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Prompt neutrons from fission
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Nuclear Physics 4 8 (1963) 4 3 3 - - 4 4 2 ; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
PROMPT NEUTRONS FROM FISSION J. C. H O P K I N S a n d B. C. D I V E N
Los Alamos Scientific Laboratory of the University of California Los Alamos, New Mexico t Received 11 J u n e 1963 Abstract: A n absolute m e a s u r e m e n t of~, the average n u m b e r o f n e u t r o n s emitted per fission, h a s been m a d e for t h e s p o n t a n e o u s fission o f C f ~62. T h i s n u m b e r is 3.7714-0.031 p r o m p t n e u t r o n s per fission. M e a s u r e m e n t s o f ~ for t h e s p o n t a n e o u s fission o f P u u ° a n d for n e u t r o n induced fission o f U ~a3, U ~ss a n d P u an9 have been m a d e relative to t h e s p o n t a n e o u s fission ~ o f C f 258. Several incident n e u t r o n energies between zero a n d 14.5 M e V were used. A universal ~ versus incident n e u t r o n energy curve for U 2as, U 2a6 a n d P u 2s9 was c o n s t r u c t e d by a d d i n g a c o n s t a n t energy to t h e incident n e u t r o n energy for each nucleide. T h e c o n s t a n t s for U ~sa, U n6 a n d P u m were 0.46 MeV, 0 M e V a n d 3.3 MeV, respectively. T h e d a t a c a n be fitted with two straight lines o f slopes 0.085 n e u t r o n s per M e V u p to a b o u t 1.6 M e V a n d 0.16 n e u t r o n s per M e V above 1.6 MeV. A t t h e r m a l energy the ~ value is 2.412 p r o m p t n e u t r o n s per fission.
1. Introduction An absolute measurement of ~, the average number of prompt neutrons emitted per fission, has been made for the spontaneous fission of Cf 252. Measurements of for the spontaneous fission of Pu 24° and for neutron induced fission of U 2an, U 2a5 a n d Pu 239 were made relative to the spontaneous fission ~ of Cf 252. Several incident neutron energies between thermal energies and 14.5 MeV have been used. Two absolute measurements of ~ for the spontaneous fission of C f 252 have been reported recently 1, 2). Asplund et al. used a large cadmium-loaded scintillator as a 4~ detector to count the neutrons emitted in fission. The efficiency of their liquid scintillator was determined with a neutron scattering experiment. This procedure yielded a ~ of 3.80___0.03 p r o m p t neutrons per fission. Moat et al. also used a large liquid scintillator. The efficiency of their scintillator was determined with the use of a calibrated Pu 24° source. After correction for the difference in the neutron spectra, they obtained a ~ value of 3.77___0.07 prompt neutrons per fission. In the present experiment we used a large cadmium-loaded liquid scintillator to detect the neutrons. The efficiency was determined by scattering neutrons from protons in an N E 102 plastic scintillator. We obtained a value of 3.77_ 0.03 p r o m p t neutrons per fission. The weighted average of these three results is 3.784___0.020. The ~-values for neutron-induced fission of U 23a, U 2 a s and Pu 2a9 were determined by measuring a ratio of ~ for the nucleide of interest to ~ for the spontaneous fission t W o r k p e r f o r m e d u n d e r the auspices o f the U.S. A t o m i c Energy C o m m i s s i o n . 433
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of Cf 252. The remainder of this article will be devoted to an elaboration of the experimental considerations of the absolute measurement and to a discussion of the results of the relative measurements.
2. A b s o l u t e
Measurement
A 1.0 m-diameter by 1.0 m long liquid scintillator, shown infig, l, was used as a ~-ray and neutron detector. The C f 252 sample was placed in a fission counter that was inserted into the centre of the liquid scintillator. The scintillator is large enough to cause most of the fission neutrons to be thermalized and finally captured by the cadmium in the scintillation solution. Neutron capture in the cadmium results in
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Fig. 1. End view and cross section of the scintillator, neutron source, and shielding. A collimated beam of neutrons is passed through the sample at the Centre of the scintillator. about 9 MeV of ~ radiation which is detected with a high efficiency by the scintillating liquid. The cadmium concentration is adjusted so that the mean ]ife of neutrons in the scintillator is long compared to the resolving time of the electronics. A pulse in the fission counter is used to open an electronic gate which is long compared to the mean life of a neutron in the liquid scintillator. The number of pulses which occur in the scintillator during the gate is determined and recorded for each fission event. In this way the fission neutrons are counted individually. The most conspicuous problem associated with any absolute ~ measurement is the determination of the efficiency of the neutron detector. A Monte Carlo calculation of neutron leakage for a 76 em liquid scintillator was modified for the 1.0 m scintillator and the results checked experimentally for one neutron energy and angle. The experimental method involved the n-p scattering technique originally developed
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by Diven et aL 3) at Los Alamos. A 3.8 cm diameter by 0.6 cm thick plastic scintillator (NE 102), mounted on a 6810A photomultiplier tube, was inserted into the axial opening of the liquid scintillator. The plastic scintillator was at the centre of the large liquid scintillator. A beam of 3.9 MeV neutrons from the D(d, n)He 3 reaction or 14.5 MeV neutrons from the T(d, n)He 4 reaction was directed through the tube along the liquid scintillator axis and into the plastic scintillator. The proton recoil spectrum from the plastic scintillator is approximately flat out to the maximum energy of the neutrons and then falls to zero rapidly. A differential discriminator was used to select a proton energy band and consequently a scattered neutron energy band and scattered neutron angle. Using the T(d, n)He 4 reaction, two neutron energy bands were selected: 0-2 MeV and 6-8 MeV. The proton recoil counter pulses were used to open an electronic gate associated with the large liquid scintillator. The circuitry, described by Diven and Hopkins 4) and Diven et aL 5) yields the number of proton recoil pulses followed by zero, one, two, etc., pulses from the liquid scintillator during the 64-/zsec gate. Three separate determinations of the number of pulses in a gating interval can be made in cyclic order: (I) for gates opened for low energy scattered neutrons, (2) for gates opened for high energy scattered neutrons, and (3) for background gates. The background gate is opened several milliseconds after one of the scattered neutron gates. The background gate is considered to be opened at random since the mean life of neutrons in the liquid scintillator is about 20 #sec. Background runs were also made with helium in the target. Let Co be the fraction of proton recoil pulses not followed by any liquid scintillator pulse, after correction for background. The fraction Co is related to the leakage and efficiency by the expression 1 - Co = e ( 1 - L ) . The leakage L is the fraction of neutrons that escape from the large liquid scintillator. The fraction of neutrons that do not emerge from the liquid scintillator and are observed is (1 - L ) times e, where e is defined as the efficiency for detection of neutrons that are captured in the scintillator. For 0 to 2 MeV neutrons the leakage was estimated at 0.5%. From this estimate and the measured C O the efficiency was found to be about 94 %. This efficiency and the measured Co for neutrons in the 6 to 8 MeV energy range yielded a leakage of about 6 %. This is the leakage for neutrons in the 6 to 8 MeV energy range entering the liquid scintillator at 45 ° in the laboratory system. Monte Carlo calculations for leakage are available for a 76 cm long by 76 cm diameter liquid scintillator. These calculations provided the leakage at various energies as a function of neutron angle. We applied these calculations to the present problem by assuming that as the liquid scintillator is increased in size the number o f mean free paths is increased proportionately, or, conversely, the number of mean free paths remains fixed and the neutron energy scale is expanded. This is tantamount to assuming that the n-p scattering cross section is linear on a log a, the cross section, versus log energy curve. The neutron leakage from the liquid scintillator is almost entirely out of the axial openings. This provides a fiat leakage versus angle relationship for all neutrons emitted at angles greater than about 15° to the scintillator
