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A method of evaluating fast-neutron differential scattering cross sections with short experimental runs
NUCLEAR
INSTRUMENTS
A METHOD
AND METHODS
52 (I967) 1 8 I - I 9 2 ;
© NORTH-HOLLAND
PUBLISHING
CO.
OF EVALUATING FAST-NEUTRON DIFFERENTIAL SCATTERING CROSS SECTIONS WITH SHORT EXPERIMENTAL
RUNS*
V. V. VERBINSKI, J. C. COURTNEY* and N. BETZ Oak Ridge National Laboratory, Oak Ridge, Tennessee, U.S.A.
Received 16 February 1967 The method utilized a pulsed neutron source with a smooth, broad spectrum, making it possible to measure neutron scattering from 0.5 to 10 MeV in a single run of 1 to 2 h duration for each scattering angle 0. Scattering samples of carbon, aluminum, iron, lithium hydride and concrete about 5 cm in dia. were located about ½m from the pulsed neutron source, and neutrons scattered through an angle 0 were directed down a 55-m flight path to a liquid organic scintillator used to measure the time-of-flight spectrum of scattered neutrons. The energy-dependent neutron intensity thus obtained was compared with Monte Carlo calculations whose inputs were the measured neutron source term and neutron elastic, inelastic, and reaction cross sections compiled from the existing literature. The comparison provides direct corrections to the cross sections for the lighter elements because
single scattering is about ten times more probable than multiple scattering with the sample sizes chosen. These corrections can be further improved by repeating the calculation with the improved cross-section values. Inelastic scattering into any given energy region was small compared with elastic scattering for low Z scatterers because of the shape of the source spectrum. In this case, the method provides an unambiguous check on the elastic differential scattering cross sections used as input for the Monte Carlo calculations, and good first-order corrections to these cross sections. Several modifications of both experiment and calculation are proposed for reducing the statistical uncertainty, for improving the experimental and calculational efficiencies, and for increasing the range of energy covered.
1. Introduction
describe the i n t e r a c t i o n o f n e u t r o n s with nuclei to v a r y i n g degrees o f a p p r o x i m a t i o n . I t is clear t h a t a fast, accurate m e t h o d of checking n e u t r o n cross-section d a t a is o f great value. Such a m e t h o d can be used to select the m o s t accurate o f the detailed cross-section m e a s u r e m e n t s that a p p e a r in the literature, to i n t e r p o l a t e between these values in a m o r e realistic m a n n e r , a n d even to test the basic a s s u m p tions o f a n y calculations that m a y have been used for p r e d i c t i n g n e u t r o n differential scattering cross sections. The c o m b i n e d e x p e r i m e n t a l a n d c a l c u l a t i o n a l m e t h o d s p r e s e n t e d here for evaluating a n d t h e r e b y i m p r o v i n g cross-section d a t a have been carried o u t for a few t a r g e t m a t e r i a l s with g o o d accuracy. A b o u t a decade o f n e u t r o n energy was covered with a single measurement. The m e a s u r e m e n t s described below were carried o u t in 1964 w i t h engineering s a m p l e s such as concrete, l i t h i u m h y d r i d e , s t r u c t u r a l a l u m i n u m , a n d steel. These m a t e r i a l s were selected to p r o v i d e a m a x i m u m coverage of cross-section e v a l u a t i o n for the fixed accelerator t i m e a l l o t t e d to this p i l o t project. The concrete, a l u m i n u m a n d steel cross-section checks were o f interest to the Defense A t o m i c S u p p o r t Agency, with the transmission of neutrons t h r o u g h multilegged concrete ducts being o f p r i m a r y concern. The L i H d a t a were of p a r t i cular interest for the design of S N A P (Space N u c l e a r A u x i l i a r y Power) r e a c t o r systems in which n e u t r o n scattering f r o m the edge o f the L i H s h a d o w shield a n d f r o m a p p a r a t u s p r o j e c t i n g out b e y o n d the circum-
A c c u r a t e differential scattering cross sections are needed for reliable calculations of n e u t r o n p e n e t r a t i o n s in r e a c t o r a n d accelerator shields, for n e u t r o n transm i s s i o n t h r o u g h multilegged ducts, a n d for n e u t r o n fluxes in breeder b l a n k e t s l o c a t e d n e a r the fuel regions o f reactors1). T h e need has g r o w n w i t h the a d v e n t o f m o d e r n n e u t r o n t r a n s p o r t codes2-4), which utilize the m o m e n t s m e t h o d , direct n u m e r i c a l i n t e g r a t i o n o f the Boltzmann equation, and Monte Carlo methods and which r o u t i n e l y use u p to P8 t e r m s in the L e g e n d r e p o l y n o m i a l a n g u l a r a p p r o x i m a t i o n s to the differential scattering cross sections. This need will e x p a n d with the c o n t i n u e d i m p r o v e m e n t in speed a n d storage c a p a c i t y o f m o d e r n c o m p u t e r s which are b e g i n n i n g to m a k e the slower b u t m o r e reliable a n d versatile M o n t e C a r l o calculations feasible for d e e p - s h i e l d - p e n e t r a t i o n calculations. Such c a l c u l a t i o n s have used up to a P16 a n g u l a r a p p r o x i m a t i o n on occasion. I n c o m p i l i n g a crosszsection l i b r a r y for these transp o r t codes, s o m e initial d a t a are first o b t a i n e d f r o m the s m a l l n u m b e r o f m e a s u r e d values t h a t a p p e a r in the literature, values t h a t often disagree by m a n y times the q u o t e d s t a n d a r d deviations. T h e gaps b e t w e e n these d a t a p o i n t s m u s t be filled in b y v a r i o u s i n t e r p o l a t i o n schemes, a n d in some cases by c a l c u l a t i o n s which t Research sponsored by the Defense Atomic Support Agency under Union Carbide Corporation's contract with the U.S. Atomic Energy Commission. * Now with U. S. Air Force, McClellan Air Force Base, Sacramento, California. JUNE II
1967
181
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, ~x,,,.~ ALT ERNATE POSITION OF SCATTERING CYLINDER Fig. 1. Experimental arrangement showing photoneutron source, scatterer, flight path with input collimator, and liquid organic scintillator. Two alternate positions are shown for the scatterer in which the same "source angle" 0t is utilized, but for which the net scattering angle is either 0z or zt-0z. Note that 0~-0~ = 90°. ference of both the reactor and the shield can result in an important contribution to neutron dosage in the peripheral regions of the instrument payload located behind the shield.
