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Measurements of prompt v̄ and variance for the spontaneous fission of 252Cf and 242Pu
Ann. nucl. Energy,Vol. 9, pp. 127 to 135, 1982 Printed in Great Britain
03064549/82[0301274)9503.00/0 Pergamon Press Ltd
M E A S U R E M E N T S OF P R O M P T ~ A N D V A R I A N C E F O R THE S P O N T A N E O U S FISSION OF 252Cf A N D 242pu G. EDWARDS,* D. J. S. FINDLAY and E. W. LEES Nuclear Physics Division, AERE Harwell, Oxon OXI 1 0RA, U.K.
(Received 16 October 1981) Abstract-- Measurements of the mean (v-)and variance (a 2) of the prompt neutron multiplicity distribution for
the spontaneous fission of 2s2Cf and 242pu have been made. Quantities of 2s 2Cfand 2'~2pu were incorporated in ionization chambers placed at the centre of a large oil-moderated neutron detector. The dependence of both f and tr2 on the fission-fragment detection efficiency of the ionization chambers was investigated in detail and led to a correction in 242pu of 0.68~ for ~ and 1.04~ for tr2. The values deduced are: ~(252Cf) = 3.752-1-0.029, o'2(252Cf)= 1.562--+0.011 v(242pu) = 2.153___0.019, o'2(242pu) = 1.298-+0.008. The ratio ~(Pu)/~(Cf)is determined more accurately than either absolute measurement, and is 0.5738 -+0.0033. 1. I N T R O D U C T I O N
In this paper we report measurements of the mean and variance ~ and tr 2 of the distribution of fission neutrons from 252Cf and 242pu measured using the Harwell oilmoderated assembly o f B F 3 counters (Lees et al., 1980). For 252Cf, our precision (0.8~o) compares favourably with existing measurements, but since our measurements rely on the calibration of the N P L manganese bath for determination of absolute neutron strengths, we cannot hope to resolve the discrepancies between the manganese bath and liquid scintillator measurements of ~7(seethe review articles of Smith 1979,1980 for a full discussion of the importance of ~ for 252Cf as a standard). However we can confirm the fission counting efficiency of the manganese bath measurements by an independent technique. For 242pu, the existing set of measurements of ~7 is not nearly so comprehensive as for 252Cf, there being only one measurement (Boldeman, 1968, 1974) of better than 2~o accuracy, and so it was felt that a second precise measurement of ~7for 242pu was necessary. Most of the uncertainty of our measurements is due to uncertainties in the neutron detector efficiency; since these are largely c o m m o n to both measurements, our value of the ratio ~ ( 2 4 2 p u ) / ~ ( 2 5 2 C ~ is more accurate than either absolute measurement. 2. E X P E R I M E N T A L
DETAILS
The experimental technique used in making these measurements is similar to that described by Lees et al. * Attached to the University of Oxford.
(1980) (hereinafter called Method I) in which the spontaneously fissioning source is incorporated in an ionization chamber placed at the centre of a highefficiency neutron detector consisting of 56 BF 3 counters connected in five rings and immersed in an oil moderator. After each fission-chamber pulse, the number of neutrons captured in the neutron detector in a gate ~ 300-#s long (the spectrum gate) is recorded and stored in a P D P - 11/45 computer. After a further ~ 1000 /~s, the background in a gate of the same length (the background gate) is also recorded and stored.
2.1. Modifications to Detector and Data Collection System For the present measurements a few changes were made to the procedure described in Method I : (1) The neutron detector assembly was taken apart, moved to the low energy area of the new Harwell 136 MeV electron linear accelerator, and reassembled inside a shielded blockhouse. (2) The E H T for the BF 3 counters was raised from 3.6 to 3.8 kV, thereby enabling amplifier gains to be lowered and consequently eliminating r.f. pick-up from the new higher power accelerator. (3) The gate width (measured using a random pulse generator whose output was shaped to simulate real neutron counts) was increased from 170 to 297.3 +0.2 #s; this had the effect of significantly increasing the detection efficiency for high multiplicity events and of eliminating the energy dependence of the gating factor (see point (7)). 127
128
G.
et
EDWARDS
al.