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axis. From these data the leakage as a function of neutron energy for an isotropic neutron source was obtained. The neutron spectrum from the spontaneous fission of Cf 252 reported by Bonner 6) was multiplied by the neutron leakage and integrated from 0 to 10 MeV. The procedure for Cf 252 fission neutrons resulted in a calculated leakage of 1 . 6 7 % . The effective efficiency is defined as 1 - C o. The leakage is a constant for a given neutron spectrum, but e, which depends u p o n the electronic adjustments, must be determined for each set of runs. The Cf 252 was inserted into the large liquid scintillator in the form of a Cf 252 fission counter. A pulse from the fission counter in coincidence with a fission y-ray pulse from the liquid scintillator indicated that a fission took place, and an electronic gate was opened between the large liquid scintillator and the circuit that determined how many liquid scintillator pulses occurred during the gate. Series of runs were made with the Cf 2s 2 fission counter and the proton recoil counter alternately placed in the centre of the large liquid scintillator. The D(d, n)He 3 reaction was used during the runs with the proton recoil counter. The incident neutron energy was 3.9 MeV, and the scattered neutron energy ranged from 0 to 1.3 MeV. The neutron leakage for the p r o t o n recoil counter runs was about 0.4 %. With the 1.67 % leakage for the C f 252 fission neutrons, the effective efficiency for C f 252 neutrons was about 86 %. The data consisting of the number of pulses following a gating pulse and the appropriate background measurements were analysed on an IBM 7090 computer for the emission probabilities, for r~, and for the standard deviations. The purpose of calculating the emission probabilities for the proton recoil runs is to test the operation of the equipment. For example, any tendency of the photomultiplier tubes to emit double pulses would show up dearly. The Cf 252 data had to be corrected for the possible pile-up of two or more neutron pulses in a gate. This correction was explained in a previous report a) on multiplicities of fission neutrons. The pile-up correction required a knowledge of the resolving time of the electronics. This turned out to be the limiting factor in accuracy. The pile-up correction was about 1% of ~ and contributed about 0.6 % uncertainty to ~. The total uncertainty, or standard deviation, is due to the statistical uncertainty in the proton recoil runs, to the uncertainty in the leakage, to the pile-up correction, and to the statistical uncertainty in the Cf 2s2 runs. The final answer for ~ of Cf 252 is 3.771 +0.030 prompt neutrons per fission. 3. Relative Measurements
The ~-values for neutron induced fission of U 233, U 235 and PU 239, and for the spontaneous fission of P u 24° were measured relative to ~ for the spontaneous fission of C f 252. Double fission counters were placed in the centre of the large liquid scintillator. One fission counter contained C f 252, and the other contained the sample material. For neutron induced fission a beam of neutrons was directed through the axial tube in the liquid scintillator and into the sample material. Coincident signals from th- fission counter and the liquid scintillator identify fission events and
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open electronics gates between the large liquid scintillator and the counting apparatus. The gates are open for 64/~sec, during which time the pulses from the liquid scintillator are counted. The data appear as the number o f fissions with 0, 1, 2, etc., pulses from the liquid scintillator during the gating interval. The gating pulses are accepted in a lyclic fashion from the Cf 252 counter, from the sample material fission counter, and from a background trigger, as explained in the discussion of the avsolute measurement. With this arrangement the effects of drifts of bias level, gate length, and amplifier gain are minimized since they effect the mean number of pulses per gate from C f 252 in the same way as they effect the sample material. A detailed investigation of the neutron beam quality was made. A gas target of tritium or deuterium was used which gave a neutron energy spread of about 80 keV depending upon the proton or deuteron energy and upon the gas pressure. The neutron energy could be degraded by scattering from the walls of the collimator. This effect was studied in two ways. The first technique was to insert photographic emulsions into the centre of the large liquid scintillator and analyse them for the neutron spectrum down to 1 MeV. Almost no degradation of the neutron energy was found for 4-MeV neutrons, but at 15 MeV the average energy was found to be decreased by about 0.5 MeV. The second technique involved a pulsed beam and time-of flight measurement. A 50 nsec wide beam pulse was directed onto the target at a 1 MHz rate. A fission counter on stilbene scintillator mounted on a 6810A photomultiplier tube was inserted into the center of the large liquid scintillator and exposed to the pulsed beam. The pulses from the fission counter or stilbene scintillator and from a beam pickup were fed into a time-to-pulse-height converter. The spectra from the time-to-pulse-height converter were displayed on a 100-channel pulse-height analyser. An analysis of these data showed that about 4% o f the neutrons at a nominal 14.5 MeV were random, and hence of very low energies. At 4 MeV approximately 9 ~o of the neutrons are of low energies. The uncertainty in the 9 values due to the uncertainty in these corrections is small. Thermal neutrons were obtained by moderating a 400 keV neutron beam with a polyethylene plug in the neutron collimator. The non-thermal contamination was monitored by measuring the cadmium ratio. The cadmium ratio varied between 10 and 20, depending upon the fission counter material. For the runs with thermal neutrons the non-thermal contribution was subtracted. The data were analysed on an IBM 7090 computer for 9, the neutron emission probabilities, and for the standard deviations due to statistical fluctuations and uncertainties in the pile-up corrections. A chi-square analysis was performed on the emission probabilities to verify consistency. An analysis o f the standard deviations is complicated by the fact that there are systematic uncertainties that influence all of the relative measurements. These consist o f the uncertainties in pile-up correction, in the absolute ~ of C f 25 z, and in the amount of thermal neutron contamination o f the neutron beam. The independent errors consist of statistical fluctuations in the individual runs.
