G.
OE LEEue-GI ERTS,
BIG M l
I »pr.
5.
Dl LEEU»
i97">i
«»»LTSI5 JF TrtE ME«5URE»E»T PROi-EOURE »»0 OF IwPOPTAwT
E*P£Rllif*jTAL
Summery. -
PARAMETERS IK
The spectrum « « i s u r w t n t l
important
:h.uictiriiticj
E
* E.
l
and
E
'
a
After
mined B e f o r e
the
Li
i n B i g t e n [ 10]
spectrometry
description
attention
is
TECHwlQUE
were used te
technique,
of
the fundamentals necessary
drawn to t h e p a r a m e t e r s
*nd ^ u r i o ; t h e measurement.
parameters j n
illustrated,
analyse
Including
the
making use of
Sensitivity
the
before
epplyinç
to be c a r e f u l l y
deter-
t e s t s on some o f
eiperimental
Bijten
these
results
interpretation.
f i n a l I y the ^ u t r o n
compared with
i.
of
SPECTROMETRY
parameter.
i sho'T
the t e c h n i a u e ,
and t h e ! '
THE L I T x l u H - 6
f*e
BE L E EU*-Gl EOTS,
BLG 501 I »pr.
spectrum,
Theoretical
S.
measured between ^ 5 kev
end 7 " e " ,
is
spectrum.
0E LEEU»
1975'
f » S L » S l S C*
E'PERIMEHTAL
THE ME*SUR£<":»T PROCEDURE ««0 Of
PipaxfTfRS
in
THE L I T H i i m - 6
IMPORTAIT
SPECTROMETRY
TECHwIO/UE
3 amen va 11 i n a. - fan de hand van evper imen t el e neu t ronen spek t r a , gemeten i n
8 i g t e n , worden e r k e f e voorname ka > ak t e r * s t i eh en van de l i t h ï u m - 6 t e c h n i e k
geanalyseerd,
zowel voor c a t b e t r e f t de E, ;i I s de E • E. p a r a m e t e r ,
1
01
'
Ma een k o r t e b e s c h r i j v i n g van de f u n d a m e n t e l e w e t t e n van de t e c h n i e k ,
wordt de aandacht g e t r o k k e n op de p a r a m e t e r s d i e , i n d i e n n i e t n a u w k e u r i g b e p a a l d , vóó ' en gedurende de m e t i n g , a a n l e i d i n g kunnen geven t o t s y s t é m a t i s é e
f o u t e n , j e . o e l i g h e ! d s t e s t e n op v e r s c h i l l e n d e van d e i e p a r a m e t e r s worden o,ei l l u s t r e e r d , d a a r b i j g e b r u i k makend ^tên het Bi gten e i p e r i m e n t en z i j n i n t e r pretatie.
u i t e i n d e l i j k wordt het n eu t ron enspek t rum, b e p a a l d tussen ^ 5 kev en 7 WeV,
vergeleken
pretatie
bij
verschillende
trend
set
hef
teoretische
van de gemeten
lithium-ï
van de w i j z i g i n g
zou b e s c h i k b a a r
E
spektrum berekend door
en t~*
E, d i s t r i b u t i e s
werkzame doorsneden
dit
"
L
se p r ê t a i t ,
om h e t m o g e l i j k
in h e t neut ron an spek t rum ta
PARAMETERS III
THE LITHIUM-6
bepalen
interdrie
t e maken een
Indian
«HO Of
tan nieuwe
l'absence
c a r a c t é r i s t i dues de l a
de n e u t r o n s
lents,
IMPORTANT
SPECTROMETRY
' ' " t a r p r é t a t ion das mesures de s p e c t r a »
de p a r
Oe
DE LEEUW
4» AL T SI S Of THE M£ASuR£"ï«T PR0C0URE
îii"-!'
Hansen.
komen.
G. OE LEEUw-GI ERTS, S.
HLG 501 ( Apr. 19751
E*PERIME»T»L
G. E.
werd d o o r g e v o e r d met
E
et
E_»
a l'analysa
t e c h n i q u e de spect romét r i e
TECMRICUE
E
dans
Bigten
d'importantes
llthlum-6.
« p r e s une c o u r t e d e s c r i p t i o n des données f o n d a m e n t a l e s n é c e s s a i r e s a
l ' u t i l i s a t i o n de la t e c h n i q u e , l ' a t t e n t i o n e s t t i r é e sur das p a r a m è t r e s a
d é t e r m i n e r avec t r i s grande p r é c i s i o n . Les données e x p é r i m e n t a l e s da B i g t e n
e t l e u r i n t e r p r é t a t i o n sont u t i l i s é e s pour i l l u s t r e r des t e s t s da s e n s i b i l i t é s sur c e r t a i n s de ces p a r a m é t r a s .
A l a f i n du r a p p o r t l a s p e c t r e de n e u t r o n s , mesuré e n t r a "V 5 keV et 7 "eV
e s t comparé au s p e c t r e t h é o ' l q u e , c a l c u l é p a r G.E, Hansen, Las s p e c t r e s E. e t
E • E { sont I n t e r p r é t é s a l ' a i d a da t r o i s j a t s de s e c t i o n * e f f i c a c e * dl f f é r e n ' l e l l e s , a f i n de p e r m e t t r e une e s t i m a t i o n du t r e n d d a * m o d i f i c a t i o n s qua
p o u r r a i t s u b i r l e s p e c t r e de n e u t r o n s si un nouveau set da « a c t i o n * « a r a l t
dl sponi b l e .
