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The calibration of 6Li semiconductor sandwich spectrometers
NUCLEAR
INSTRUMENTS
AND
METHODS
127
(1975)
61--72;
©
NORTH-HOLLAND
PUBLISHING
CO,
THE CALIBRATION OF 6Li S E M I C O N D U C T O R S A N D W I C H S P E C T R O M E T E R S P. J. C L E M E N T S
Materials Physics Dioision (Building 521), A.E.R.E., Harwell, Didcot, Oxon., OWll ORA, U.K. Received 8 April 1975 T h e 6Li Semiconductor Sandwich Spectrometers which are c o m m o n l y used for the m e a s u r e m e n t o f fast-neutron spectra, especially in reactors, are subject to a variety o f effects which, if n o t taken into account, can lead to significant calibration errors. T h e effects which are here discussed in detail are: (1) the energy degradation in the sensitive layer o f the spectrometer, (2) the alpha-particle contribution to the " r e s p o n s e f u n c t i o n "
(3)
It can ~30
1. Introduction 6Li semiconductor sandwich spectrometers are widely used for the measurement of fast-neutron spectra in reactors 1-6), and have recently found other applications 7, 8). The accuracy with which the spectrometer needs to be calibrated depends on the measurement for which it is being used, but for most purposes a calibration uncertainty leading to an uncertainty of more than a few per cent in the results of the measurement being made would probably be undesirable. It is the intention of the present discussion to demonstrate that of the several levels of sophistication of calibration corrections which can be made, some are sufficiently simple that they ought normally to be included as a routine part of the data-analysis procedure. The use of more detailed corrections would have to be justified by the overall increase in accuracy which could be obtained in view of the presence of other sources of error in any particular measurement. The modes of operation of 6Li sandwich spectrometers have been described elsewhere1), and a knowledge of the techniques used will therefore be assumed in the discussion which follows. The calibration of a 6ti sandwich spectrometer involves several separate stages. Some of the various calibration uncertainties which can arise during these stages have been considered by other authors for their spectrometer systems+'9). However, discussion of the major uncertainties which can arise during the use of the most common system, i.e. a sandwich spectrometer with the sensitive layer deposited on the face of one of the diodes and used in the " s u m - p e a k " and " t r i t o n " modes1), have not previously been collected together. In the first stage of calibration, the efficiency with which neutrons are detected must be specified as a
used to deconvolve the lower-energy part o f the n e u t r o n spectra, a n d the superposition o f a high-energy contribution on the lower part o f the m e a s u r e d s p e c t r u m in one m o d e o f operation o f the spectrometer. will be s h o w n that the failure to take account o f these effects in s o m e circumstances lead to energy-calibration errors o f keV a n d errors o f up to 50% in m e a s u r e d n e u t r o n spectra.
function of neutron energy. It has been demonstrated that for some designs of spectrometer the usual expression for the efficiency is inadequate1°), and that the efficiency should be written as: /3( E ) = Z O'n~t ( E ) G ( E ) B ( E ) ,
where A is a constant, E is the neutron energy, a,~ (E) is the 6Li(n, cot cross section, G(E) is a calculable geometrical efficiency, and B(E) is a calculable internal background factor. The methods of calculation of G(E)and B(E)have been described elsewhere1°-12), and values for these factors and for an~(E ) may be updated as more accurate values of the relevant nuclear data become available. The second stage of calibration is the assignment of an energy scale to the data collected during the measurement. The calibration in the sum-peak mode is usually carried out by detecting thermal neutrons using two different gain settings to generate spectral peaks at energies corresponding to known multiples of 4.785 MeV, the Q value of the reaction. The calibration in the triton mode is accomplished by using thermal neutrons to generate peaks corresponding to energies of 2.056 MeV and 2.729 MeV, the energies of the particle and triton produced by thermal-neutron detection. A 4.785 MeV peak would probably also be included in this calibration. The energy calibration in either mode of operation is subject to two sources of uncertainty. Firstly, the presence of electronic noise makes the position of the calibration peaks difficult to determine precisely. Secondly, in order that a neutron interacting in the sensitive region of the spectrometer should be recorded, the alpha particle and the triton produced by the interaction must together have travelled a total distance through 6LiF, the sensitive material 61
62
P. J. C L E M E N T S
of the spectrometer, of at least the thickness of the 6LiF layer. The alpha-particle, triton, and sum peaks therefore all have their own characteristic shapes due to energy loss in the 6LiF layer, and this can lead to significant errors in energy calibration unless the effect is taken into account. (There is also a small energy loss, typically an average of ~ 15 keV in the total energy, in the gold-layer electrodes on the diodes. A relatively crude correction for this is adequate.) The energy loss in the 6LiF layer is particularly important when fluxes of high-energy neutrons are being measured, where it may be necessary to use a thick layer of 6LiF in order to detect enough neutrons before the spectrometer suffers significant radiation damage. For example, if a 2.0 pg/mm 2 layer is used, no event in the summed calibration peak can have suffered an energy loss less than ,-~40 keV, and the average energy loss is considerably more than this. Calculation of the energy losses involved for one particular spectrometer design have been reported 9), but accurate corrections for these losses are not generally made. The third stage of calibration is the generation of suitable response functions for the spectra recorded in the triton and sum-peak modes. The generation of a simple triton response function has been described previouslyla), but both this matrix and response matrices used elsewhere generally omit two effects. Firstly, the triton suffers energy degradation as described above. Secondly, measurements made in the triton mode are usually regarded as being valid up to ,-~600 keV neutron energy. At this energy the lowerenergy end of the part of the triton spectrum generally used in the analysis is overlapped by the higherenergy section of the alpha-particle spectrum. Omission of this extra contribution to the calculated triton response matrix leads to an overestimate of the relative neutron flux at low energies. The response function for the sum-peak mode is usually taken to be a diagonally dominant matrix with each column of the matrix containing a Gaussian resolution function centered on the diagonal. The energy degradation in the 6LiF layer shifts each resolution function slightly away from the diagonal of the matrix and alters the shape of the function in a manner dependent on the neutron energy, on the thickness of the 6LiF layer, and on the peak width due to electronic noise. The sizes of all these effects can be calculated. One further effect, which may in a sense be regarded in the same category as the calibration correction described above, is the calculation of the contribution to the so called "triton spectrum" from neutrons of
higher energies than those included in the response matrix. This contribution is quite easily calculated, yet is usually only included as an approximation. Most of the calculations which will be described in this paper were carried out to assist the analysis of data obtained in measurements other than reactorspectra measurements and therefore do not form a comprehensive set. However, the general principles involved could equally well be applied to the analysis of the results of any measurement made with 6Li sandwich spectrometers.
2. Energy degradation in the 6LiF layer The amount of energy lost by any charged particle travelling through a medium depends on the nature and initial energy of the particle and on the nature, density, and thickness of the medium through which it passes. For the particular case of alpha-particle and triton energy losses in a layer of 6LiF, the energy loss for each particle depends only on its initial energy and the path length in the layer. 2.1. TH E ENERGY LOSSES AS FUNCTIONS OF ENERGY
The energy losses for alpha particles and tritons traversing a layer of defined thickness can be deduced by interpolation between values given in nuclear-data tables l4), and are conveniently expressed as losses relative to the energy losses AE~(T) and AEt(T) suffered by the alpha particle and triton produced by the 6Li(n,~t)t reaction for thermal neutrons. The following empirical relationships were found to reproduce very closely the interpolated tabulated values:
AE~(E~) = AE~(T) {1-0.245(E~-2.056) + + 0.0283 (E~- 2.056)2},
AEt(E,) = AEt(T) { 1 - 0 . 2 1 7 ( E t - 2 . 7 2 9 ) + + 0.0265(E t - 2.729)1}. The values of AE~,(T) and AEt(T ) for a 1.0 pg/mm 2 layer of 6LiF are approximately 130 keV and 21 keV, respectively. 2.2.
THE ENERGY DISTRIBUTION OF PARTICLES WH1CH ARE DETECTED
The effects of energy losses on the response of a spectrometer are conveniently considered in two separate stages. In the first idealised stage the distributions of particle path lengths in the degrading layer are calculated on the assumption that all the alpha particles
6Li
SEMICONDUCTOR
and tritons are detected, while in the second stage the detailed effects of spectrometer geometry can be introduced. 2.2.1, The idealised distribution of path lengths Consider an energy-degrading layer of thickness t units with a charged particle generated a distance x from the lower surface, as shown in fig. 1. For a fixed value of x the number of particles having a path length between z and z + dz in the layer is given by: dN (z, x) =
dN dO d0
Particles can be generated with equal probability at all values of x, as long as x is very much smaller than the mean free path of neutrons in the layer. This is certainly true in practice, so the distribution of path lengths of particles generated in the layer can be calculated from the above expression for dN(z, x). The probability of finding a path length z may be written as: dN(z) = f0 K 1(x/z 2) dx dz for z ~ t,
dz,
= K2(t2/z2),
d(2 dO dz where dN/d~2 is the probability of the particle path lying within a defined solid angle; i.e. it is proportional to the differential cross section. I f the differential cross section is for the moment assumed to be independent of 0 then:
but:
x/z,
.. sin 0 dO = ( x / 2 2) dz
for constant x.
