A facility for the measurement of neutron-capture cross sections from 0.01 eV to 1 MeV

NUCLEAR INSTRUMENTS AND METHODS 93 ( I 9 7 I ) 4 7 7 - 4 9 2 ;

© NORTH-HOLLAND

A FACILITY FOR THE MEASUREMENT NEUTRON-CAPTURE

CROSS SECTIONS

FROM

PUBLISHING CO.

OF

0.01 eV T O 1 MeV*

s. J. FRIESENHAHN, W. M. LOPEZ?, A. D. CARLSON and M. P. FRICKE Gulf Radiation Technology+, Division of Gulf Energy & Environmental Systems, Co., San Diego, California 92112, U.S.A.

Received 7 December 1970 ik facility has been constructed at Gulf Energy & Environmental Systems, Inc., to measure neutron-capture cross sections throughout the full neutron-energy region of interest in reactor design. Neutron-flux measurement techniques have been developed that yield absolute values with greater precision than has been previously achieved in time-of-flight measurements. The 10B(n,ct)TLi and the hydrogen-scatttering cross sections are used as standard cross sections for flux measurements below and above 80 keV, respectively. The 3He(n,p)T cross section was also measured to

allow detectors based on this cross section to be used as secondary flux standards. Two neutron flight paths with lengths of 20 and 230 m are used in a complementary fashion to optimize data accumulation, and large liquid scintillators are used at both flight paths to detect the capture gamma rays. These scintillators have been designed to achieve good gamma-ray energy resolution and timing characteristics while preserving a maximum of experimental flexibility.

I. Introduction

often f o u n d to be in strong d i s a g r e e m e n t with the measurements, p a r t i c u l a r l y a b o v e 100keV. Thus calculations o f the n e u t r o n e c o n o m y in h a r d - s p e c t r u m reactors m u s t at present rely a l m o s t exclusively u p o n m e a s u r e d c a p t u r e cross sections a b o v e this energy. O f the various m e t h o d s used to measure c a p t u r e cross sections, only the sphere-transmission technique avoids the difficulties associated with the m e a s u r e m e n t o f the n e u t r o n flux a n d reaction rate. U n f o r t u n a t e l y , however, the i n t e r p r e t a t i o n o f sphere t r a n s m i s s i o n in terms o f the c a p t u r e cross section requires very detailed i n f o r m a t i o n on the average r e s o n a n c e statistics o f the m a t e r i a l to allow accurate corrections to be m a d e for multiple elastic scattering, inelastic scattering a n d resonance self-shielding. The lack o f such inform a t i o n for m e d i u m a n d h e a v y nuclei severely limits the usefulness o f this technique. M a n y experiments have been p e r f o r m e d using highenergy, m o n o - e n e r g e t i c n e u t r o n b e a m s to o b t a i n c a p t u r e cross sections by activation techniques. This m e t h o d is a p p l i c a b l e only to c o m p o u n d nuclei with a suitable decay p r o d u c t , a n d the lack o f time-of-flight discrimin a t i o n against m o d e r a t e d neutrons has led to form i d a b l e c o m p l i c a t i o n s in m a n y o f these measurements. D e t e c t i o n o f the p r o m p t g a m m a rays with b o t h lowefficiency ( M o x o n - R a e ) a n d high-efficiency (large liquid scintillator) detectors have also been used in m o n o - e n e r g e t i c e x p e r i m e n t s ; however the absolute efficiency o f these detectors is difficult to obtain, as will be discussed in sec. 3. This is p a r t i c u l a r l y u n f o r t u n a t e in view o f the fact t h a t the precision o f absolute flux m e a s u r e m e n t s using associated-particle o r p r o t o n - r e c o i l techniques is quite good. B o t h the M o x o n - R a e a n d liquid-scintillator detectors

The d e v e l o p m e n t o f large t h e r m a l - s p e c t r u m reactors gave impetus to the m e a s u r e m e n t o f low-energy n e u t r o n cross sections. T o t a l cross-section measurements have yielded m u c h valuable i n f o r m a t i o n on c a p t u r e in nonfissionable nuclei. H o w e v e r , the advent o f i m p r o v e d g a m m a - r a y detectors in the early p a r t o f the past decade allowed the direct m e a s u r e m e n t o f the energy d e p e n d e n c e o f the c a p t u r e cross section, tlhus r e m o v i n g m o s t o f the uncertainties due to scattering. C a p t u r e techniques also yielded i m p r o v e d values o f the r e s o n a n c e p a r a m e t e r s a n d allowed m e a s u r e m e n t s for resonances t o o w e a k to be observed in total cross-section measurements. The r a t i o o f c a p t u r e to fission in fissionable nuclei tends to decrease with increasing n e u t r o n energy, thus e n c o u r a g i n g the design o f h a r d - s p e c t r u m reactors to achieve i m p r o v e d neutron e c o n o m y a n d fissilem a t e r i a l breeding. This tendency t o w a r d the use o f higher-energy neutrons in r e a c t o r design requires k n o w ledge o f c a p t u r e cross sections up to at least the m e a n fission n e u t r o n energy o f a b o u t 1 MeV. F o r m o s t heavy nuclei, the energy region a b o v e I keV is one in which the levels o f the c o m p o u n d nucleus are strongly overlapping, a n d theoretical predictions o f the energy d e p e n d e n c e o f the average c a p t u r e cross sections are * This work was supported by the National Aeronautics and Space Administration under Contracts NAS 3-11188 and 3-11844 and by the U.S. Atomic Energy Commission under Contract AT(04-3)-167, P.A. No. 11. t Present address: University of California at San Diego, La Jolla, California 92027. + Formerly the Defense Sciences Department of Gulf General Atomic Incorporated. 477

478

s.J.