ANALYSIS OF THE
MEASUREMENT PROCEDURE AND
OF IMPORTANT EXPERIMENTAL
PARAMETERS IN THE LITHIUM-6
SPECTROMETRY TECHNIQUE
6 . DE LEEUW-GIERTS, S. DE LEEUW
A p r i l 1975
BLG 501
-
1 -
INTRODUCTION
As p a r t of tr.e c o l l a b o r a t i o n between U.S. l a b o r a t o r i e s and C.E.N./S.C.K.
linked
t o t h e U.S. l a b o r a t o r y LKFBR Reaction Rate programme, t h e c e n t r a l n e u t r o n
spectrum of th^ Bigten c r i t i c a l assembly was measured by means of t h e l i t h i u m - 6
spectrometry t e c h n i q u e , using the E • E. parameter and t h e E. parameter as
a t
t
v
developed in Mol I 3] • The Bigten assen> ly i s a c l e a n , c r i t i c a l uranium (10 %
^„
J
U,
90 % ~" U) assembly a t Los Alamos [ 1) ; i t i s i n c o r p o r a t e d i n t o t h e U.S. Benchmarks.
The neutron spectrum deduced from the I i t h i u m - 6 measurements , performed in September 1973 in c o l l a b o r a t i o n with Drs H.H. Heimir.k aid G.E. Har.sen, being published
elsewhere ( 10} , t h e aim of t h e present paper i s t o use t h e experimental data to
analyse t h e s y s t e m a t i c s and most important parameters appearing in t h e a p p l i c a t i o n
of t h e
Li t e c h n i q u e . Indeed t h e t o t a l absence of slow neutron energy t a i l i n thic-
f a s t r e a c t o r type neutron spectrum was very -well s u i t e d t o p o s t u l a t e p o s s i b l e
systematic e r r o r s in fundamental experimental d a t a and p e r m i t t e d a s t u d y , down t o
a few KeV, of the r e p e r c u s s i o n of u n c e r t a i n t i e s i n t h e s e d a t a on t h e unfolded
neutron spectrum.
1 . DESCRIPTION OF THE SPECTROMETER
6
The "Li spectrometer box, loaded with heme made d e t e c t o r s , c u r r e n t l y used
for t h e Fast Reactor Programme at Mol, had to be modified t o enable i t s p o s i t i o n i n g
in the c e n t r e of B i g t e n . The maximum c u t e r diameter allowed was 3.65 cm. Since t h e
corresponding maximum height was 3 cm, a new vacuum system had t o be developed.
Easy replacement of t h e d e t e c t o r s mounted in a sandwich o r c o l l i m a t e d geometry and
minimum p e r t u r b a t i o n of t h e neutron population t o be analysed were mandatory. The
new design i s shown in Fig. 3a. A ceramic mounting system was fixed t o t h e cover
t o r e c e i v e two s o l i d s t a t e d e t e c t o r s of 3 cm diameter maximum, with or without
spacing between. The d e t e c t o r s , f i x e ! in a ceramic r i n g w i t h tvo small drops of
SISS n - t y p e g l u e , had a r e s i s t i v i t y of U, 000 Q cm and were operated a t TO V,
n e t t o r e v e r s e b i a s on the d e t e c t o r s . A LiF
d e p o s i t of 0.07 vm w *s evaporated
onto one of t h e d e t e c t o r s for t h e f i r s t experimental r u n .
2.FUNDAMENTALS OF THE 6 U SPECTROMETRY TECHNIQUE
2.1. Principle
- Using t h e
E. * E
t
a
L i ( n , a ) t r e a c t i o n , t h e neutron spectrum can be deduced from the
and E. d i s t r i b u t i o n s ,
t
t h e neutron energy i s deduced in t h e f i r s t case from t h e r e l a t i o n E
a
Q + E
where E • energy of a particle
E • energy of triton
+ E. •
t
= neutron energy
= energy released = ".787 MeV
m the
' /<• v ?
"t
M
+y
a
A! M E
y (M • M )
t
where M , '•' *r.d M
"
M Q + E (M
2
M
- M ) |
a * Mt
J
indicate respectively the nasses of the neutron, the alpha
an,-»
t i
and S = «r.çle between r.eutrcr. and t r i ten [2]
in l a b o r a t o r y
co-ordinates.
The setiiod using t h e E^. parameter i s , as in t h e proton r e c o i l c a s e , i n d i r e c t ;
consequently t c i n t e r p r e t trie E„ d i s t r i b u t i o n s , in supplement t o the
t i a l c r e s s - s e c t i o n s , t h e knowledge of t h e angular " L i ( n , a ) t
cross-secticne
With the.- ^
is
differen-
differential
required.
