Coppola, M.

Knitter , H.-H.

Archive of European Integration

•·*:Μ»Ηι ¿113 llSi^'iáig? H t 1 1 y ãíS iiüiüi Ηβ™ Joint Nuclear Research Center r CE HS Geel Establishm nt — Belgium itiiaiiium1".!·" Μ } · " ; Ϊ Μ ' !is π ;·ΊΤΠΗ I ί ώ entrai Bureau for Nuclear Measurements fflïîïllrîSÏÏTOKEiiei ,Üü 1 iy^ltøp-friSi 'JL'íi. llUíh»! ■t ftff iii ι,.«·'Β m Neither the HUKA i t acting on their behalf: Untat i .;„ Λ4.'ιίΛΐ>->νΙ. . i l l f ï * n t * ' i t t i : U: ι LEGAL NOTICE 'tø ! 'ÆT jfplfe . vas prepared under the sponsorship of the Commission of the European Atomic Energy Community (EURATOM). Neither the EURATOM Commission, its contractors nor any person Make any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information con­tained in this document, or that the use of any information, apparatus, method, or process disclosed in this document may not infringe privately owned rights; or Assume any liability with respect to the use of, or for damages resulting process disclosed This report is on sale at the addresses listed on at the price of FF 2.50 FB 25.­ D M 2 . — Lit. 310 Fl. 1.80 When ordering, please quote the EUR number and the title, which are indicated on the cover of each report. vi.írjtf Se ¡ «S'ìwWfiM ¡mm EUR 2798.e ELASTIC SCATTERING OF NEUTRONS FROM NATURAL SILICON by M. COPPOLA and H-Η. KNITTER European Atomic Energy Community — EURATOM Joint Nuclear Research Center Geel Establishment (Belgium) Central Bureau for Nuclear Measurements (CBNM) Brussels, April 1966 - 10 Pages - FB 25 Angular distributions of neutrons elastically scattered from natural Si were measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron time-of-flight spectrometer. Corrections for beam attenuation and multiple scattering in the sample were performed. Differential cross section results were fitted with a Legendre polynomial expansion and the coefficients for the best fits are presented. EUR 2798.e ELASTIC SCATTERING OF NEUTRONS FROM NATURAL SILICON by M. COPPOLA and H-Η. KNITTER European Atomic Energy Community — EURATOM Joint Nuclear Research Center Geel Establishment (Belgium) Central Bureau for Nuclear Measurements (CBNM) Brussels, April 1966-10 Pages - FB 25 Angular distributions of neutrons elastically scattered from natural Si were measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron time-of-flight spectrometer. Corrections for beam attenuation and multiple scattering in the sample were performed. Differential cross section results were fitted with a Legendre polynomial expansion and the coefficients for the best fits are presented. EUR 2798.e ELASTIC SCATTERING OF NEUTRONS FROM NATURAL SILICON by M. COPPOLA and H-Η. KNITTER European Atomic Energy Community — EURATOM Joint Nuclear Research Center Geel Establishment (Belgium) Central Bureau for Nuclear Measurements (CBNM) Brussels, April 1966 - 10 Pages - FB 25 Angular distributions of neutrons elastically scattered from natural Si were measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron time-of-flight spectrometer. Corrections for beam attenuation and multiple scattering in the sample were performed. Differential cross section results were fitted with a Legendre polynomial expansion and the coefficients for the best fits are presented. EUR 2 7 9 8 . e EUROPEAN ATOMIC ENERGY COMMUNITY — EURATOM ELASTIC SCATTERING OF NEUTRONS FROM NATURAL SILICON by M. COPPOLA and H.