FRIESENHAHN et al.

have also been used with white-spectrum neutron sources using the time-of-flight technique. The counting rate from such a detector can be expressed by

C(t)

= eS~p(t)

[(l

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+ P~] ,

(I)

where is the efficiency of the gamma-ray detector, is the area of the sample exposed to the beam, S is the flux incident at the flight time t, is the neutron transmission o f the sample, T O'7~ O" are the capture and total cross sections, respectively, is the probability for capture after the first collision. The product ~S~o(t) can be obtained either from normalization to a well-known thermal cross section or to a low-energy " s a t u r a t e d " resonance with a precision o f 1% in favorable cases. A saturated resonance is one in which the quantity [ ] o f eq. (1) approaches unity, i.e., becomes insensitive to the parameters o f the resonance in question. Since the response o f the detectors can be made very insensitive to changes in the gamma-ray cascade mode, the normalized product e S q , ( t ) can be used to obtain the cross section at any energy for which the flux is known relative to that at the normalization energy. Thus, the ability to obtain accurate time-offlight measurements of the relative neutron and capture gamma-ray intensities from the thermal to the MeV region avoids the difficulties associated with determinations of the detection efficiencies for neutrons and capture g a m m a rays. Since the large liquid scintillator possesses the advantages of higher efficiency and pulse-height discrimination against backgrounds and g a m m a rays from inelastic scattering, this detector was chosen for this facility in preference to the M o x o n - R a e detector. In the following sections we will describe the two flight paths and their associated capture gamma-ray detectors as well as the flux measuring techniques used to cover the approximately eight orders of magnitude in neutron energy spanned by our present capture cross-section measurements.

TABLE l Linear accelerator p e r f o r m a n c e specifications ~'.

Energy range

4-100 MeV

Long pulse mode (0.5-4.5 ltsec) Peak beam current Average beam power

750 mA 35 kW

Short pulse mode Peak beam current

10 A

~' These specifications apply to operation at 16 MW of rf power in each of the four sections, A maximum of 20 MW of rf power/section is available. uncertainties and or the recovery of the detectors from the large pulse due to Bremsstrahlung from the neutron source. The second requirement is due to the need for maintaining reasonably high repetition rates without overlap between neutron bursts. For example, the 14-#sec flight time of a I-MeV neutron over 230 m is more than adequate for detector recovery, but a 0.01-eV neutron requires ~ 140msec which would

~,

2. Flight paths and neutron source To cover such a large neutron-energy range using time-of-flight techniques, one is faced with the conflicting requirements of achieving reasonably long flight times at the highest energies and yet reasonably short flight times at the lowest energies. The first requirement is dictated by considerations of timing

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Fig. I. Linear accelerator and flight-path facilities.

NEUTRON-CAPTURE CROSS SECTIONS FROM 0.01 eV TO 1 MeV limit the burst repetition rate to < 7/sec. This would result in prohibitively low counting rates at such a long flight path. Thus, the use of two flight paths of different lengths vastly improves the utilization of the accelerator, and flight paths of 20 and 230 m were chosen for the present facility. The relative locations of the two flight paths with respect to the linear accelerator are shown in fig. 1, and the performance specifications of the accelerator are listed in table 1. As indicated, the two flight paths join at a point common to the Linac electron-beam path, and this

allows both flight paths to be operated simultaneously if desired. The electron target configuration is shown in fig. 2. The electron beam from the accelerator passes through a 0.003-cm tantalum window and then strikes a watercooled tungsten-alloy target located at the center of a six-inch diameter right circular cylinder of depleted uranium. The Bremsstrahlung produced in the target yields neutrons via the (y, n) process, and these neutrons have a broad energy distribution with median energy of ~ 1 MeV. Since most experiments require more

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low-energy neutrons than are contained in the primary spectrum, some moderation is desirable. Part of this moderation is achieved via inelastic scattering in the uranium, and additional moderation occurs in a 2.5-cm thick slab of polyethylene placed perpendicular to the appropriate flight path. The polyethylene also eliminates structure in the flux shape introduced by the uranium. The uranium drastically attenuates the Bremsstrahlung that escapes from the target, and hence reduces detector recovery times after the Linac burst. Various other target configurations have been investigated (such as shadow cones and off-axis electron targets), and all have been found inferior to the present design in terms of the number of neutrons produced relative to the Bremsstrahlung signal in the detector. The use of uranium as part of the target assembly raises the question of effects due to delayed neutrons resulting from gamma-ray and neutroninduced fission. However, measurements made with a similar target assembly in which the uranium was replaced by lead produced no observable change in the capture yield. The uranium is enclosed in a gas-tight container pressurized to ~ 10 psi with helium. The container contains fission products from the uranium, and the helium conducts the heat generated in the uranium to the container cooling coils. Since the power dissipation may be as high as 35 kW, the cooling is of considerable importance. Water flow rates of 5 gpm and 1 gpm are maintained through the target and container cooling coils, respectively. Both flight paths are evacuated over the majority of their length by mechanical pumps which maintain a pressure < 0.1 torr, and all of the flight-path windows are composed of 0.04-cm mylar. These precautions are taken to avoid the introduction of significant fine structure in the neutron beam which would require neutron flux-shape measurements with better timing resolution and statistical precision than are presently required. It is necessary to use neutron filters in both flight paths to avoid overlap of neutron bursts at the higher repetition rates. The filter used in the 20-m flight path is composed of a 0.20-cm-thick solid slab of very high purity, natural boron nitride. This filter was checked for resonant capture by placing it in the sample position of the 4000-1 scintillator. No such capture was detected, and thus the attenuation over the energy region of interest was assumed to be represented by a (l/v) absorption cross section plus a constantscattering cross section. This assumption was confirmed by a transmission measurement for the filter which