Daraneter one can determine t h e neutron spectrum from a few keV [ 2)
r -
up to atcut ~~C keV;a higher limit is meaningless,the F. • E
parameier covering
the energy range above the 2'50 keV resonance region.
To avoid any normalization between these tve cctr.pleKer.tary method'-- and tr. eliir.i nate the overlap of the triton distribution resulting from interactions with
neutrons of energies higher than 1 MeV {= variable limit), a two-parameter analysis was performed. Other advantages of this method are described-in 13).
Many correction factors, described in [2, I] are to be taken into acccurt for
the interpretation of the E
and E
+ E^ distributions recorded in a completely
unknown neutron population, because the measurement must be done in a real . -rt
geometry. This involves for instance an energy dependent correction related to
the angle between a and triton, and a highly deformed signal of the monoenergetic distributions, commonly assimilated in the interpretation to Gaussian
ones.
In Fig. 1 are compared the theoretical mono-energetic E , E
ar.d E
+ E
responses,
for a deposit of 1 urn, in case of a 2 1 and collimatod detection. It is presently
possible to avoid these correction factors and sources of errors because of the
cylindrical geometry, homogeneity and overall dimensions of the assembly. Indeed
one may use a sandwich of detectors separated by a distance, as is the case for
energy independent collimation [ 2]. Moreover, although the angular neutron
distribution must be close to isotropy, we intentionally positioned the detectors perpendicular to the symmetry axis, 30 that, by the E
analysis in the tvo
detectors, we could verify whether the perturbation due to the entrance hole
and cables was negligible.
2.2. Measurements
2.2.1. Distributions to be recorded
Tc deiermine the neutron spectrin ir. Eigten, the following distributions
had to be measured and analysed :
1. the F, • E spectrum;
a
t
?. for reasons outlined abcve, the E^ spectrum recorded in each détecter. ?r.e is
analysed in the X-APC cf a two-par-uaeter analyser, the Y-ADC analysing the
r • ii. signal:
a
t
1. _c avoid nonnili zation factors, related i'cr instance to reactor pover and
stability, Lieasjiring time, analyser dead time, etc.;
?.
to reduce "by direct elimination, the background to a negligible «count;
?. to avoid inaccuracies related to the presence of tritons issued fr^ni interactions with neutrons of energies higher than about 1 MeV; these inaccuracies are principally due to the fact that no sufficiently accurate theoretical representation for the angular crocs-sections exists, vhich allows
interpolation of the experimental data;
4. to eliminate, if not negligible, the partial superposition of the a-distributior..
The second solid utate detector response is analysed in e. single-parameter
analyser, the first one corroborating a clean response from the high neutron
energy tail and the
t's.
2.2.2. Erergy calibration method
The energy calibration of the analysers is established using a puiser and
the thermal a, triton and sum responses. Compatibility tests were performed all
along the experiment, using
gain comparisons and stability for the puiser and
the theoretical energy losses, respectively for the a, triton and sum peaks and
for the two deposit thicknesses used I 2) , for the mono-energetic responses.
2.2.3. Fast neutrcn measurements
7
The neutron flux asked for lies between 10
7 - 2 - 1
and about 5.10 n.cm
s
, the
final value depending on the "y" over "fast neutron dese" ratio. The final spectrum is the sum of partial spectra. These sequential measurements over short
periods (about 1 h) are necessary because the solid state detector characteristics
vary when irradiated by fast neutrons.
Recording the partial spectra enables one to correct for shifts introduced by the
degradation of the detector characteristics and to hold th* detector depletion
depth rather constant all along the measurement, by adjusting the polarization to
correct for the increase of the inverse current.
- u -
Puiser calibration is dene between two successive measurements to survey electronic and g-iir. stability.
2.2.4. Background substractton method
The background component, mostly due to parasitic (n,a) and (n,p) reactions
with tr.-^ Si-nuclei, is very important when measuring the E
a
+ E. distribution;
t
its absolute value depends on the depletion depth. Due to the changing characteristics of the solid state detector under fast neutron irradiation, it is very
difficult :c ensure that the background was measured under the same conditions
as the spectrum. The depletion depth can be kept constant, as explained earlier,
but shifts between background and spectrum are difficult to detect. Because of
the steep decrease of the spectra above about 700 keV this may introduce large
errors. To monitor possible shifts two solutions exist. The first consists cf
putting a none-energetic a source in front of the detectors; for practical reasons
this solution is abandoned for the two-deposit technique ( 5] • Here a first set
of measurements is done with a thin LiF deposit (^ C O T u m ) . The specific shape
of the F. • r, distribution is used to find the shifts and to correct for them
a
t
when substra:tin.ç these measurements from the second set performed with a deposit
about ten times rr.ickor.
lue reliability of this method was tested by comparing the results with those
obtained by using a new recently developed method. This rather complicated method
eliminates the background during the spectrum recording itself; elimination is
based on the analysis of the stopping power of the particle in the space between
the two solid state detectors [ 6] .
The same method is used for the E
configuration. For the E
measurements, not recorded in a two-parameter
parameter, the background is however much less important.