-H. KNITTER 1 9 6 6 Joint Nuclear Research Center Geel Establishment — Belgium Central Bureau for Nuclear Measurements — CBNM Summary Angular distributions of neutrons elastically scattered from natural Si were measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron time-of-flight spectrometer. Corrections for beam attenuation and multiple scattering in the sample were performed. Differential cross section results were fitted with a Legendre polynomial expansion and the coefficients for the best fits are presented. _ 3 ­Introduction (°) An accurate study of elastic scattering of neutrons from natu­ral silicon was undertaken as part of a program to provide da­ta, needed for reactor design. Scarce systematic efforts were made in the last few years in order to determine differential cross sections for scattering of fast neutrons in the energy region up to 3 MeV. Using BF­, ( ]) J counters as detectors, Lane et al. ' measured scattering of neutrons from natural silicon in the energy range from 50 keV to 2.3 MeV. later, with the same technique hut with narrow e­nergie resolution, they measured scattering on natural silicon in the energy range from 0.2 to 0.7 MeV, and determined P0 (Θ) (?) (ï) using partially polarized neutrons v . Bredin w / measured one angular distrihution of elastic neutron scattering and polari­sation at E ­ 1.95 MeV, using time­of­flight technique. His attempt of fitting the experimental results with calculations "based on a local optical model failed when trying to fit ¿both ­elastic scattering and polarisation. Optical model calculations using a non­local potential were made by Wilmore ^ . No good fit with the available data of differential cross sections was generally reached in the neutron energy region "below 2 MeV. Data on neutron total elastic scattering are available from ref. <1>. Experimental Equipment and Procedure The measurements were made at the 3 MeV Van de Graaff accelera­tor of CBNM, using conventional fast neutron time­of­flight ( 5 ) techniques v . A pulsed proton "beam, with 1 ns hurst width and 1 MHz repetition rate was focused on an occluded TiT target, 1 mg/cm thick. The ­produced neutrons were scattered by a natural silicon cylinder of 2.2 cm diameter and 3.0 cm height. The weight of this sample was (26.676 _+ 0.001)g. The sample was placed at 15.0 cm distance from the target, under 0° with respect to the accelerated beam. The average proton current was between 4 and 7 pA. The neutron flux from the target was monitored with a long counter of the Hansoh­Mc Kibben type^ '. His stability had been checked and was found to be always within the statistical error of 1$ required during the testing runs. The detector was inserted in a shielding which collimated the scattered neutrons. (°) Manuscript received on Marche 26, 1966 The distance between scatterer and detector was H 8 . 6 cm. The shielding including the detector could be rotated around the sample position in the horizontal plane. As an additional shielding of the detector against the direct neutrons, a sha­dow cone made out of brass was placed between neutron source and detector. The detector itself was a 56 AVP photomultiplier tube facing a stilbene crystal of 45 mm diameter and 30 mm thickness. The counting threshold was set to about 220 keV neutron energy, and the overall time resolution, observed on the time-of-flight spectrum of Y-rays from the target, was 2.1 ns. The stability of the threshold position was checked before starting the measurements and was controlled