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O n l y very small samples o f fissionable m a t e r i a l were tolerable because o f the pile-up o f ~-particle pulses. This results in a negligible c o r r e c t i o n to ~ due to fission induced by fission neutrons. TABLE 1 Prompt neutrons per fission Nucleide
Neutron energy and energy spread (MeV)
Prompt neutrons per fission ~
Total relative error
Total systematic error
u ~sa+ n
thermal 0.2804-0.090 0.4404-0.080 0.9805:0.050 1.084-4-0.05 3.93 4-0.29
2.473 2.489 2.502 2.553 2.510 2.983
0.026 0.033 0.033 0.035 0,030 0,040
0.022 0.023 0.023 0.023 0.023 0.030
U2S~+ n
thermal 0.2804-4-0.090 0.4704-0.080 0.815 4-0.060 1.08 4-0.05 3.93 ±0.29 14,5 4-4-1.0
2.425 2.438 2.456 2.471 2.530 2.937 4.626
0,020 0,022 0.022 0.026 0.026 0.030 0.075
0.022 0.022 0.022 0.022 0.023 0.029 0.066
2.189 2.83 ! 2.93 i 2.957 2.904 3.004 3.422 4.942
0.026 0.028 0.039 0.046 0.041 0.041 0.039 0.119
0.019 0.028 0.029 0.030 0.029 0.030 0.038 0.076
Pu z'° Pu ~9 + n
spontaneous fission thermal 0.250 4- 0.050 0.4204-0.110 0.6104-0,070 0.900 4- 0.080 3.90 i0 . 2 9 14.5 4-1.0
These results are based on ~ for spontaneous fission of Cf uz of 3.771 4-0.000. Absolute measurement of spontaneous fission ~ of Cf u2 yields ~ = 3.771 :~0.030. T a b l e 1 shows the ~-values f o r the three nucleides. T h e s p o n t a n e o u s fission o f P u 24° p r o v i d e d a negative energy p o i n t at - 6 . 3 MeV, f o r the nucleide f o r m e d by the P u 239 + n reaction. T h e energy spread is due to target thickness. T h e total relative e rr o r an d the t o t al systematic errors are shown. T h e total systematic e r r o r is the square r o o t o f the s u m o f the squares o f the i n d i v i d u a l systematic errors. This procedure is sufficiently accurate c o n s i d e r i n g the uncertainties in the s t a n d a r d deviations. All o f the ~-values are based u p o n a ~ o f 3.771 p r o m p t n e u t r o n s per fission for the s p o n t a n e o u s fission o f C f 252.
4. Discussion T h e ~-values vs incident n e u t r o n energy f o r U 235 are p l o t t ed in fig. 2. Th e circles represent o u r m e a s u r e m e n t s a n d the triangles represent the data t a k e n by M a t h e r et al. 7). N o t s h o w n o n this c u r v e are the recent d a t a o f M e a d o w s an d W h a l e n a).
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NEUTRONS
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FROM FISSION
Their data, covering a region from 0 to 1.76 MeV, agree well with the present data. The insert in the upper left corner shows the 0 to 2 MeV region in more detail. The dashed lines are separated by approximately twice the relative error of each point. The data can be represented by two straight lines with a slope of 0.085 neutrons per MeV in the region up to 2 MeV and a slope of 0.160 neutrons per MeV in the region above 2 MeV. I f we use only the present data and a least-squares fit, the standard deviations in the slopes become 0.02 and 0.01, respectively. More complicated functions, such as hyperbolic tangents and various polynomials, can be devised to fit these data, but there is no theoretical motive to do so. / i I
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INCIDENT NEUTRON ENERGY IN MeV Fig. 2. N u m b e r o f p r o m p t neutrons emitted per fission f o r neutron induced fission o f U " s plotted against incident n e u t r o n energy in MeV. T h e circles are the d a t a o f Diven a n d H o p k i n s *), a n d the triangles are the d a t a o f M a t h e r , F i e l d h o u s e a n d M o a t 7). T h e solid line is the so-called " U n i v e r s a l C u r v e " . T h e d a s h e d lines r e p r e s e n t the relative s t a n d a r d deviations.
A first guess of the energy dependence of 9 is a linear relationship with a slope 9) of about one neutron per 7 MeV. Seven MeV is the sum of the binding energy and kinetic energy of an emitted neutron. This pre-supposes that all other terms in an energy-balance expression are independent of incident neutron energy. There is no experimental justification for this assumption. If, for example, the kinetic energy of the fission fragments increased as the incident neutron energy increased, then the slope of f versus energy of the incident neutron would be less than one neutron per 7 MeV. Conversely, if the fragment kinetic energy decreased with increasing incident neutron energy, then the ~ versus incident neutron energy curve would have a higher
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slope. The change in fragment kinetic energy necessary to explain the observed change in slope from 0 to 14 MeV is only about 1 MeV out of a total of about 180 MeV. The experimental data on the fragment kinetic energies show that within an accuracy of perhaps +__3 MeV the kinetic energy is independent of incident neutron energy lo, 11) up to 14 MeV. Recent data by Okolovich et aL 12) indicate that within an accuracy of 0.1% the fragment kinetic energy is the same for thermal neutron induced fission as it is for 5 MeV neutron induced fission. Other sources for a change in slope can be found, but again there is a lack of experimental information for verification. There is no evidence either for or against a discontinuity in ~ versus incident neutron energy at the threshold for second chance fission la). 5.2 _-
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ADJUSTED INCIDENT NEUTRON ENERGY IN MeV
Fig. 3. Number o f prompt neutrons emitted per fission for neutron induced fission of U ~ss (circles) and Pu == (triangles), plotted against the adjusted incident neutron energy. For U us 0.456 M e V is a d d e d to the actual incident n e u t r o n energy, a n d for Pu =s9 3.286 M e V is added. T h e solid line is the so-called " U n i v e r s a l C u r v e . " T h e relative s t a n d a r d d e v i a t i o n s are s h o w n .