Thus:
d N ( z , x ) = Kt(x/z2)" dz
I ! Fig. 1. The path length z for a particle generated at a depth x within the sensitive layer. U "o N
1
Z "o >I...J en
2t
CO O
0
I t
I
2t D
and: dN(z) = dz =
;0
K 1(x/z 2) dx for z ~< t.
K2,
Normalisation of the resulting distribution curve for z gives the path-length distribution shown in fig. 2, and it can be demonstrated that the areas under the fiat and curved portion of the distribution are equal. This leads to the important conclusion that the average path length of particles generated within the layer and with an isetropic distribution is equal to the thickness of the layer.
dN(z, x____~)= K(27r sin0) dO dz dz cos 0 =
63
SANDWICH SPECTROMETERS
Z
Fig. 2. The distribution of path lengths within the sensitive layer.
2.2.2. The effects of spectrometer geometry The energy distributions of alpha particles and tritons which are detected and recorded by the spectrometer depend both on the distributions of path lengths within the sensitive layer of the spectrometer and on the geometry of the spectrometer. In general, particles travelling at very shallow angles in the 6LiF layer are preferentially associated with a companion particle which does not meet the geometrical criteria for recording the event. This has the effect of shortening the tail of the distribution in fig. 2. A second general conclusion is that, while the individual energy distributions of the alpha particle and triton would be expected to be closely related to the path-length distribution shown in fig. 2, the total energy distribution cannot start at zero energy loss, because the smallest total path length through the layer must be equal to the layer thickness. The energy spectra of alpha particles and tritons and the summed energy spectrum could all be calculated for any spectrometer used in any way. However, the benefits to be gained from carrying out such calculations are rather different for the two most usual modes of operation.
64
P. J. C L E M E N T S
In the triton mode, the average energy loss in the 6LiF layer is only of the order of 20 keV for a typical spectrometer. The average energy-loss value discussed in the previous section is rendered approximate by geometrical effects, but the error introduced by its use
is so small as to be insignificant. The effective width of the distribution caused by energy degradation is considerably less than the normal electronic noise width and can be included in an overall resolution width. Bearing in mind both the narrowness of the
TRITON PEAK 1000
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600
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100
150
C H A N N E L NUMBER ( 1 CHANNEL ~ 1 3 . 5 k e y )
Fig. 3. T h e a l p h a - p a r t i c l e a n d t r i t o n e n e r g y / p u l s e - h e i g h t d i s t r i b u t i o n s p r o d u c e d b y the d e t e c t i o n o f t h e r m a l n e u t r o n s . 51f 4
q ~
B4
O ~
:z
>= w
,=,
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200
i
,~o
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,~o
=
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CHANNEL NUMBER (1 CHANNEL ~ 13.SkeV)
Fig. 4 T h e s u m m e d e n e r g y / p u l s e - h e i g h t d i s t r i b u t i o n p r o d u c e d b y the d e t e c t i o n o f t h e r m a l n e u t r o n s
6Li SEMICONDUCTOR
SANDWICH
distribution and the shortening of its tail by geometrical effects, the shape of the resolution function is expected to be closely Gaussian. Fig. 3 shows the alpha-particle and triton energy distributions produced by the detection of thermal neutrons in a spectrometer with a nominal 2.4 gg/mm 2, layer of 6LiF. It can be seen that the triton peak is nearly symmetrical, though the alpha-particle peak is considerably less so, having an energy-degradation factor approximately six times as large as for the triton distribution. The triton response matrix is slightly dependent on the alpha-particle distributions as will be demonstrated shortly. Nevertheless, a sufficiently accurate response function in the triton mode can be calculated by subtracting the appropriate energy- dependent average energy loss from the triton and alpha-particle energies used during the calculation and by broadening the resolution functions to match experimental values. The average energy loss in the summed energy peak is considerably larger than for the triton alone and the
asymmetries of the alpha-particle and triton energyloss distributions are reflectedin the shape of the summed peak, as shown in fig. 4. The considerable asymmetry of the peak shape suggests that a calculation not only of the average energy loss but also of the detailed peak shape would be justified. The economy with which these calculations could be performed was determined by the availability of computer programs which could be adapted for the purpose. A complete set of calculations was therefore not carried out, but it was nevertheless possible to deduce a useful amount of information about the spectrometer response in a range of practical circumstances. A Monte-Carlo program was available for calculating the geometrical efficiency of the spectrometer for a neutron beam incident in a direction parallel to the axis and incident either from the front or the rear of the spectrometer11). This program was extended to calculate the total path length distributions in the 6LiF layer for those particles which were geometrically acceptable and were therefore recorded. It would also
xXX x 3
Xx x x x
x
x
65
SPECTROMETERS
x
x x
0 MeV
x
x
•5 MeV
x
x
x X x
Xx x
x I
Xx x
xx x
Xxx
x x Xx
I
Xxxxll~xxX x I I XXXXxx
1
2
0
3
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2
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Xx
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Fig. 5. The distributions o f total energy loss at various energies for a neutron b e a m incident f r o m the front o f a Harwell-design spectrometer (see text for scales).
66
P. J. CLEMENTS
have been possible to include the effects o f the gold electrode layers in this p r o g r a m , but in view o f the flelatively small energy losses involved the increase in c o m p u t a t i o n a l c o m p l e x i t y which w o u l d have been involved was n o t t h o u g h t to be justified. Similar p a t h length distribution calculations for the case o f an isotropic n e u t r o n flux could n o t be so readily carried out. However, it is p r o b a b l e t h a t the path-length distributions in an isotropic flux have some average shape between those o f the two different b e a m - g e o m e t r y distributions. The exact shapes o f the path-length a n d hence the energy-loss distributions d e p e n d p r i m a r i l y on the c o u n t e r g e o m e t r y a n d n e u t r o n spatial distribution a n d 1-01
Xxr 0.9/~r~ x
HARWELL DESIGN BEAM FROM FRONT x
TABLE ] The geometrical specifications of the Harwell and 20th Century design spectrometers
Spectrometer Harwell Effective area of each diode (ram2) Diode separation (mm) Area of 8LiF (ram2) Range of 6LiF layer thicknesses (/tg/ mm 2) Range of gold-layer thicknesses (/~g/ mm 2) 0.c.
xx
Xx
x
0.4-2.8
0.8-2.4
0.5-1.0
Not known
x
05
0.8I
x
x
x x
~
~
1.0~
200 3.75 154
x
x X
0.7
154 1 113
20th C DESIGN BEAM FROM FRONT
x
0.8
20th Century
~
0.1~
.-~x--
HARWELL DESIGN BEAM FROM REAR
I
I
I
x I
20 th C DESIGN BEAM FROM REAR
0.8,~x
0-~ ~x
0,8
0.7
x
x.
*~
x x
x
0.6
x x
x x
0.7
x
x
x
0.5
x x
0.5
~ 1
= 2
~ 3
~x-4
I
I
I
I
1
2
3
4
NEUTRON ENERGY (NeV)
Fig. 6. The average total energy losses as functions of neutron energy in MeV (see text for vertical scales). lI ~ 1.1
HARWELL DESIGxN BEAM FROM FRO T
1.1~ .x x
09 x
x
* ~
1.1I_x,~ ~,,~ 09
i
x
xXx x
r
t
HARWELL DESIGN BEAM FROM REAR
~ x
0'71
. I
''
I
I
20th C DESIGN BEAM FROM REAR
x
X-~x x x
x
X XX
091 13.7
X
0.7
x
xx
0,9F n. t u ,' / -L
20th C DESIGN I BEAM FROM FRONT I
X
.
x
x x
x x
0..=
ix
4 0.5 1 NEUTRON ENERGY (MeV)
x
,L_
Fig. 7. The widths of the total-energy-loss distributions as functions of neutron energy in MeV (see text for vertical scales).