2. Experimental configuration In fig. I is shown the experimental arrangement for measuring the energy dependence of the neutron flux scattered by cylindrical samples. The General Atomic
electron linear accelerator (linac) was used to provide 14-nsec bursts of 33-MeV electrons which irradiated a lead slug. The electrons produced bremsstrahlung radiation which in turn produced photoneutrons whose spectrum and intensity varied slowly with 01, the angle of emission with respect to the electron beam. Neutrons scattered by the cylindrical sample at a net scattering angle 02 traveled down a long flight path which was terminated by a fast liquid organic scintillator (NE-213)
FAST-NEUTRON
DIFFERENTIAL
used to detect their time of arrival. (An NE-211 detector was used for measuring the source spectrum, as described in sect. 3.) Background measurements were made by simply removing the scatterer. In addition, a separate background measurement was made by leaving the scatterer in place and shielding it from the neutron source by a shadow shield made from laminations of iron and polyethylene An increase in background was observed, beyond that obtained by simply removing the scatterer and shadow shield. Since this increase was about equal to calculated neutron leakage through the shadow shield and since the backgrounds contributed only about 10% to the total count rate, the simple scattererout backgrounds were accurate enough. During each scattering experiment, a sulfur monitor foil placed at 45 ° to the electron beam, as shown in fig. 1, was used to determine the time-integrated source strength. Since the monitor foil was also used while the source spectral intensity was being measured, simple monitor ratios could be used to determine the absolute, time-integrated spectral intensity of the neutron source for each scattering measurement. The measurement of the spectral intensity of neutrons leaving the source at 01 was accomplished by bending the electron beam clockwise through 0 t - 9 0 ° before it crossed the flight path and by locating the lead slug alongthe flight path center line (fig. 1). The axis of the disk-shaped slug was always kept parallel to the electron beam so that the self-shielding of the lead slug would be a constant factor. To further assure that the self-shielding was constant, steps were taken to keep the electron beam size and position constant. The size was monitored periodically with film-type beam profile measurements. Positioning of the beam was accomplished with a small, thin foil centrally located in the beam tube of the linac (not shown in fig. 1) and electrically connected to an oscilloscope. A narrow ionization chamber located behind the lead slug was also used for beam positioning. Note that two scatterers are shown in fig. 1 for which the source angle 01 is the same but for which the net scattering angle is either 02 or n -02. Thus, only a single source measurement and a single background measurement were necessary for the scattering measurements performed at two supplementary scattering angles. (In sect. 7, a simple method of keeping the source spectrum constant for all scattering angles is described.) 3. Electronics
A block diagram of the data-gathering electronics is shown in fig, 2. The fast scintillator and photomultiplier
SCATTERING
CROSS SECTIONS
183
tube located near the neutron source produced a pulse of constant shape for each linac burst. This timefi.ducial pulse was sent to the 55-m flight path station of the General Atomic linear accelerator facility, where it was used to start a 1-nsec clock.* The fiducial pulse was also used to activate a gating circuit which turned on the neutron-detector photomultiplier tube after the bremsstrahlung passed this detector and just before the fastest neutrons arrived. The tube-base diagram for the neutron detector shown in fig. 2 illustrates how a neutron event produces three signals in the Phillips XP-1040 photomultiplier tube - a fast timing signal at dynode 13, a linear signal at dynode 12 used for an accurate and stable bias level and set at approximately 0.43-MeV recoil-proton energy, a n d a pulse-shapediscriminator (PSD) signal from a modified Fort6 circuit connected to dynode 14 and anode. The effective bias of the PSD circuit was below the 0.43-MeV linearbias level, so that a sharp cutoff could be obtained. The PSD circuit was used to reject gamma-ray counts which were appreciable for the scattering runs. During the scattering measurements the presence of these three simultaneous signals was required for the fast signal to stop the 1-nsec clock and activate the command module which caused the clock datum to be stored directly in the memory of a TMC-400 channel analyzer. * The dividing circuit + shown in fig. 2 was needed to divide the 1-nsec clock reading by a factor such that the complete time span (corresponding to 0.4 to 14 MeV neutrons) could be contained in the 400 channels available from the T M C analyzer used. The channel number corresponding to zero time was deduced from the time of arrival of the bremsstrahlung pulse at the neutron detector. Zero drift was always within one channel (8 or 12 nsec). When the spectral intensity of the neutron source was being measured, the scintillators viewed the neutron source (the lead slug shown in fig. 1) directly. In thia case, the bremsstrahlung radiation and positron-decay radiation in the lead slug illuminated the NE-213~ scintillator to such an intensity that the slow component of light emission was intolerably high at the time that the photomultiplier was gated on (just before the fastest neutrons arrived). Consequently the gating circuit was of no avail, and an NE-211 scintillator, which has almost no slow component of light emission, • M o d e l 793-A 1-nsec Clock, E l d o r a d o Electronics, 601 C h a l a m a r
Road, Concord, California. t Model 401B6 400-channel pulse height analyzer, Technical Measurements Corporation, North Haven, Connecticut. + Model 3-3031 Computing Unit (Dividing Unit), Applied Development Corporation, Monterey Park, California. § Nuclear Enterprises, Ltd., Winnepeg, Canada.
184
v . v . VERBINSKI et al.
XP ~040 PHILLIPS FHOTCMULTIPLIER 300k
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Fig. 2. Block diagram of tinae-of-flight electronics, showing tube-base diagram of XP-1040 Phillips photomultiplier tube, gating arrangement, pulse shape discriminator circuit (from dynode 14 and anode), fast signal, and slow, linear signal. was used. Good pulse shape discrimination is not feasible with this scintillator, but a separate run with an NE-213 scintillator (with very low linac current) showed that the relative intensity of the delayed gamma background was negligibly small for the sourcemeasurement runs.
Since the controlling bias level was determined by the linear-amplifier discriminator setting, it had to be checked at periodic intervals by using the end point of the 6°Co pulse-height distribution as a standard of reference. The detector efficiency as a function of bias setting was determined in an extensive program of
FAST-NEIJTRON
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Fig. 3. Two typical neutron-detection efficiency functions fcr 5" x 5" dia. NE-211 and NE-213 scintillators. A pulse height unit
of 1 "cobalt" is the extrapolated endpoint of a ~°Co pulse height distribution, linear plot. The XP-1040 photomultiplier tube was used. detector calibration 5) in which all neutron pulse heights were referred to the 6°Co endpoint (equal to 1 "cobalt" in pulse height). The NE-211 and NE-213 scintillators were found to be identical for neutrons in this respect (i.e., with respect to the calibration point obtained from the 6°Co pulse-height distribution). Both were 5" dia. x 5" hgt cylinders, glass-encapsulated, deoxygenated, sealed, and covered with a white reflective coating at the factory. Two efficiency-vs-energy curves are shown in fig. 3 for two different bias settings. Typ!cal bias settings were 0.038 to 0.042 "cobalt". 4. Data handling The time-of-flight spectrometer could accept only one count per linac burst. The linac current therefore had to be kept at a level where the average count rate was not greater than 0.15 per burst. The occurrence of two counts or more during one burst could then be accurately corrected for by assuming that the linac current was constant during a given run. High count rates (0.15 per burst) were realized only during the source spectrum measurements, and the linac current was held constant to within 4- 30% during these relatively short runs. The error in the count loss correction was about 2°/0 maximum, which is generally much smaller than the statistical accuracy of the present data. All time-of-flight spectra were analyzed with a datahandling code developed by R. Cowperthwaite at O R N L which utilizes the relativistic relationship between neutron velocity and energy, subtracts the background, propagates the variances or statistical uncertainties, corrects for the occurrence of more than one event per burst, divides by the energy-dependent detector efficiency, corrects for neutron scattering by
SCATTERING
CROSS SECTIONS
185
materials in the flight path, and groups time channels into uniform energy fractions (1°/0 to 5%, which could be preselected). The materials in the beam included an argon-filled dr~ft tube, thin aluminum windows and a g a m m a filter of lead up to 5 cm thick. In one measurement of source spectrum, at 0t = 160 °, it was possible to decrease the lead filter to ¼ cm. A 5-cm thickness was also used in this measurement to determine the validity of the lead-scattering correction. The two corrected spectra agreed in shape within counting statistics, which were better than for most runs. It was possible to use the total neutron cross section 6) as the removal cross section because of the good-geometry arrangement (the g a m m a filter was located about 17 m down a rather tightly collimated flight path). The sulfur monitors were located at 45 ° to the electron beam for both source and scattering measurements. For the source measurements, where the detector at 55 m viewed the source directly, the linac output had to be kept very low, and so the sulfur-monitor activation was difficult to determine with good counting statistics. Therefore a separate high-intensity run was made in which sulfur monitor pills were also placed at angles of 110, 135, 160, and 170 ° to the source. By convoluting the sulfur (n,p) cross section with each of the neutron spectra the absolute source strength was obtained at each of the source angles and was properly correlated to the activation of the sulfur monitor located at the standard position, i.e., 45 ° to the electron beam. The sulfur counting was not started until several days after exposure in order to eliminate short-lived background activity. The 32S(n,p)32p cross sections were taken from BNL-325, ref. 6). 5. The Monte Carlo calculations 5.1. DESCRIPTION The 05R Monte Carlo system of Coveyou et al. 2) was adapted to the scattering problem by Betz and Courtney. The actual source spectrum, source angular distribution, geometry of the system, and a neutron crosssection compilation were used as inputs to the calculations. For each source angle 01 (i.e., for the two scattering angles shown in fig. 1) histories of 100000 source neutrons were calculated. The neutrons were followed until they either escaped the system or fell below the cutoff energy. Absorption was treated by multiplying the weight of the neutron by the nonabsorption probability at each collision. After each collision the appropriate parameters (energy, direction components, weight, position coordinates) were written onto a collision tape. The collision tapes were then
v . v . VERBINSKI et al.