An attempt is made to provide a universal ~ versus incident neutron energy curve for the three fissioning even nucleides (U 234, U 236, and Pu 24°) formed by the absorption o f a neutron by U 233, U 235 and P u 239. The shapes of the curves are similar. There are three ways to combine the data into one curve: 1) adjust the energy scales leaving the ~ scale fixed, 2) adjust the ~ scale leaving the energy scale fixed, and 3) adjust the energy scale and the ~ scale simultaneously. The fission barriers o f the three nucleides are different. For this reason it is to be expected that an adjustment of the
PROMPT NEUTRONS FROM FISSION
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energy scales corresponding to the differences in the fission barriers might be necessary. This results in an adjustment o f less than 1 MeV. Fission of the three nucleides results in three different mass distributions. The difference in the mass distribution can be related to differences in the average number of neutrons emitted. This difference would be approximately 0.08 neutrons per mass unit t4). For example, the difference between U 23s and P u 239 ~-values for thermal neutron induced fission would be expected to be about 0.32 neutrons per fission. This is approximately what is observed. I f only the energy scale is varied, the shift is much greater than c a n b e explained by just the differences in barrier height. It is reasonable to suppose that some combination of ~ scale shift and energy scale shift would be necessary, but there are no theoretical guide lines. Fig. 3 shows the U 233 and P u 239 V data plotted as a function o f the adjusted incident neutron energy. A constant 3.286 MeV has been added to the energy scale of the PU 239 data and a constant 0.456 MeV to the energy scale of the U 2a3 data. The energy shifts were found by making a least-squares fit to the data, using the slopes from the U 235 data, and adjusting the energy scale so that the zero incident neutron energy value falls on the U 235 curve. The error bars represent the relative errors. The agreement of the data shown in fig. 3 is good. However, almost as good agreement is found if only the ~-value scale is adjusted. Unfortunately these data do not provide a sensitive recipe for producing a universal curve of ~ versus incident neutron energy. However, the fact that the result is not sensitive to the assumptions should be comforting to the reactor engineer who is forced to make a best guess of in a region where no data exist. Table 2 gives results of the least-squares fits to the data in the energy region shown. TABLE 2 for thermal n e u t r o n induced fission
Target nucleide
Energy region (MeV)
Assumed slope
U ~a
0 - - 1.08
0.085
U us
0 - - 1.08
0.085
Pu 2a°
0--14.5
0.160
Zero energy intercept 2.458 4-.028 2.412 4-.026 2.831 4-.038
Sher and Delayed Total number neutrons of neutrons Felberbaum per fission per fission least-squares analysis
0.007 0.016 0.006
2.465 4-0.028
2.503
2.428 4-0.026
2.430
2.837
2.882
±0.038
The slopes are 0.085 neutrons per MeV for U 233 and U 235 and 0.160 neutrons per MeV for Pu 239. These are the slopes of the so-called "Universal Curve." The zero energy intercept is the ~ value o f the fitted straight line at zero energy. These are our best values for the thermal ~ of the three nucleides. The standard deviations were
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calculated b y c o n s i d e r i n g the deviations o f the p o i n t s f r o m a straight line, the uncertainty in the slopes a n d the systematic e r r o r s Is). These c o n t r i b u t i o n s were considered t o be i n d e p e n d e n t o f each other. T h e final e r r o r was c a l c u l a t e d as the square r o o t o f t h e s u m o f the squares o f the i n d i v i d u a l errors. T h e n u m b e r o f delayed n e u t r o n s p e r fission 16) is given in the fifth c o l u m n t, a n d the t o t a l n u m b e r o f n e u t r o n s p e r fission a n d the a b s o l u t e errors in the sixth c o l u m n . T h e relative errors o n the values are a p p r o x i m a t e l y one h a l f o f the a b s o l u t e errors shown. A c o m p a r i s o n is m a d e with the results o f a least squares analysis o f previous d a t a 17), s h o w n in the last c o l u m n o f T a b l e 2. These calculations d o n o t include the m o s t recent results o f Colvin a n d S o w e r b y i s ) , which w o u l d also t e n d to lower very slightly ~ for U 233 a n d P u 239. H o w e v e r , there is n o statistically significant d i s a g r e e m e n t b e t w e e n o u r results a n d those o b t a i n e d f r o m the least squares analysis o f the p r e v i o u s data. t See Asplund-Nilsson le) for a compilation of the experimental data.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)
17) 18)
Asplund-Nilsson, Cond6 and Starfelt, to be published Moat, Mather, and McTaggart, Reactor Sci. and Technol., J. Nucl. Energy A and B 15 (1961) 102 Diven, Martin, Taschek and Terrell, Phys. Rev. 101 (1956) 1012 Diven and Hopkins, in Physics of fast and intermediate reactors, Vol. I (Intern. At. Energy Agency, Vienna, 1962) Diven, Terrell and Hemmendinger, Phys. Rev. 109 (1958) 144 T. W. Bonnet, Nuclear Physics 23 (1961) 116 Mather, Fieldhouse and Moat, private communication Meadows and Whalen, Phys. Rev. 126 (1962) 197 R. B. Leachman, Phys. Rev. 101 (1956) 1005; J. Terrell, Phys. Rev. 108 (1957) 783 Stevenson, Hicks, Armstrong and Gunn, Phys. Rev. 117 (1960) 186 Baranov, Protopopov, and Eismont, Soviet J. At. Energy (English Transl.) 12 (1962) 162 Okolovich, Smirenkin, and Bondarenko, Soviet J. At. Energy (English Transl.) 12 (1963) 491 Vasilev, Zamyatnin, II'in, Sirotinin, Toropov and Fomushkin, JETP (Soviet Physics) 11 (1960) 483 J. Terrell, Phys. Rev. 127 (1962) 880 R. T. Birge, Phys. Rev. 40 (1932) 207 G. R. Keepin, TID-7547, p. 130; Keepin, Wimett and Zeigler, Phys. Rev. 107 (1957) 1044; Keepin, Wimett and Zeigler, J. Nucl. Energy 6 (1957) 1; I. Asplund-Nilsson, F6rsvarets Forksningsanstalt (Stockholm) Report FOA 4 report A 4290411 (1963) Sher and Felberbaum, Brookhaven National Laboratory Report BNL-722, June 1962 Colvin and Sowerby, private communication
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Nuclear Physics 4 8 (1963) 4 3 3 - - 4 4 2 ; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
PROMPT NEUTRONS FROM FISSION J. C. H O P K I N S a n d B. C. D I V E N
Los Alamos Scientific Laboratory of the University of California Los Alamos, New Mexico t Received 11 J u n e 1963 Abstract: A n absolute m e a s u r e m e n t of~, the average n u m b e r o f n e u t r o n s emitted per fission, h a s been m a d e for t h e s p o n t a n e o u s fission o f C f ~62. T h i s n u m b e r is 3.7714-0.031 p r o m p t n e u t r o n s per fission. M e a s u r e m e n t s o f ~ for t h e s p o n t a n e o u s fission o f P u u ° a n d for n e u t r o n induced fission o f U ~a3, U ~ss a n d P u an9 have been m a d e relative to t h e s p o n t a n e o u s fission ~ o f C f 258. Several incident n e u t r o n energies between zero a n d 14.5 M e V were used. A universal ~ versus incident n e u t r o n energy curve for U 2as, U 2a6 a n d P u 2s9 was c o n s t r u c t e d by a d d i n g a c o n s t a n t energy to t h e incident n e u t r o n energy for each nucleide. T h e c o n s t a n t s for U ~sa, U n6 a n d P u m were 0.46 MeV, 0 M e V a n d 3.3 MeV, respectively. T h e d a t a c a n be fitted with two straight lines o f slopes 0.085 n e u t r o n s per M e V u p to a b o u t 1.6 M e V a n d 0.16 n e u t r o n s per M e V above 1.6 MeV. A t t h e r m a l energy the ~ value is 2.412 p r o m p t n e u t r o n s per fission.