3. EXPERIMENTAL PARAMETERS GENERATING INACCURACIES
3.1. Determination of the zero of the neutron energy scale
Because of the
Li(n,a)t cross-section shape, the zero of the neutron
energy scale must be very accurately known. For the E. parameter, the repercussion of an erroneous zero is mostly noticed in the resonance region, while for
E 0 + E_ the spectrum is completely perturbed in the energy region corresponding
to the high-energy side of the resonance i.e. from 300 up to about 800 keV.
The precision of the zero deduced by means of the puiser measuremnts, performed for reasons described in § ?,2., is insufficient. Indeed, due to the high
Q value, an accuracy of 0.1 channel is required. A good accuracy is obtained when
using the mean energy of the E t or E o + E^ prominent peak, resulting from inter-
- 5 -
actions vith the slow neutron energy tail present in almost all spectra.
The method used up to now was not practicable in Bigten, where no such peaks
were observable. Fig. 2 compares, for instance, the triton distribution measured
in 11 and Bigten. To reach the accuracy required, a programme was written using
indirectly the 250 keV resonance.
3.2. Energy calibration
3.2.1. E. parameter
The thicker the deposit, xhe more it is diflicult to assure a high accuracy
in the channel width determination by means of the thermal neutron calibration
method. Indeed, the energy loss of the a particles and even tritons is then no
longer negligible and is not accurately known. Therefore a calibration is never
based solely on one method. Combining puiser calibration and theoretical knowledge of a energy ?.oss, and taking into account compatibility tests between the
mean energy displacement of the a and a + t thermal distributions [ 2 ] , an accuracy
sufficiently high was obtained, as will be shown in § 5- The highest accuracy and
compatibility is obtained when considering as calibration points the maximum
energy of the a and triton distributions (cf. § 5)3-?.2. E • E. parameter
a
t
As for E , inaccuracies are again due to an inaccurate knowledge of the
mean energy of the thermal distribution as a function of the deposit thickness.
But again, using the method described for E
and following the procedure
described in 2.2.2., sufficient accuracy is obtained.
3.3. Resolution
To correct for the resolution, the resolution function was previously assumed to be well approximated by a Qaussian*, only a partial unfolding is done by
the Uclis code to avoid oscillations. This may introduce local inaccuracies
(cf. $ 7). Indeed, because of the finite resolution of the E
parameter, local
errors are introduced in the resonance region. The use of bin widths equal to
the resolution width attenuates te som? extent these systematic deviations
around 250 keV.
The errors introduced by this partial unfolding in the E
avoided by restricting the lower validity limit to about 3 A
+ E,. case are
o
t
. . (FWHM). This
O T t
limit might be lowered when using other interpretation approaches, as does the
programme mentioned under § 3 . 1 .
If one wishes to interpret below * 600 keV, the res'lution must be quite accurately known.
- o -
The inaccuracies expected on the resolution are principally due to th* degradation of the characteristics of the detectors, if all oth»*r experimental conditions have been carefully
3.4.
defined.
Geometry
Using the ?nergy independent, collimation set-up, the use of Oaussian as
the resolution function for the E
• E. , and certainly for the E^. distributions,
a t
t
is sufficiently accurate. Having no corrections to carry out for the angle
between a and t r i t o n , another source of inaccuracies is avoided.
Finally, to verify that no error is introduced by the hypothesis on the angular
neutron distributions (mentioned under 2 . 1 . and allowing us to work under present
conditions) the E responses of the two detectors are compared.
3.5. Background
Because of its high value, the background subtraction may easily introduce
unexpected errors. However, using the method described in § 2.2.U., this source
of inaccuracy is greatly reduced, especially in the MeV energy region, where the
background can reach up to 5û %.
4. ELECTRONIC SET-UP
The normally used electronic scheme is r-ported in I 7)• For reasons of nonavailability of certain modules or availability of more appropriate ones, some
modifications may occur as long as the basic principle in conserved. A schematic
drawing of the electronics used here is given in Fig. 3b. The fast coincidences
eliminate almost entirely the 7-hackground, but when usiner the constant fraction
of pulse height trigger, or any other module with the same function, particular
attention must be given to the lower level discriminator. Indeed not to lose any
event, especially for the E
parameter, one must make sure no alphas are cut off
by the lower level setting. Knowing that the lowest theoretical a energy equals
1.595 MeV, the level should be put at least 2 A
U
: full width at half maximum
a a
of a mono-energetic distribution) lower. To be safe in case of possible level
s h i f t s , i t s height should not exceed 0.5 to 0.75 MeV.
- 7-
5. CALIBRATION MEASUREMENTS
5.1. Thermal neutron results
5.1.1. The energy calibration was performed as outlined atcve, using puiser and
thermal neutrons.