186
e s t i m a t i o n for each collision. This weighted c o u n t was a d d e d to the p r o p e r energy bin. In this way, the a b s o l u t e spectral intensity o f scattered neutrons was o b t a i n e d with a relatively small statistical u n c e r t a i n t y for the n u m b e r of case histories carried out. B o t h the calculat i o n a l a n d e x p e r i m e n t a l results given b e l o w were normalized to a n e u t r o n source strength o f 1 n e u t r o n / sterad, so t h a t differences give a direct cross section c o r r e c t i o n in t e r m s o f n e u t r o n energy before scattering t h r o u g h the net scattering angle 02.
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T h e n e u t r o n source was a s s u m e d to be a p o i n t source a n d to be i s o t r o p i c over the solid angle segment s u b t e n d e d b y the scatterer. The actual source d i a m e t e r was a b o u t 1 cm, which was small c o m p a r e d with the 22.9- a n d 33-cm distan.ces to the scatterers. The source s p e c t r a for 01 = 110, 135, a n d 160 ° are shown in fig. 4, n o r m a l i z e d to 1 n e u t r o n p e r M e V per sterad. The 0 t = 110 ° source s p e c t r u m was used for 02 = 10 ° scattering because no difference was observed between the 100 ° a n d 110 ° source spectra, within c o u n t i n g statistics. 5.3. SCATTERER GEOMETRY AND COMPOSITION
2
5
4
5
NEUTRON
6
7
ENERGY
8
9
10
11
12
(MeV)
Fig. 4. Neutron source spectra for three source angles 01 shown in fig. 1. The 110° spectrum was used for 10° scattering as well as for 20 and 160° scattering, since it was nearly identical to the 100° spectrum. All source spectra are shown normalized to 1 neutron/ sterad when integrated over neutron energy. analyzed with a last-flight statistical analysis routine7). A t each collision p o i n t the p r o b a b i l i t y of the n e u t r o n scattering t h r o u g h such an angle as to reach the detector a n d the p r o b a b i l i t y o f the n e u t r o n e s c a p i n g f r o m the cylinder in this direction w i t h o u t further collisions were calculated. The p r o d u c t of these two p r o b a b i l i t i e s times the n e u t r o n weight gave the last-flight statistical
Both the geometries a n d chemical c o m p o s i t i o n s o f the scatterers were r e q u i r e d i n p u t s to the M o n t e C a r l o code. Except for LiH, all scatterers were smaller t h a n the f l i g h t - p a t h - i n p u t - c o l l i m a t o r d i m e n s i o n s shown in fig. 1. Thus every collision resulting in an energy a b o v e 0.5 M e V in the direction o f the d e t e c t o r c o n t r i b u t e d to the scattered intensity. T h e 3" dia. x 6" high L i H scatterer was larger t h a n the 3" high × 2.5" wide precollimator. Since the p r e c o l l i m a t o r was l o c a t e d 53/55 o f the distance f r o m the source to the d e t e c t o r only collisions within a central region 3" x (55/53) high a n d 2.5"× (55/53) wide were accepted. The e l e m e n t a l c o m p o s i t i o n for s o m e o f the samples is shown in table 1, which gives b o t h the a c t u a l e s t i m a t e d c o m p o s i t i o n a n d the simplified c o m p o s i t i o n used for
TABLE 1 Chemical com )osition of scatterers (wt %). Scatterer type 5083 aluminum ~,density = 2.65 g/cma) lrype 4340 steel ~density = 7.82 g/cm3) Concrete ',density = 2.07 g/cm3)
H
C
O
Na
Mg 4.5
A1
Si
94 (100)*
0.4
K
Ca
0.4 O.5 + (1.7)*
1.9
5O.O (58.7)*
2.5
0.9
6.8
23.8 (27.2)*
2.0
8.5 (12.4)*
Mn
Fe
0.7
0.4
0.7
96.3 (100)* 1.9
Ni
Cr
1.8
0.8
* The values listed represent the actual estimated content (analysis, manufacturers catalog, etc.), with the values in parentheses being the calculational composition (assumed for the Monte Carlo scattering calculation).
FAST-NEUTRON DIFFERENTIAL SCATTERING CROSS SECTIONS I00
graphite, assumed to be 100% pure carbon, with a density of 1.6 g/cm 3. The LiH was composed of natural Li which was crystalized, ground, isostatically pressed to a density of 0.76 g/cm a, machined, and jacketed in a 0.01" thick stainless steel container. The LiH container wall was taken to be pure iron, and the Monte Carlo calculation was made to perform a 2-region-scatterer problem for LiH and Fe.
2 t0-t
2
5.4. CROSS SECTIONS
tO-Z
The 05R code utilizes scattering cross sections to a Ps angular approximation for the more routine applications. These were obtained from the cross-section library maintained by the 05R system. Both elastic and inelastic scattering cross sections were used. The natural lithium was taken to be composed Of 6Li and 7Li, with the two being treated as separate elements. Cross sections for 6Li(n,dn) and 7Li(n,tn) were also used. The
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CARBON C Y L I N D E R -
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5 6 7 8 9 NEUTRON ENERGY (MeV)
iO
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12
13
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Fig. 5. Calculated and measured scattering by carbon at 20°. Both were normalized to a total neutron source strength of 1 neutron/ sterad so that cross-section corrections may be derived from differences in neutron flux vs neutron energy. the Monte Carlo calculations. For calculation purposes, little error is made in assuming that the type 5083 aluminum is 100% Al, because the impurities are small and close to aluminum in mass and total cross section. Similar simplifications were made for iron in the type 4340 steel and for concrete. For the concrete scattering sample, a chemical analysis for both free and bound water gave a minimum of 0.5% hydrogen by weight. Since the analysis was carried out about six months after the sample had been used in the scattering experiment (the sample had been kept under high humidity conditions until a few days before the experiment), the estimated hydrogen content was arbitrarily raised to a value of 1.7%, or about three times the value obtained from the analysis. Any error in this estimate is not evident in the comparison between calculation and measurement that is presented below. The carbon scatterer consisted of reactor-grade
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1
2
3
4
5
6
7
8
9
10
11
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NEUTRON ENERGY [MeV)
Fig. 6. Measured and calculated scattering from carbon at net scattering angles of 20, 70 and 160°. The cross-sectioncompilation that was usedn) is off by a factor of about 3 for the broad peak at 7 to 8 MeV for 20° scattering and at 3.5 to 4.5 MeV for 160° scattering.
188
v.v.
eta[.
VERBINSKI
publications and compilations from which these crosssection values were obtained are given for hydrogen6), lithium 6, 8 - to), carbon 11), oxygen 12 - 14), aluminum and siliconlO, 12), calciumlO, 15) and iron12).