6Li SEMICONDUCTOR SANDWICH SPECTROMETERS considerably less on the differential cross section for the 6Li(n, c~)t reaction. The conclusions which will be reached should therefore not be changed except in detail by any future improvement in the accuracy of the nuclear data. Calculations were carried out for the two designs of spectrometer which were available at Harwell when 6Li spectrometers were in regular use there. These will be referred to as the Harwell and 20th Century designs and their geometrical specifications are given in table 1. Calculations for other designs could be carried out if required. 2.3. RESULTSOF THE ENERGY-DEGRADATION CALCULATIONS The results of the energy-degradation calculations are given in figs. 5-7. Fig. 5 shows the energy-degradation distributions calculated for neutrons of various energies incident from the front of a Harwell-design spectrometer. The horizontal scales in fig. 5 are in terms of the energy loss suffered by an alpha particle passing directly through the whole thickness of the 6LiF layer. The area under each distribution is a measure of the geometrical efficiency at that energy. Similar distributions were obtained for the rear-incidence beam and for the 20th-Century-design spectrometer. In fig. 6 the average energy losses for front- and rear-incidence neutron beams for each of the spectrometer designs are given as functions of neutron energy. The vertical scales are in the same alpha-particle energy-loss units as the horizontal scales of fig. 5. Fig. 7 shows the energy variation of the full widths at half maximum of the various energy-loss distributions. The bulk of the energy dependence of both the average energy loss and spread of the energy loss arises from the reduction with increasing neutron and hence average particle energy in the amount of energy lost by a charged particle as it passes through a medium. However, some further geometrical effects would be expected to be present and these are indeed evident, particularly at an energy of approximately 300400 keV where the 6Li(n, ~)t cross section is strongly anisotropic. The differences between the results shown for the Harwell- and 20th-Century-design spectrometer are also due to geometrical effects. A further geometrical effect is that both the average energy lost and the width of the energy-loss distribution are larger for a neutron beam incident from the front of the spectrometer than from the back. This is a result of the net momentum of both the alpha particle and the triton in the direction of the beam. In the case of the front-incidence beam, the forward-moving particle is progressively more
67
likely to be detected as the neutron energy rises, without placing any great restraint on the angle at which the backward-moving particle must pass through th6 layer in order to be detected. When the beam is incident from the rear of the spectrometer one particle must be emitted into the appropriate backward angle to be detected and this contains the forward-moving particle within a narrower forward cone than in the front-incidence case. On average, therefore, it travels a shorter distance through the degrading layer and thus loses less energy. An analogous shortening of the tail of the energy-loss distribution has been reported to take place, although for a rather different spectrometer design in an isotropic flux, when the separation of the diodes is increased9). 3. The response matrices 3.1. THE TRITONRESPONSE MATRIX The triton response function for any incident neutron energy is normally taken to be that part of the triton energy-distribution function which is at a higher energy than 2.73 MeV, the position of the peak produced by the detection of thermal neutrons. At energies below 600 keV the triton mode affords better energy resolution than the summed peak, but has the disadvantage that measurements need deconvolution to derive the neutron spectrum. The accuracy of the deconvolution depends primarily on the accuracy with which the response matrix has been calculated, and this calculation, as well as containing unavoidable errors due to
_ NEUTRON - 3 1 ENERG IES IN MeV
?
1.0
"8
8 ALPHA / ~ ~CONTRIBUTIONSJ
NEUTRON ENERGIES
I
n
~ °o
I
-2
[
.4
I
.6
Ik
.8
~.
i ~,
1.0
TRITON ENERGY (MeV}
Fig. 8. The triton response function for various neutron energies.
68
P.J.
CLEMENTS
105
x
x
CALCULATED TRITON x
x x x
.SPECTRUM
FROM
WHOLE
NEUTRON
x'~
SPECTRUM
ld x xxxx x x ~ X ~ x = ~
~
Z w
x
z
x
10 3
x
x
~
g
x
xj
X
x
CALCULATED TRITO
~x x x
Q.
x
x
:~
SPECTRUM
FROM N E U T R O N
~.
SPECTRUM
ABOVE 6 0 0 k e Y
,Y
x x
10~
g
x x
w
z
x x
...1 I1:
x
1Q10_2 10-3
IO-Z
10-I
NEUTRON
ENERGY
10°
i
i
101
I
I
I 10 0
,
,
101
TRITON ENERGY (MoV)
(MeV)
Fig. 10. The calculated triton spectrum with and without the contribution from neutrons o f energy lower than 600 keV.
Fig. 9. A typical fast-neutron'_'spectrum in the " Z e b r a " reactor.
I
I 10-1
I
t
I
I
Ud <~ >
40% --
bJ t~ l-Ld
30%bJ CO
20% W Z m UJ C~
10%
Z ~C bJ a.
lo-3
lo-2 NEUTRON
lo-~
ENERGY ( M e V )
Fig. 11. The percentage increase in calculated neutron flux produced by omitting the alpha-particle contribution to the response matrix.
6Li SEMICONDUCTOR SANDWICH SPECTROMETERS nuclear-data uncertainties, has in the past contained an unnecessary approximation. It can easily be shown that at a neutron energy greater than ,-,370 keV the maximum energy in the alpha-particle distribution exceeds 2.73 MeV and so contributes to the so-called triton response. The alpha-particle energy distribution is slightly wider than that for the triton, so the contribution to the response function from alpha particles is always somewhat smaller than from tritons, but it is nevertheless certainly significant. Complete alphaparticle and triton distributions have been calculated and reported elsewhere*), but were discussed in the context of a bi-dimensional mode of data collection. This mode is not in general use, so it is worthwhile investigating the effect of the alpha-particle contribution to the triton response matrix in more normal usage. The triton response functions for a range of neutron energies are given in fig. 8, where the alpha-particle contribution can be clearly seen. The functions shown have been calculated from the usual kinematic and geometrical factors, but also include noise broadening with a full width half maximum of ,-~65 keV, and average energy-degradation factors appropriate to a 6LiF layer thickness of 0.8/~g/mm 2 as discussed in the previous section. The use of an average energydegradation factor for the triton response is justified by the narrowness of the triton degradation distribution, while the justification for an average value for the alpha particle lies in the fact that the long tail of the degradation distribution is at low energies, and is therefore not included in the calculated response functions. In view of the results given in section 2.3 it might be argued that an average energy degradation equal to the energy loss in passing vertically through the sensitive layer is not exact. However, the errors introduced by this assumption are considerably smaller than the purely experimental errors in defining the energy scale. Fig. 9 shows a typical fast reactor spectrum, and the upper curve of fig. 10 shows the calculated triton response to this spectrum, with the alpha-particle contributions included in the response matrix used to perform the convolution. (The lower curve in fig. 10 is discussed in section 4.) Fig. I 1 shows the percentage difference between the spectrum obtained by deconvolving the data of fig. 10 with the matrices firstly including and secondly excluding the alpha-particle contribution. It can be seen that, although the difference is negligible at energies of above ~ 5 0 keV, it rises very rapidly as the neutron energy falls towards what is normally regarded as the lower limit of usefulness of the spectrometer at ~ 5-10 keV.
69
3.2. THE SUMMED-PEAKRESPONSE MATRIX If a neutron-spectrum measurement in the summedpeak mode is made with very good resolution it may not be necessary to deconvolve the measurement to derive the desired neutron spectrum. It is more often the case that some deconvolution is required, particularly in the lower-energy region where an overlap with results from the triton mode measurement is desirable. Satisfactory deconvolution requires a realistic response matrix, which is usually taken to be a set of Gaussian functions centred about the diagonal of the matrix. It can be seen from the results of section 2.3 that, particularly in cases where a thick 6LiF layer has been used in order to obtain sufficient sensitivity to the higher end of the neutron spectrum, the response function is not Gaussian. This is illustrated in fig. 12, which shows various experimentally obtained spectral peaks with curves fitted to them using the distributions as in fig. 5 with appropriate degradation and electronicnoise factors. The validity of the degradation theory is confirmed by the good agreement between calculation and measurement. It is therefore reasonable to suppose that the average energy-loss curves given in fig. 6 are also correct. It can be seen from these curves that when a thick sensitive layer is used there are non linearities of up to ~ 30 keV on the energy scale. An error of this size is not insignificant, and in view of the ease with which at least an approximate correction can be made the omission of such a correction seems unnecessary.
4. The high-energy contribatioa to the triton spectrum One further effect which may be regarded as influencing the calibration of the 6Li spectrometer is the calculation of the contribution to the recorded spectrum from neutrons of energy outside the range of the response matrix. This matrix is usually calculated up to a maximum neutron energy of ~600 keV, corresponding to a maximum triton energy of 1 MeV relative to the thermal-neutron value. Neutrons of energy greater than 600 keV can all contribute to the triton distribution within the triton energy range of 0-1 MeV. The relative size of this contribution is reduced by the rapid fall in spectrometer efficiency as the neutron energy rises, and in many spectrum measurements is also further reduced by the rapid fall in neutron flux with increasing energy. However, it will be increased by the fact that the alpha-particle and triton distributions overlap to a greater extent as the neutron energy increases, so a larger proportion of alpha particles from high-energy neutrons will contribute to the triton spectrum.