The energy width of a channel vas determined, using the majciauE energy of
the thermal alpha and triton distribution and the mean energy of the sum peak ;
indeed the channel width was too large in this case tc obtain high accuracy on
the positioning of the maximum energy. To determine the mean energy cf the sun
peak, the theoretical values of [2) were considered; it was assured equal to
'•*.6 MeV for the thick LiF deposit. The resolution for the triton ir. the detector
with the LiF deposit and tr• •> sum distributions were found respectively tc be 35
and 75 keV for the thin deposit, 65 and 25C keV for the thick one. The accuracy
of the channel width is estimated to be equal or less than 1 % for the E distribution, and equal t~ ? % for the E • E one. Fis. h represents the thermal o,
a
t
t and sum d i s t r i b u t i o n s , measured with the t h i n d e p o s i t and recorded in t h e two
ADC's coupled to t h e PDP 8. Fig. 5 and 6 show the same d i s t r i b u t i o n s , but measured
with the t h i c k d e p o s i t . The alpha and t r i t o n d i s t r i b u t i o n s a r e those measured i n
the other d e t e c t o r and recorded by t h e single-parameter
analyser.
5 . 1 . 2 . The determination of the r a t i o of the number of Li n u c l e i in both d e p o s i t s
(value needed for t h e background s u b t r a c t i o n ) i s a l s o deduced from t h e thermal
neutrcn measurements. A r a t i o of 11.5 was found;the thermal count r a t e s were equal
t o 36.35 c t s / s and U18.8 c t s / s r e s p e c t i v e l y for t h e t h i n and t h i c k d e p o s i t .
5.1.3. Counter e f f i c i e n c y
The loss in count rate due to the collimation geometry was determined by
comparing the triton count rate in the detector with the LiF deposit, recorded
once with and once without applying coincidences.
5.1.4. The neutron spectra deduced from the E
distributions are directly com-
parp.ble if there are no differences in dead-time losses or corrections for the
different systems used. The thick deposit thermal calibration showed a difference
of about 5 % in absolute count rates between the PDP system used and the others.
To a value of 1*16.8 cts/s, measured with the PDP set-up, corresponded U00 cts/s
with the single-parameter analyser. No inaccuracy is introduced by ';his loss,
because E
+ E. was, together with the E. spectrum of one detector, recorded on
G
t
the PD? system.
w
-8$.2. Lower and upper neutron energy limits that can be reached 1n the present
conditions
The lower energy validity limit is deduced from the resolution of the E.
thermal distribution. When slow neutrons are present in an amount comparable to
Mol-EE, one may accept a lewer energy limit equal to the neutron energy corresponding to a triton, forward emitted, and with an energy equal to E^ • 2 o
(I.
* 2.73 MeV). This would correspond here to about 5 keV. But because of the
o
absence of any slow neutron component in the spectrum one might even go down to
1 i
• 1 a ; this corresponds to about 1.5 keV. Indeed no slow Qaussian tail,
due ?o slow neutrons, is then superposed on the low neutron energy response.
The upper energy limit depends on the depletion depth of the detector.
To hold the background to a reasonable amount, avoiding in that way new sources
of inaccuracy, a compromise must be made. To not exceed 25 t (background percentage
reached at 1» MeV neutron energy), we opted to lose a bit in resolution by taking
a rather thick deposit (% 0.8 \sm) and to limit the depletion depth to about 270 ym.
This amount corresponds to the range of a triton of 9 MeV, incident perpendicularly
on the detector plane ; the corresponding neutron energy equals about 6 MeV.
Because of the reaction cinematics and the isotropy of the distributions, the
underestimation m?de by interpreting the E
a
• E,, spectrum up to 7 MeV neutron
t
energy is less than 10 %. The lower energy limit resulting from the E
• E
distribution is related to the limit of compatibility between the two methods of
interpretation. For a FWHM of 250 keV, this equals about 600 keV (cf, 5 7 ) .
6. SPECTRUM MEASUREMENTS IN 8I6TEN ( 10]
Fast üeutron spectra were recorded in sequences of one hour, first with the
thin, then with the thick deposit. Thermal neutron calibrations preceded and
followed each set of measurements. Polarization adjustments and puiser calibrations were performed each hour. The sequential spectra were compared and corrected
fox Shifts before final summation.
The spectrum recorded in the two-parameter configuration showed that the superposition of the a distribution to the triton one introduced a negligible correction in the region of interest} consequently no problems were raised by this
parameter for the interpretation of the triton distribution recorded in the
•ingle-parameter configuration.
It was also established that the high-energy neutrons contributed less than a
few percent below -v 600 keV. To estimate the inaccuracies that flight be introduced
by the inaccuracies on the angular
Li differential cross-sections above * 700 keV,
the triton spectrum recorded in the 8.P. analyser was once interpreted up to a
triton energy corresponding to 750 keV neutron energy, once corresponding to
•Mtvmil nf 1.9
MaV.
- 9 -
In the present experiment al?
• -measuremente vith the thin deposit were
used for background purposes throu
*1
(E
o * Et
or E
H
(E
o * Et
or
2
->ving relations :
t'measured * H ,
* background
V m e a s u r e d " H2real * Kbackground
Indices 1 and 2 corrspond respectively to the thin and the thick deposit. N. (Et)
is for instance the triton distribution measured vith the thin deposit.
Having
J *»2 r e a l -11-5 J »i
real
R
2real "
wff
(
*2 "
H
we
°* t a ^ n
0
Local effects, e.g. in the thermal and resonance region, due to the difference
in resolution functions are easily eliminated.
In the single-parameter recorded E+ distributions, the background component is
less than 3 It up to 250 keV; it reaches 10 % at about 500 keV neutron energy.