Table 1. BF 3 detector efficiency calibration sources, and corrections applied to raw efficiencies for neutron absorption by the fission-chamber materials and Be impurities in the other (~, n) sources Source type
Neutron mean energy (MeV)
Am/Li Am/F Am/B Am/Be
0.45+0.1 1.25+0.15 2.70___0.25 4.20 _ 0.20
Neutron absorption correction (~o) 1.48+0.38 0.15+0.05 0.49___0.15 0.08 ___0.04
Be correction (~)
Final efficiency
+0.94+0.15 +0.17+0.03 +0.21___0.03
0.4825 + 0.0033 0.4602+0.0031 0.4331+0.0025 0.3993 __+0.0031
The mean energies of the neutron sources were deduced from Geiger and Van der Zwan (1975), Lorch (1973) and Werle (1970). (4) A 2 ms paralysis time was applied to the output of the fission ionization chamber so that data processing could not be triggered by any further fissions occurring within this period. (5) The data collection system has been extended to record ring ratios* as a function of neutron multiplicities 1, 2 and >~3 ; these data may give neutron energies as a function of multiplicity. (6) The efficiency of the neutron detector assembly has been redetermined more accurately using the same 24tAm/Li, /F, /B a n d / B e sources calibrated with the National Physical Laboratory manganese bath as in Method I. However for the present measurements the strengths of these neutron sources as determined from the N P L calibration were increased by 0.5~o to account for chemical impurities in the bath solution (Axton and Bardell, 1982). The reflection and capture of neutrons in the materials of the source were computed by the Monte Carlo programme MONK(Sherriffs, 1978) which uses the U.K. Nuclear Data Library. The percentage corrections to the measured efficiencies are given in Table 1. Also given in Table 1 are corrections for Be impurities in the A m / L i , / F a n d / B sources (Lees and Lindley, 1977). The final neutron detection efficiency e as a function of neutron energy E (MeV) is well represented by the straight line (see Fig. 1) e = (0.4907_0.0038)-(0.0218 +0.0016)E
and e = 0.4492+0.0034
for 2 4 2 p U ( E = 1.9+0.1 MeV).
(7) The capture time distribution was measured with better resolution for both 2s2cf and 242pu fission chambers with a multishot time analyser having ½ #s bins (Chapman et al., 1977) using a fission-fragment pulse as a start and the detected neutron pulses as stops. The distributions for the two fission chambers were different due to the shorter time constants used on the amplifier and preamplifier for the 242pu chamber (see Table 2). The gating factor, or fraction of neutron captures occurring within the time the gate is open, 8-305.3 #s, was evaluated directly from these data after background subtraction. The gating factors obtained were ]-~os.3 f ( t ) d t = 0.8777+0.0004 for 252Cf and 0.8801 + 0.0004 for 242pu. These data were also used to evaluate the integrals .fsa°5"3f2(t) dt and S]°s'af3(t) dt which are required for deadtime corrections (described in Method I).
2.2. Spontaneous Fission Sources 2.2.1.2s2cffission chamber An oxide source of high chemical purity was used in the 2~2Cf fission chamber (see Table 2). Analysis by the 10
(1) 08
with a correlation coefficient of --0.743. The fitting procedure took account of the covariances in the neutron source strengths due to all sources being measured at NPL. Hence at the energiest of the two fission sources used in this experiment,
06 E
.----___._,.
O~
= 0.4438+0.0028
for 2 5 2 C f ( E = 2.15+0.05 MeV)
* The ratio of counts in the outermost to innermost rings in the detector is a monotonically increasing function of neutron energy. t The mean energy for 2~2Cfwas deduced from a survey of the literature; the mean energy for 242pu was deduced from our ring ratio measurements, equation (4) in Terrell (1965) and Belov et al. (1969).
02
i 1
i 2
i 3
i
E (MeV)
Fig. 1. Neutron detection efficiency e as a function of neutron energy E for the Harwell BF 3 counter assembly.
f and a 2 for spontaneous fission of 2s2cf and 2'*2pu
129
Table 2. Properties of fission chambers Property Mass of fissionable material (g) Diameter of fissionable material (mm) Backing material and thickness (mm) Initial isotopic composition (~o)
Chamber gas pressure (mm Hg) Electronic time constants (#s) Integration (I) Differentiation (D)
252Cf
2'*2pu
7.36 x l0 - i t
1.092 X 10 -2 40 Pt, 0.13 242pu : 89.37
--
Pt, 0.13 252Cf; 74.48 2s°Cf: 25.52
24tpu :0.93 24°pu : 4.57 239pu : 5.13
760 Preamp: 100(I) Amp : 1 (I)
190 Preamp: 0.2(I) Amp : 0.2 (I)
1 (D)
0.2 ( D )
The isotopic composition of the Cf during measurements of ~ also included 248'246'2't4Cm, these, however, made a negligible contribution to neutron output, The isotopic composition of Pu is that taken immediately after 2*tAm separation in October, 1979. Chemical Division at Harwell showed the presence of 2s°cf, and by the time of measurement, daughter impurities of 24SCm and 246Cm were present; these led to only a 0.025~ correction to the measured ~7value. The fission rate deduced from the measured ~t activity implied that the chamber was > 9 9 % efficient in detecting fission fragment pulses. The half-life of 2szcf is 2.63 yr, so over the period of data collection (June 1980-January 1981) the fission rate changed significantly.
2.2.2. 242pit fission chamber Details of the 242pUO2 s o u r c e used are also given in Table 2. The only other isotope contributing fission neutrons is 24°Pu, having a ~ value very similar to that o f 242pu (Boldeman, 1974), implying a negligibly small correction. A spontaneous fission rate of 8.03 +_0.08 s - 1 was deduced from a measurement of the total neutron output of the source* (after correction for the (~t,n) contribution of 0.13 ns-1). The gas pressure in the chamber for early runs was 760 m m Hg. At this pressure the fission rate was only 62~o of the expected value, owing to the need to discriminate against severe • pileup. Subsequently two reductions in pressure were made, first to 380 mm, then to 190 mm. The final fission fragment detection efficiency was 889/o,slightly less than * The spontaneous fission rate was confirmed with poorer precision using a neutron coincidence counter designed for safeguards applications (Lambert, 1977). ~"Fission fragments recoiling in the plane of the foil will not be detected. Neutrons emitted in the direction of fragment recoil will, on average, have higher energies. Furthermore, neutrons emitted in the direction of the BF 3 detector symmetry axis will escape along the through tube. The highest energy neutrons from fragment recoils parallel to the detector axis are therefore always lost. However, such fragment recoils are not detected when the foil is arranged parallel to the axis, and hence the average kinetic energy for detected neutrons is higher.
that expected from fission fragment ranges (James and de Saussure, 1981), but probably accounted for by irregularities in target deposition. An extrapolation to 100~o detection efficiency was made (see Section 2.3.3).