70
P. J. C L E M E N T S
20TH CENTURY DESIGN SPECTROMETER
/ 500
/
\
,x'
\
/
LAYER THICKNESS = . 8 0 p g m l m m 2 NOISE FULL WIDTH HALF MAX.- 130keV NEUTRON ENERGY = 0
\
x/ ¢
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x"-x"x"x"¢'x"x'-250 ~
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k
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HARWELL DESIGN SPECTROMETER LAYER THICKNESS w 2' 0 p gmlmm 2 NOISE FULL WIDTH HALF MAX. " 1 / , 0 keV NEUTRON ENERGY - 0 (SAME DATA AS FIG./,)
k
ix
t
0
: 200
I 250 CHANNEL NUMBER
I
x x x x~(; A(x~'----'~x ~ x / / xX ~._ KI/ X X X )P~ X
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I
X
HARWELL DESIGN SPECTROMETER LAYER THICKNESS" 2.8Hom/mm2 NOISE FULL WIDTH HALF MAX. m 450keV NEUTRON ENERGY - STSkeV
~,~
/x/x
\xX xx~x
.s
I
~
t
I
I 350 CHANNEL NUMBER
I
I
I
I
~
~
II
Fig. 12, T h e observed ( x ) and calculated ( - - ) s u m m e d - p e a k pulse-height distributions, produced by the detection o f neutrons in three different spectrometers. (One channel ,~13.5 keV in each case.)
6Li S E M I C O N D U C T O R
SANDWICH
It can be argued that, because no neutrons of energy below ,-~600 keV can produce a triton response at an energy of more than 1 MeV above the zero value, then the contribution to the measured triton spectrum at 600 KeV must have arisen from neutrons of higher energy. This gives an approximate value for the highenergy background contribution at this energy which can be taken to be an approximation for the value at lower energies. The necessity for making an estimate of the highenergy contribution is removed if the bi-dimensional data-collection mode mentioned in section 3.1 4) is used, but as has been pointed out, this method is not in general use, so a calculation of the high-energy contribution observed in more normal use is necessary. A precise estimate of the background contribution in any spectrum may be derived by calculating not only a triton response matrix covering a relative maximum triton-energy range from 0-1 MeV, but also a further matrix for the range 0 to some suitable upper limit, e.g. 4 MeV. The neutron spectrum above a neutron energy of 600 keV is assumed to be known from the summed-peak measurement. The convolution of the extended response matrix with a neutron spectrum assumed to have a zero value below a neutron energy of ~ 600 keV and the measured value above this energy produces the high-energy contribution to the triton spectrum in the lower-energy range. Fig. 9 shows a typical reactor spectrum and fig. 10
71
SPECTROMETERS
shows the triton response to this spectrum with the relative contribution from neutrons of energies above and below 600 keV shown separately. It can be seen that at a triton energy of less than about 500 keV the contribution to the triton spectrum caused by the detection of neutrons of energy greater than 600 keV is only 4-5 %, but that at higher triton energies it rises rapidly to become the entire contribution at a triton energy of 1 MeV. The effects of the presence of the high-energy contribution were investigated by deconvolving the triton spectrum in the triton energy range 0-1 MeV in three different ways. Firstly the deconvolution was carried out with a correct subtraction made, i.e. by deconvolving the difference between the two curves shown in fig. 10. Further deconvolutions were also carried out by ignoring the high-energy contribution altogether and by assuming, as previously suggested, that this contribution is flat and equal to the number of events in the triton distribution at 1 MeV. The results of these calculations are shown in fig. 13 as deviations from the results obtained by deconvolving the properly corrected triton spectrum. It can be seen that omission of the correction for the high-energy contribution leads to oscillations of total amplitude ,-,10% below a neutron energy of ,--500 keV, but rising very rapidly above this energy. The oscillations are considerably reduced by the fiat contribution correction, but again lead to very large errors above ,,~ 500 keV. Errors above x
BOTH x AND o RISE TO VERY LARGE VALUES
x NO SUBTRACTION OF THE HIGH ENERGY CONTRIBUTION O SUBTRACTION OF A FLAT HIGH ENERGY CONTRIBUTION
uJ
3+sI
x o
ooO~
x 0
0 ~
0
X
X
0
%°°
~
"x OoX
X 0 x 0 x X O0 X
°x/t~,~
~ x
X X X X
oo
0
o°
0
0
X
o x
x
g
o x
N
x o
x
x x
x Xx x
x
o o
x I
I 10-3
LOGARITHMIC I I
SCALE CHANGEI !
10-2
~
LINEAR ---~ I •1
I '2 NEUTRON ENERGY (MeVI
I -3
I .&
I .5
.6
Fig. 13. T h e errors in the calculated n e u t r o n s p e c t r u m produced by: (a) Omitting the high-energy contribution to the triton spectrum, a n d (b) subtracting a fiat high-energy contribution.
72
P. J. C L E M E N T S
500 keV are not serious as long as the neutron spectrum derived from the summed-peak spectrum can be satisfactorily extended down to this energy. Whether this is so will depend primarily on the width of the summed peak and difficulty may be encountered if the peak is more than a few hundred keV broad, as is sometimes the case. It could also be difficult if a spectrometer with a very thick 6LiF layer had been used, because the resulting asymmetry in summedpeak shape would have its greatest effect at the lowerenergy end of the spectrum. The errors below 500 keV may in some cases be on the borderline of significance, especially if the flat-contribution approximation is used, but there nevertheless seems to be little justification for not making the proper correction for the high-energy contribution to the triton spectrum, considering the ease with which this can be carried out. 5. Conclusions It has been suggested that the accuracy of neutronspectrum measurements made using 6LiF semiconductor sandwich spectrometers could be improved by adding several relatively straightforward refinements to the methods normally used for data analysis. Both the improvements which can thus be obtained and the benefits to be obtained by making them will of course vary from measurement to measurement. It has been shown that the accuracy of the calibration of the energy scale in both the triton and summed-peak modes depends on an understanding of the energy-loss mechanism in the sensitive layer of the spectrometer. For example, for spectrometers with a sensitive layer thickness of ~ 2.4/~g/mm 2 a non-linearity of ~ 30 keV i s introduced over the energy range of the summed-peak measurement. Considerably greater errors would be expected with more sensitive spectrometers whose use might occasionally be necessary. However, the energy losses within the sensitive layer have been calculated to give good agreement with experimentally obtained data and to allow accurate correction of the energy scales in both the triton and summed-peak modes.
The calculation of the triton response matrix does not normally include the contribution from alpha particles. This contribution has now been calculated and included, because its omission leads to unnecessary errors in neutron spectra generated by deconvolution with the incomplete matrix. It was shown that the omission of the alpha-particle contribution leads to errors of nearly 50 % at the lower-energy end of a typical neutron spectrum which might be measured with the spectrometer. Two other possible sources of calibration error, caused by approximate subtraction of the high-energy contribution to the triton spectrum and by the approximation of the sum-peak response function by a Gaussian shape, were also discussed. Although the errors from these sources were likely to be small, they could in some circumstances lead to undesirably large errors in the energy region from ~ 500-600 keV, where the triton and sum-peak measurements are respectively at their upper and lower limits of usefulness.
References
1) I. C. Rickard, Nucl. Instr. and Meth. 105 (1972) 399. 2) A.M. Broomfield, W.J. Paterson and J.E. Sanders, AEEW-M.997 (1970). a) M. G. Silk and S. B. Wright, AERE-R. 6060 (1970). 4) G. De Leeuw-Gierts and S. De Leeuw, BLG-450(Dec. 1970). 5) S. K. I. Pattenden and J. M. Stevenson, Proc. CEGB Conf. on Radiation measurements in nuclear power (September 1966). 6) C. Beets, S. De Leeuw and G. De Leeuw-Gierts, Proc. CEGB Conf. on Radiation measurements in nuclear power (September 1966). 7) p.j. Clements and I. C. Rickard, AERE-R.7075 (1972). s) p.j. Clements, AERE-R.7600 (1973). 9) H. Bluhm and D. Stegemann, Nucl. Instr. and Meth. 70 (1969) 141. 10) p. j. Clements, AERE-R.7512 (1973). 11) M. G. Silk, J. Nucl. Energy 22 (1973) 163. 12) M.G. Silk and Margaret E. Windsor, J. Nucl. Energy 21 (1966) 17. 1~) M. G. Silk, AERE-M.2009 (1968). 14) j. B. Marion and F. C. Young, Nuclear reaction analysis graphs and tables (North-Holland Publ. Company, Amsterdam, 1968).