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6. Comparison of measured and calculated results 6.1. DERWATION Or C~OSS SECTION ~NVO~MaT~ON Fig. 5 shows a source spectrum and both a measured and calculated spectrum for 20 ° scattering from carbon, all normalized to a source strength of 1 neutron/sterad. This figure illustrates the lSroblem of obtaining crosssection information from such data. At all scattering energies the Monte Carlo calculation showed the inelastic scattering component to be negligible for carbon, so that the data of fig. 5 involve only the differential elastic scattering cross section. In addition, 90°/0 of the scattered neutrons are singly scattered at 20 ° , according to the Monte Carlo calculation, and the energy loss due to elastic scattering from carbon at this angle is negligible. Therefore, for this case, we can directly conclude from the data that the calculational cross section ~1) at 20 ° is about 50% too high in the 2- to 3-MeV region. At 7.5 MeV, it should be increased by over 100°/0. The error in these corrections, due to multiple scattering, must be about 10°/0, which is generally better than the statistical accuracy of the present results. For results with better statistics, the correction can be further improved by repeating the Monte Carlo calculation with corrected cross section values. However, a 10°/0 error on a correction is small, considering that cross section accuracy is improved by an order of magnitude. For all light elements, the inelastic scattering was found to be completely negligible, according to the Monte Carlo calculations. For elements such as alumin u m and iron, the inelastically scattered neutrons contribute several percent to the total scattering. A spectral breakdown of scattering shows 15 to 20°/0 of the neutrons scattered at 20 ° by iron to be due to inelastic scattering near the low-energy cutoff (i.e. 0.5 to 1.5 MeV). However, this is a small part of the total energy region covered. In any case, 80 to 85% elastic scattering is still a manageable fraction of the combined scattering, in that a first-order correction to the cross section at 20 ° can be obtained which results in a considerable improvement. The source spectrum could be further softened by adding a moderating material to the neutron source, and thus the elastic scattering fraction could be raised well above the 80 to 85% figure in the 0.5- to 1.5-MeV region. The inelastic events are generally masked at forward angles (at all angles for light elements) because they must scatter down from
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a higher energy, where the source neutrons are less abundant by about an order of magnitude per 4 MeV (fig. 5). Therefore, a good estimate of the correction to the differential scattering cross section can be obtained simply by correcting for energy loss by elastic scattering (negligible correction at 20 ° and about 25% at 160 ° for the case of carbon). This scheme is workable for the light elemental scatterers~ but for lithium hydride and concrete, a comparison of measurement and calculation can only serve as a check on the cross section data for each agglomerate of target material. If the cross sections are found to be inadequate, then the scattering experiments described here should obviously be repeated using single constituent elements for each measurement. 6.2° RESULTS Fig. 6 shows the comparison of measured and calculated spectral intensities for natural carbon. The 20 ° scattering was discussed above. The 70 ° scattering results show that the carbon cross section is reasonably well known below 5 MeV, where the experimental statistics are reasonably good. At 160 °, the calculational cross section appears to be a bit too high from 1 to 2 MeV, considerably high at 3 to 5 MeV, and somewhat too low above 5 MeV. The aluminum data (fig. 7) show very good overall agreement between the measurement and the Monte Carlo calculation. Most of the disagreement appears to be within the statistical uncertainty in both the measurement and the calculation. The calculational cross section is about 20% low at 5 to 7 MeV and 20 ° and 20% high at 2 to 4 MeV and 70 °. The iron data (fig. 8) also show reasonably good overall agreement. However, the calculational results for 20 ° scattering are everywhere about 20% lower than the experimental results. Such disagreement is almost certainly due to an experimental error in monitoring the source neutrons during the scattering measurement, and not to the cross-section values used in the Monte Carlo calculation. The use of three sulfur monitor pills instead of one can eliminate most errors of this nature, since a single error in three is easily detected. In fig. 9, it can be seen that the cross sections for the constituents of concrete are known to a good accuracy. The chemical composition was determined with fair accuracy, except for the hydrogen content. However, Fig. 8. M e a s u r e d a n d calculated scattering f r o m Fe at 6 angles• T h e compilation 12) used for this calculation appears to be quite accurate. T h e bodily shift (upwards) o f the m e a s u r e d curve over that calculated at 20 ° c a n be reasonably explained o n l y by a n experimental error in the n e u t r o n - m o n i t o r reading.
190
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the good agreement between measurements and calculations at all energies and scattering angles clearly indicates that the hydrogen content was estimated to good accuracy for present purposes. Fig. 10 shows the results for scattering from a 3" cylinder of LiH. The calculation is in very good agreement with the measurements, indicating that the cross section compilation is accurate within the statistical uncertainty of these measurements.
energy range of the measurement. At low energies, the neutron source strength can be increased by the simple expedient of increasing the volume of coolant water in
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high energy neutrons can be greatly improved 17) by placing a generous slab of light material, such as beryllium or boron, on the downstream side of the lead slug shown in fig. 1. The lead slug would act mostly as a very efficient bremsstrahlung converter. The pseudodeuteron effect in light elements results in a relatively large yield of neutrons up to nearly half the electron energy.
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8. Conclusions The method of obtaining cross-section data presented here is straightforward in that it makes use of a comparison of the measured and calculated values of differential (or angular) neutron flux scattered by a small scattering sample. Differences between the two provide direct first-order corrections to the scattering cross sections used as input to the scattering calculation after correcting for energy loss by elastic scattering. The use of a lead photoneutron source greatly deemphasizes the inelastic scattering, so that only differential elastic cross section data are obtained for low Z elements. The advantages of the method are that good energy resolution was easily attained with timeof-flight methods using a modern electron linear accelerator (linac), the efficiency of the neutron detector was accuractely known, and good discrimination against g a m m a counts was achieved. The greatest disadvantage is that only indirect cross-section data are obtained. A sophisticated Monte Carlo calculation was required before any useful conclusions could be drawn. However, in most optimally designed cross section measurements, Monte Carlo calculations for multiple scattering corrections are usually required in any case. The present experiment can therefore be thought of as a compromise in which a little more burden than usual is placed on a reliable scattering calculation, with the result that a disproportionately greater burden is removed from the experimental costs and time consumption involved when making the measurements with thin scatterers and with monoenergetic neutron sources. With the constant improvement in computer speed, the justification of this method will be even greater in the future.
References 1) Compilation of requests for nuclear cross section measurements, issued periodically by the USAEC Cross Section Advisory Group. See, for example, WASH-1057 (August 1965). 2) R. R. Coveyou et al., 05R: a general purpose Monte Carlo neutron transport code, ORNL-3622, Oak Ridge National Laboratory (Febr. 1965). 3) K. D. Lathrop, DTF-IV, a FORTRAN-IV program for solving the multigroup transport equation with anisotropic scattering, LA-3373, Los Alamos ScientificLaboratory (1965).
192
V. V: VERBINSKI et al.
4) D. Yetman, B. Eisenman and G. Rabinowitz, Description of input preparation and operating procedures for 9-NIOBE, an IBM-7090 code, Advanced shield calculational techniques 1, UNUCOR-631 (1963); also S. Preiser, G. Rabinowitz and E. deDufour, A program for the numerical integration of the Boltzmann transport equation, NIOBE, Advanced shieM calculational techniques 2, UNUCOR-632 (1963). 5) V. V. Verbinski et al., Trans. Am. Nucl. Soc. 7 (1964) 374. Also V. V. Verbinski et al., The response of some organic scintillators to fast neutrons, ANS-SD-2, Proc. special session on fast neutron spectroscopy (Dec. 1964) Meeting of Am. Nucl. Soc., San Francisco, California. ~) J. R. Stehn et al., Neutron cross sections, BNL-325, Suppl. no. 2, Brookhaven National Laboratory (1964) also 2 na ed. (1958) by D. J. Hughes and R. B. Schwartz. 7) F. Kam, ACTIFK, a general purpose analysis code for 05R, ORNL-3856, Oak Ridge National Laboratory (1966). 8) E. D. Pendlebury, Neutron cross sections of eLi in the energy range 0.001 eV-15 MeV, AWRE 0-60/64, Harwell, England (July 1964). 9) E. D. Pendlebury, Neutron cross sections of 7Li in the energy range 0.001 eV-15 MeV, AWRE-0-61/64, Harwell, England (July 1964). lO) M. D. Goldberg, V. M. May and J. R. Stehn, Angular
distributions in neutron induced reactions, BNL-400, 2nd ed., Brookhaven National Laboratory (Oct. 1962). 11) K. Parker, Neutron cross sections for carbon in the energy range 0.025 eV-15 MeV, AWRE 0-71/60, Harwell, England (August 1961). 12) E. S. Troubetzkoy, Fast neutron cross sections of iron, silicon, aluminum and oxygen, NDA-2111-3, Vol. C., United Nuclear Corporation (Nov. 1959). 13) G. D. Joanou and H. Fenech, Reactor Sci. Yechn. 17 (•963) 425. 14) M. K. Kalos, H. Goldstein and J. Ray, Revised cross sections for neutron interactions with oxygen and deuterium, NDLTR-40, United Nuclear Corporation (August 1962). 15) E. S. Troubetzkoy, Fast neutron cross sections of manganese, calcium, sulfur, and sodium, N D A 2133-4, United Nuclear Corporation (June 1960). 16) W. M. Good, J. H. Neiler and J. H. Gibbons, Phys. Rev. 109 (1958) 926. 17) j. Winhold, P. Yergin and H. Medicus, Rensselaer Polytechnic Institute, private communication. 18) D. B. Gayther and P. D. Goode, Neutron energy spectra and angular distributions from targets bombarded by 45 MeV electrons, A ERE-R 5331, Atomic Energy Research Establishment (Dec. 1966).