1. Introduction An absolute measurement of ~, the average number of prompt neutrons emitted per fission, has been made for the spontaneous fission of Cf 252. Measurements of for the spontaneous fission of Pu 24° and for neutron induced fission of U 2an, U 2a5 a n d Pu 239 were made relative to the spontaneous fission ~ of Cf 252. Several incident neutron energies between thermal energies and 14.5 MeV have been used. Two absolute measurements of ~ for the spontaneous fission of C f 252 have been reported recently 1, 2). Asplund et al. used a large cadmium-loaded scintillator as a 4~ detector to count the neutrons emitted in fission. The efficiency of their liquid scintillator was determined with a neutron scattering experiment. This procedure yielded a ~ of 3.80___0.03 p r o m p t neutrons per fission. Moat et al. also used a large liquid scintillator. The efficiency of their scintillator was determined with the use of a calibrated Pu 24° source. After correction for the difference in the neutron spectra, they obtained a ~ value of 3.77___0.07 prompt neutrons per fission. In the present experiment we used a large cadmium-loaded liquid scintillator to detect the neutrons. The efficiency was determined by scattering neutrons from protons in an N E 102 plastic scintillator. We obtained a value of 3.77_ 0.03 p r o m p t neutrons per fission. The weighted average of these three results is 3.784___0.020. The ~-values for neutron-induced fission of U 23a, U 2 a s and Pu 2a9 were determined by measuring a ratio of ~ for the nucleide of interest to ~ for the spontaneous fission t W o r k p e r f o r m e d u n d e r the auspices o f the U.S. A t o m i c Energy C o m m i s s i o n . 433
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of Cf 252. The remainder of this article will be devoted to an elaboration of the experimental considerations of the absolute measurement and to a discussion of the results of the relative measurements.
2. A b s o l u t e
Measurement
A 1.0 m-diameter by 1.0 m long liquid scintillator, shown infig, l, was used as a ~-ray and neutron detector. The C f 252 sample was placed in a fission counter that was inserted into the centre of the liquid scintillator. The scintillator is large enough to cause most of the fission neutrons to be thermalized and finally captured by the cadmium in the scintillation solution. Neutron capture in the cadmium results in
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Fig. 1. End view and cross section of the scintillator, neutron source, and shielding. A collimated beam of neutrons is passed through the sample at the Centre of the scintillator. about 9 MeV of ~ radiation which is detected with a high efficiency by the scintillating liquid. The cadmium concentration is adjusted so that the mean ]ife of neutrons in the scintillator is long compared to the resolving time of the electronics. A pulse in the fission counter is used to open an electronic gate which is long compared to the mean life of a neutron in the liquid scintillator. The number of pulses which occur in the scintillator during the gate is determined and recorded for each fission event. In this way the fission neutrons are counted individually. The most conspicuous problem associated with any absolute ~ measurement is the determination of the efficiency of the neutron detector. A Monte Carlo calculation of neutron leakage for a 76 em liquid scintillator was modified for the 1.0 m scintillator and the results checked experimentally for one neutron energy and angle. The experimental method involved the n-p scattering technique originally developed
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by Diven et aL 3) at Los Alamos. A 3.8 cm diameter by 0.6 cm thick plastic scintillator (NE 102), mounted on a 6810A photomultiplier tube, was inserted into the axial opening of the liquid scintillator. The plastic scintillator was at the centre of the large liquid scintillator. A beam of 3.9 MeV neutrons from the D(d, n)He 3 reaction or 14.5 MeV neutrons from the T(d, n)He 4 reaction was directed through the tube along the liquid scintillator axis and into the plastic scintillator. The proton recoil spectrum from the plastic scintillator is approximately flat out to the maximum energy of the neutrons and then falls to zero rapidly. A differential discriminator was used to select a proton energy band and consequently a scattered neutron energy band and scattered neutron angle. Using the T(d, n)He 4 reaction, two neutron energy bands were selected: 0-2 MeV and 6-8 MeV. The proton recoil counter pulses were used to open an electronic gate associated with the large liquid scintillator. The circuitry, described by Diven and Hopkins 4) and Diven et aL 5) yields the number of proton recoil pulses followed by zero, one, two, etc., pulses from the liquid scintillator during the 64-/zsec gate. Three separate determinations of the number of pulses in a gating interval can be made in cyclic order: (I) for gates opened for low energy scattered neutrons, (2) for gates opened for high energy scattered neutrons, and (3) for background gates. The background gate is opened several milliseconds after one of the scattered neutron gates. The background gate is considered to be opened at random since the mean life of neutrons in the liquid scintillator is about 20 #sec. Background runs were also made with helium in the target. Let Co be the fraction of proton recoil pulses not followed by any liquid scintillator pulse, after correction for background. The fraction Co is related to the leakage and efficiency by the expression 1 - Co = e ( 1 - L ) . The leakage L is the fraction of neutrons that escape from the large liquid scintillator. The fraction of neutrons that do not emerge from the liquid scintillator and are observed is (1 - L ) times e, where e is defined as the efficiency for detection of neutrons that are captured in the scintillator. For 0 to 2 MeV neutrons the leakage was estimated at 0.5%. From this estimate and the measured C O the efficiency was found to be about 94 %. This efficiency and the measured Co for neutrons in the 6 to 8 MeV energy range yielded a leakage of about 6 %. This is the leakage for neutrons in the 6 to 8 MeV energy range entering the liquid scintillator at 45 ° in the laboratory system. Monte Carlo calculations for leakage are available for a 76 cm long by 76 cm diameter liquid scintillator. These calculations provided the leakage at various energies as a function of neutron angle. We applied these calculations to the present problem by assuming that as the liquid scintillator is increased in size the number o f mean free paths is increased proportionately, or, conversely, the number of mean free paths remains fixed and the neutron energy scale is expanded. This is tantamount to assuming that the n-p scattering cross section is linear on a log a, the cross section, versus log energy curve. The neutron leakage from the liquid scintillator is almost entirely out of the axial openings. This provides a fiat leakage versus angle relationship for all neutrons emitted at angles greater than about 15° to the scintillator