2.2.3. Fission chamber absorption Absorption by the materials comprising the fission chambers necessitates a correction to the neutron detection efficiency of the BF a counter assembly. These corrections, again computed by MONK, resulted in reductions of (0.59 + 0.11)~o for the 252Cf chamber and (1.01 + 0 . 1 4 ) ~ for the 242pu chamber. The final gated detection efficiencies es were : eg(252C0
=
0.3872 +_0.0025
eg(2*2pu) = 0.3914+_0.0030.
2.3. Consistency and Sensitivity Checks 2.3.1. Background correction To check the accuracy of the background correction procedure described in Method I, a measurement of for 252Cf was made with the background increased (using an Am/Be neutron source) by a factor of 20 over that occurring naturally. The value of f was unchanged within statistics.
2.3.2. Fission chamber orientation The design of the two fission chambers used was different. The 242pu chamber had its foil orientated perpendicular to the symmetry axis of the detector; the 2s 2Cfchamber, however, had its foil parallel to this axis. A check on the effect of orientation of the chambers with respect to the detector axis was carried out. When the foils were arranged perpendicular to the axis, the ring ratio, and hence the mean detected neutron energy, was lower than when the foils were parallel to the axis.t
130
G. EDWARDSet al. I
I
I
I
Variation of P with Fission Fragment Detection E f f i c i e n c y
I T
376
3 72
370 P
252Cf
354
352
36°
do
I0
9'o
5'
I~0
Fig. 2. Measured ~ as a function of fission-fragment detection efficiency ~/for the 252 Cf fission chamber. Errors shown are the statistical errors for each point appropriately increased to account for the very small fluctuations in neutron detector efficiency (Section 2.3.4). Appropriately correcting the efficiency for the small change in neutron mean energy with orientation (equation (1)) and for the slightly different position of the fission foils in the two orientations led to values of different by only 0.38+0.14% and to values of a 2 different by only 0.46+0.42%; these amounts were included as errors (see Table 5). The values of ~7and a 2 quoted in this paper are for the parallel orientation. I
2.3.3. Variation o f measured ~ and a 2 with fragment
detection efficiency Since the fission-fragment detection efficiency of the 242pu chamber was ~ 88%, an extrapolation to 100% efficiency was necessary. Therefore a study of the variation of measured ~and a 2 with fragment detection efficiency was made for both 242pu and 2s2Cf. The results for ¢ are illustrated in Figs 2 and 3.
I
[
I
I
I 90
l 100
Variahon of ~ with Fission Fragment Detection E f f i c i e n c y 216
2.15
214
213
212
211
242pu
210
209
I 60
I 70
I 80 n I°/o)
Fig. 3. Measured ~ as a function of fission-fragment detection efficiency ~ for the 242Pu fission chamber. Errors as in Fig. 2.
and a 2 for spontaneous fission of 252Cf and 242Pu I
i
I
I
Variation of 0.2 with Fission Fragment Defection Efficiency
131 I
rt
'1 ' 6 2
1 60
1 58
oz
1 56
1 5/*
1 52 252Cf 1.50
1 1.8
I 60
I 70
I 80 n i%)
i 90
1 100
Fig. 4. Measured o 2 as a function of fission-fragment detection efficiency ~/for the 252Cf fission chamber. Errors as in Fig. 2. i
I Variation of a 2 with Fission Fragment Detection Efficiency
i
I
I
I 90
1 100
r/
1 31
1 3C
12S
o 2 128
1 27
242 PH
12E
12~
I 60
I 70
I S0 n (%}
Fig~5~Measured~2asafuncti~n~ffissi~n-fragmentdetecti~nef~ciencyqf~rthe242Pufissi~nchamber~Err~rs as in Fig. 2. Reducing fission-fragment detection efficiency by increasing the discrimination threshold preferentially excludes those fragments of lowest kinetic energy. Since fission fragments with low kinetic energy tend to have high excitation energy, and high excitation energy leads to high emitted neutron multiplicity, a reduction in q is expected. Based on the general trend of the data points, th~ results for q were fitted by the straight lines
* This effect is analogous to the variation in measured ~with fission-foil thickness (Boldeman and Frehaut, 1980).