The relative importât ;e of the background in the analysis of the E
• E. parameter
reaches % 5 f at 500 keV, 10 % at about 1 MeV and nearly 25 % at I» MeV neutron
energy. In the following figures, typical experimental results are given.
The triton distribution resulting from a one-hour measurement vith a thick deposit,
and recorded in the S.P. analyser, is drtvn in Pig. 7* The final E
distribution
recorded in a tvo-parameter configuration is represented in Pig. 8. Partial spectra
deduced from the summation of a fev (E
+ E.) energy groups are compared in Fig. 9-
Curve one corresponds to the summation over all E
+ E. energy groups i.e. from
9
h.2 MeV up to 5.6 MeV (E
v
• 1 MeV); curves 2, 3 and 1» are partial E. distributions
V
11
limited by the y-axis between I*.2 and 5-2 MeV, U.2 and U.95 MeV (En » 350 keV),
k.9 and 5.6 MeV respectively.
The ï + 1 distribution meast
measured vith the thick deposit, and from vhich backa
o
t
ground vas subtracted, is represented in Fig. 10.
7. INTERPRETATION
The E* and E . • E. spectra «re interprets* by means of the Uclis code (to
be published» S. De Leeuv). This cod* uses implicitly the
Li reaction character-
istics and a priori information. Partial unfolding of the resolution curve is
performed on the experimental I* and C
v
• E. distributions.
S t
All spectra are interpreted vitb the cross-section drawn in Pig. 11, used
for the interprétation of the Mol-ÎI spectra. Reasons for the choice of this
cross-section curve ere outlined in ( 8 ) . The B Q , B. and B„ constants used for
- 10 -
the interpolation of the experimental angular triton distributions are taken
from 191 •
In § 9 an attempt is made to give trends of spectrum modifications when
changing the cross-section. Because the angular data are not changed when passing
from one cross-section set to another, the differential and angular data are not
necessarily compatible and these results may only be considered as possible trends.
7.1. E t distributions
7.1.1. Unfolding of the triton distributions
In Fig. 12 we compare the neutron spectra deduced from the S.P. distribution
(curve 1 ) , the PDP ADC response (curve 2) and the two-parameter distribution
(curve 3) limited betveen k.2 and 5.6 MeV, E • E. values. Curve 1 corresponds to
ct
t
the neutron spectrum seen by the detector without a deposit, curves 2 and 3 by
the detector with the LiF deposit. The differences between curves 2 and 3 result
only from the fact that whereas curve 2 is deduced from an E. distribution where
the background was subtracted by using the thin deposit method, curve 3 is obtained by the two-parameter analysis. The differences observed between the twodetector responses do not display a significant difference in the spectral shape
of the forward and backward 2 n neutron distributions. The power of a two-parameter analysis (beside the elimination of normalization problems) when dealing
with ft hard spectrum is illustrated in Fig. 13. It represents the interpretation
of the partial E t distributions corresponding to the curves 1, 2 and 3 of Fig. 9.
When comparing the partial spectra one must not lose sight of the resolution
function on the E • E. mono-energetic distributions. For a nearly Gaussian resoCI
U
lution function, i.e. thin deposit, the unfolding of the triton responses recorded
in aa isotropic neutron population and collapsed in narrow E • B«. intervals may
s
a t
provide very good tests on the angular Li data.
Around the resonance peak, systematic errors are introduced by the only
partial unfolding of the resolution function. The spectrum being rather flat
between 200 and 300 keV, the difference between 250 keV and 200 or 280 k«V should
not exceed * 15 %; these errors almost cancel out when collapsing into the fol
loving energy groups : 180 - 220, 220 - 350 keV. The 350 - l»20 keV interval i s
underestimated by about 5 %. The restatement of a new method is presently under
waf to correct for these deviations.
7.1.2. Sensitivity tests to zero uncertainties
In order tc show the importance of a high accuracy on the «ero of the
neutron energy scale, we compare in Fig. 11» neutron spectra obtained fro» the
- 11 ~
seae E. distribution but where ve shifted intentionally the zero of the neutron
energy scale. Frost the differences observed it appears that, if it is known that
no fine structures are present in the neighbourhood of the resonance peak, the
resolution of the E. parameter is sufficiently good to point out errors on the
zero. Because of the steep slopes around Et-;- " ^ &t_M corresponding to
E * 1^0 keV, once the zero is precisely known, shifts can be easily displayed
even if no slow neutron response is present.
7.1.3. Sensitivity tests to other parameters
- In Fig. 15 we have drawn the neutron spectrn unfolded from the triton distribution, recorded in the S.P., respectively for 6.1» and 6.5 keV/ch to illustrate
the errors that may be due to channel width inaccuracies. The zero of the
neutron energy scale is of course respected. The best value for the channel
width i» 6.U5 keV.
- Fig. 16 reports the neutron spectra obtained from the seme triton distribution,
once considering a triton cut-off corresponding to 1.2 MeV neutron energy, once
to 0.75 MeV. The differences observed are partly due to inaccuracies on the
theoretically calculated angular crosa-section data above 0.700 MeV.