INSTRUMENTS
A METHOD
AND METHODS
52 (I967) 1 8 I - I 9 2 ;
© NORTH-HOLLAND
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OF EVALUATING FAST-NEUTRON DIFFERENTIAL SCATTERING CROSS SECTIONS WITH SHORT EXPERIMENTAL
RUNS*
V. V. VERBINSKI, J. C. COURTNEY* and N. BETZ Oak Ridge National Laboratory, Oak Ridge, Tennessee, U.S.A.
Received 16 February 1967 The method utilized a pulsed neutron source with a smooth, broad spectrum, making it possible to measure neutron scattering from 0.5 to 10 MeV in a single run of 1 to 2 h duration for each scattering angle 0. Scattering samples of carbon, aluminum, iron, lithium hydride and concrete about 5 cm in dia. were located about ½m from the pulsed neutron source, and neutrons scattered through an angle 0 were directed down a 55-m flight path to a liquid organic scintillator used to measure the time-of-flight spectrum of scattered neutrons. The energy-dependent neutron intensity thus obtained was compared with Monte Carlo calculations whose inputs were the measured neutron source term and neutron elastic, inelastic, and reaction cross sections compiled from the existing literature. The comparison provides direct corrections to the cross sections for the lighter elements because
single scattering is about ten times more probable than multiple scattering with the sample sizes chosen. These corrections can be further improved by repeating the calculation with the improved cross-section values. Inelastic scattering into any given energy region was small compared with elastic scattering for low Z scatterers because of the shape of the source spectrum. In this case, the method provides an unambiguous check on the elastic differential scattering cross sections used as input for the Monte Carlo calculations, and good first-order corrections to these cross sections. Several modifications of both experiment and calculation are proposed for reducing the statistical uncertainty, for improving the experimental and calculational efficiencies, and for increasing the range of energy covered.
1. Introduction
describe the i n t e r a c t i o n o f n e u t r o n s with nuclei to v a r y i n g degrees o f a p p r o x i m a t i o n . I t is clear t h a t a fast, accurate m e t h o d of checking n e u t r o n cross-section d a t a is o f great value. Such a m e t h o d can be used to select the m o s t accurate o f the detailed cross-section m e a s u r e m e n t s that a p p e a r in the literature, to i n t e r p o l a t e between these values in a m o r e realistic m a n n e r , a n d even to test the basic a s s u m p tions o f a n y calculations that m a y have been used for p r e d i c t i n g n e u t r o n differential scattering cross sections. The c o m b i n e d e x p e r i m e n t a l a n d c a l c u l a t i o n a l m e t h o d s p r e s e n t e d here for evaluating a n d t h e r e b y i m p r o v i n g cross-section d a t a have been carried o u t for a few t a r g e t m a t e r i a l s with g o o d accuracy. A b o u t a decade o f n e u t r o n energy was covered with a single measurement. The m e a s u r e m e n t s described below were carried o u t in 1964 w i t h engineering s a m p l e s such as concrete, l i t h i u m h y d r i d e , s t r u c t u r a l a l u m i n u m , a n d steel. These m a t e r i a l s were selected to p r o v i d e a m a x i m u m coverage of cross-section e v a l u a t i o n for the fixed accelerator t i m e a l l o t t e d to this p i l o t project. The concrete, a l u m i n u m a n d steel cross-section checks were o f interest to the Defense A t o m i c S u p p o r t Agency, with the transmission of neutrons t h r o u g h multilegged concrete ducts being o f p r i m a r y concern. The L i H d a t a were of p a r t i cular interest for the design of S N A P (Space N u c l e a r A u x i l i a r y Power) r e a c t o r systems in which n e u t r o n scattering f r o m the edge o f the L i H s h a d o w shield a n d f r o m a p p a r a t u s p r o j e c t i n g out b e y o n d the circum-
A c c u r a t e differential scattering cross sections are needed for reliable calculations of n e u t r o n p e n e t r a t i o n s in r e a c t o r a n d accelerator shields, for n e u t r o n transm i s s i o n t h r o u g h multilegged ducts, a n d for n e u t r o n fluxes in breeder b l a n k e t s l o c a t e d n e a r the fuel regions o f reactors1). T h e need has g r o w n w i t h the a d v e n t o f m o d e r n n e u t r o n t r a n s p o r t codes2-4), which utilize the m o m e n t s m e t h o d , direct n u m e r i c a l i n t e g r a t i o n o f the Boltzmann equation, and Monte Carlo methods and which r o u t i n e l y use u p to P8 t e r m s in the L e g e n d r e p o l y n o m i a l a n g u l a r a p p r o x i m a t i o n s to the differential scattering cross sections. This need will e x p a n d with the c o n t i n u e d i m p r o v e m e n t in speed a n d storage c a p a c i t y o f m o d e r n c o m p u t e r s which are b e g i n n i n g to m a k e the slower b u t m o r e reliable a n d versatile M o n t e C a r l o calculations feasible for d e e p - s h i e l d - p e n e t r a t i o n calculations. Such c a l c u l a t i o n s have used up to a P16 a n g u l a r a p p r o x i m a t i o n on occasion. I n c o m p i l i n g a crosszsection l i b r a r y for these transp o r t codes, s o m e initial d a t a are first o b t a i n e d f r o m the s m a l l n u m b e r o f m e a s u r e d values t h a t a p p e a r in the literature, values t h a t often disagree by m a n y times the q u o t e d s t a n d a r d deviations. T h e gaps b e t w e e n these d a t a p o i n t s m u s t be filled in b y v a r i o u s i n t e r p o l a t i o n schemes, a n d in some cases by c a l c u l a t i o n s which t Research sponsored by the Defense Atomic Support Agency under Union Carbide Corporation's contract with the U.S. Atomic Energy Commission. * Now with U. S. Air Force, McClellan Air Force Base, Sacramento, California. JUNE II
1967
181
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2. Experimental configuration In fig. I is shown the experimental arrangement for measuring the energy dependence of the neutron flux scattered by cylindrical samples. The General Atomic
electron linear accelerator (linac) was used to provide 14-nsec bursts of 33-MeV electrons which irradiated a lead slug. The electrons produced bremsstrahlung radiation which in turn produced photoneutrons whose spectrum and intensity varied slowly with 01, the angle of emission with respect to the electron beam. Neutrons scattered by the cylindrical sample at a net scattering angle 02 traveled down a long flight path which was terminated by a fast liquid organic scintillator (NE-213)
FAST-NEUTRON
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used to detect their time of arrival. (An NE-211 detector was used for measuring the source spectrum, as described in sect. 3.) Background measurements were made by simply removing the scatterer. In addition, a separate background measurement was made by leaving the scatterer in place and shielding it from the neutron source by a shadow shield made from laminations of iron and polyethylene An increase in background was observed, beyond that obtained by simply removing the scatterer and shadow shield. Since this increase was about equal to calculated neutron leakage through the shadow shield and since the backgrounds contributed only about 10% to the total count rate, the simple scattererout backgrounds were accurate enough. During each scattering experiment, a sulfur monitor foil placed at 45 ° to the electron beam, as shown in fig. 1, was used to determine the time-integrated source strength. Since the monitor foil was also used while the source spectral intensity was being measured, simple monitor ratios could be used to determine the absolute, time-integrated spectral intensity of the neutron source for each scattering measurement. The measurement of the spectral intensity of neutrons leaving the source at 01 was accomplished by bending the electron beam clockwise through 0 t - 9 0 ° before it crossed the flight path and by locating the lead slug alongthe flight path center line (fig. 1). The axis of the disk-shaped slug was always kept parallel to the electron beam so that the self-shielding of the lead slug would be a constant factor. To further assure that the self-shielding was constant, steps were taken to keep the electron beam size and position constant. The size was monitored periodically with film-type beam profile measurements. Positioning of the beam was accomplished with a small, thin foil centrally located in the beam tube of the linac (not shown in fig. 1) and electrically connected to an oscilloscope. A narrow ionization chamber located behind the lead slug was also used for beam positioning. Note that two scatterers are shown in fig. 1 for which the source angle 01 is the same but for which the net scattering angle is either 02 or n -02. Thus, only a single source measurement and a single background measurement were necessary for the scattering measurements performed at two supplementary scattering angles. (In sect. 7, a simple method of keeping the source spectrum constant for all scattering angles is described.) 3. Electronics