also verified the calculated attenuation. The transmission is 1% at ~ 0.08 eV, which allows the 20-m flight path to be operated with a repetition rate of 180pps for capture samples with relatively low thermal-capture cross sections and at the rate of 120 pps for high-thermal cross section samples. Neutrons of much higher energy must be attenuated for the 230-m flight path, and this requires the use of a much thicker filter. Boron enriched to 93% I°B was available only as a fine powder, thus necessitating the use of either a binder material or a container to form the uniform layer required. Binder materials tend to produce undesirable scattering and attenuation of the neutron beam, and hence an 18-cm-diameter layer of I°B powder, 0.116 atom/barn in thickness, was contained between two 0.02-cm-thick sheets of mylar. One sheet of mylar was stretched and cemented to a 0.25-cm-thick spacer ring, and the boron powder was evenly distributed within the ring. A second sheet of mylar was stretched and vacuum sealed to the top of the ring, and the air between the sheets was evacuated. The air pressure on each side of the filter serves to hold the powder in position during use. Densitometer measurements of a radiograph of the filter indicated a thickness uniformity of + 4 % . This filter transmits 1% of the neutrons at 2.4 eV, which allows a repetition rate of 120 pps for capture samples which do not have a strong resonance at this energy. Somewhat lower repetition rates are used when a resonance exists near this energy.

3. Capture gamma-ray detectors The large liquid scintillators used at this facility were designed to yield a signal representing a large portion of the total gamma-ray energy emitted from neutron capture. A capture event usually results in the emission of several prompt gamma rays with a total energy equal to the neutron separation energy plus the incident neutron kinetic energy. The ideal large scintillator would yield a constant-amplitude signal proportional to this total energy. Practical devices fail to do this for a number of reasons which are described briefly below. 1. Finite size: Since the scintillator cannot be made infinitely large, some of the gamma energy will escape. The statistical nature of this escape process produces a spreading of the total gamma-ray energy peak on the low-energy side. This effect is most important for compound nuclei which decay primarily by emission of a few high-energy gamma rays.

NEUTRON-CAPTURE

CROSS SECTIONS FROM 0.01 e V

2. Gamma absorption: In general there will be absorbing materials between the point of emission of the capture gamma rays and the scintillating liquid. This absorbing material may be the capture sample itself, structural materials or neutron absorbers used to reduce the inscattering effect, as is discussed later. Such absorption produces an effect on the pulse-height distribution similar to the finite-size effect, but this effect is most important for compound nuclei that decay by the emission of a large number of low-energy gamma rays. 3. Geometric effects: The light emission due to the interaction of a single gamma ray in the liquid (usually a Compton-scattering event) is highly localized, and hence there will be a spreading of the capture peak if the fraction of the light collected from all active regions of the scintillator is not constant. It has been shown that significant geometrical nonuniformities can exist in common

TO

1 MeV

481

scintillator configurations1'2), and hence the uniformity of light collection is an important factor in scintillator performance. . Photoelectron statistics: The number of electrons emitted from the photocathodes of the photomultiplier tubes is usually small enough to produce an appreciable statistical broadening of the capture gamma peak. The number of photocathode electrons emitted will depend upon the average light-collection efficiency as well as the photomultiplier quantum efficiency for'converting incident photons into electrons. . Nonlinear summing: The median response of the scintillator to a single gamma ray will not, in general, be equal to that of several simultaneous gamma rays with the same total energy. This is due to the asymmetric nature of the response function that arises from the effects mentioned above. Fortunately this is a relatively small effect for typical capture gamma-ray cascades.

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482

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et al.

Fig. 4. 2400-1 scintillator during construction.

NEUTRON-CAPTURE CROSS SECTIONS FROM 0.01 eV TO 1 MeV Practical large scintillators thus exhibit an asymmetric capture gamma-ray pulse-height distribution, the high-energy portion of which can be accounted for largely on the basis of effects 3 and 4. The slope of the low-energy side of the distribution is due primarily to effects 1 and 2. It is of considerable importance to keep the major portion of the capture gamma-ray peak out of the low gamma-ray energy region in order to avoid large background and to reduce the spectrum fraction corrections as will be discussed in sec. 4. The two large liquid scintillators constructed for this facility have been designed with all of the above effects taken into consideration. Of the commonly used scintillator geometries, the cylinder observed from both ends through light pipes yields good lightcollection efficiency and also good uniformity. Both of the scintillators are composed of modules based on this geometry, and possess essentially the same design features, differing primarily in the number of modules. The larger scintillator, containing 4000 1 of liquid, is located at the 20-m flight path; and the smaller detector, containing 2400 l, is located at the 230flight path. The former scintillator has been described previouslyS), and hence only its over-all features will be mentioned here. The 4000-1 scintillator, shown in fig. 3, is composed of 45 cylindrical plastic containers 198 cm long. The central, 61-cm-diameter cylinder is viewed by 16 photomultiplier tubes and surrounds the evacuated neutron beam pipe which contains the capture sample. The remaining liquid is contained in forty-four, 23-cmdiameter cylinders, which are viewed at each end by a photomultiplier tube through a 23-cm-long light pipe. The scintillator solvent is commercial grade decahydronapthalene (decalin) which was filtered through 1.2-meter-long columns filled with 100 mesh alumina. ,One gram per liter p-terpenyl and 2 g/1 PPO act as the scintillating solute, and 0.05 g/l of dimethyl POPOP was used as a wavelength shifter. After the larger :scintillator was constructed, the light collection from the cylindrical scintillators was investigated, taking into account effects such as the light attenuation of the solution, scattering, imperfect internal and external reflection and absorption in the plastic4). The results of this investigation indicated that the contribution ~Lo the resolution width due to nonuniformities in light collection is ~ _+7%, and that the mean lightcollection efficiency is approximately 20%. These investigations also showed that slightly better perfornlance could be achieved by modification of the wavelength shifter concentration, and thus the 2400liter scintillator was filled with decalin containing 1 g/l