INSTRUMENTS
AND
METHODS
127
(1975)
61--72;
©
NORTH-HOLLAND
PUBLISHING
CO,
THE CALIBRATION OF 6Li S E M I C O N D U C T O R S A N D W I C H S P E C T R O M E T E R S P. J. C L E M E N T S
Materials Physics Dioision (Building 521), A.E.R.E., Harwell, Didcot, Oxon., OWll ORA, U.K. Received 8 April 1975 T h e 6Li Semiconductor Sandwich Spectrometers which are c o m m o n l y used for the m e a s u r e m e n t o f fast-neutron spectra, especially in reactors, are subject to a variety o f effects which, if n o t taken into account, can lead to significant calibration errors. T h e effects which are here discussed in detail are: (1) the energy degradation in the sensitive layer o f the spectrometer, (2) the alpha-particle contribution to the " r e s p o n s e f u n c t i o n "
(3)
It can ~30
1. Introduction 6Li semiconductor sandwich spectrometers are widely used for the measurement of fast-neutron spectra in reactors 1-6), and have recently found other applications 7, 8). The accuracy with which the spectrometer needs to be calibrated depends on the measurement for which it is being used, but for most purposes a calibration uncertainty leading to an uncertainty of more than a few per cent in the results of the measurement being made would probably be undesirable. It is the intention of the present discussion to demonstrate that of the several levels of sophistication of calibration corrections which can be made, some are sufficiently simple that they ought normally to be included as a routine part of the data-analysis procedure. The use of more detailed corrections would have to be justified by the overall increase in accuracy which could be obtained in view of the presence of other sources of error in any particular measurement. The modes of operation of 6Li sandwich spectrometers have been described elsewhere1), and a knowledge of the techniques used will therefore be assumed in the discussion which follows. The calibration of a 6ti sandwich spectrometer involves several separate stages. Some of the various calibration uncertainties which can arise during these stages have been considered by other authors for their spectrometer systems+'9). However, discussion of the major uncertainties which can arise during the use of the most common system, i.e. a sandwich spectrometer with the sensitive layer deposited on the face of one of the diodes and used in the " s u m - p e a k " and " t r i t o n " modes1), have not previously been collected together. In the first stage of calibration, the efficiency with which neutrons are detected must be specified as a
used to deconvolve the lower-energy part o f the n e u t r o n spectra, a n d the superposition o f a high-energy contribution on the lower part o f the m e a s u r e d s p e c t r u m in one m o d e o f operation o f the spectrometer. will be s h o w n that the failure to take account o f these effects in s o m e circumstances lead to energy-calibration errors o f keV a n d errors o f up to 50% in m e a s u r e d n e u t r o n spectra.
function of neutron energy. It has been demonstrated that for some designs of spectrometer the usual expression for the efficiency is inadequate1°), and that the efficiency should be written as: /3( E ) = Z O'n~t ( E ) G ( E ) B ( E ) ,
where A is a constant, E is the neutron energy, a,~ (E) is the 6Li(n, cot cross section, G(E) is a calculable geometrical efficiency, and B(E) is a calculable internal background factor. The methods of calculation of G(E)and B(E)have been described elsewhere1°-12), and values for these factors and for an~(E ) may be updated as more accurate values of the relevant nuclear data become available. The second stage of calibration is the assignment of an energy scale to the data collected during the measurement. The calibration in the sum-peak mode is usually carried out by detecting thermal neutrons using two different gain settings to generate spectral peaks at energies corresponding to known multiples of 4.785 MeV, the Q value of the reaction. The calibration in the triton mode is accomplished by using thermal neutrons to generate peaks corresponding to energies of 2.056 MeV and 2.729 MeV, the energies of the particle and triton produced by thermal-neutron detection. A 4.785 MeV peak would probably also be included in this calibration. The energy calibration in either mode of operation is subject to two sources of uncertainty. Firstly, the presence of electronic noise makes the position of the calibration peaks difficult to determine precisely. Secondly, in order that a neutron interacting in the sensitive region of the spectrometer should be recorded, the alpha particle and the triton produced by the interaction must together have travelled a total distance through 6LiF, the sensitive material 61
62
P. J. C L E M E N T S
of the spectrometer, of at least the thickness of the 6LiF layer. The alpha-particle, triton, and sum peaks therefore all have their own characteristic shapes due to energy loss in the 6LiF layer, and this can lead to significant errors in energy calibration unless the effect is taken into account. (There is also a small energy loss, typically an average of ~ 15 keV in the total energy, in the gold-layer electrodes on the diodes. A relatively crude correction for this is adequate.) The energy loss in the 6LiF layer is particularly important when fluxes of high-energy neutrons are being measured, where it may be necessary to use a thick layer of 6LiF in order to detect enough neutrons before the spectrometer suffers significant radiation damage. For example, if a 2.0 pg/mm 2 layer is used, no event in the summed calibration peak can have suffered an energy loss less than ,-~40 keV, and the average energy loss is considerably more than this. Calculation of the energy losses involved for one particular spectrometer design have been reported 9), but accurate corrections for these losses are not generally made. The third stage of calibration is the generation of suitable response functions for the spectra recorded in the triton and sum-peak modes. The generation of a simple triton response function has been described previouslyla), but both this matrix and response matrices used elsewhere generally omit two effects. Firstly, the triton suffers energy degradation as described above. Secondly, measurements made in the triton mode are usually regarded as being valid up to ,-~600 keV neutron energy. At this energy the lowerenergy end of the part of the triton spectrum generally used in the analysis is overlapped by the higherenergy section of the alpha-particle spectrum. Omission of this extra contribution to the calculated triton response matrix leads to an overestimate of the relative neutron flux at low energies. The response function for the sum-peak mode is usually taken to be a diagonally dominant matrix with each column of the matrix containing a Gaussian resolution function centered on the diagonal. The energy degradation in the 6LiF layer shifts each resolution function slightly away from the diagonal of the matrix and alters the shape of the function in a manner dependent on the neutron energy, on the thickness of the 6LiF layer, and on the peak width due to electronic noise. The sizes of all these effects can be calculated. One further effect, which may in a sense be regarded in the same category as the calibration correction described above, is the calculation of the contribution to the so called "triton spectrum" from neutrons of
higher energies than those included in the response matrix. This contribution is quite easily calculated, yet is usually only included as an approximation. Most of the calculations which will be described in this paper were carried out to assist the analysis of data obtained in measurements other than reactorspectra measurements and therefore do not form a comprehensive set. However, the general principles involved could equally well be applied to the analysis of the results of any measurement made with 6Li sandwich spectrometers.
2. Energy degradation in the 6LiF layer The amount of energy lost by any charged particle travelling through a medium depends on the nature and initial energy of the particle and on the nature, density, and thickness of the medium through which it passes. For the particular case of alpha-particle and triton energy losses in a layer of 6LiF, the energy loss for each particle depends only on its initial energy and the path length in the layer. 2.1. TH E ENERGY LOSSES AS FUNCTIONS OF ENERGY
The energy losses for alpha particles and tritons traversing a layer of defined thickness can be deduced by interpolation between values given in nuclear-data tables l4), and are conveniently expressed as losses relative to the energy losses AE~(T) and AEt(T) suffered by the alpha particle and triton produced by the 6Li(n,~t)t reaction for thermal neutrons. The following empirical relationships were found to reproduce very closely the interpolated tabulated values:
AE~(E~) = AE~(T) {1-0.245(E~-2.056) + + 0.0283 (E~- 2.056)2},
AEt(E,) = AEt(T) { 1 - 0 . 2 1 7 ( E t - 2 . 7 2 9 ) + + 0.0265(E t - 2.729)1}. The values of AE~,(T) and AEt(T ) for a 1.0 pg/mm 2 layer of 6LiF are approximately 130 keV and 21 keV, respectively. 2.2.
THE ENERGY DISTRIBUTION OF PARTICLES WH1CH ARE DETECTED
The effects of energy losses on the response of a spectrometer are conveniently considered in two separate stages. In the first idealised stage the distributions of particle path lengths in the degrading layer are calculated on the assumption that all the alpha particles
6Li
SEMICONDUCTOR
and tritons are detected, while in the second stage the detailed effects of spectrometer geometry can be introduced. 2.2.1, The idealised distribution of path lengths Consider an energy-degrading layer of thickness t units with a charged particle generated a distance x from the lower surface, as shown in fig. 1. For a fixed value of x the number of particles having a path length between z and z + dz in the layer is given by: dN (z, x) =
dN dO d0
Particles can be generated with equal probability at all values of x, as long as x is very much smaller than the mean free path of neutrons in the layer. This is certainly true in practice, so the distribution of path lengths of particles generated in the layer can be calculated from the above expression for dN(z, x). The probability of finding a path length z may be written as: dN(z) = f0 K 1(x/z 2) dx dz for z ~ t,
dz,
= K2(t2/z2),
d(2 dO dz where dN/d~2 is the probability of the particle path lying within a defined solid angle; i.e. it is proportional to the differential cross section. I f the differential cross section is for the moment assumed to be independent of 0 then:
but:
x/z,
.. sin 0 dO = ( x / 2 2) dz
for constant x.