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axis. From these data the leakage as a function of neutron energy for an isotropic neutron source was obtained. The neutron spectrum from the spontaneous fission of Cf 252 reported by Bonner 6) was multiplied by the neutron leakage and integrated from 0 to 10 MeV. The procedure for Cf 252 fission neutrons resulted in a calculated leakage of 1 . 6 7 % . The effective efficiency is defined as 1 - C o. The leakage is a constant for a given neutron spectrum, but e, which depends u p o n the electronic adjustments, must be determined for each set of runs. The Cf 252 was inserted into the large liquid scintillator in the form of a Cf 252 fission counter. A pulse from the fission counter in coincidence with a fission y-ray pulse from the liquid scintillator indicated that a fission took place, and an electronic gate was opened between the large liquid scintillator and the circuit that determined how many liquid scintillator pulses occurred during the gate. Series of runs were made with the Cf 2s 2 fission counter and the proton recoil counter alternately placed in the centre of the large liquid scintillator. The D(d, n)He 3 reaction was used during the runs with the proton recoil counter. The incident neutron energy was 3.9 MeV, and the scattered neutron energy ranged from 0 to 1.3 MeV. The neutron leakage for the p r o t o n recoil counter runs was about 0.4 %. With the 1.67 % leakage for the C f 252 fission neutrons, the effective efficiency for C f 252 neutrons was about 86 %. The data consisting of the number of pulses following a gating pulse and the appropriate background measurements were analysed on an IBM 7090 computer for the emission probabilities, for r~, and for the standard deviations. The purpose of calculating the emission probabilities for the proton recoil runs is to test the operation of the equipment. For example, any tendency of the photomultiplier tubes to emit double pulses would show up dearly. The Cf 252 data had to be corrected for the possible pile-up of two or more neutron pulses in a gate. This correction was explained in a previous report a) on multiplicities of fission neutrons. The pile-up correction required a knowledge of the resolving time of the electronics. This turned out to be the limiting factor in accuracy. The pile-up correction was about 1% of ~ and contributed about 0.6 % uncertainty to ~. The total uncertainty, or standard deviation, is due to the statistical uncertainty in the proton recoil runs, to the uncertainty in the leakage, to the pile-up correction, and to the statistical uncertainty in the Cf 2s2 runs. The final answer for ~ of Cf 252 is 3.771 +0.030 prompt neutrons per fission. 3. Relative Measurements
The ~-values for neutron induced fission of U 233, U 235 and PU 239, and for the spontaneous fission of P u 24° were measured relative to ~ for the spontaneous fission of C f 252. Double fission counters were placed in the centre of the large liquid scintillator. One fission counter contained C f 252, and the other contained the sample material. For neutron induced fission a beam of neutrons was directed through the axial tube in the liquid scintillator and into the sample material. Coincident signals from th- fission counter and the liquid scintillator identify fission events and
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open electronics gates between the large liquid scintillator and the counting apparatus. The gates are open for 64/~sec, during which time the pulses from the liquid scintillator are counted. The data appear as the number o f fissions with 0, 1, 2, etc., pulses from the liquid scintillator during the gating interval. The gating pulses are accepted in a lyclic fashion from the Cf 252 counter, from the sample material fission counter, and from a background trigger, as explained in the discussion of the avsolute measurement. With this arrangement the effects of drifts of bias level, gate length, and amplifier gain are minimized since they effect the mean number of pulses per gate from C f 252 in the same way as they effect the sample material. A detailed investigation of the neutron beam quality was made. A gas target of tritium or deuterium was used which gave a neutron energy spread of about 80 keV depending upon the proton or deuteron energy and upon the gas pressure. The neutron energy could be degraded by scattering from the walls of the collimator. This effect was studied in two ways. The first technique was to insert photographic emulsions into the centre of the large liquid scintillator and analyse them for the neutron spectrum down to 1 MeV. Almost no degradation of the neutron energy was found for 4-MeV neutrons, but at 15 MeV the average energy was found to be decreased by about 0.5 MeV. The second technique involved a pulsed beam and time-of flight measurement. A 50 nsec wide beam pulse was directed onto the target at a 1 MHz rate. A fission counter on stilbene scintillator mounted on a 6810A photomultiplier tube was inserted into the center of the large liquid scintillator and exposed to the pulsed beam. The pulses from the fission counter or stilbene scintillator and from a beam pickup were fed into a time-to-pulse-height converter. The spectra from the time-to-pulse-height converter were displayed on a 100-channel pulse-height analyser. An analysis of these data showed that about 4% o f the neutrons at a nominal 14.5 MeV were random, and hence of very low energies. At 4 MeV approximately 9 ~o of the neutrons are of low energies. The uncertainty in the 9 values due to the uncertainty in these corrections is small. Thermal neutrons were obtained by moderating a 400 keV neutron beam with a polyethylene plug in the neutron collimator. The non-thermal contamination was monitored by measuring the cadmium ratio. The cadmium ratio varied between 10 and 20, depending upon the fission counter material. For the runs with thermal neutrons the non-thermal contribution was subtracted. The data were analysed on an IBM 7090 computer for 9, the neutron emission probabilities, and for the standard deviations due to statistical fluctuations and uncertainties in the pile-up corrections. A chi-square analysis was performed on the emission probabilities to verify consistency. An analysis o f the standard deviations is complicated by the fact that there are systematic uncertainties that influence all of the relative measurements. These consist o f the uncertainties in pile-up correction, in the absolute ~ of C f 25 z, and in the amount of thermal neutron contamination o f the neutron beam. The independent errors consist of statistical fluctuations in the individual runs.