every few days during the experiment, by comparison with the 60 keV Ύ-2 A 1 photopeak of a ' A m source. The long-time stability, over about 4 months, was found to be better than 1$ or 2.2 keV neu­tron energy. The relative detector efficiency was obtained by comparing the measured yield of neutrons scattered on hydrogen, at several angles between 20° and 67.5°, with the known η-p scattering ( 7) differential cross section '. These data on hydrogen were corrected for attenuation in the sample of outgoing scattered neutrons v . As a scatterer a hollow polyethylene cylinder of 1.00 cm outside diameter, 0.60 cm inside diameter and 4.00 cm height was used. The weight was 1.84O g and the hydrogen con­tent (14.31 + 0.06)$. Angular distributions of elastically scattered neutrons on Si were obtained at scattering angles between 20° and I480. With the sample in position, a spectrum was taken for a certain pre­set number of counts in the monitor. The sample was then moved away from the detector collimation, and background was sub-stracted for the same number of monitor counts. The contribu­tion of the background was in the order of 20 to 30$ of the counts within the peak of the elastic scattered neutrons. This procedure was repeated for each measured point several times till enough events were collected in the elastic peak. Statis­tical errors on the measured points were always in the order of or better than 2.0$. - 5 -Seven angular distributions were measured at incident neutron energies of 0.57, 0.84, 1.00, 1.41, 1.74, 1.94, and 2.28 MeV. The neutron energy spreads due to target thickness and finite geometry were 122, 110, 104, 92, 84, 82, and 71 keV, respecti-vely. Absolute values of the differential scattering cross sections were obtained by comparing the angular distribution data for Si with scattering data on hydrogen. For each angular distribution one calibration point was measured on the poly-ethylene sample at an angle choosen between 30° and 50°. Experimental Results Fig. .1 shows a typical time-of-flight spectrum for primary neutron energy of 2.28 MeV. The channel width is about 0.7 ns. The small peak which appears in fig. 1 is due to the inelastic neutron group corresponding to the first excited level in Si at 1.78 MeV. The elastic scattering data were fully corrected for finite geometry, beam attenuation and multiple scattering. Corrections were calculated with a modified version of the program MAGGIE3^ y' The importance of multiple scattering is clearly shown in fig. 2 and 3. Corrected differential elastic cross section data were then fitted with a Legendre polynomial expansion of the form 42:(^)=¿BLPL(cos^ dn ¿Q and the resulting best fits are shown in fig. 2 and 3. Overall accuracies of the absolute cross sections are estimated to be (11 around 6$. The available results of lane et al.1 ; at about the same neutron energies are also shown. The agreement between the two sets of measurements, which are made with completely diffe-rent techniques, is reasonably good. Discrepancies in the shape of the angular distributions as well as in the absolute values can also be understood, considering the differences in energy and energy spread of primary neutrons,since the total neutron * by courtesy of Dr. R.Batchelor ­ 6 ­cross section for Si shows a very pronounced resonance struc­ture below 4 MeV. The values of the six Bv coefficients obtained from the least squares fits are indicated in table I together