for 252Cf" 17(~]) =
(3.424_+0.017)+ 10 -3 (3.26+0.18)q
(2)
with a correlation coefficient of -0.989 for 2 4 2 p u " 17(?/) ~-~ (2.028+0.012)+ 10 - 3
(1.25 _+0.15)q
(3) with a correlation coefficient of --0.995 where r/is the fragment detection efficiency (~).* Similar plots were made for o 2 (Figs 4 and 5), and
G. EDWARDSet al.
132
Table 3. Summary of 252Cf data
a l t h o u g h a linear dependence is perhaps not quite so obvious now, the d a t a are represented by the lines for
Date of run
Fission rate (s - 1)
~
0.2
10.87 10.81 10.69 10.74 9.88 9.67 9.29
3.759 3.759 3.746 3.744 3.745 3.751 3.757
1.554 1.568 1.557 1.586 1.571 1.541 1.560
--
3.752
1.562
252Cf: tr2(q) = (1.494 _ 0.042) + 10- a (0.684 + 0.459)r/
(4) with a correlation coefficient of - 0 . 9 9 0 for
242pu • o"2(/1) ---~(1.200 ~ 0.018) q-- 10- 3 (0.983 + 0.218)r/
(5)
9 June 1980 10 June 1980 11 June 1980 26 June 1980 12 November 1980 24 November 1980 29 January 1981 Mean
with a correlation coefficient of - 0 . 9 9 6 This b e h a v i o u r m a y also be u n d e r s t o o d in terms of preferential exclusion of high multiplicity. A small but significant dependence of ring ratio with fission-fragment detection efficiency was noted. It is possible to interpret this as a slight variation of n e u t r o n average kinetic energy with n e u t r o n multiplicity.
in the b a c k g r o u n d gate is slightly higher t h a n that occurring d u r i n g the spectrum gate since fissions c a n n o t have occurred before the spectrum gate but m a y occur during a n d after the spectrum gate. The ratio of the b a c k g r o u n d s is given by the formula
2.3.4. Long-term consistency The present m e a s u r e m e n t s were carried out between J u n e 1980 a n d July 1981. Over this period the detector efficiency was checked m a n y times a n d was found to vary on average by only 0.17~o. T h e statistical errors on ~Tandtr 2 values from individual runs were appropriately increased to account for this variation. Table 3 shows the consistency between individual 252Cf runs over this period. 3. D A T A
Bb~'¢k = (1 +fz) Bspec
(6)
where Bspec is the effective b a c k g r o u n d d u r i n g the spectrum gate Bback is the m e a s u r e d b a c k g r o u n d in the b a c k g r o u n d gate f i s the unparalysed fission rate z is the m e a n lifetime of a n e u t r o n in the detector,
ANALYSIS
Several corrections to the raw d a t a are m a d e before a value of ~7is obtained.
F o r a m e a n n e u t r o n lifetime in our detector of 135/~s, the correction to ~ a n d a 2 is <0.0001 for 252Cf a n d completely negligible for 242pu.
3.1. Paralysis Correction to Background Most of the b a c k g r o u n d (82Voofor 252Cfand 65~o for 242pu) is due to n e u t r o n s from other fission events. As s h o w n by Colvin a n d Sowerby (1965), however, when a paralysis period is imposed the b a c k g r o u n d measured
3.2. Other Corrections to Data B a c k g r o u n d a n d dead time corrections are m a d e as described in M e t h o d I. The changes in ~ a n d tr 2 m a d e by including these corrections are given in Table 4, where
Table 4. Effect of the various corrections made to the data on the values of ~ and a2 Average change when correction is included 0-2
Nature of correction Background Deadtime Background paralysis q extrapolation + 6eg* change in eg Isotopic impurities Fission-chamber absorption
2~2Cf
242pu
252Cf
242pu
- 0.022 + 0.009 < 10- 4
- 0.011 + 0.003 <<10 - 4 + 0.014 - 0.017 Negligible + 0.022
- 0.057 + 0.038 < 10 - 4 -+ 0.004 Negligible - 0.004
- 0.020 + 0.014 <<10- 4 + 0.013 - 0.004 Negligible + 0.005
- 0.024 + 0.001 + 0.022
* 6eg = 0.0025 for 252Cf, 0.0030 for 2d'2pu.
and a 2 for spontaneous fission of 2s2Cfand 242Pu the effects of all other corrections are also listed. In computing the neutron detector efficiency for 252Cfan d 242pu we have assumed that equation (1) is a true representation of the efficiency above the mean energy of the Am/Be source 4.2 MeV. We have performed sensitivity checks based on the following extremely unlikely two assumptions : if e = 0 for E > 7.5 MeV then the present ~ values would increase by 1.09/o; if below 0.3 MeV e rises rapidly towards e = 1 as E ~ 0 the present q values would decrease by 0.45%. However these two assumptions are highly improbable. Further support for our use of equation (1) is that the neutron spectrum from an Am/Be source extends up to 10.3 MeV and marked deviations of e from linearity would be expected to markedly lower the measured Am/Be efficiency.
133
3.4. Evaluation of Errors As mentioned in Section 2.3.4, the statistical errors on ~7 and a 2 values from individual runs were appropriately increased (in quadrature) to account for the very small fluctuations in neutron detector efficiency. A detailed list of the components of the final errors in ~7and a 2 are given in Table 5 ; all components are + l a and were added in quadrature to give the final errors quoted in the next section. 4. RESULTS AND DISCUSSION
4,1. Absolute Values of ~ and a2 for 252Cfand 242pu The values oflTand 172for 2 s2Cfwere obtained from a weighted mean of seven runs, and are ~7(2s2cf) = 3.752 +0.029
3.3. Direct Determination of ~ and 172
a2(2s2Cf) = 1.562+0.011.