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O n l y very small samples o f fissionable m a t e r i a l were tolerable because o f the pile-up o f ~-particle pulses. This results in a negligible c o r r e c t i o n to ~ due to fission induced by fission neutrons. TABLE 1 Prompt neutrons per fission Nucleide
Neutron energy and energy spread (MeV)
Prompt neutrons per fission ~
Total relative error
Total systematic error
u ~sa+ n
thermal 0.2804-0.090 0.4404-0.080 0.9805:0.050 1.084-4-0.05 3.93 4-0.29
2.473 2.489 2.502 2.553 2.510 2.983
0.026 0.033 0.033 0.035 0,030 0,040
0.022 0.023 0.023 0.023 0.023 0.030
U2S~+ n
thermal 0.2804-4-0.090 0.4704-0.080 0.815 4-0.060 1.08 4-0.05 3.93 ±0.29 14,5 4-4-1.0
2.425 2.438 2.456 2.471 2.530 2.937 4.626
0,020 0,022 0.022 0.026 0.026 0.030 0.075
0.022 0.022 0.022 0.022 0.023 0.029 0.066
2.189 2.83 ! 2.93 i 2.957 2.904 3.004 3.422 4.942
0.026 0.028 0.039 0.046 0.041 0.041 0.039 0.119
0.019 0.028 0.029 0.030 0.029 0.030 0.038 0.076
Pu z'° Pu ~9 + n
spontaneous fission thermal 0.250 4- 0.050 0.4204-0.110 0.6104-0,070 0.900 4- 0.080 3.90 i0 . 2 9 14.5 4-1.0
These results are based on ~ for spontaneous fission of Cf uz of 3.771 4-0.000. Absolute measurement of spontaneous fission ~ of Cf u2 yields ~ = 3.771 :~0.030. T a b l e 1 shows the ~-values f o r the three nucleides. T h e s p o n t a n e o u s fission o f P u 24° p r o v i d e d a negative energy p o i n t at - 6 . 3 MeV, f o r the nucleide f o r m e d by the P u 239 + n reaction. T h e energy spread is due to target thickness. T h e total relative e rr o r an d the t o t al systematic errors are shown. T h e total systematic e r r o r is the square r o o t o f the s u m o f the squares o f the i n d i v i d u a l systematic errors. This procedure is sufficiently accurate c o n s i d e r i n g the uncertainties in the s t a n d a r d deviations. All o f the ~-values are based u p o n a ~ o f 3.771 p r o m p t n e u t r o n s per fission for the s p o n t a n e o u s fission o f C f 252.
4. Discussion T h e ~-values vs incident n e u t r o n energy f o r U 235 are p l o t t ed in fig. 2. Th e circles represent o u r m e a s u r e m e n t s a n d the triangles represent the data t a k e n by M a t h e r et al. 7). N o t s h o w n o n this c u r v e are the recent d a t a o f M e a d o w s an d W h a l e n a).
PROMPT
NEUTRONS
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FROM FISSION
Their data, covering a region from 0 to 1.76 MeV, agree well with the present data. The insert in the upper left corner shows the 0 to 2 MeV region in more detail. The dashed lines are separated by approximately twice the relative error of each point. The data can be represented by two straight lines with a slope of 0.085 neutrons per MeV in the region up to 2 MeV and a slope of 0.160 neutrons per MeV in the region above 2 MeV. I f we use only the present data and a least-squares fit, the standard deviations in the slopes become 0.02 and 0.01, respectively. More complicated functions, such as hyperbolic tangents and various polynomials, can be devised to fit these data, but there is no theoretical motive to do so. / i I
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INCIDENT NEUTRON ENERGY IN MeV Fig. 2. N u m b e r o f p r o m p t neutrons emitted per fission f o r neutron induced fission o f U " s plotted against incident n e u t r o n energy in MeV. T h e circles are the d a t a o f Diven a n d H o p k i n s *), a n d the triangles are the d a t a o f M a t h e r , F i e l d h o u s e a n d M o a t 7). T h e solid line is the so-called " U n i v e r s a l C u r v e " . T h e d a s h e d lines r e p r e s e n t the relative s t a n d a r d deviations.
A first guess of the energy dependence of 9 is a linear relationship with a slope 9) of about one neutron per 7 MeV. Seven MeV is the sum of the binding energy and kinetic energy of an emitted neutron. This pre-supposes that all other terms in an energy-balance expression are independent of incident neutron energy. There is no experimental justification for this assumption. If, for example, the kinetic energy of the fission fragments increased as the incident neutron energy increased, then the slope of f versus energy of the incident neutron would be less than one neutron per 7 MeV. Conversely, if the fragment kinetic energy decreased with increasing incident neutron energy, then the ~ versus incident neutron energy curve would have a higher
440
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slope. The change in fragment kinetic energy necessary to explain the observed change in slope from 0 to 14 MeV is only about 1 MeV out of a total of about 180 MeV. The experimental data on the fragment kinetic energies show that within an accuracy of perhaps +__3 MeV the kinetic energy is independent of incident neutron energy lo, 11) up to 14 MeV. Recent data by Okolovich et aL 12) indicate that within an accuracy of 0.1% the fragment kinetic energy is the same for thermal neutron induced fission as it is for 5 MeV neutron induced fission. Other sources for a change in slope can be found, but again there is a lack of experimental information for verification. There is no evidence either for or against a discontinuity in ~ versus incident neutron energy at the threshold for second chance fission la). 5.2 _-
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Fig. 3. Number o f prompt neutrons emitted per fission for neutron induced fission of U ~ss (circles) and Pu == (triangles), plotted against the adjusted incident neutron energy. For U us 0.456 M e V is a d d e d to the actual incident n e u t r o n energy, a n d for Pu =s9 3.286 M e V is added. T h e solid line is the so-called " U n i v e r s a l C u r v e . " T h e relative s t a n d a r d d e v i a t i o n s are s h o w n .