Thus:
d N ( z , x ) = Kt(x/z2)" dz
I ! Fig. 1. The path length z for a particle generated at a depth x within the sensitive layer. U "o N
1
Z "o >I...J en
2t
CO O
0
I t
I
2t D
and: dN(z) = dz =
;0
K 1(x/z 2) dx for z ~< t.
K2,
Normalisation of the resulting distribution curve for z gives the path-length distribution shown in fig. 2, and it can be demonstrated that the areas under the fiat and curved portion of the distribution are equal. This leads to the important conclusion that the average path length of particles generated within the layer and with an isetropic distribution is equal to the thickness of the layer.
dN(z, x____~)= K(27r sin0) dO dz dz cos 0 =
63
SANDWICH SPECTROMETERS
Z
Fig. 2. The distribution of path lengths within the sensitive layer.
2.2.2. The effects of spectrometer geometry The energy distributions of alpha particles and tritons which are detected and recorded by the spectrometer depend both on the distributions of path lengths within the sensitive layer of the spectrometer and on the geometry of the spectrometer. In general, particles travelling at very shallow angles in the 6LiF layer are preferentially associated with a companion particle which does not meet the geometrical criteria for recording the event. This has the effect of shortening the tail of the distribution in fig. 2. A second general conclusion is that, while the individual energy distributions of the alpha particle and triton would be expected to be closely related to the path-length distribution shown in fig. 2, the total energy distribution cannot start at zero energy loss, because the smallest total path length through the layer must be equal to the layer thickness. The energy spectra of alpha particles and tritons and the summed energy spectrum could all be calculated for any spectrometer used in any way. However, the benefits to be gained from carrying out such calculations are rather different for the two most usual modes of operation.
64
P. J. C L E M E N T S
In the triton mode, the average energy loss in the 6LiF layer is only of the order of 20 keV for a typical spectrometer. The average energy-loss value discussed in the previous section is rendered approximate by geometrical effects, but the error introduced by its use
is so small as to be insignificant. The effective width of the distribution caused by energy degradation is considerably less than the normal electronic noise width and can be included in an overall resolution width. Bearing in mind both the narrowness of the
TRITON PEAK 1000
u')
~. aoo I.IJ
0 tU m Z
600
Z ALPHA-PARTICLE PEAK a e,0 U W
~00
%.o - . . %;
o °.
20(;
°o oO
•~e
° °°.*~''
ol,r•,~••.,.°•.-,
0 0
"°
"':'.-,.~-'-........ ""'i
I 50
"'"""
,
100
150
C H A N N E L NUMBER ( 1 CHANNEL ~ 1 3 . 5 k e y )
Fig. 3. T h e a l p h a - p a r t i c l e a n d t r i t o n e n e r g y / p u l s e - h e i g h t d i s t r i b u t i o n s p r o d u c e d b y the d e t e c t i o n o f t h e r m a l n e u t r o n s . 51f 4
q ~
B4
O ~
:z
>= w
,=,
3l(
(]D
Z Z o
2K
°, .•°•o °°°°•••|"°"••°°
200
i
,~o
•o
o., •
i
,~o
=
,~,o
i
,8o'"•
CHANNEL NUMBER (1 CHANNEL ~ 13.SkeV)
Fig. 4 T h e s u m m e d e n e r g y / p u l s e - h e i g h t d i s t r i b u t i o n p r o d u c e d b y the d e t e c t i o n o f t h e r m a l n e u t r o n s
6Li SEMICONDUCTOR
SANDWICH
distribution and the shortening of its tail by geometrical effects, the shape of the resolution function is expected to be closely Gaussian. Fig. 3 shows the alpha-particle and triton energy distributions produced by the detection of thermal neutrons in a spectrometer with a nominal 2.4 gg/mm 2, layer of 6LiF. It can be seen that the triton peak is nearly symmetrical, though the alpha-particle peak is considerably less so, having an energy-degradation factor approximately six times as large as for the triton distribution. The triton response matrix is slightly dependent on the alpha-particle distributions as will be demonstrated shortly. Nevertheless, a sufficiently accurate response function in the triton mode can be calculated by subtracting the appropriate energy- dependent average energy loss from the triton and alpha-particle energies used during the calculation and by broadening the resolution functions to match experimental values. The average energy loss in the summed energy peak is considerably larger than for the triton alone and the
asymmetries of the alpha-particle and triton energyloss distributions are reflectedin the shape of the summed peak, as shown in fig. 4. The considerable asymmetry of the peak shape suggests that a calculation not only of the average energy loss but also of the detailed peak shape would be justified. The economy with which these calculations could be performed was determined by the availability of computer programs which could be adapted for the purpose. A complete set of calculations was therefore not carried out, but it was nevertheless possible to deduce a useful amount of information about the spectrometer response in a range of practical circumstances. A Monte-Carlo program was available for calculating the geometrical efficiency of the spectrometer for a neutron beam incident in a direction parallel to the axis and incident either from the front or the rear of the spectrometer11). This program was extended to calculate the total path length distributions in the 6LiF layer for those particles which were geometrically acceptable and were therefore recorded. It would also
xXX x 3
Xx x x x
x
x
65
SPECTROMETERS
x
x x
0 MeV
x
x
•5 MeV
x
x
x X x
Xx x
x I
Xx x
xx x
Xxx
x x Xx
I
Xxxxll~xxX x I I XXXXxx
1
2
0
3
I
I
X x x x x x X X X x x x x,~Xxx !
1
2
3
X X X 41
X
xXx x
3
x
x
3.5 MeV
X
1"5 MeV
X
X x x x x x
Xx
x xx
I 0
1
2
3
4
0
1
XXxxxxxxxxxXx
I
2
xfXx~
3
xxx
x 4
Fig. 5. The distributions o f total energy loss at various energies for a neutron b e a m incident f r o m the front o f a Harwell-design spectrometer (see text for scales).
66
P. J. CLEMENTS
have been possible to include the effects o f the gold electrode layers in this p r o g r a m , but in view o f the flelatively small energy losses involved the increase in c o m p u t a t i o n a l c o m p l e x i t y which w o u l d have been involved was n o t t h o u g h t to be justified. Similar p a t h length distribution calculations for the case o f an isotropic n e u t r o n flux could n o t be so readily carried out. However, it is p r o b a b l e t h a t the path-length distributions in an isotropic flux have some average shape between those o f the two different b e a m - g e o m e t r y distributions. The exact shapes o f the path-length a n d hence the energy-loss distributions d e p e n d p r i m a r i l y on the c o u n t e r g e o m e t r y a n d n e u t r o n spatial distribution a n d 1-01
Xxr 0.9/~r~ x
HARWELL DESIGN BEAM FROM FRONT x
TABLE ] The geometrical specifications of the Harwell and 20th Century design spectrometers
Spectrometer Harwell Effective area of each diode (ram2) Diode separation (mm) Area of 8LiF (ram2) Range of 6LiF layer thicknesses (/tg/ mm 2) Range of gold-layer thicknesses (/~g/ mm 2) 0.c.
xx
Xx
x
0.4-2.8
0.8-2.4
0.5-1.0
Not known
x
05
0.8I
x
x
x x
~
~
1.0~
200 3.75 154
x
x X
0.7
154 1 113
20th C DESIGN BEAM FROM FRONT
x
0.8
20th Century
~
0.1~
.-~x--
HARWELL DESIGN BEAM FROM REAR
I
I
I
x I
20 th C DESIGN BEAM FROM REAR
0.8,~x
0-~ ~x
0,8
0.7
x
x.
*~
x x
x
0.6
x x
x x
0.7
x
x
x
0.5
x x
0.5
~ 1
= 2
~ 3
~x-4
I
I
I
I
1
2
3
4
NEUTRON ENERGY (NeV)
Fig. 6. The average total energy losses as functions of neutron energy in MeV (see text for vertical scales). lI ~ 1.1
HARWELL DESIGxN BEAM FROM FRO T
1.1~ .x x
09 x
x
* ~
1.1I_x,~ ~,,~ 09
i
x
xXx x
r
t
HARWELL DESIGN BEAM FROM REAR
~ x
0'71
. I
''
I
I
20th C DESIGN BEAM FROM REAR
x
X-~x x x
x
X XX
091 13.7
X
0.7
x
xx
0,9F n. t u ,' / -L
20th C DESIGN I BEAM FROM FRONT I
X
.
x
x x
x x
0..=
ix
4 0.5 1 NEUTRON ENERGY (MeV)
x
,L_
Fig. 7. The widths of the total-energy-loss distributions as functions of neutron energy in MeV (see text for vertical scales).