with the com­puted errors. The authors wish to thank Dr. J.Spaenen, director of CBNM, for supporting these measurements and Mr. K.H.Böckhoff for his kind interest in this work. Especial thanks are due to Dr. H.Horst­mann for carrying out the computer calculations. We gratefully acknowledge the help given to us by Mr. C.Rousseau on the elec­tronics side, and by the accelerator staff, as well as by the Sample Preparation Group of CBNM. References (1) R.O.Lane et al., Ann.Phys. J_2, 135 (1961) (2) R.O.Lane et al., Phys.Rev. _126, 1105 (1962) (3) D.J.Bredin, Phys.Rev. 135, Β 412 (1964) (4) D.Wilmore, AERE­R4649 (1964) (5) A.Jacquot and C.Rousseau, submitted to Nucl.Phys. (6) Hanson and Mc Kibben, Phys.Rev. 72, 673 (1947) and Rev.Sci.Instr. _25, 334 (1954) (7) J.L.Gammel, Fast Neutron Physics, Part II, New York and London, 1963. (8) L.Cranberg and J.S.Levin, LA­2177 (1959) (9) G.B.Parker et al., Nucí.Instr.Meth. 30, 77 (1964) TABLE I Values of the Coefficients in the Legendre Polynomial Expansions, Expressed in mb/sr E(MeV) 0 . 5 7 i 0 .84 1 ! 1.00 ι ¡ 1.41 j i 1 1 1.75 1.94 2 . 2 8 I I! 1! I j ¡\ II li ί I! II II II -Il II II 1 1 II 1! li 1. Il II II II II II II II II II II II II­II II li II II 1. li II lì li =,J. Β 0 + 3 5 0 . 5 + 2 . 8 + 3 5 5 . 2 + 2 . 8 + 3 4 2 . 1 + 3 . 0 + 2 1 0 . 6 + 1.7 + 144.4 + 1.3 + 2 6 0 . 9 + 2 .5 + 2 0 6 . 1 + 3 . 1 B 1 i + 2 1 1 . 8 ! + 6 .3 L . . _ 1 1 + 3 3 2 . 7 + 5 .0 + 4 3 9 . 1 + 6 .3 + 211 .4 + 3 .3 + 111.1 + 2 .4 + 3 5 4 . 9 + 6 . 1 + 2 6 5 . 4 + 5 .8 i " · - -i i + ι _ . J - — _ J ! + 1 + + + + ♦ + + + + + + ^mm B 2 169.8 9 . 2 170.3 6 .6 2 1 9 . 7 9 . 1 103.7 4 . 6 121.5 3 . 4 2 8 7 . 0 8 . 2 222 . 1 8 . 4 -_+ + + — + + -I . I . + + + + + — · » . mm. + 4-B 3 13.7 18.7 8 . 2 6 . 6 3 . 4 5.3 2 2 . 6 5 .4 6 8 . 4 4 . 5 117.6 10 .2 7 2 . 5 11.3 i ι ! + i i _ ι + + + + + + + + + B 4 3 . 2 3 . 1 2 8 . 6 9 . 1 5 . 0 8 . 1 8 . 0 9 . 1 2 3 . 0 4 . 5 i "" " ~ 8 . 4 ¡ 4 . 8 15.3 15.3 I ; ! - 2 8 . 6 1 ± 1 ^.3 ¡ - 14 .7 i + 9 . 3 + 3 . 3 + 16 .2 + 9 . 2 + 6 .9 - 14 .8 + 5 . 6 + 3 . 0 + 4 . 5 - 12 .4 + 15 .4 1 3000 2500 2000 1500 WOO 500 0 k i < . f i t/) κ« I 8 -• • • · . * . ■ En=2.2ô MeV \at>=20° Inelastic 1772 MeV ♦ • / ï X5 / V.· · * . . . . . • . . . • . • Elastic —+-. · \Zf* * V.... ·.. . CHANNEL NUMBER ■ ■ 150 200 250 300 Fig.1 Typical time-of-flight spectrum. woo 900 800 700 600 500 400 300 200 WO WOO 900 eoo 700 600 500 400 300 200 WO O — Ή > \ oN da \mb dtì[sr. ~ ^ v 1 S ( A V \ N i da \mti dÇi[sr. S>\ Λ V Δ o ELaD =0.57'MeV, this work ^ ^ ^-Μ *~~^ νί Λ/ ^ o ELab =1.00 MeV, this work Δ Δ^ i-Lab-\ -LUI η ^ ινν, ι ^ ο . VI. | /> • f i ö ^ $Lab u*· ι ~~* ·^< *^^_ k \ [As i ■ "SJVS k \ > Δ V o ELab=0.84 MeV, this work Δ \ Δ \ CLab=uaomev, rer.( υ k \ \ ' " ^ ^ ^ ^ » - Λ - Q Δ o E\jjb=UlMeV, this work Δ L-Latr x> /.time V, 1 Cf. I ι J $Lab I 0" 20° 40° 60° 80° 100° 120° 140° 160° 0° 20° 40° 60° 80" W0° 120° K0° 160° Fig. 2 Elastic scattering of neutrons from Si. Best fits through uncorrected experimental data of this work. Angular distributions corrected for multiple scattering. woo 900 800 700 600 500 400 300 200 100 O WOO 900 800 700 600 500 400 300 200 WO Λ da \mb dn [sr. : ^ A ^v da \mb dñ\JF_ ~^S V i \ o ELab =1.75MeV, this work Δ V A cLab: -■I./JM ev ,r sr. f /7 .. ο ELab=2.28MeV, this work *^TL ^^^^Ä ^ — .ab — t -^ \ S \ \ i · V \ \ \ \ \ o ELab = W4MeV, this work Δ s \ cLab- -LSDmev, rer. \JJ **Lab »· 0° 20° 40° 60° 80° 100° 120° 140° K0° ■ 0° 20° 40° 60° 80° 100° 120° 140° 160° Fig. 3 Elastic scattering of neutrons from Si. Best fits through uncorrected experimental data of this work. Angular distributions corrected for multiple scattering. l i t im· ,x'i «•••VitabËîtci All Euratom reports are on sale at the offices listed below, at the pnces given on the bad cover (when ordering, specify clearly the EUR number and the title of the report, which are shown on the cover). 