483

p-terphenyl, 0.5 g/1 PPO and 0.03 g/l dimethyl POPOP. Fig. 4 is a photograph of the 2490-1 scintillator under construction. In order to obtain an experimental measure of the effect of the size of the scintillator on the pulse-height distribution, the effective size of the 4000-1 scintillator was varied by turning off successive rings of cylinders. The effect of this size reduction is illustrated for goldcapture gamma rays in fig. 5. The curve labeled "center section + 2 rings" corresponds to the size of the 2400-1 scintillator. It can be seen that only minimal improvements in pulse-height resolution are obtained by going beyond this size. 3.1. ELECTRONICCONFIGURATION CBS No. 7819 and Dumont No. 6364 photomultipliers were used on the 4000-1 scintillator largely for reasons of economy. These tubes have S-11 photocathode response and ~ 11-15% quantum efficiency. The dynode structure is of the box and grid type, which yields a moderate transit-time spread ( ~ 20 nsec) and only fair uniformity of photocathode response

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Fig. 5. i 9 7 A u + n capture g a m m a - r a y pulse-height distributions as the effective size is c h a n g e d by t u r n i n g off the high voltage to the outer rings of logs. Curve C corresponds to the size o f the 2400-1 scintillator.

484

s.J. FRIESENHAHN et al.

( + 30%). EMI No. 9530 photomultiplier tubes selected for highest quantum efficiency were used on the 2400-1 detector. These tubes have a venetian-blind dynode structure which exhibits excellent uniformity (_+ 10%) and high quantum efficiency ( ~ 25%) at the sacrifice of a somewhat greater transit-time spread ( ~ 44 nsec). This type of structure has the added advantage of being relatively insensitive to after pulsing, which is quite important in achieving rapid recovery after the Bremsstrahlung burst from the neutron source. The anodes of the photomultiplier tubes are summed on closed loops of RG62U coaxial cable in such fashion as to form separate signals from four quadrants of the scintillator defined by vertical planes perpendicular and parallel to the neutron beam. Each of these four signals is fed to a two-stage grounded-base transistorterminating amplifier which provides a characteristic impedance termination for the coaxial cable ( ~ 93 Q) and ~ 1 M(~ output impedance. A typical electronic configuration used for recording capture events is illustrated in fig. 6. It will be noted in the figure that the outputs of the terminating amplifiers are connected in two pairs to form signals corresponding to events in either of the two optically isolated halves of the scintillator. Each of these signals passes

~DISCRIMINATOR II

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through a preamplifier and a linear amplifier with 0.25-/~sec shaping time constants. The output is fed to a discriminator set to accept events above a pulse height corresponding to 1 MeV. The two amplifier outputs are also summed and sent to two zero-crossover differential discriminators set to accept events in the 3.5 to 10 MeV and 4.5 to 10 MeV energy intervals, respectively. A third acceptance condition is established by demanding an 0.080-/~sec coincidence between the two I-MeV discriminators and the 3.5 to 10 MeV discriminator. This coincidence mode results in an order of magnitude improvement in the signal-to-background ratio, since capture usually results in multi-gamma-ray cascades and most backgrounds are single gamma events.

4. Background and efficiency corrections In general three types of backgrounds are of importance in capture measurements for non fissionable nuclei. We shall describe briefly the methods used to assess each one. 1. Ambient: The steady-state background due to cosmic rays and radioactivity in structural materials typically varies from 500 to 20 000 counts/sec depending on bias conditions.

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DETEC?OHRLUNG

NEUTRON-CAPTURE CROSS SECTIONS FROM 0.01 eV TO 1 MeV This counting rate is measured both by observing the count rate with the accelerator off and by using passive, 50-/~sec delay lines to allow observation of the count rate immediately prior to the accelerator burst. 2. Machine (sample out): The background observed with the sample removed and with the accelerator on represents events due to imperfect collimation of the neutron beam and accelerator-produced g a m m a rays which penetrate the scintillator shielding. Since the background is small, and only slightly affected by the sample attenuation of the neutron beam, it can be satisfactorily measured by observing the net capture rate with the sample out. 3. Inscattered neutrons: The background due to the detection of sample-scattered neutrons is usually the most difficult to assess precisely. Samples of carbon or lead are used to simulate the inscattering effect, since their average capture cross sections are small. The energy dependence of the scattering cross section of these materials will not in general be identical to that of the scattering cross section of the capture sample, which introduces an unavoidable error in the correction. The majority of the inscattered neutrons slow to thermal energy before being detected. This requires about 10/~sec in a scintillator containing 10% methyl borate and 170/~sec in an unpoisoned scintillator. This time delay is approximately compensated by choice of the scattering cross section ratio used for normalizing the inscattering effect at an energy corresponding to the flight time less than the time delay. An additional source of error is the energy loss suffered by the neutron when it scatters from the sample. Since carbon and lead represent the extremes of the mass range encountered in capture measurements, the comparison of the normalized inscattering of carbon versus lead yields a measure of the energy-loss effect. The carbon typically yields a 20% smaller inscattering effect in the 2400-1 detector, but this may be due in part to the relative cross-section uncertainties. An over-all uncertainty of ~ 30% is typically assigned to the inscattering correction. The magnitude of the inscattered neutron background is reduced by the addition of trimethyl borate to the c e n t r a l - scintillator and also by the use of liners around the capturing sample made of I°B (at 20 m) or 6LiH (at 230 m). The use of the coincidence mode of operation typically produces an additional factor o f t e n improvement in the signal/scattered-neutron background.