A block diagram of the data-gathering electronics is shown in fig, 2. The fast scintillator and photomultiplier
SCATTERING
CROSS SECTIONS
183
tube located near the neutron source produced a pulse of constant shape for each linac burst. This timefi.ducial pulse was sent to the 55-m flight path station of the General Atomic linear accelerator facility, where it was used to start a 1-nsec clock.* The fiducial pulse was also used to activate a gating circuit which turned on the neutron-detector photomultiplier tube after the bremsstrahlung passed this detector and just before the fastest neutrons arrived. The tube-base diagram for the neutron detector shown in fig. 2 illustrates how a neutron event produces three signals in the Phillips XP-1040 photomultiplier tube - a fast timing signal at dynode 13, a linear signal at dynode 12 used for an accurate and stable bias level and set at approximately 0.43-MeV recoil-proton energy, a n d a pulse-shapediscriminator (PSD) signal from a modified Fort6 circuit connected to dynode 14 and anode. The effective bias of the PSD circuit was below the 0.43-MeV linearbias level, so that a sharp cutoff could be obtained. The PSD circuit was used to reject gamma-ray counts which were appreciable for the scattering runs. During the scattering measurements the presence of these three simultaneous signals was required for the fast signal to stop the 1-nsec clock and activate the command module which caused the clock datum to be stored directly in the memory of a TMC-400 channel analyzer. * The dividing circuit + shown in fig. 2 was needed to divide the 1-nsec clock reading by a factor such that the complete time span (corresponding to 0.4 to 14 MeV neutrons) could be contained in the 400 channels available from the T M C analyzer used. The channel number corresponding to zero time was deduced from the time of arrival of the bremsstrahlung pulse at the neutron detector. Zero drift was always within one channel (8 or 12 nsec). When the spectral intensity of the neutron source was being measured, the scintillators viewed the neutron source (the lead slug shown in fig. 1) directly. In thia case, the bremsstrahlung radiation and positron-decay radiation in the lead slug illuminated the NE-213~ scintillator to such an intensity that the slow component of light emission was intolerably high at the time that the photomultiplier was gated on (just before the fastest neutrons arrived). Consequently the gating circuit was of no avail, and an NE-211 scintillator, which has almost no slow component of light emission, • M o d e l 793-A 1-nsec Clock, E l d o r a d o Electronics, 601 C h a l a m a r
Road, Concord, California. t Model 401B6 400-channel pulse height analyzer, Technical Measurements Corporation, North Haven, Connecticut. + Model 3-3031 Computing Unit (Dividing Unit), Applied Development Corporation, Monterey Park, California. § Nuclear Enterprises, Ltd., Winnepeg, Canada.
184
v . v . VERBINSKI et al.
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Since the controlling bias level was determined by the linear-amplifier discriminator setting, it had to be checked at periodic intervals by using the end point of the 6°Co pulse-height distribution as a standard of reference. The detector efficiency as a function of bias setting was determined in an extensive program of
FAST-NEIJTRON
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of 1 "cobalt" is the extrapolated endpoint of a ~°Co pulse height distribution, linear plot. The XP-1040 photomultiplier tube was used. detector calibration 5) in which all neutron pulse heights were referred to the 6°Co endpoint (equal to 1 "cobalt" in pulse height). The NE-211 and NE-213 scintillators were found to be identical for neutrons in this respect (i.e., with respect to the calibration point obtained from the 6°Co pulse-height distribution). Both were 5" dia. x 5" hgt cylinders, glass-encapsulated, deoxygenated, sealed, and covered with a white reflective coating at the factory. Two efficiency-vs-energy curves are shown in fig. 3 for two different bias settings. Typ!cal bias settings were 0.038 to 0.042 "cobalt". 4. Data handling The time-of-flight spectrometer could accept only one count per linac burst. The linac current therefore had to be kept at a level where the average count rate was not greater than 0.15 per burst. The occurrence of two counts or more during one burst could then be accurately corrected for by assuming that the linac current was constant during a given run. High count rates (0.15 per burst) were realized only during the source spectrum measurements, and the linac current was held constant to within 4- 30% during these relatively short runs. The error in the count loss correction was about 2°/0 maximum, which is generally much smaller than the statistical accuracy of the present data. All time-of-flight spectra were analyzed with a datahandling code developed by R. Cowperthwaite at O R N L which utilizes the relativistic relationship between neutron velocity and energy, subtracts the background, propagates the variances or statistical uncertainties, corrects for the occurrence of more than one event per burst, divides by the energy-dependent detector efficiency, corrects for neutron scattering by
SCATTERING
CROSS SECTIONS
185
materials in the flight path, and groups time channels into uniform energy fractions (1°/0 to 5%, which could be preselected). The materials in the beam included an argon-filled dr~ft tube, thin aluminum windows and a g a m m a filter of lead up to 5 cm thick. In one measurement of source spectrum, at 0t = 160 °, it was possible to decrease the lead filter to ¼ cm. A 5-cm thickness was also used in this measurement to determine the validity of the lead-scattering correction. The two corrected spectra agreed in shape within counting statistics, which were better than for most runs. It was possible to use the total neutron cross section 6) as the removal cross section because of the good-geometry arrangement (the g a m m a filter was located about 17 m down a rather tightly collimated flight path). The sulfur monitors were located at 45 ° to the electron beam for both source and scattering measurements. For the source measurements, where the detector at 55 m viewed the source directly, the linac output had to be kept very low, and so the sulfur-monitor activation was difficult to determine with good counting statistics. Therefore a separate high-intensity run was made in which sulfur monitor pills were also placed at angles of 110, 135, 160, and 170 ° to the source. By convoluting the sulfur (n,p) cross section with each of the neutron spectra the absolute source strength was obtained at each of the source angles and was properly correlated to the activation of the sulfur monitor located at the standard position, i.e., 45 ° to the electron beam. The sulfur counting was not started until several days after exposure in order to eliminate short-lived background activity. The 32S(n,p)32p cross sections were taken from BNL-325, ref. 6). 5. The Monte Carlo calculations 5.1. DESCRIPTION The 05R Monte Carlo system of Coveyou et al. 2) was adapted to the scattering problem by Betz and Courtney. The actual source spectrum, source angular distribution, geometry of the system, and a neutron crosssection compilation were used as inputs to the calculations. For each source angle 01 (i.e., for the two scattering angles shown in fig. 1) histories of 100000 source neutrons were calculated. The neutrons were followed until they either escaped the system or fell below the cutoff energy. Absorption was treated by multiplying the weight of the neutron by the nonabsorption probability at each collision. After each collision the appropriate parameters (energy, direction components, weight, position coordinates) were written onto a collision tape. The collision tapes were then
v . v . VERBINSKI et al.
186
e s t i m a t i o n for each collision. This weighted c o u n t was a d d e d to the p r o p e r energy bin. In this way, the a b s o l u t e spectral intensity o f scattered neutrons was o b t a i n e d with a relatively small statistical u n c e r t a i n t y for the n u m b e r of case histories carried out. B o t h the calculat i o n a l a n d e x p e r i m e n t a l results given b e l o w were normalized to a n e u t r o n source strength o f 1 n e u t r o n / sterad, so t h a t differences give a direct cross section c o r r e c t i o n in t e r m s o f n e u t r o n energy before scattering t h r o u g h the net scattering angle 02.