98, chaussée de Charleroi, Bruxelles 6 Banque de la Société Générale - Bruxelles compte N° 964.558, Banque Belgo Congolaise - Bruxelles compte N° 2444.141, Compte chèque postal - Bruxelles - N° 167.37, Belgian American Bank and Trust Company - New York compte No. 22.186, Lloyds Bank (Europe) Ltd. - 10 Moorgate, London E.C.2, Postcheckkonto - Köln - Nr. 160.861 ö > o K) oo m o OFFICE CENTRAL D E V E N T E DES PUBLICATIONS DES COMMUNAUTES E U R O P E E N N E S 2. place de Metz, Luxembourg (Compte chèque postal N° 191-90) BELGIQUE — BELGIË MONITEUR BELGE 40-42, rue de Louvain - Bruxelles BELGISCH STAATSBLAD Leuvenseweg 4042 - Brussel DEUTSCHLAND BUNDESANZEIGER Postfach - Köln 1 FRANCE SERVICE DE VENTE EN FRANCE DES PUBLICATIONS DES COMMUNAUTES EUROPEENNES 26, rue Desaix - Paris 15e W*i û I GRAND-DUCHE DE LUXEMBOURG OFFICE CENTRAL DE VENTE DES PUBLICATIONS DES COMMUNAUTES EUROPEENNES 9, rue Goethe - Luxembourg (TALIA LIBRERIA DELLO STATO Piazza G. 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Elastic Scattering of Neutrons from Natural Silicon. EUR 2798.

•·*:Μ»Ηι 
¿113 llSi^'iáig? 
H t 1 1 y ãíS 
iiüiüi Ηβ™ 
Joint Nuclear Research Center 
r CE 
HS Geel Establishm nt — Belgium itiiaiiium1".!·" Μ } · " ; Ϊ Μ ' !is π ;·ΊΤΠΗ I ί 
ώ 
entrai Bureau for Nuclear Measurements 
fflïîïllrîSÏÏTOKEiiei 
,Üü 
1 iy^ltøp-friSi 
'JL'íi. llUíh»! ■t 
ftff iii 
ι,.«·'Β 
m 
Neither the HUKA i t 
acting on their behalf: 
Untat i .;„ Λ4.'ιίΛΐ>->νΙ. . i l l f ï * n t * ' i t t i : U: ι 
LEGAL NOTICE 
'tø ! 'ÆT jfplfe 
. vas prepared under the sponsorship of the Commission 
of the European Atomic Energy Community (EURATOM). 
Neither the EURATOM Commission, its contractors nor any person 
Make any warranty or representation, express or implied, with respect 
to the accuracy, completeness, or usefulness of the information con­
tained in this document, or that the use of any information, apparatus, 
method, or process disclosed in this document may not infringe privately 
owned rights; or 
Assume any liability with respect to the use of, or for damages resulting 
process disclosed 
This report is on sale at the addresses listed on 
at the price of FF 2.50 FB 25.­ D M 2 . — Lit. 310 Fl. 1.80 
When ordering, please quote the EUR number and the title, 
which are indicated on the cover of each report. 
vi.írjtf 
Se 
¡ «S'ìwWfiM ¡mm 
EUR 2798.e 
ELASTIC SCATTERING OF NEUTRONS FROM NATURAL SILICON 
by M. COPPOLA and H-Η. KNITTER 
European Atomic Energy Community — EURATOM 
Joint Nuclear Research Center 
Geel Establishment (Belgium) 
Central Bureau for Nuclear Measurements (CBNM) 
Brussels, April 1966 - 10 Pages - FB 25 
Angular distributions of neutrons elastically scattered from natural Si were 
measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron 
time-of-flight spectrometer. Corrections for beam attenuation and multiple 
scattering in the sample were performed. Differential cross section results were 
fitted with a Legendre polynomial expansion and the coefficients for the best 
fits are presented. 