485

At the upper end of the neutron-energy region of interest the kinetic energy of the incident neutron is an appreciable lYaction of the neutron separation energy of the compound nucleus. Consequently the data must be corrected for the change in detection efficiency due to the increase in the fraction of the gamma-ray energy observed above the electronic bias. We make the simplifying assumption that the kinetic energy contribut ed by the neutron produces a linear stretching of the pulse-height distribution. This is a satisfactory assumption below 1 MeV since this energy is still a small fraction of the neutron separation energy for most nuclei. Thus the pulse-height distribution measured at low energies f(E~) is replaced by the distribution f[E~B,/(B,+E,)] where E~ is the gamma-ray energy and B, is the neutron separation energy. In the case of coincidence data an additional correction is made for the change in the coincidence efficiency due to the linear stretching of the pulse-height distribution 9(Er) as observed in either of the two identical coincidence channels. The coincidence efficiency varies as the square of the biasing efficiency in either channel as calculated from the stretched single-channel distribution 9 [E~B,/(B, + E,)]. The capture data acquired under each of the three biasing conditions have different sensitivities to both background-subtraction errors and gamma-spectrum fraction changes. Thus a powerful check on the validity of the three capture data sets, after the above corrections have been applied, is a comparison of the neutron-energy dependence of the capture yield. Such comparisons are routinely made before the data are reduced to cross-section values. 5. Neutron flux measurements

5.1.

NEUTRON DETECTOR DESIGN CONSIDERATIONS

The ideal device for a time-of-flight flux measurement would have unit probability for the absorption of the incident neutron and yield a prompt output signal. Unfortunately, absorption cross sections tend to become small compared to scattering at high energies, and hence any attempt to construct a high-efficiency detector based on absorption reactions results in a poor time response due to the scattering of neutrons before absorption. Many detection devices have been constructed exhibiting various degrees of compromise between efficiency and timing uncertainty, but none of these devices have proved to be suitable for precision flux measurements. Excellent timing properties can be achieved using a variety of reactions in low-efficiency

486

s.J.

FRIESENHAHN

detectors. Since the energy dependence of the efficiency of such a detector is directly related to the cross section involved, it is imperative that this cross section be well known. A reaction with a large positive Q value is desirable since the contribution to the total energy deposition due to the kinetic energy of the incident neutron will tend to have less effect upon the detection efficiency. The l°B(n, c07Li,3He(n,p)T and the 6Li(n,c0T reactions are the best prospects for the low and intermediate energy region. All of these absorption cross sections can be obtained accurately by analysis of slab or sphere transmission measurements or by targetactivation techniques since the corresponding total cross sections vary slowly with neutron energy. The 6Li(n,~)T cross section is the smallest of the three, and lithium is rather difficult to introduce into a suitable detector; thus its use in a precision fluxmeasuring device has been somewhat limited. The aHe(n,p)T reaction can be easily implemented using gas proportional counters, but no direct measurements of this reaction in the kV region existed until the recent measurements of Costello et al. s) and Lopez et al. 6) performed at this facility. In the former measurement the aHe(n,p)T cross section was related to the 3He total cross section between 300 keV and 1.16 MeV by analysis of two parameter time of flight versus pulse-height data for aHe(n,p)T and aHe recoil events observed in a 3He proportional counter. In the latter measurement the ratio of the 3He(n,p)T cross section to the ~°B(n, :07Li cross section was measured between 70 eV and 100 keV using proportional counters. These measurements established the aHe(n,p)T cross section with a precision of ~ + 5 % up to 1 MeV. This represented an appreciable improvement over the precision of previous values obtained in this energy region. The l°B(n,~)VLi reaction has been studied using several techniques, and the consensus is that the total (n,c0-reaction cross section varies as 1/t~ up to at least 100 keV within _+5%. This assumption has been substantiated by measurements of the l°B(n,~)TLi cross section relative to the hydrogen-scattering cross section at this facility6), and by a measurement relative to 6Li(n,c~)T by Sowerby et al.7). Since this cross section has the smallest uncertainty, it has been chosen as the standard cross section for flux measurements at this facility below 100 keV. Detectors based on the observation of hydrogen recoils, though difficult to implement due to the zero Q value, retain the distinct advantage of having a

et al.