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T h e n e u t r o n source was a s s u m e d to be a p o i n t source a n d to be i s o t r o p i c over the solid angle segment s u b t e n d e d b y the scatterer. The actual source d i a m e t e r was a b o u t 1 cm, which was small c o m p a r e d with the 22.9- a n d 33-cm distan.ces to the scatterers. The source s p e c t r a for 01 = 110, 135, a n d 160 ° are shown in fig. 4, n o r m a l i z e d to 1 n e u t r o n p e r M e V per sterad. The 0 t = 110 ° source s p e c t r u m was used for 02 = 10 ° scattering because no difference was observed between the 100 ° a n d 110 ° source spectra, within c o u n t i n g statistics. 5.3. SCATTERER GEOMETRY AND COMPOSITION
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Fig. 4. Neutron source spectra for three source angles 01 shown in fig. 1. The 110° spectrum was used for 10° scattering as well as for 20 and 160° scattering, since it was nearly identical to the 100° spectrum. All source spectra are shown normalized to 1 neutron/ sterad when integrated over neutron energy. analyzed with a last-flight statistical analysis routine7). A t each collision p o i n t the p r o b a b i l i t y of the n e u t r o n scattering t h r o u g h such an angle as to reach the detector a n d the p r o b a b i l i t y o f the n e u t r o n e s c a p i n g f r o m the cylinder in this direction w i t h o u t further collisions were calculated. The p r o d u c t of these two p r o b a b i l i t i e s times the n e u t r o n weight gave the last-flight statistical
Both the geometries a n d chemical c o m p o s i t i o n s o f the scatterers were r e q u i r e d i n p u t s to the M o n t e C a r l o code. Except for LiH, all scatterers were smaller t h a n the f l i g h t - p a t h - i n p u t - c o l l i m a t o r d i m e n s i o n s shown in fig. 1. Thus every collision resulting in an energy a b o v e 0.5 M e V in the direction o f the d e t e c t o r c o n t r i b u t e d to the scattered intensity. T h e 3" dia. x 6" high L i H scatterer was larger t h a n the 3" high × 2.5" wide precollimator. Since the p r e c o l l i m a t o r was l o c a t e d 53/55 o f the distance f r o m the source to the d e t e c t o r only collisions within a central region 3" x (55/53) high a n d 2.5"× (55/53) wide were accepted. The e l e m e n t a l c o m p o s i t i o n for s o m e o f the samples is shown in table 1, which gives b o t h the a c t u a l e s t i m a t e d c o m p o s i t i o n a n d the simplified c o m p o s i t i o n used for
TABLE 1 Chemical com )osition of scatterers (wt %). Scatterer type 5083 aluminum ~,density = 2.65 g/cma) lrype 4340 steel ~density = 7.82 g/cm3) Concrete ',density = 2.07 g/cm3)
H
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1.8
0.8
* The values listed represent the actual estimated content (analysis, manufacturers catalog, etc.), with the values in parentheses being the calculational composition (assumed for the Monte Carlo scattering calculation).
FAST-NEUTRON DIFFERENTIAL SCATTERING CROSS SECTIONS I00
graphite, assumed to be 100% pure carbon, with a density of 1.6 g/cm 3. The LiH was composed of natural Li which was crystalized, ground, isostatically pressed to a density of 0.76 g/cm a, machined, and jacketed in a 0.01" thick stainless steel container. The LiH container wall was taken to be pure iron, and the Monte Carlo calculation was made to perform a 2-region-scatterer problem for LiH and Fe.
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The 05R code utilizes scattering cross sections to a Ps angular approximation for the more routine applications. These were obtained from the cross-section library maintained by the 05R system. Both elastic and inelastic scattering cross sections were used. The natural lithium was taken to be composed Of 6Li and 7Li, with the two being treated as separate elements. Cross sections for 6Li(n,dn) and 7Li(n,tn) were also used. The
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188
v.v.
eta[.
VERBINSKI
publications and compilations from which these crosssection values were obtained are given for hydrogen6), lithium 6, 8 - to), carbon 11), oxygen 12 - 14), aluminum and siliconlO, 12), calciumlO, 15) and iron12).
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6. Comparison of measured and calculated results 6.1. DERWATION Or C~OSS SECTION ~NVO~MaT~ON Fig. 5 shows a source spectrum and both a measured and calculated spectrum for 20 ° scattering from carbon, all normalized to a source strength of 1 neutron/sterad. This figure illustrates the lSroblem of obtaining crosssection information from such data. At all scattering energies the Monte Carlo calculation showed the inelastic scattering component to be negligible for carbon, so that the data of fig. 5 involve only the differential elastic scattering cross section. In addition, 90°/0 of the scattered neutrons are singly scattered at 20 ° , according to the Monte Carlo calculation, and the energy loss due to elastic scattering from carbon at this angle is negligible. Therefore, for this case, we can directly conclude from the data that the calculational cross section ~1) at 20 ° is about 50% too high in the 2- to 3-MeV region. At 7.5 MeV, it should be increased by over 100°/0. The error in these corrections, due to multiple scattering, must be about 10°/0, which is generally better than the statistical accuracy of the present results. For results with better statistics, the correction can be further improved by repeating the Monte Carlo calculation with corrected cross section values. However, a 10°/0 error on a correction is small, considering that cross section accuracy is improved by an order of magnitude. For all light elements, the inelastic scattering was found to be completely negligible, according to the Monte Carlo calculations. For elements such as alumin u m and iron, the inelastically scattered neutrons contribute several percent to the total scattering. A spectral breakdown of scattering shows 15 to 20°/0 of the neutrons scattered at 20 ° by iron to be due to inelastic scattering near the low-energy cutoff (i.e. 0.5 to 1.5 MeV). However, this is a small part of the total energy region covered. In any case, 80 to 85% elastic scattering is still a manageable fraction of the combined scattering, in that a first-order correction to the cross section at 20 ° can be obtained which results in a considerable improvement. The source spectrum could be further softened by adding a moderating material to the neutron source, and thus the elastic scattering fraction could be raised well above the 80 to 85% figure in the 0.5- to 1.5-MeV region. The inelastic events are generally masked at forward angles (at all angles for light elements) because they must scatter down from
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a higher energy, where the source neutrons are less abundant by about an order of magnitude per 4 MeV (fig. 5). Therefore, a good estimate of the correction to the differential scattering cross section can be obtained simply by correcting for energy loss by elastic scattering (negligible correction at 20 ° and about 25% at 160 ° for the case of carbon). This scheme is workable for the light elemental scatterers~ but for lithium hydride and concrete, a comparison of measurement and calculation can only serve as a check on the cross section data for each agglomerate of target material. If the cross sections are found to be inadequate, then the scattering experiments described here should obviously be repeated using single constituent elements for each measurement. 6.2° RESULTS Fig. 6 shows the comparison of measured and calculated spectral intensities for natural carbon. The 20 ° scattering was discussed above. The 70 ° scattering results show that the carbon cross section is reasonably well known below 5 MeV, where the experimental statistics are reasonably good. At 160 °, the calculational cross section appears to be a bit too high from 1 to 2 MeV, considerably high at 3 to 5 MeV, and somewhat too low above 5 MeV. The aluminum data (fig. 7) show very good overall agreement between the measurement and the Monte Carlo calculation. Most of the disagreement appears to be within the statistical uncertainty in both the measurement and the calculation. The calculational cross section is about 20% low at 5 to 7 MeV and 20 ° and 20% high at 2 to 4 MeV and 70 °. The iron data (fig. 8) also show reasonably good overall agreement. However, the calculational results for 20 ° scattering are everywhere about 20% lower than the experimental results. Such disagreement is almost certainly due to an experimental error in monitoring the source neutrons during the scattering measurement, and not to the cross-section values used in the Monte Carlo calculation. The use of three sulfur monitor pills instead of one can eliminate most errors of this nature, since a single error in three is easily detected. In fig. 9, it can be seen that the cross sections for the constituents of concrete are known to a good accuracy. The chemical composition was determined with fair accuracy, except for the hydrogen content. However, Fig. 8. M e a s u r e d a n d calculated scattering f r o m Fe at 6 angles• T h e compilation 12) used for this calculation appears to be quite accurate. T h e bodily shift (upwards) o f the m e a s u r e d curve over that calculated at 20 ° c a n be reasonably explained o n l y by a n experimental error in the n e u t r o n - m o n i t o r reading.