EUR 2798.e 
ELASTIC SCATTERING OF NEUTRONS FROM NATURAL SILICON 
by M. COPPOLA and H-Η. KNITTER 
European Atomic Energy Community — EURATOM 
Joint Nuclear Research Center 
Geel Establishment (Belgium) 
Central Bureau for Nuclear Measurements (CBNM) 
Brussels, April 1966-10 Pages - FB 25 
Angular distributions of neutrons elastically scattered from natural Si were 
measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron 
time-of-flight spectrometer. Corrections for beam attenuation and multiple 
scattering in the sample were performed. Differential cross section results were 
fitted with a Legendre polynomial expansion and the coefficients for the best 
fits are presented. 
EUR 2798.e 
ELASTIC SCATTERING OF NEUTRONS FROM NATURAL SILICON 
by M. COPPOLA and H-Η. KNITTER 
European Atomic Energy Community — EURATOM 
Joint Nuclear Research Center 
Geel Establishment (Belgium) 
Central Bureau for Nuclear Measurements (CBNM) 
Brussels, April 1966 - 10 Pages - FB 25 
Angular distributions of neutrons elastically scattered from natural Si were 
measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron 
time-of-flight spectrometer. Corrections for beam attenuation and multiple 
scattering in the sample were performed. Differential cross section results were 
fitted with a Legendre polynomial expansion and the coefficients for the best 
fits are presented. 

EUR 2 7 9 8 . e 
EUROPEAN ATOMIC ENERGY COMMUNITY — EURATOM 
ELASTIC SCATTERING OF NEUTRONS 
FROM NATURAL SILICON 
by 
M. COPPOLA and H.-H. KNITTER 
1 9 6 6 
Joint Nuclear Research Center 
Geel Establishment — Belgium 
Central Bureau for Nuclear Measurements — CBNM 
Summary 
Angular distributions of neutrons elastically scattered from natural Si were 
measured in the energy range between 0.57 and 2.28 MeV, using a fast neutron 
time-of-flight spectrometer. Corrections for beam attenuation and multiple 
scattering in the sample were performed. Differential cross section results were 
fitted with a Legendre polynomial expansion and the coefficients for the best 
fits are presented. 
_ 3 ­
Introduction (°) 
An accurate study of elastic scattering of neutrons from natu­
ral silicon was undertaken as part of a program to provide da­
ta, needed for reactor design. 
Scarce systematic efforts were made in the last few years in 
order to determine differential cross sections for scattering 
of fast neutrons in the energy region up to 3 MeV. Using BF­, 
( ]) J 
counters as detectors, Lane et al. ' measured scattering of 
neutrons from natural silicon in the energy range from 50 keV 
to 2.3 MeV. later, with the same technique hut with narrow e­
nergie resolution, they measured scattering on natural silicon 
in the energy range from 0.2 to 0.7 MeV, and determined P0 (Θ) (?) (ï) using partially polarized neutrons v . Bredin w / measured one 
angular distrihution of elastic neutron scattering and polari­
sation at E ­ 1.95 MeV, using time­of­flight technique. His 
attempt of fitting the experimental results with calculations 
"based on a local optical model failed when trying to fit ¿both ­
elastic scattering and polarisation. Optical model calculations 
using a non­local potential were made by Wilmore ^ . No good 
fit with the available data of differential cross sections was 
generally reached in the neutron energy region "below 2 MeV. 
Data on neutron total elastic scattering are available from 
ref. <1>. 