response that can be related to the extremely wellknown hydrogen-scattering cross section. Hydrogen recoils may be observed above ~ 100 keV using an organic scintillator, However, the low sensitivity to gamma rays and the more linear response of the hydrogen-filled proportional counter make it the better choice in situations where the much slower time response of the proportional counter can be tolerated. Gas mixtures or hydrogen compounds may be used to limit the range of the recoil protons to a small fraction of the counter dimensions, thus reducing the corrections required for wall and end effects. Methane (CH4) is an attractive proportional-counter filling gas for flux measurements above 100 keV since it combines a relatively fast response with acceptable proton range. The elimination of carbon recoils requires a nonzero bias, and hence an extrapolation must be made to determine the counting efficiency. The distribution of recoiling protons is rectangular with a leading edge corresponding to the incident neutron energy. The distribution of observed events deviates from the proton recoil distribution due to wall and end effects, and to the energy dependence of the protonenergy loss per ion pair (W). The wall and end effects are usually small below 1 MeV and can be satisfactorily calculated using published range-energy measurements. The energy dependence of W has been measured by Allen and Ferguson 8) and by Rogersg). Since this quantity may be a function of impurities and mode of operation, it is preferable to determine the dependence from observations of the leading edges of the distributions versus incident neutron energy. Since each distribution contains events extending to zero energy, it is desirable to extend the leading edge observations to as low an energy as possible. The data of Rogers were obtained using monoenergetic neutron beams and extends down to ~ 2 keV. It is thus necessary to extrapolate to zero energy in the calculation of the response function. The uncertainty in this extrapolation is not a serious source of error in biasing efficiency calculations for neutron energies > 80 keV. Determinations of W from analysis of time-of-flight versus pulse-height data obtained at this facility down to 30 keV indicate good agreement with the results of Rogers: the largest deviation amounting to ~ 2.6% occurs near 100 keV. Rogers' results have been used in our response-function calculations. The methane ionpair defect as observed by Rogers and at this facility is illustrated in fig. 7. The number of ion pairs/eV for carbon recoils is substantially smaller than the value corresponding to protons of the same energy. Allen and Ferguson 8)

NEUTRON-CAPTURE

C R O S S S E C T I O N S F R O M 0.01 e V TO

The pulse height of a practical porportional counter will depend upon the location of the interaction in the counter due to nonuniformities in the central wire and to fringing effects in the electric field. Since it is customary to add a small percentage of nitrogen to the counter to allow a preliminary energy calibration using the 14N(n,p)~4C reaction, it is possible to obtain a measure of this nonuniformity by observation of the width of the peak observed for uniform illumination with thermal neutrons. This width, when corrected for wall and end effects, is used as one of the contributions to the resolution function in the calculations of the response functions. The other contributions are the electronic noise which can be measured with a mercury pulser, and the width of the neutron-energy interval used in obtaining the pulse-height distribution. All of these resolution-width contributions along with the dependence of W on proton energy have been included in the calculated response functions discussed in the next section. Since the neutron-energy bin width is always chosen larger than the energy uncertainty clue to time jitter in the counter, it was not necessary to include timing uncertainty in the resolution width.

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5.2. IMPLEMENTATIONOF FLUX MEASUREMENTS We will now describe the techniques used to obtain the energy dependence of the neutron flux (flux shape) at each of the two flight paths. In both cases a lowerenergy flux shape overlaps a higher-energy flux shape which allows a composite flux shape to be formed via normalization.

fbund a value of 0.6 for the carbon/proton ion pair/eV ratio, however our data indicate a ratio ~ 0.7. This latter effect is of little consequence unless the bias is c.hosen low enough to include substantial number of carbon recoils, a condition which is easily avoided.

I

1 MeV

5.2.1. Flux shape at 20 m In the neutron-energy region from 0.01 eV to 1 eV the observation of the capture rate in a thin gold foil using the 20-m flight path is the most convenient method of flux measurement since excellent counting rates and signal-to-background ratios are easily achieved. A previous measurement 1°) in which the flux determination was based on the observation of the 470-keV gamma rays from a thick ~°B4C slab confirmed that the gold-resonance parameters yield a correct representation of the low-energy gold-capture cross section when a l/v contribution is added to obtain the recommended thermal cross section. Small corrections are applied to the observed gold counting rate for self-shielding and multiple scattering to obtain a flux shape with a precision of ~ 2% in this energy region. Either a thin 3He- or a thin ~°BF3-gas proportional counter is used to extend the flux-shape measurements from 1 eV to ~ 20 keV. As pointed out earlier the

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488

s . J . FRIESENHAHN et al.

3He(n,p)T cross section is known to a precision of a few percent in this energy region. The cross section is calculated from the formula developed by Schmidt ~l), cr(n,p)E~ =

847.3_+ 1.6 6 ' 1 + 1 4 . 6 x 1 0 - 4 E ~ + 3 . 8 x 10- E .

5.2.2. F l u x shape at 230 m During the 3He(n,p)T cross-section measurements described in sec. 4 a pair of 3He-filled proportional counters were calibrated using the ~°B(n,~)VLi cross section, thus allowing these counters to serve as flux-shape standards below 100 keV as well as fluxshape and intensity monitors during capture measurements at the 230-m flight path. The 10-atm filing pressure of the 2.54-cm diameter 3He counter produces a good counting rate in a volume small enough to allow the perimeter of the neutron beam to be observed without interfering with the central part of the beam used for capture measurements. Fig. 8 illustrates the relative positions of the proportional counters with respect to the 2400-1 scintillator.