Following Lazarev (1977), ~ and 172 have been determined directly from the data using the relations =
F o r 242pu 15 runs were used to define the linear extrapolation to 100% shown in Figs 3 and 5, and the final results are
(7)
--
~g :
~(242pu) = 2.153 +0.019
,~ )
=
a2(242pu) = 1.298_ 0.008.
(8)
4.2. f for 242pu Relative to 252Cf where 9
9
nQ(n), ~ = ~ n2Q(n),
~ =
n=O
n=O
the Q(n) are the measured neutron distribution probabilities, and e, is the efficiency of the neutron detector.
As explained in Section 1, the ratio ~(242pu/~(252C0 is more accurate than either absolute value. The error in the ratio was computed from the components given in Table 5 by omitting the errors due to source orientation (the two fission chambers had their fission foils in the same orientation) and by replacing the errors due to detector efficiency calibration and fission neutron/~ by
Table 5. Contributions to errors quoted on the final f and a 2 results in Section 4.1 tr2 Source
Background Deadtime Fission-chamber absorption Gating factor Detector eft. calibration* Fission neutron E Statistical error Statistical error in extrapolated value 1% in fission rate Fission chamber position error Source orientation Total
2s2Cf
2*2pu
2s2Cf
2'*2pu
0.001 0 0.004 0.002 0.022 0.009 0.003
0* 0 0.003 0.001 0.012 0.010
0.002 0.002 0.002 0.001 0.004 0.002 0.008
0 0.001 0.001 0 0.003 0.002
-0.003 0.002 0.014
0.003 0.001 0.001 0.008
0.001 0 0.006
0.004 0.001 0 0.006
0.029
0.019
0.011
0.008
* Contributions less than 0.001 are denoted 0. t Includes covariance terms (see Section 2.1).
134
G. EDWARDSet al. Table 6. Experimental values of ~ and a 2 for the spontaneous fission of 242pu
the error in the efficiency difference arising from the two different neutron mean energies/~ of 242pu and 252Cf. The ratio is
Author
~(242pu) - = 0.5738+0.0033. 1~(25 2Ct)
Hicks et al. ( 1 9 5 6 ) Crane et al. ( 1 9 5 6 ) Prokhorova et al. (1969) Boldeman (1974) Present work
4.3. Comparisons with Previous Measurements of ~ Smith (1980) summarizes the various measurements of ~ for 252Cf, pointing out the discrepancies between manganese bath and liquid scintillator measurements, and attempting to reduce the discrepancies by improved data corrections. The weighted average of the manganese bath measurements for ~7T, the total number of neutrons emitted per fission, is 3.750; removing the delayed neutron fraction of 0.009 per fission (Lemmel, 1975) gives a value of 3.741_+0.009 prompt neutrons per fission. Smith's evaluation of the group average of liquid scintillator measurements is 3.771_+0.009 (prompt). However a recent liquid scintillator measurement by Zhang and Liu (1979), published since the Smith review, gives a value of 3.743_+0.018, in excellent agreement with the weighted mean of the manganese bath measurements. The value from our experiment of 3.752_+ 0.029 agrees very well with both the manganese bath and most recent liquid scintillator measurements. As we mentioned previously the present measurements are tied to the N P L manganese bath through the neutron detector efficiency. However, manganese bath measurements of ~involve very precise measurements of the spontaneous fission rate, whereas our measurements of neutron multiplicity per fission event are not nearly so sensitive to absolute fission rates (see Section 2.3.3). The good agreement between our value of ~7and the N P L value of 3.734-+ 0.019 validates the N P L fission counting technique. Of the previous 242pu measurements (see Table 6), only Boldeman has good statistical precision. Our value of 2.153_+0.019 is slightly higher than Boldeman's value of 2.120-+ 0.007. The only previous measurement of the ratio V(242pu)/v(252Cf) was by Boldeman (1968, 1974). His revised value of 0.5663 _+0.0028 is not inconsistent with the value of 0.5738_+0.0033 obtained in the present work. However Boldeman's result has not been
~
a2
2.07___0.09 2.46+0.16
1.20+0.10 --
2.11 +0.05 2.120 + 0.007 2.153__+0.019
1.31 + 0.01 1.298+0.008
Results measured relative to 252Cfhave been renormalized to ~ (2 s2Cf) = 3.744 (the weighted mean of all measurements excluding the recent tentative value of Spencer (see Smith, 1980; Spencer, 1980)); otherwise the data of Lazarev (1977) are used for renormalization. corrected for fission-foil thickness (Boldeman and Frehaut, 1980), and this would increase his ratio and his absolute value of ~for 242pu. In addition it may be that a further revision of the effects of delayed 7-rays to which his results are sensitive (Boldeman, 1968, 1974) would bring the two measured ratios into closer agreement. 4.4. Comparisons with Other Measurements oft& The evaluation of Lazarev (1977) lists a 2 for 2s2cf as 1.57+0.01, in excellent agreement with the present value of 1.562+0.011. Previous experimental measurements o f a 2 for 242pu are shown in Table 6, and are in excellent agreement with the present value of 1.298 + 0.008. 4.5. Comparisons with Neutron Multiplicity Distribution Formulae The measured multiplicities have been fitted with two models : (1) Terrell's (1965) model (2) The Truncated Renormalized Double-Gaussian (TRDG) distribution of Edwards et al. (1981). Comparisons are presented in Table 7 between the ~7 and a 2 as determined directly, and as fitted by Terrell's model and the T R D G . In all cases the T R D G provides a more accurate description, particularly for the low distribution of 242pu, providing further validation of Edwards et al. (1981).