Experimental Equipment and Procedure 
The measurements were made at the 3 MeV Van de Graaff accelera­
tor of CBNM, using conventional fast neutron time­of­flight 
( 5 ) techniques v . A pulsed proton "beam, with 1 ns hurst width and 
1 MHz repetition rate was focused on an occluded TiT target, 1 
mg/cm thick. The ­produced neutrons were scattered by a natural 
silicon cylinder of 2.2 cm diameter and 3.0 cm height. The weight 
of this sample was (26.676 _+ 0.001)g. The sample was placed at 
15.0 cm distance from the target, under 0° with respect to the 
accelerated beam. The average proton current was between 4 and 
7 pA. The neutron flux from the target was monitored with a 
long counter of the Hansoh­Mc Kibben type^ '. His stability had 
been checked and was found to be always within the statistical 
error of 1$ required during the testing runs. The detector was 
inserted in a shielding which collimated the scattered neutrons. 
(°) Manuscript received on Marche 26, 1966 
The distance between scatterer and detector was H 8 . 6 cm. The 
shielding including the detector could be rotated around the 
sample position in the horizontal plane. As an additional 
shielding of the detector against the direct neutrons, a sha­
dow cone made out of brass was placed between neutron source 
and detector. The detector itself was a 56 AVP photomultiplier 
tube facing a stilbene crystal of 45 mm diameter and 30 mm 
thickness. The counting threshold was set to about 220 keV 
neutron energy, and the overall time resolution, observed on 
the time-of-flight spectrum of Y-rays from the target, was 
2.1 ns. The stability of the threshold position was checked 
before starting the measurements and was controlled every few 
days during the experiment, by comparison with the 60 keV Ύ-
2 A 1 photopeak of a ' A m source. The long-time stability, over 
about 4 months, was found to be better than 1$ or 2.2 keV neu­
tron energy. 
The relative detector efficiency was obtained by comparing the 
measured yield of neutrons scattered on hydrogen, at several 
angles between 20° and 67.5°, with the known η-p scattering 
( 7) 
differential cross section '. These data on hydrogen were 
corrected for attenuation in the sample of outgoing scattered 
neutrons v . As a scatterer a hollow polyethylene cylinder of 
1.00 cm outside diameter, 0.60 cm inside diameter and 4.00 cm 
height was used. The weight was 1.84O g and the hydrogen con­
tent (14.31 + 0.06)$. 
Angular distributions of elastically scattered neutrons on Si 
were obtained at scattering angles between 20° and I480. With 
the sample in position, a spectrum was taken for a certain pre­
set number of counts in the monitor. The sample was then moved 
away from the detector collimation, and background was sub-
stracted for the same number of monitor counts. The contribu­
tion of the background was in the order of 20 to 30$ of the 
counts within the peak of the elastic scattered neutrons. This 
procedure was repeated for each measured point several times 
till enough events were collected in the elastic peak. Statis­
tical errors on the measured points were always in the order of 
or better than 2.0$. 
- 5 -
Seven angular distributions were measured at incident neutron 
energies of 0.57, 0.84, 1.00, 1.41, 1.74, 1.94, and 2.28 MeV. 
The neutron energy spreads due to target thickness and finite 
geometry were 122, 110, 104, 92, 84, 82, and 71 keV, respecti-
vely. Absolute values of the differential scattering cross 
sections were obtained by comparing the angular distribution 
data for Si with scattering data on hydrogen. For each angular 
distribution one calibration point was measured on the poly-
ethylene sample at an angle choosen between 30° and 50°. 
Experimental Results 
Fig. .1 shows a typical time-of-flight spectrum for primary 
neutron energy of 2.28 MeV. The channel width is about 0.7 ns. 
The small peak which appears in fig. 1 is due to the inelastic 
neutron group corresponding to the first excited level in Si 
at 1.78 MeV. 
The elastic scattering data were fully corrected for finite 
geometry, beam attenuation and multiple scattering. Corrections 
were calculated with a modified version of the program MAGGIE3^ y' 
The importance of multiple scattering is clearly shown in fig. 