(2)

where E, is the incident neutron energy in eV. The l°B(n, c07Li cross section is assumed to be l / r in this energy region, and the agreement between measurements of the energy dependence of the neutron flux using these two detectors and the cross sections just described is excellent. The electron-drift velocity in BF3 is much lower than that in 3He, and hence proportional counters with the latter filling recover from the Linac Bremsstrahlung burst more rapidly and thus allow measurements to somewhat higher energies. In order to reduce statistical uncertainties, the measured flux shape is fitted to an expression of the form: ~p(t)

=

k[e.(t)] ~ ,

Above 100 keV the uncertainties in the ~°B(n,~)TLi cross section and the large time jitter of the ~°BF3 proportional counters preclude the use of ~°BF3-filled proportional counters. As pointed out earlier, the hydrogen-scattering cross section is very well known, and hence a methane (CH4)-filled proportional counter was used in this energy region. The construction of the counter is essentially the same as that of the ~°BF3 counters. The counter specifications are listed in table 2. As noted in the table, the counter contains a small admixture of nitrogen which allows the approximate energy scale of the counter to be established via the [4N(n,p)14C reaction with thermal neutrons. The effective active length of the counter was experimentally determined to be 61.8-+0.6cm using a collimated SVCo source to scan an identical xenonfilled counter. A 0.203-cm alumina disk forms the entry end of the counter, and thus end-window transmission corrections are small at most neutron energies and can be made

(3)

where k is a normalization constant, E, the neutron kinetic energy, and c~is the fit parameter which depends upon the neutron-source configuration and is approximately c~= 0.57 for the moderator-target geometry of fig. 1. Without a filter to remove low-energy neutrons, repetition rates are limited to ~ 20 pps. If only the data above 1 eV are of interest, a 0.20-cm boron nitride filter is inserted in the beam to allow repetition rates of up to 180 pps. When the BN filter is used the flux shape is fitted to an expression of the form: q)(t) = k [E,,(t)] ~ exp(/~E~- 'q.

(4)

Both c~ and/7 are treated as variables, but the fit yields values of c~ in good agreement with those obtained for the unfiltered flux [eq. (3)]. The values of/3 agree with those calculated from the parameters of the filter.

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NEUTRON-CAPTURE CROSS SECTIONS FROM 0.01 eV TO 1 MeV TABLE 2 Methane-gas counter specifications.

Cathode: Anode: End window: Connector: Gas filling:

2.00±0.01-in. (5.08 ±0.025-cm) o.d., 304 S.S., 0.036-in. (0.0914-cm) wall 0.002-in. (0.005-cm) diam. tungsten 0.080-in. (0.203-cm) thick aluminiumoxide ceramic (A1,903) HN, magnesium with A1203 insulator Total pressure = 31.20 ±0.16 psia Constituents by volume (%) Nitrogen 5.0:~0.2 Methane 94.0±0.2 Oxygen 0.0012 Carbon dioxide 0.0010 Argon 0.0032

Measured active length of counter:

61.8 -[-0.6 cm)

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see text

deadtime effects, transmission of the alumina end window, self-shielding, and the residual energy dependence of the detection efficiency. This efficiency calculation is performed with a modified version of the computer code WEND12). A few examples of pulseheight distributions obtained by sorting the data with 10% neutron energy bin widths are compared to the calculated response functions in fig. 9. All of the resolution-width contributions and the dependence of W on the proton energy have been included in the calculations and normalized in the region from 0.4 to 0.6 E,. After the above corrections are applied, the time-offlight data are divided by the hydrogen cross section

% °

with confidence. The largest transmission correction is 22 -t- 2% which occurs at the 434-keV oxygen resonance. Throughout the majority of the energy region studied, the absolute detection efficiency can be calculated with a precision of ~ _+4% when uncertainties in gas composition and filling pressure as well as counter misalignment and wall scattering are considered. However, since the product eSk ofeq. (1) is normalized independently using the capture data, only the relative efficiency is required for a capture measurement. The proton recoil data are accumulated in twoparameter form using a CDC-1700 computer equipped with a disk drive. The neutron flight time and the proton recoil pulse height are stored as pairs of binary numbers on a magnetic disk. A subsequent sorting operation into 10% AE,/E, energy bins allows an accurate proton recoil energy scale to be established from the leading edges of the proton recoil distributions. A time-of-flight spectrum is then formed by selecting the time-of-flight data for which the proton recoil pulse height is > 0.3 En. In this way, carbon and nitrogen recoil events are rejected. The fast neutron contribution to the background of methane-filled counter is negligible. The chief background contribution arises from detection of Comptonscattered electrons produced by the ambient gammaray background. This background is small, and can be obtained by observing the events at very long flight times when no high-energy neutrons are present. The sorted time-of-flight data are corrected for

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490

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recommended by Gamme113) to obtain the flux shape above 80 keV. As mentioned previously, the 3He flux-shape monitors were calibrated during the 3He and I°B crosssection measurements. Thus the flux shape below 100 keV is obtained directly from the 3He data by use of the calibration function after subtraction of a background typically equal to 5% of the foreground. These two flux shapes are normalized in the 80 to 100 keV region to obtain a composite flux shape extending from ~ 10 eV to 1 MeV (see fig. 10). 5.2.3. Capture yield normalization The composite flux shape is normalized either to the area of a resonance with known parameters or to the area contained within an energy region measured with the 20-m flight path. If the latter alternative is chosen the flux normalization can be referred to a saturated resonance or known thermal cross section as described in the introduction. In either case the effects of multiple scattering at the calibration point are calculated with the Monte Carlo code TACAS114).