- To estimate the inaccuracies on the spectra unfolded from a single-parameter
recorded triton distribution and due to background, ve compare, in Fig. 17*
the neutron spectra unfolded from a S.P. triton distribution with and without
background subtraction in the way described in S 6.
7.2. E + E. distributions
7.2.1. Unfolding methods
After subtraction of the background tne E + E . spectrum was interpreted
in two ways.
The first one uses the Uclis code. Because only half of the resolution is unfolded, a dip at the resonance energy subsists in the unfolded spectrum. To determine up to what energy the spectrum is perturbed, another, iterative, procedure
hat been written, which may be suosserized as follows :
let
**(0
*exp
— W
: tne
neutron spectrum at the i
iteration
'' **e
1 «periaental Io • IL
t distribution
RjU)
? J 0(B, ta) a(Efl) # i (B n ) âSa
G(l, E Î : resolution function
rttj n
i (n,e) cross-section of wLi
-
then
R
•i—
with
(E)
RTHÊT *
i-r
12 -
'i-V
• (E ) : the starting spectrum,
o n
In the present c a s e , t o reduce the number o f i t e r a t i o n s , we started from the
f i t t e d t h e o r e t i c a l spectrum. The method proved to be s t a b l e and has a quite f a s t
convergence r a t e . Prom the comparison of the two methods a compatibility was
obtained above 600 keV. The E • E. spectrum was interpreted using s u c c e s s i v e l y
a
t
0.5 and 1 uncertainty limit
of the real zero of the energy scale. Results from
both interpretation methods are drawn in Fig. l8.
7.2.2. Sensitivity tests for channel width and resolution inaccuracies
To illustrate the influence <f a 2 % difference in the channel width we
compare in Fig. 19 the spectra unfolded from the same E
+ E
distribution and
conserving the same channel number for the zero of the neutron energy scale, but
once with U8.9 and once with 50 keV/ch (a normalization factor of 1.022 was introduced for the comparison of the spectral shapes). Although spectra are accumulated during short times it may be possible that the thermal resolution
function is enlarged during the fast neutron measurement. The curves given in
Fig. 20 and corresponding to the unfolding of the same E
+ E
Cl
distribution
X
correspond to full width at half maximum for the resolution function of 200,
250 and 300 keV respectively.
7.2.3. Sensitivity tests for zero Inaccuracies
The second interpretation method is a very sensitive tool to reveal
wrong
sere's for the neutron energy scale. With Uclis, systematic tests showed that,
when moving the zero, the dip in the spectrum was displaced and no longer corresponded to the maximum of the resonance. When using the second method a wrong
aero is displayed by the oscillations between 300 and 6C0 keV, becoming larger
and larger when iteration convergence is approached. This is illustrated in Fig.
21. Curves 1 correspond to •., curves 2 are the results after several iterations.
The differences between 1 and 2 are of course due to the fact that there are differences between the theoretical and experimental spectrum, but the large peaks
and dips result from erroneous data : cross-sections» forced shifts in the zero
of the neutron energy scale, simplified model for the resolution function.
An additional test to ensure correct parameter estimations is the flux obtained at 300 keV ± 20 keV, because, at that energy for a 7VHH of 250 keV, the
resolution function should have a negligible influence and the result obtained
- 13 -
must be compatible with the E data. From all pre ious remarks it is seen that,
although the 250 keV resonance may introduce local, but computable errors, it
is the basis of many compatibility and vality tests and can be considered as
the detective of otherwise undetectable errors.
7.2.4. Normalization between E. and E • E. results
t
a
t
The E and E • E d i s t r i b u t i o n s beins recorded by a two-parameter analyser,
no normalization e r r o r s , resulting from dead-time l o s s e s , power f l u c t u a t i o n s ,
counting time, e t c . are p o s s i b l e . Here the two ADC's coupled to a PDP 8 computer
played t h i s r ô l e . The only error that may subsist when using t h i s method i s
related t o the channel width inaccuracy, presently 1 t for E. and 2 % for E + E .
Because of the compatibility t e s t s performed between the X and Y-ADC energy
c a l i b r a t i o n s , these errors are not considered cumulative and 2 % seems a reasonable estimation for the possible systematic error between the two p a r t i a l spectra.
Fig. 22 reports the unfolded PDP 8 , E. , and E + E. , spectra without, as mentioned
t
a t
above, any intermediate normalization factor.
8. COMPARISON OF THE EXPERIMENTAL RESULTS WITH THEORY
To compare experiment and theory [ 10] the spectra were normalized for the
same total flux between 0.0055 and 5-35 MeV. The results are drawn in Fig. 23.
When comparing the differences between experiment and theory, with those encountered in the Mol-EE experiment (Fig. 2h) J 8] , we observe around U00 keV the
same trend in the discrepancies: underestimation below 1*00 KeV, overestimation
above. Because the spectral shape for Mol-EE is highly influenced in that energy
region by the B.C screen, it is almc ;t certain that some of th«îse local discrepancies are related to errors in the Li cross-section. The marked disagreement
at about 2 MeV observed for Mol-EE is not present here. As in the case of the
Mol-EE
fast assembly experiment, the E. and E • E. spectra were also inter-
t
a t
preted by mean» of the ENDF/B I and ENDF/B II cross-section sets. Results deduced
from the three sets are compared in Fig. 25 and 26.