2 and 3. 
Corrected differential elastic cross section data were then 
fitted with a Legendre polynomial expansion of the form 
42:(^)=¿BLPL(cos^ dn ¿Q 
and the resulting best fits are shown in fig. 2 and 3. Overall 
accuracies of the absolute cross sections are estimated to be 
(11 around 6$. The available results of lane et al.1 ; at about the 
same neutron energies are also shown. The agreement between the 
two sets of measurements, which are made with completely diffe-
rent techniques, is reasonably good. Discrepancies in the shape 
of the angular distributions as well as in the absolute values 
can also be understood, considering the differences in energy 
and energy spread of primary neutrons,since the total neutron 
* by courtesy of Dr. R.Batchelor 
­ 6 ­
cross section for Si shows a very pronounced resonance struc­
ture below 4 MeV. 
The values of the six Bv coefficients obtained from the least 
squares fits are indicated in table I together with the com­
puted errors. 
The authors wish to thank Dr. J.Spaenen, director of CBNM, for 
supporting these measurements and Mr. K.H.Böckhoff for his kind 
interest in this work. Especial thanks are due to Dr. H.Horst­
mann for carrying out the computer calculations. We gratefully 
acknowledge the help given to us by Mr. C.Rousseau on the elec­
tronics side, and by the accelerator staff, as well as by the 
Sample Preparation Group of CBNM. 
References 
(1) R.O.Lane et al., Ann.Phys. J_2, 135 (1961) 
(2) R.O.Lane et al., Phys.Rev. _126, 1105 (1962) 
(3) D.J.Bredin, Phys.Rev. 135, Β 412 (1964) 
(4) D.Wilmore, AERE­R4649 (1964) 
(5) A.Jacquot and C.Rousseau, submitted to Nucl.Phys. 
(6) Hanson and Mc Kibben, Phys.Rev. 72, 673 (1947) and 
Rev.Sci.Instr. _25, 334 (1954) 
(7) J.L.Gammel, Fast Neutron Physics, Part II, New York and 
London, 1963. 
(8) L.Cranberg and J.S.Levin, LA­2177 (1959) 
(9) G.B.Parker et al., Nucí.Instr.Meth. 30, 77 (1964) 
TABLE I 
Values of the Coefficients in the Legendre Polynomial Expansions, Expressed in mb/sr 
E(MeV) 
0 . 5 7 
i 
0 .84 
1 
! 1.00 ι 
¡ 1.41 
j 
i 
1 
1 
1.75 
1.94 
2 . 2 8 
I 
I! 
1! 
I j 
¡\ 
II 
li 
ί 
I! 
II 
II 
II 
-Il 
II 
II 
1 
1 
II 
1! 
li 1. 
Il 
II 
II 
II 
II 
II 
II 
II 
II 
II 
II 
II 
II­
II 
II 
li 
II 
II 
1. 
li 
II 
lì 
li 
=,J. 
Β 
0 
+ 3 5 0 . 5 
+ 2 . 8 
+ 3 5 5 . 2 
+ 2 . 8 
+ 3 4 2 . 1 
+ 3 . 0 
+ 2 1 0 . 6 
+ 1.7 
+ 144.4 
+ 1.3 
+ 2 6 0 . 9 
+ 2 .5 
+ 2 0 6 . 1 
+ 3 . 1 
B 1 
i 
+ 2 1 1 . 8 
! + 6 .3 
L . . _ 
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900 
800 
700 
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Best fits through uncorrected experimental data of this work. 
Angular distributions corrected for multiple scattering. 
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Fig. 3 Elastic scattering of neutrons from Si. 
Best fits through uncorrected experimental data of this work. 
Angular distributions corrected for multiple scattering. 

l i t im· ,x'i 
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Elastic Scattering of Neutrons from Natural Silicon. EUR 2798.

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