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The effect of the resolution function and transmission are included in the saturated resonance calibrations and the self-shielding of the sample in thermal energy calibrations. It should be noted here that when the capture sample is thick enough to produce large attenuation of the gamma rays a second order effect can appear that will introduce a detection efficiency which is a function of both the capture and total cross sections. This second order effect results from the fact that the mean attenuation of gamma rays produced at the surface of the sample is smaller than that of those produced at the center. Thus the detection efficiency will be larger in high cross-section regions such as in the saturated resonances. The magnitude of this effect can be obtained by careful shape analysis of low-energy saturated resonances or by obtaining several saturated resonance flux calibrations in the same material using various sample thicknesses. When capture cross-section information is obtained using thick samples it is also necessary to correct for the attenuation of the neutron beam in the sample and

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NEUTRON-CAPTURE

C R O S S S E C T I O N S F R O M 0.01 e V TO 1 M e V

for multiple scattering and self-shielding effects. In the very low energy region the resolution width is very small compared to the cross-section structure except near the resonance peaks, and hence the neutron-beam attenuation and multiple scattering calculations can be performed by iteration using only the total cross section as an input parameter. At very high energies the Doppler-broadened resonance widths will exceed the resonance spacing, thus producing a smooth microscopic cross section and allowing the very low e,nergy techniques to be applied. In the intermediate e,nergy region, the resonance structure will produce attenuation and multiple-scattering effects dependent upon the average resonance parameters of the material. Corrections in this case can be obtained using Monte

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Carlo resonance sampling techniques ~6) provided that average resonance parameters are known and the resolution function is broad enough to include a statistically significant sample of resonances. With the exception of measurements on monoisotopic materials, capture will occur in more than one isotope. In such cases, it is necessary to obtain the detector efficiency for capture in each of the isotopes and the capture cross section of the contaminant isotopes. This is best achieved by a set of measurements in which samples enriched in each of the isotopes are used to obtain a capture probability matrix which can be solved for the capture cross section of each of the isotopes via iterationS°). An illustration of gold-capture data from I eV to

,

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492

s . J . FRIESENHAHN et al.

l MeV obtained with both flight paths is contained in fig. 11. In this case the 4.906-eV saturated resonance was used to normalize the yield measured with the 20-m flight path. The yield measured with the 230-m flight path was then normalized to the 20-m result in the 2 to 8 keV region. To date the radiative capture cross sections of eight elements have been measured at this facility from 1 keV to 1 MeV using this technique. For details of these measurements see ref. 15.

proton-recoil measurements could reduce the uncertainty in the flux shape to ~ 2%. Further study of the response of the large liquid scintillators to the gamma spectra produced by neutrons with energies on the order of the compound nucleus excitation energy would allow the energy range of the capture cross-section measurements to be extended above 1 MeV with precision comparable to that achieved at lower energies.

6. Conclusions

The apparatus and techniques described here allow the measurement of the energy dependence of the neutron flux by time-of-flight methods from 0.01 eV to 1 MeV with uncertainties of < 4%. Capture measurements over the same energy span can then be normalized to known thermal cross sections or saturated resonances, thus avoiding the difficulties associated with determinations of absolute detector efficiencies. In most cases the over-all uncertainties in the absolute capture cross sections determined at this facility are ~< 10% over the full neutron-energy region. The practical necessity of using thick capture samples in some cases requires reasonably accurate resonance parameters for calculations of resonance self-shielding and multiple scattering in the intermediate energy region. In many cases these parameters are poorly known, particularly for isotopes with a relatively large level spacing. Further measurements of these resonance parameters spanning an energy region sufficient to include a statistically significant number of resonances would be of great value not only in the interpretation of average cross-section measurements, but also in the calculation of neutron interactions in bulk media. Further improvements in the precision of the standard cross sections used for flux measurements and in the response functions of gas counters used for

References 1) W. A. Shurcliff and R. Clark Jones, J. Opt. Soc. Am. 39, no. 11 (1959) 912. 2) D. Brini, L. Peli, A. Rimondi and P. Veronesi, Nuovo Cimento 10, no. 2, suppl, no. 4 (1955) 1048. 3) E. Haddad, R. B. Walton, S. J. Friesenhahn and W. M. Lopez, Nucl. Instr. and Meth. 31 (1964) 125. 4) S. J. Friesenhahn, Rev. Sci. Instr., to be published. 5) D. G. Costello, S. J. Friesenhahn and W. M. Lopez, Nucl. Sci. Eng. 39, no. 3 (1970) 409. ~) W. M. Lopez, M. P. Fricke, D. G. Costello and S. J. Friesenhahn, unpublished data. 7) M. G. Sowerby, B. H. Polrick, C. A. Uttley and K. M. Diment, A E R E - R 6316 (1970). 8) W. D. Allen and A. T. G. Ferguson, A E R E N P / R 1720 (1955). 9) j. W. Rogers, Nucl. Instr. and Meth. 80 (1970) 313. 10) S. J. Friesenhahn, E. Haddad, F. H. Frohner and W. M. Lopez, Nucl. Sci. Eng. 26 (1966) 487. ll) j. j. Schmidt, K F K 120/11 (1965). 12) j. B. Parker et al., Nucl. Instr. and Meth. 23 (1963) 61. 13) j. L. Gammel, Fast neutronphysies, part II (eds. J. B. Marion and J. L. Fowler; lnterscience Publ., Inc., New York, 1963) p. 2185. 14) F. H. Frohner, Gulf Energy & Environmental Systems, inc. Report GA-6906, unpublished. 15) M. P. Fricke, W. M. Lopez, S. J. Friesenhahn, A. D. Carlson and D. G. Costello, I A E A 2nd Intern. Conf. Nuclear data ['or reactors, Paper CN-26/43 (Helsinki, Finland, June 15-19, 1970). 16) F. H. Frohner, Gulf Energy & Environmental Systems, Inc. Report GA-8380, unpublished.