An attempt is made to provide a universal ~ versus incident neutron energy curve for the three fissioning even nucleides (U 234, U 236, and Pu 24°) formed by the absorption o f a neutron by U 233, U 235 and P u 239. The shapes of the curves are similar. There are three ways to combine the data into one curve: 1) adjust the energy scales leaving the ~ scale fixed, 2) adjust the ~ scale leaving the energy scale fixed, and 3) adjust the energy scale and the ~ scale simultaneously. The fission barriers o f the three nucleides are different. For this reason it is to be expected that an adjustment of the
PROMPT NEUTRONS FROM FISSION
441
energy scales corresponding to the differences in the fission barriers might be necessary. This results in an adjustment o f less than 1 MeV. Fission of the three nucleides results in three different mass distributions. The difference in the mass distribution can be related to differences in the average number of neutrons emitted. This difference would be approximately 0.08 neutrons per mass unit t4). For example, the difference between U 23s and P u 239 ~-values for thermal neutron induced fission would be expected to be about 0.32 neutrons per fission. This is approximately what is observed. I f only the energy scale is varied, the shift is much greater than c a n b e explained by just the differences in barrier height. It is reasonable to suppose that some combination of ~ scale shift and energy scale shift would be necessary, but there are no theoretical guide lines. Fig. 3 shows the U 233 and P u 239 V data plotted as a function o f the adjusted incident neutron energy. A constant 3.286 MeV has been added to the energy scale of the PU 239 data and a constant 0.456 MeV to the energy scale of the U 2a3 data. The energy shifts were found by making a least-squares fit to the data, using the slopes from the U 235 data, and adjusting the energy scale so that the zero incident neutron energy value falls on the U 235 curve. The error bars represent the relative errors. The agreement of the data shown in fig. 3 is good. However, almost as good agreement is found if only the ~-value scale is adjusted. Unfortunately these data do not provide a sensitive recipe for producing a universal curve of ~ versus incident neutron energy. However, the fact that the result is not sensitive to the assumptions should be comforting to the reactor engineer who is forced to make a best guess of in a region where no data exist. Table 2 gives results of the least-squares fits to the data in the energy region shown. TABLE 2 for thermal n e u t r o n induced fission
Target nucleide
Energy region (MeV)
Assumed slope
U ~a
0 - - 1.08
0.085
U us
0 - - 1.08
0.085
Pu 2a°
0--14.5
0.160
Zero energy intercept 2.458 4-.028 2.412 4-.026 2.831 4-.038
Sher and Delayed Total number neutrons of neutrons Felberbaum per fission per fission least-squares analysis
0.007 0.016 0.006
2.465 4-0.028
2.503
2.428 4-0.026
2.430
2.837
2.882
±0.038
The slopes are 0.085 neutrons per MeV for U 233 and U 235 and 0.160 neutrons per MeV for Pu 239. These are the slopes of the so-called "Universal Curve." The zero energy intercept is the ~ value o f the fitted straight line at zero energy. These are our best values for the thermal ~ of the three nucleides. The standard deviations were
442
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calculated b y c o n s i d e r i n g the deviations o f the p o i n t s f r o m a straight line, the uncertainty in the slopes a n d the systematic e r r o r s Is). These c o n t r i b u t i o n s were considered t o be i n d e p e n d e n t o f each other. T h e final e r r o r was c a l c u l a t e d as the square r o o t o f t h e s u m o f the squares o f the i n d i v i d u a l errors. T h e n u m b e r o f delayed n e u t r o n s p e r fission 16) is given in the fifth c o l u m n t, a n d the t o t a l n u m b e r o f n e u t r o n s p e r fission a n d the a b s o l u t e errors in the sixth c o l u m n . T h e relative errors o n the values are a p p r o x i m a t e l y one h a l f o f the a b s o l u t e errors shown. A c o m p a r i s o n is m a d e with the results o f a least squares analysis o f previous d a t a 17), s h o w n in the last c o l u m n o f T a b l e 2. These calculations d o n o t include the m o s t recent results o f Colvin a n d S o w e r b y i s ) , which w o u l d also t e n d to lower very slightly ~ for U 233 a n d P u 239. H o w e v e r , there is n o statistically significant d i s a g r e e m e n t b e t w e e n o u r results a n d those o b t a i n e d f r o m the least squares analysis o f the p r e v i o u s data. t See Asplund-Nilsson le) for a compilation of the experimental data.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)
17) 18)
Asplund-Nilsson, Cond6 and Starfelt, to be published Moat, Mather, and McTaggart, Reactor Sci. and Technol., J. Nucl. Energy A and B 15 (1961) 102 Diven, Martin, Taschek and Terrell, Phys. Rev. 101 (1956) 1012 Diven and Hopkins, in Physics of fast and intermediate reactors, Vol. I (Intern. At. Energy Agency, Vienna, 1962) Diven, Terrell and Hemmendinger, Phys. Rev. 109 (1958) 144 T. W. Bonnet, Nuclear Physics 23 (1961) 116 Mather, Fieldhouse and Moat, private communication Meadows and Whalen, Phys. Rev. 126 (1962) 197 R. B. Leachman, Phys. Rev. 101 (1956) 1005; J. Terrell, Phys. Rev. 108 (1957) 783 Stevenson, Hicks, Armstrong and Gunn, Phys. Rev. 117 (1960) 186 Baranov, Protopopov, and Eismont, Soviet J. At. Energy (English Transl.) 12 (1962) 162 Okolovich, Smirenkin, and Bondarenko, Soviet J. At. Energy (English Transl.) 12 (1963) 491 Vasilev, Zamyatnin, II'in, Sirotinin, Toropov and Fomushkin, JETP (Soviet Physics) 11 (1960) 483 J. Terrell, Phys. Rev. 127 (1962) 880 R. T. Birge, Phys. Rev. 40 (1932) 207 G. R. Keepin, TID-7547, p. 130; Keepin, Wimett and Zeigler, Phys. Rev. 107 (1957) 1044; Keepin, Wimett and Zeigler, J. Nucl. Energy 6 (1957) 1; I. Asplund-Nilsson, F6rsvarets Forksningsanstalt (Stockholm) Report FOA 4 report A 4290411 (1963) Sher and Felberbaum, Brookhaven National Laboratory Report BNL-722, June 1962 Colvin and Sowerby, private communication