Table 7. Comparison between predictions of Terrell and TRDG fits and direct determination of ~Tanda 2 from equations (7) and (8), AffTerreU = 100 ((l~Tetr¢ll-- Vdirect)/Vdirect) etc. Fissioning nucleus
Fission-fragment det. eft. t/(~o)
f Direct
Terrell At7(~)
TRDG Af (~)
0-2 Direct
Terrell A°'2 (~oo)
TRDG A 0"2 (~o)
242Pu 2s 2Cf
88 100
2.139 3.751
-- 4.14 - 0.55
0.04 - 0.34
1.289 1.541
17.15 4.58
-- 0.25 2.66
and ~r2 for spontaneous fission of 252Cf and 242pu 5. CONCLUSIONS Absolute determinations of the prompt ~and a 2 have been obtained for the spontaneous fission of 252Cf and 242pu to <0.9~o precision. The importance of correcting 9 and a 2 for fission-fragment detection efficiency has been emphasized; for 242pu this increase amounts to 0.68~o for f and 1.04~o for tr 2. For 252Cf, the values of ~ and tr 2 agree within experimental error with those of previous workers. For 242pu, our ~ measurement is consistent with the only other precise measurement ; and our value of tr 2, deduced with greater precision, is also in agreement. The ratio ~(242pu) : ~7(252Ci) has been measured with greater accuracy than either absolute measurement. This value is not inconsistent with the only comparable measurement (Boldeman, 1974) and agreement would probably be improved if the Boldeman value were corrected for foil thickness. Acknowledgements--We are grateful to our colleagues in Chemistry Division and Instrumentation and Applied Physics Division for producing the fission foils and ionization chambers. We are indebted to Dr M. G. Sowerby for invaluable discussions throughout the project and to Dr M. S. Coates for a critical reading of the manuscript. REFERENCES
Axton E. J. and Bardell A. G. (1982) Metrologia. Submitted for publication. Belov L. M. et al. (1969) Soviet J. nucl, Phys. 9, 421. Boldeman J. W. (1968) J. nucl. Energy 22, 63. Boldeman J. W. (1974) Nucl. Sci. Engng 55, 188. Boldeman J. W. and Frehaut J. (1980) Nucl. Sci. Engng 76, 49. Chapman W. S. et al. (1977) AERE-R8597.
135
Colvin D. W. and Sowerby M. G. (1965) Proc. Syrup. Physics and Chemistry of Fission, Salzburg, Vol. 2, pp. 25-37. IAEA, Vienna. Crane W. W. T., Higgins G. H. and Bowman H. R. (1956) Phys. Rev. 101, 1804. Edwards G., Findlay D. J. S. and Lees E. W. (1981) Ann. nucl. Energy 8, 105. Geiger K. W. and Van der Zwan L. (1975) Nucl. lnstrum. Meth. 131, 315. Hicks D. A., Ise J. and Pyle R. V. (1956) Phys. Rev. 101, 1016. James G. D. and Saussure G. de (1981) Nuclear Fission and Neutron Induced Fission Cross-Sections, Chapter 4. Pergamon Press, Oxford. Lambert K. P. (1977) AERE-R8303 (revised). Lazarev Yu. A. (1977) Atom. Energy Rev. 15, 75. Lees E. W. and Lindley D. (1977) AERE-R8891. Lees E. W., Patrick B. H. and Bowey E. M. (1980) Nucl. Instrum. Meth. 171, 29. Lemmel H. D. (1975) Nuclear Cross-Sections and Technology, Washington, Vol. 1, pp. 286-292. N.B.S. Spec. Publ. No. 425. N.B.S., Washington. Lorch E. A. (1973) Int. J. appl. Radiat. Isotopes 24, 585. Prokhorova L, I., Smirenkin G. N. and Turchin Yu. M. (1969) BNL-tr-266, Sherriffs V. S. W. (1978) SRD R86 UKAEA. Smith J. R. (1979) Proc. Syrup. Nuclear Data Problems for Thermal Reactor Applications, Brookhaven, 5.1-5.27. EPRI NP-1098. Smith J. R. (1980) Proc. Int. Conf. Nuclear Cross-Sections.for Technology, Knoxville, 1979, pp. 738-742. N.B.S. Spec. Publ. No. 594. N.B.S., Washington. Spencer R. R. (1980) Proc. Int. Conf. Nuclear Cross-sections for Technology, Knoxville, 1979, pp. 728-732. N.B.S. Spec. Publ. No. 594. N.B.S., Washington. Terrell J. (1965) Proc. Syrup. Physics and Chemistry of Fission, Salzburg, Vol. 2, pp. 3-24. IAEA, Vienna. Werle H. (1970) Nuclear Research Centre, Karlsruhe. Report INR-4/70-25. Zhang H.-Q. and Liu Z.-H. (1979) Chin. J. nucl. Phys. 1, 9. (Available in translation from IAEA Nuclear Data Section).