CONCLUSIONS
Putting aside the r^obleas related to the limited lifetime of the solid
state detectors, the Li technique may be considered as one of the most powerful
methods to determine the neutron spectra inside fast subcritical assemblies. If
carefully applied* several possibilities exist to Beveel
systematic errorsfthus
avoiding all other errors except those related to limited statistics and crosssection uncertainties.
- 1U -
Local discrepancies observed betveen theory and experiment are not necessarily to be attributed to computation, because similar local trends were observed in the intercomparison vork performed in Mol-EE. In the present state of
knowledge of the technique, apart from statistical inaccuracies and local uncertainties, no errors other than those analysed (<_2 %) and cross-section uncertainties interfere vhen comparing the theoretical spectrum to the experimental
one covering, as a whole, the three energy decades.
-
15 -
FIGURE CAPTIONS
Fig. 1
Fig. 2
Comparison of the theoretical E , E. and E • E. responses for a LiF
a x
o x
deposit of 1 to thickness» in case of a 2w and collimated detection
ge-cmetry
Comparison of an E distribution measured in Mol-IE and Bigten
Fig. 3a Drawing of the spectrometer
3b Schematic drawing of the Bigten electronics
Fig. b
Thermal a, triton and sua distributions for the thin LiF deposit
Fig. 5
Thermal a and triton distribution of the thick LiF deposit
Fig. 6
Thermal sua distribution for the thick LiF deposit
Fig. T
E. distribution recorded for 1 hour in the S.P. analyser
Fig. 8
Two-parameter distribution
Fig. 9
Partial E. distributions deduced from the two-parameter one
Fig. 10 Experimental E • E. distribution after background subtraction
a
Fig. 11
t
Li(n,o)t cross-section sets
Fig. 12 Neutron spectra unfolded from the E. distributions
Fig. 13 Neutron spectra unfolded from the partial E. distribution of Fig. 9
Fig. 11* Sensitivity tests to zero
shifts of the E. energy scale
Fig. 15 Sensitivity testa to channel width inaccuracies for the E. parameter
Fig. 16 Importance of the high neutron energy tails in the interpretation of
the single-parameter E. distributions
Fig. 17 Importance of the background for the E t distribution
Fig. 18 Unfolding of the Z • ! , distribution by means of the Uclis and
a
x
iterative code
Fig. 19 Sensitivity testa to channel inaccuracies for the E + E
parameter
Fig. 20 Influence of the resolution on the interpretation of the E„ • I.
distribution
Fig. 21 Sensitivity tests to aero shifts of the E_ + E. energy scale
o
x
Fig. 22 Neutron spectrum deduced from the E» and E • E. distribution recorded
x
a x
by the PDF 8 system (without any normalisation)
Fig. 23 Comparison of the experimental and theoretical Bigten spectra
- 16 -
Pig. 2h
Comparison of the experimental and theoretical Mol-II spectra
Pig. 25
Comparison of the neutron spectra deduced from the E results using
g
t
successively the ENDF/B I, EBDF/B III and Mol Li(n,o)t cross-section
sets
Pig. 26
Comparison of the neutron spectra deduced from the E
using the same three sets
• E
disvnoution
- 17 -
BIBLIOGRAPHY
11)
L.J. Sapir, H.H. Helmie», J.D. Orndoff
Trans, ta. Hucl. Soc. 15, 312 (1972)
(2)
1. G. De Leeuv-Gierts, S. De Leeuv
BLG 1*28 (1968)
2 . G. De Leéuv-Oierts
Thèse de Doctorat (1968)
(3]
G. De Leeuv-Gierts, S. De Leeuv
BLG 1*50 (1970)
(M
R.A. Rydin
Eur 27930 (1966)
(5)
G. De Leeuv-Gierts, S. De Leeuv
BLG U67 (1972) p. 3-62 and 3-63
(6J
G. De Leeuv-Gierts et a l .
BLG 1*93 (197U)
[7]
H. Bluhn et a l .
KPK 1658, RCH 172, BLG U71 (1972)
(8)
G. De Leeuv-Gierts, S. De Leeuv
LMPBR Reaction Rate and Dosimetry 7th Progress Report HEDL-39 (1973)
(9) J.C. Bluet, E. Port, J.C. Leroy
Centre d'Etudes Nucléaires de Cadarache SMNF 6h/0k
196U
Internal report
1965
Proceedings of the International Conference on the study of Nuclear
Structure with Neutrons, Antwerp (Amsterdam : North Holland)
(10) G. De Leeuv-Gierts, 8. De Leeuv, G.E. Hansen, H.H. lelaicx
LASL report to be published
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LOWER VALIDITY ENERGY LIMIT
A :ENDF/6 I
X ; ENDF/B III
+ :MOL
ICT»
6
7
8
9
ICf
ENERGIES (MEV)
SENSITIVITY OF THE SPECTRAL SHAPE TO OIFFERENT CROSS-SECTION SETS
«
«
7 » «
FIO. 2 6 .
jtf