6Li SEMICONDUCTOR SANDWICH SPECTROMETERS considerably less on the differential cross section for the 6Li(n, c~)t reaction. The conclusions which will be reached should therefore not be changed except in detail by any future improvement in the accuracy of the nuclear data. Calculations were carried out for the two designs of spectrometer which were available at Harwell when 6Li spectrometers were in regular use there. These will be referred to as the Harwell and 20th Century designs and their geometrical specifications are given in table 1. Calculations for other designs could be carried out if required. 2.3. RESULTSOF THE ENERGY-DEGRADATION CALCULATIONS The results of the energy-degradation calculations are given in figs. 5-7. Fig. 5 shows the energy-degradation distributions calculated for neutrons of various energies incident from the front of a Harwell-design spectrometer. The horizontal scales in fig. 5 are in terms of the energy loss suffered by an alpha particle passing directly through the whole thickness of the 6LiF layer. The area under each distribution is a measure of the geometrical efficiency at that energy. Similar distributions were obtained for the rear-incidence beam and for the 20th-Century-design spectrometer. In fig. 6 the average energy losses for front- and rear-incidence neutron beams for each of the spectrometer designs are given as functions of neutron energy. The vertical scales are in the same alpha-particle energy-loss units as the horizontal scales of fig. 5. Fig. 7 shows the energy variation of the full widths at half maximum of the various energy-loss distributions. The bulk of the energy dependence of both the average energy loss and spread of the energy loss arises from the reduction with increasing neutron and hence average particle energy in the amount of energy lost by a charged particle as it passes through a medium. However, some further geometrical effects would be expected to be present and these are indeed evident, particularly at an energy of approximately 300400 keV where the 6Li(n, ~)t cross section is strongly anisotropic. The differences between the results shown for the Harwell- and 20th-Century-design spectrometer are also due to geometrical effects. A further geometrical effect is that both the average energy lost and the width of the energy-loss distribution are larger for a neutron beam incident from the front of the spectrometer than from the back. This is a result of the net momentum of both the alpha particle and the triton in the direction of the beam. In the case of the front-incidence beam, the forward-moving particle is progressively more
67
likely to be detected as the neutron energy rises, without placing any great restraint on the angle at which the backward-moving particle must pass through th6 layer in order to be detected. When the beam is incident from the rear of the spectrometer one particle must be emitted into the appropriate backward angle to be detected and this contains the forward-moving particle within a narrower forward cone than in the front-incidence case. On average, therefore, it travels a shorter distance through the degrading layer and thus loses less energy. An analogous shortening of the tail of the energy-loss distribution has been reported to take place, although for a rather different spectrometer design in an isotropic flux, when the separation of the diodes is increased9). 3. The response matrices 3.1. THE TRITONRESPONSE MATRIX The triton response function for any incident neutron energy is normally taken to be that part of the triton energy-distribution function which is at a higher energy than 2.73 MeV, the position of the peak produced by the detection of thermal neutrons. At energies below 600 keV the triton mode affords better energy resolution than the summed peak, but has the disadvantage that measurements need deconvolution to derive the neutron spectrum. The accuracy of the deconvolution depends primarily on the accuracy with which the response matrix has been calculated, and this calculation, as well as containing unavoidable errors due to
_ NEUTRON - 3 1 ENERG IES IN MeV
?
1.0
"8
8 ALPHA / ~ ~CONTRIBUTIONSJ
NEUTRON ENERGIES
I
n
~ °o
I
-2
[
.4
I
.6
Ik
.8
~.
i ~,
1.0
TRITON ENERGY (MeV}
Fig. 8. The triton response function for various neutron energies.
68
P.J.
CLEMENTS
105
x
x
CALCULATED TRITON x
x x x
.SPECTRUM
FROM
WHOLE
NEUTRON
x'~
SPECTRUM
ld x xxxx x x ~ X ~ x = ~
~
Z w
x
z
x
10 3
x
x
~
g
x
xj
X
x
CALCULATED TRITO
~x x x
Q.
x
x
:~
SPECTRUM
FROM N E U T R O N
~.
SPECTRUM
ABOVE 6 0 0 k e Y
,Y
x x
10~
g
x x
w
z
x x
...1 I1:
x
1Q10_2 10-3
IO-Z
10-I
NEUTRON
ENERGY
10°
i
i
101
I
I
I 10 0
,
,
101
TRITON ENERGY (MoV)
(MeV)
Fig. 10. The calculated triton spectrum with and without the contribution from neutrons o f energy lower than 600 keV.
Fig. 9. A typical fast-neutron'_'spectrum in the " Z e b r a " reactor.
I
I 10-1
I
t
I
I
Ud <~ >
40% --
bJ t~ l-Ld
30%bJ CO
20% W Z m UJ C~
10%
Z ~C bJ a.
lo-3
lo-2 NEUTRON
lo-~
ENERGY ( M e V )
Fig. 11. The percentage increase in calculated neutron flux produced by omitting the alpha-particle contribution to the response matrix.
6Li SEMICONDUCTOR SANDWICH SPECTROMETERS nuclear-data uncertainties, has in the past contained an unnecessary approximation. It can easily be shown that at a neutron energy greater than ,-,370 keV the maximum energy in the alpha-particle distribution exceeds 2.73 MeV and so contributes to the so-called triton response. The alpha-particle energy distribution is slightly wider than that for the triton, so the contribution to the response function from alpha particles is always somewhat smaller than from tritons, but it is nevertheless certainly significant. Complete alphaparticle and triton distributions have been calculated and reported elsewhere*), but were discussed in the context of a bi-dimensional mode of data collection. This mode is not in general use, so it is worthwhile investigating the effect of the alpha-particle contribution to the triton response matrix in more normal usage. The triton response functions for a range of neutron energies are given in fig. 8, where the alpha-particle contribution can be clearly seen. The functions shown have been calculated from the usual kinematic and geometrical factors, but also include noise broadening with a full width half maximum of ,-~65 keV, and average energy-degradation factors appropriate to a 6LiF layer thickness of 0.8/~g/mm 2 as discussed in the previous section. The use of an average energydegradation factor for the triton response is justified by the narrowness of the triton degradation distribution, while the justification for an average value for the alpha particle lies in the fact that the long tail of the degradation distribution is at low energies, and is therefore not included in the calculated response functions. In view of the results given in section 2.3 it might be argued that an average energy degradation equal to the energy loss in passing vertically through the sensitive layer is not exact. However, the errors introduced by this assumption are considerably smaller than the purely experimental errors in defining the energy scale. Fig. 9 shows a typical fast reactor spectrum, and the upper curve of fig. 10 shows the calculated triton response to this spectrum, with the alpha-particle contributions included in the response matrix used to perform the convolution. (The lower curve in fig. 10 is discussed in section 4.) Fig. I 1 shows the percentage difference between the spectrum obtained by deconvolving the data of fig. 10 with the matrices firstly including and secondly excluding the alpha-particle contribution. It can be seen that, although the difference is negligible at energies of above ~ 5 0 keV, it rises very rapidly as the neutron energy falls towards what is normally regarded as the lower limit of usefulness of the spectrometer at ~ 5-10 keV.
69
3.2. THE SUMMED-PEAKRESPONSE MATRIX If a neutron-spectrum measurement in the summedpeak mode is made with very good resolution it may not be necessary to deconvolve the measurement to derive the desired neutron spectrum. It is more often the case that some deconvolution is required, particularly in the lower-energy region where an overlap with results from the triton mode measurement is desirable. Satisfactory deconvolution requires a realistic response matrix, which is usually taken to be a set of Gaussian functions centred about the diagonal of the matrix. It can be seen from the results of section 2.3 that, particularly in cases where a thick 6LiF layer has been used in order to obtain sufficient sensitivity to the higher end of the neutron spectrum, the response function is not Gaussian. This is illustrated in fig. 12, which shows various experimentally obtained spectral peaks with curves fitted to them using the distributions as in fig. 5 with appropriate degradation and electronicnoise factors. The validity of the degradation theory is confirmed by the good agreement between calculation and measurement. It is therefore reasonable to suppose that the average energy-loss curves given in fig. 6 are also correct. It can be seen from these curves that when a thick sensitive layer is used there are non linearities of up to ~ 30 keV on the energy scale. An error of this size is not insignificant, and in view of the ease with which at least an approximate correction can be made the omission of such a correction seems unnecessary.
4. The high-energy contribatioa to the triton spectrum One further effect which may be regarded as influencing the calibration of the 6Li spectrometer is the calculation of the contribution to the recorded spectrum from neutrons of energy outside the range of the response matrix. This matrix is usually calculated up to a maximum neutron energy of ~600 keV, corresponding to a maximum triton energy of 1 MeV relative to the thermal-neutron value. Neutrons of energy greater than 600 keV can all contribute to the triton distribution within the triton energy range of 0-1 MeV. The relative size of this contribution is reduced by the rapid fall in spectrometer efficiency as the neutron energy rises, and in many spectrum measurements is also further reduced by the rapid fall in neutron flux with increasing energy. However, it will be increased by the fact that the alpha-particle and triton distributions overlap to a greater extent as the neutron energy increases, so a larger proportion of alpha particles from high-energy neutrons will contribute to the triton spectrum.