03064549/82[0301274)9503.00/0 Pergamon Press Ltd
M E A S U R E M E N T S OF P R O M P T ~ A N D V A R I A N C E F O R THE S P O N T A N E O U S FISSION OF 252Cf A N D 242pu G. EDWARDS,* D. J. S. FINDLAY and E. W. LEES Nuclear Physics Division, AERE Harwell, Oxon OXI 1 0RA, U.K.
(Received 16 October 1981) Abstract-- Measurements of the mean (v-)and variance (a 2) of the prompt neutron multiplicity distribution for
the spontaneous fission of 2s2Cf and 242pu have been made. Quantities of 2s 2Cfand 2'~2pu were incorporated in ionization chambers placed at the centre of a large oil-moderated neutron detector. The dependence of both f and tr2 on the fission-fragment detection efficiency of the ionization chambers was investigated in detail and led to a correction in 242pu of 0.68~ for ~ and 1.04~ for tr2. The values deduced are: ~(252Cf) = 3.752-1-0.029, o'2(252Cf)= 1.562--+0.011 v(242pu) = 2.153___0.019, o'2(242pu) = 1.298-+0.008. The ratio ~(Pu)/~(Cf)is determined more accurately than either absolute measurement, and is 0.5738 -+0.0033. 1. I N T R O D U C T I O N
In this paper we report measurements of the mean and variance ~ and tr 2 of the distribution of fission neutrons from 252Cf and 242pu measured using the Harwell oilmoderated assembly o f B F 3 counters (Lees et al., 1980). For 252Cf, our precision (0.8~o) compares favourably with existing measurements, but since our measurements rely on the calibration of the N P L manganese bath for determination of absolute neutron strengths, we cannot hope to resolve the discrepancies between the manganese bath and liquid scintillator measurements of ~7(seethe review articles of Smith 1979,1980 for a full discussion of the importance of ~ for 252Cf as a standard). However we can confirm the fission counting efficiency of the manganese bath measurements by an independent technique. For 242pu, the existing set of measurements of ~7 is not nearly so comprehensive as for 252Cf, there being only one measurement (Boldeman, 1968, 1974) of better than 2~o accuracy, and so it was felt that a second precise measurement of ~7for 242pu was necessary. Most of the uncertainty of our measurements is due to uncertainties in the neutron detector efficiency; since these are largely c o m m o n to both measurements, our value of the ratio ~ ( 2 4 2 p u ) / ~ ( 2 5 2 C ~ is more accurate than either absolute measurement. 2. E X P E R I M E N T A L
DETAILS
The experimental technique used in making these measurements is similar to that described by Lees et al. * Attached to the University of Oxford.
(1980) (hereinafter called Method I) in which the spontaneously fissioning source is incorporated in an ionization chamber placed at the centre of a highefficiency neutron detector consisting of 56 BF 3 counters connected in five rings and immersed in an oil moderator. After each fission-chamber pulse, the number of neutrons captured in the neutron detector in a gate ~ 300-#s long (the spectrum gate) is recorded and stored in a P D P - 11/45 computer. After a further ~ 1000 /~s, the background in a gate of the same length (the background gate) is also recorded and stored.
2.1. Modifications to Detector and Data Collection System For the present measurements a few changes were made to the procedure described in Method I : (1) The neutron detector assembly was taken apart, moved to the low energy area of the new Harwell 136 MeV electron linear accelerator, and reassembled inside a shielded blockhouse. (2) The E H T for the BF 3 counters was raised from 3.6 to 3.8 kV, thereby enabling amplifier gains to be lowered and consequently eliminating r.f. pick-up from the new higher power accelerator. (3) The gate width (measured using a random pulse generator whose output was shaped to simulate real neutron counts) was increased from 170 to 297.3 +0.2 #s; this had the effect of significantly increasing the detection efficiency for high multiplicity events and of eliminating the energy dependence of the gating factor (see point (7)). 127
128
G.
et
EDWARDS
al.