190
v . v . VERBINSKI et al.
the good agreement between measurements and calculations at all energies and scattering angles clearly indicates that the hydrogen content was estimated to good accuracy for present purposes. Fig. 10 shows the results for scattering from a 3" cylinder of LiH. The calculation is in very good agreement with the measurements, indicating that the cross section compilation is accurate within the statistical uncertainty of these measurements.
energy range of the measurement. At low energies, the neutron source strength can be increased by the simple expedient of increasing the volume of coolant water in
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7. Improvements of the experimental and calculation 10-3 , ~ ; -~-, configurations The most obvious possible improvement in the experir mental arrangement would be the use of a much larger o9* detector. This could be very simply cross-calibrated against the standard 5" detectors which we had pre-2~ff_e- viously calibrated. The higher count rate could not be handled by the present electronic circuitry. However, the addition of an extra 1-nsec clock, which would allow two counts per burst to be stored instead of one, would increase the permissible count rate by about a factor 6 oo of 10 according to the statistical analysis made of this 10-4 problem by one of us (VVV). The second clock could be 7 interrogated by the analyzer at any time between linac pulses, which are the order of 2000/~sec apart. Another improvement over the present arrangement is related to the choice of flight path. It should either be °~' ~ longer by a factor of about 2 or be oriented at 150 to × 170 ° to the electron beam. The problem is that of ~_ 10-4 recovery of the scintillator from the linac's large Z0 "gamma flash". The longer flight path allows the photo- I-multiplier tube to be gated on later, when the scintillator phosphorescence is practically gone. The large-angle ~-o flight path will reduce the gamma flash by a very large factor with very little corresponding decrease in neutron yield. In fact, if a bending magnet system were used, 10-4 the angle of bend can be varied so as to keep 01 constant (at 150 to 180°). This would result in a substantial reduction of computer time, with present techniques, t0-5 because the source spectrum would be the same for all scattering angles, and only one set of scattering histories (generated with this spectrum) would be needed for all angles for a given scattering material. If01 is not kept constant, then the calculation for the different source spectra, q)(E,01), could be done piece160 ° wise with several segments of an "average" source 10-7 o t spectrum. This could easily be implemented because of 0 I 2 3 4 5 6 7 8 9 10 11 12 the small changes of source spectrum over a large range NEUTRON ENERGY (MeV) of source angle 01, so that only a few energy segments Fig. 9. Measured and calculated scattering from a concrete would be needed to reconstruct any of the similar cylinder. The good overall agreement at all angles speaks well for spectra shown in fig. 3. both the cross-sectioncompilations6,10,11,lZ, 15)and the chemical Three improvements are possible for increasing the analysis (including the estimate of the hydrogen content).
f.
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191
high energy neutrons can be greatly improved 17) by placing a generous slab of light material, such as beryllium or boron, on the downstream side of the lead slug shown in fig. 1. The lead slug would act mostly as a very efficient bremsstrahlung converter. The pseudodeuteron effect in light elements results in a relatively large yield of neutrons up to nearly half the electron energy.
5-in.-diam LiH CYLINDER
'~',I
SCATTERING
12
Fig. 10. Measured and calculated scattering from a 3" dia. by 6" long LiH cylinder (natural Li) encased in a 0.010" thick stainless steel jacket. The detector viewed only a 3" x (55/53) height and a 2.5" x (55/53) width of the central portion of the cylinder. The calculations were carried out only for 45 and 135° scattering. the lead slug (the neutron source), or by replacing the lead slug with a uranium sluglS). The neutron detector can be made to go to lower energies without the onset oftroubleseome photomultiplier-tube noise by selecting low-noise tubes, by cooling them, or by using two to a scintillator and demanding a coincidence between the two. A different type of detector could be used to extend the spectral measurements to very low neutron energies. A popular detector of this type is the 1°B4C slab placed in the neutron beam at the end of the flight patha6). The a°B4C slab is viewed by a N a I scintillator (which, for linac work, must be just out of the beam). The N a I spectrometer is set to detect the 480-keV neutron-capture gammas in I°B. At high energies the present type of proton-recoil detector can hardly be surpassed in efficiency. However, the target yield of
8. Conclusions The method of obtaining cross-section data presented here is straightforward in that it makes use of a comparison of the measured and calculated values of differential (or angular) neutron flux scattered by a small scattering sample. Differences between the two provide direct first-order corrections to the scattering cross sections used as input to the scattering calculation after correcting for energy loss by elastic scattering. The use of a lead photoneutron source greatly deemphasizes the inelastic scattering, so that only differential elastic cross section data are obtained for low Z elements. The advantages of the method are that good energy resolution was easily attained with timeof-flight methods using a modern electron linear accelerator (linac), the efficiency of the neutron detector was accuractely known, and good discrimination against g a m m a counts was achieved. The greatest disadvantage is that only indirect cross-section data are obtained. A sophisticated Monte Carlo calculation was required before any useful conclusions could be drawn. However, in most optimally designed cross section measurements, Monte Carlo calculations for multiple scattering corrections are usually required in any case. The present experiment can therefore be thought of as a compromise in which a little more burden than usual is placed on a reliable scattering calculation, with the result that a disproportionately greater burden is removed from the experimental costs and time consumption involved when making the measurements with thin scatterers and with monoenergetic neutron sources. With the constant improvement in computer speed, the justification of this method will be even greater in the future.
References 1) Compilation of requests for nuclear cross section measurements, issued periodically by the USAEC Cross Section Advisory Group. See, for example, WASH-1057 (August 1965). 2) R. R. Coveyou et al., 05R: a general purpose Monte Carlo neutron transport code, ORNL-3622, Oak Ridge National Laboratory (Febr. 1965). 3) K. D. Lathrop, DTF-IV, a FORTRAN-IV program for solving the multigroup transport equation with anisotropic scattering, LA-3373, Los Alamos ScientificLaboratory (1965).
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4) D. Yetman, B. Eisenman and G. Rabinowitz, Description of input preparation and operating procedures for 9-NIOBE, an IBM-7090 code, Advanced shield calculational techniques 1, UNUCOR-631 (1963); also S. Preiser, G. Rabinowitz and E. deDufour, A program for the numerical integration of the Boltzmann transport equation, NIOBE, Advanced shieM calculational techniques 2, UNUCOR-632 (1963). 5) V. V. Verbinski et al., Trans. Am. Nucl. Soc. 7 (1964) 374. Also V. V. Verbinski et al., The response of some organic scintillators to fast neutrons, ANS-SD-2, Proc. special session on fast neutron spectroscopy (Dec. 1964) Meeting of Am. Nucl. Soc., San Francisco, California. ~) J. R. Stehn et al., Neutron cross sections, BNL-325, Suppl. no. 2, Brookhaven National Laboratory (1964) also 2 na ed. (1958) by D. J. Hughes and R. B. Schwartz. 7) F. Kam, ACTIFK, a general purpose analysis code for 05R, ORNL-3856, Oak Ridge National Laboratory (1966). 8) E. D. Pendlebury, Neutron cross sections of eLi in the energy range 0.001 eV-15 MeV, AWRE 0-60/64, Harwell, England (July 1964). 9) E. D. Pendlebury, Neutron cross sections of 7Li in the energy range 0.001 eV-15 MeV, AWRE-0-61/64, Harwell, England (July 1964). lO) M. D. Goldberg, V. M. May and J. R. Stehn, Angular
distributions in neutron induced reactions, BNL-400, 2nd ed., Brookhaven National Laboratory (Oct. 1962). 11) K. Parker, Neutron cross sections for carbon in the energy range 0.025 eV-15 MeV, AWRE 0-71/60, Harwell, England (August 1961). 12) E. S. Troubetzkoy, Fast neutron cross sections of iron, silicon, aluminum and oxygen, NDA-2111-3, Vol. C., United Nuclear Corporation (Nov. 1959). 13) G. D. Joanou and H. Fenech, Reactor Sci. Yechn. 17 (•963) 425. 14) M. K. Kalos, H. Goldstein and J. Ray, Revised cross sections for neutron interactions with oxygen and deuterium, NDLTR-40, United Nuclear Corporation (August 1962). 15) E. S. Troubetzkoy, Fast neutron cross sections of manganese, calcium, sulfur, and sodium, N D A 2133-4, United Nuclear Corporation (June 1960). 16) W. M. Good, J. H. Neiler and J. H. Gibbons, Phys. Rev. 109 (1958) 926. 17) j. Winhold, P. Yergin and H. Medicus, Rensselaer Polytechnic Institute, private communication. 18) D. B. Gayther and P. D. Goode, Neutron energy spectra and angular distributions from targets bombarded by 45 MeV electrons, A ERE-R 5331, Atomic Energy Research Establishment (Dec. 1966).