70
P. J. C L E M E N T S
20TH CENTURY DESIGN SPECTROMETER
/ 500
/
\
,x'
\
/
LAYER THICKNESS = . 8 0 p g m l m m 2 NOISE FULL WIDTH HALF MAX.- 130keV NEUTRON ENERGY = 0
\
x/ ¢
x
,' ,~
\
I
\
~"~..xx x
x"-x"x"x"¢'x"x'-250 ~
'
2'7o
-
CHANNEL NUMBER
5K
k
/
HARWELL DESIGN SPECTROMETER LAYER THICKNESS w 2' 0 p gmlmm 2 NOISE FULL WIDTH HALF MAX. " 1 / , 0 keV NEUTRON ENERGY - 0 (SAME DATA AS FIG./,)
k
ix
t
0
: 200
I 250 CHANNEL NUMBER
I
x x x x~(; A(x~'----'~x ~ x / / xX ~._ KI/ X X X )P~ X
100
X/
/ /
x
x
I 300
I
X
HARWELL DESIGN SPECTROMETER LAYER THICKNESS" 2.8Hom/mm2 NOISE FULL WIDTH HALF MAX. m 450keV NEUTRON ENERGY - STSkeV
~,~
/x/x
\xX xx~x
.s
I
~
t
I
I 350 CHANNEL NUMBER
I
I
I
I
~
~
II
Fig. 12, T h e observed ( x ) and calculated ( - - ) s u m m e d - p e a k pulse-height distributions, produced by the detection o f neutrons in three different spectrometers. (One channel ,~13.5 keV in each case.)
6Li S E M I C O N D U C T O R
SANDWICH
It can be argued that, because no neutrons of energy below ,-~600 keV can produce a triton response at an energy of more than 1 MeV above the zero value, then the contribution to the measured triton spectrum at 600 KeV must have arisen from neutrons of higher energy. This gives an approximate value for the highenergy background contribution at this energy which can be taken to be an approximation for the value at lower energies. The necessity for making an estimate of the highenergy contribution is removed if the bi-dimensional data-collection mode mentioned in section 3.1 4) is used, but as has been pointed out, this method is not in general use, so a calculation of the high-energy contribution observed in more normal use is necessary. A precise estimate of the background contribution in any spectrum may be derived by calculating not only a triton response matrix covering a relative maximum triton-energy range from 0-1 MeV, but also a further matrix for the range 0 to some suitable upper limit, e.g. 4 MeV. The neutron spectrum above a neutron energy of 600 keV is assumed to be known from the summed-peak measurement. The convolution of the extended response matrix with a neutron spectrum assumed to have a zero value below a neutron energy of ~ 600 keV and the measured value above this energy produces the high-energy contribution to the triton spectrum in the lower-energy range. Fig. 9 shows a typical reactor spectrum and fig. 10
71
SPECTROMETERS
shows the triton response to this spectrum with the relative contribution from neutrons of energies above and below 600 keV shown separately. It can be seen that at a triton energy of less than about 500 keV the contribution to the triton spectrum caused by the detection of neutrons of energy greater than 600 keV is only 4-5 %, but that at higher triton energies it rises rapidly to become the entire contribution at a triton energy of 1 MeV. The effects of the presence of the high-energy contribution were investigated by deconvolving the triton spectrum in the triton energy range 0-1 MeV in three different ways. Firstly the deconvolution was carried out with a correct subtraction made, i.e. by deconvolving the difference between the two curves shown in fig. 10. Further deconvolutions were also carried out by ignoring the high-energy contribution altogether and by assuming, as previously suggested, that this contribution is flat and equal to the number of events in the triton distribution at 1 MeV. The results of these calculations are shown in fig. 13 as deviations from the results obtained by deconvolving the properly corrected triton spectrum. It can be seen that omission of the correction for the high-energy contribution leads to oscillations of total amplitude ,-,10% below a neutron energy of ,--500 keV, but rising very rapidly above this energy. The oscillations are considerably reduced by the fiat contribution correction, but again lead to very large errors above ,,~ 500 keV. Errors above x
BOTH x AND o RISE TO VERY LARGE VALUES
x NO SUBTRACTION OF THE HIGH ENERGY CONTRIBUTION O SUBTRACTION OF A FLAT HIGH ENERGY CONTRIBUTION
uJ
3+sI
x o
ooO~
x 0
0 ~
0
X
X
0
%°°
~
"x OoX
X 0 x 0 x X O0 X
°x/t~,~
~ x
X X X X
oo
0
o°
0
0
X
o x
x
g
o x
N
x o
x
x x
x Xx x
x
o o
x I
I 10-3
LOGARITHMIC I I
SCALE CHANGEI !
10-2
~
LINEAR ---~ I •1
I '2 NEUTRON ENERGY (MeVI
I -3
I .&
I .5
.6
Fig. 13. T h e errors in the calculated n e u t r o n s p e c t r u m produced by: (a) Omitting the high-energy contribution to the triton spectrum, a n d (b) subtracting a fiat high-energy contribution.
72
P. J. C L E M E N T S
500 keV are not serious as long as the neutron spectrum derived from the summed-peak spectrum can be satisfactorily extended down to this energy. Whether this is so will depend primarily on the width of the summed peak and difficulty may be encountered if the peak is more than a few hundred keV broad, as is sometimes the case. It could also be difficult if a spectrometer with a very thick 6LiF layer had been used, because the resulting asymmetry in summedpeak shape would have its greatest effect at the lowerenergy end of the spectrum. The errors below 500 keV may in some cases be on the borderline of significance, especially if the flat-contribution approximation is used, but there nevertheless seems to be little justification for not making the proper correction for the high-energy contribution to the triton spectrum, considering the ease with which this can be carried out. 5. Conclusions It has been suggested that the accuracy of neutronspectrum measurements made using 6LiF semiconductor sandwich spectrometers could be improved by adding several relatively straightforward refinements to the methods normally used for data analysis. Both the improvements which can thus be obtained and the benefits to be obtained by making them will of course vary from measurement to measurement. It has been shown that the accuracy of the calibration of the energy scale in both the triton and summed-peak modes depends on an understanding of the energy-loss mechanism in the sensitive layer of the spectrometer. For example, for spectrometers with a sensitive layer thickness of ~ 2.4/~g/mm 2 a non-linearity of ~ 30 keV i s introduced over the energy range of the summed-peak measurement. Considerably greater errors would be expected with more sensitive spectrometers whose use might occasionally be necessary. However, the energy losses within the sensitive layer have been calculated to give good agreement with experimentally obtained data and to allow accurate correction of the energy scales in both the triton and summed-peak modes.
The calculation of the triton response matrix does not normally include the contribution from alpha particles. This contribution has now been calculated and included, because its omission leads to unnecessary errors in neutron spectra generated by deconvolution with the incomplete matrix. It was shown that the omission of the alpha-particle contribution leads to errors of nearly 50 % at the lower-energy end of a typical neutron spectrum which might be measured with the spectrometer. Two other possible sources of calibration error, caused by approximate subtraction of the high-energy contribution to the triton spectrum and by the approximation of the sum-peak response function by a Gaussian shape, were also discussed. Although the errors from these sources were likely to be small, they could in some circumstances lead to undesirably large errors in the energy region from ~ 500-600 keV, where the triton and sum-peak measurements are respectively at their upper and lower limits of usefulness.
References
1) I. C. Rickard, Nucl. Instr. and Meth. 105 (1972) 399. 2) A.M. Broomfield, W.J. Paterson and J.E. Sanders, AEEW-M.997 (1970). a) M. G. Silk and S. B. Wright, AERE-R. 6060 (1970). 4) G. De Leeuw-Gierts and S. De Leeuw, BLG-450(Dec. 1970). 5) S. K. I. Pattenden and J. M. Stevenson, Proc. CEGB Conf. on Radiation measurements in nuclear power (September 1966). 6) C. Beets, S. De Leeuw and G. De Leeuw-Gierts, Proc. CEGB Conf. on Radiation measurements in nuclear power (September 1966). 7) p.j. Clements and I. C. Rickard, AERE-R.7075 (1972). s) p.j. Clements, AERE-R.7600 (1973). 9) H. Bluhm and D. Stegemann, Nucl. Instr. and Meth. 70 (1969) 141. 10) p. j. Clements, AERE-R.7512 (1973). 11) M. G. Silk, J. Nucl. Energy 22 (1973) 163. 12) M.G. Silk and Margaret E. Windsor, J. Nucl. Energy 21 (1966) 17. 1~) M. G. Silk, AERE-M.2009 (1968). 14) j. B. Marion and F. C. Young, Nuclear reaction analysis graphs and tables (North-Holland Publ. Company, Amsterdam, 1968).