C,
).
All steps of this technique were readily performed on the IBM 7094 computer. 235
236
D. R. K O E H L E R A N D J. T. G R I S S O M
For this part of the calculation, the response function given by Birks, that is,
3oo
d P / d E = { 1 + k B ( d E / d x ) }- t wxth k B = 0.0120 m g / c m 2" keV, was approximated by d P / d E = 0.253 E ° 445. This approximation in no way causes a loss of generality to the techmque and for that matter a light response function in experimental tabular form could be used m an actual application.
~00
104
I/
~'
o
:~
I
i
i
6
~
,o
ENERGY
,~
IN MeV
Fig. 1 I n p u t neutron d~stnbution.
c
~, 103
To demonstrate the technique, a neutron spectrum was fabricated in the f o r m o
3
N.(E.) = Z
Amexp[-(En-Em) 2/2¢7z]
~ro~ o g
m=t
g
which IS displayed m fig. 1. The resulting proton recoil spectrum, eq. (2), is shown in fig. 2 where 4) o'(En) :
F3/(E n+4.30)+
F-
IOI y
1/(E.+0.08)] x X
Np
N[
"---
j
Nn
1.3l(10) -24 cm 2.
This proton recoil spectrum is further modified by the light response function to yield the final light spectrum.
300
too
t°'l /
~
z o t
0 ~: zoo l,-¢/) £3
I00
i
I
4.
i
[
l
I
L
i
i
6 8 I0 ENERGY IN MEV
I
12
l
i
14
Fig 3 Distributions: Nn = neutron spectrum; Np = proton recoil spectrum; N L = hght spectrum.
_J z o I--
2
Np)
Q.
ENERGY
IN MeV
Fig. 2. Recod proton and generated light spectra.
The resultant light spectrum is also shown in fig. 2 The p r o t o n recoil dxstribution and output light dtstrlbution are displayed again in fig. 3 on a semi-logarithmic plot where the input neutron distribution is also shown for reference purposes The dramatic lack o f structure in the light spectrum incurred through the original p r o t o n recoiling process and the subsequent light production process, seen in these figures is to be contrasted with the structured neutron distribution
A FAST N E U T R O N S P E C T R O M E T R I C T E C H N I Q U E
300
~200
I00
2
4
6
ENERCY
8
IN NleV
I0
12
Fig. 4 Unfolded neutron energy spectrum.
After applying the described data analysis technique a reconstructed neutron spectrum, the upper curve of fig. 4, was generated. This curve has been displaced along the positive ordinate axis in order to facilitate comparison with the initial input neutron spectrum which is the lower curve of this figure. For no part of the distrlbut'on was there more than a 2 ~ difference
237
and for the major portion the agreement was better than 1 ~ . We have not considered in the present work corrections for crystal end and side effects, carbon recoil effects, multiple scattering nor experimental resolution effects~); however, the crystal size effects and multiple scattering can be minimized through proper design of the scintillator. A program to unfold the experimental smearing is underway and preliminary results indicate that the techniques proposed in that area will be fruitful. In summary, the presently described work offers a spectrometric technique which should prove useful to neutron spectroscopists. This neutron spectrometer is merely a hydrogenous scintillator plus photomultlplier tube, with the associated electronics for gamma-ray discrimination and multichannel analysis. The spectroscopic information is generated from the light output spectrum through a computer oriented data analysis program and, as has been shown, this data analysis is the heart of the spectrometer system. References
1) C. D Swartz and G. E. Owen, in Fast Neutron Phystcs 1 (ed J B Marion and J. L. Fowler, Intersclence, New York, 1960) Ch II B. 2) j 8. Birks, Proc. Phys. Soc. (London) 64A (1951) 874. 3) J B. Birks, Phys. Rev. 84 (1951) 364. 4) H A. Bethe and R. F Bacher, Rev. Mod. Phys. 8 (1936) 117.