Table 1. BF 3 detector efficiency calibration sources, and corrections applied to raw efficiencies for neutron absorption by the fission-chamber materials and Be impurities in the other (~, n) sources Source type
Neutron mean energy (MeV)
Am/Li Am/F Am/B Am/Be
0.45+0.1 1.25+0.15 2.70___0.25 4.20 _ 0.20
Neutron absorption correction (~o) 1.48+0.38 0.15+0.05 0.49___0.15 0.08 ___0.04
Be correction (~)
Final efficiency
+0.94+0.15 +0.17+0.03 +0.21___0.03
0.4825 + 0.0033 0.4602+0.0031 0.4331+0.0025 0.3993 __+0.0031
The mean energies of the neutron sources were deduced from Geiger and Van der Zwan (1975), Lorch (1973) and Werle (1970). (4) A 2 ms paralysis time was applied to the output of the fission ionization chamber so that data processing could not be triggered by any further fissions occurring within this period. (5) The data collection system has been extended to record ring ratios* as a function of neutron multiplicities 1, 2 and >~3 ; these data may give neutron energies as a function of multiplicity. (6) The efficiency of the neutron detector assembly has been redetermined more accurately using the same 24tAm/Li, /F, /B a n d / B e sources calibrated with the National Physical Laboratory manganese bath as in Method I. However for the present measurements the strengths of these neutron sources as determined from the N P L calibration were increased by 0.5~o to account for chemical impurities in the bath solution (Axton and Bardell, 1982). The reflection and capture of neutrons in the materials of the source were computed by the Monte Carlo programme MONK(Sherriffs, 1978) which uses the U.K. Nuclear Data Library. The percentage corrections to the measured efficiencies are given in Table 1. Also given in Table 1 are corrections for Be impurities in the A m / L i , / F a n d / B sources (Lees and Lindley, 1977). The final neutron detection efficiency e as a function of neutron energy E (MeV) is well represented by the straight line (see Fig. 1) e = (0.4907_0.0038)-(0.0218 +0.0016)E
and e = 0.4492+0.0034
for 2 4 2 p U ( E = 1.9+0.1 MeV).
(7) The capture time distribution was measured with better resolution for both 2s2cf and 242pu fission chambers with a multishot time analyser having ½ #s bins (Chapman et al., 1977) using a fission-fragment pulse as a start and the detected neutron pulses as stops. The distributions for the two fission chambers were different due to the shorter time constants used on the amplifier and preamplifier for the 242pu chamber (see Table 2). The gating factor, or fraction of neutron captures occurring within the time the gate is open, 8-305.3 #s, was evaluated directly from these data after background subtraction. The gating factors obtained were ]-~os.3 f ( t ) d t = 0.8777+0.0004 for 252Cf and 0.8801 + 0.0004 for 242pu. These data were also used to evaluate the integrals .fsa°5"3f2(t) dt and S]°s'af3(t) dt which are required for deadtime corrections (described in Method I).
2.2. Spontaneous Fission Sources 2.2.1.2s2cffission chamber An oxide source of high chemical purity was used in the 2~2Cf fission chamber (see Table 2). Analysis by the 10
(1) 08
with a correlation coefficient of --0.743. The fitting procedure took account of the covariances in the neutron source strengths due to all sources being measured at NPL. Hence at the energiest of the two fission sources used in this experiment,
06 E
.----___._,.
O~
= 0.4438+0.0028
for 2 5 2 C f ( E = 2.15+0.05 MeV)
* The ratio of counts in the outermost to innermost rings in the detector is a monotonically increasing function of neutron energy. t The mean energy for 2~2Cfwas deduced from a survey of the literature; the mean energy for 242pu was deduced from our ring ratio measurements, equation (4) in Terrell (1965) and Belov et al. (1969).
02
i 1
i 2
i 3
i
E (MeV)
Fig. 1. Neutron detection efficiency e as a function of neutron energy E for the Harwell BF 3 counter assembly.
f and a 2 for spontaneous fission of 2s2cf and 2'*2pu
129
Table 2. Properties of fission chambers Property Mass of fissionable material (g) Diameter of fissionable material (mm) Backing material and thickness (mm) Initial isotopic composition (~o)
Chamber gas pressure (mm Hg) Electronic time constants (#s) Integration (I) Differentiation (D)
252Cf
2'*2pu
7.36 x l0 - i t
1.092 X 10 -2 40 Pt, 0.13 242pu : 89.37
--
Pt, 0.13 252Cf; 74.48 2s°Cf: 25.52
24tpu :0.93 24°pu : 4.57 239pu : 5.13
760 Preamp: 100(I) Amp : 1 (I)
190 Preamp: 0.2(I) Amp : 0.2 (I)
1 (D)
0.2 ( D )
The isotopic composition of the Cf during measurements of ~ also included 248'246'2't4Cm, these, however, made a negligible contribution to neutron output, The isotopic composition of Pu is that taken immediately after 2*tAm separation in October, 1979. Chemical Division at Harwell showed the presence of 2s°cf, and by the time of measurement, daughter impurities of 24SCm and 246Cm were present; these led to only a 0.025~ correction to the measured ~7value. The fission rate deduced from the measured ~t activity implied that the chamber was > 9 9 % efficient in detecting fission fragment pulses. The half-life of 2szcf is 2.63 yr, so over the period of data collection (June 1980-January 1981) the fission rate changed significantly.
2.2.2. 242pit fission chamber Details of the 242pUO2 s o u r c e used are also given in Table 2. The only other isotope contributing fission neutrons is 24°Pu, having a ~ value very similar to that o f 242pu (Boldeman, 1974), implying a negligibly small correction. A spontaneous fission rate of 8.03 +_0.08 s - 1 was deduced from a measurement of the total neutron output of the source* (after correction for the (~t,n) contribution of 0.13 ns-1). The gas pressure in the chamber for early runs was 760 m m Hg. At this pressure the fission rate was only 62~o of the expected value, owing to the need to discriminate against severe • pileup. Subsequently two reductions in pressure were made, first to 380 mm, then to 190 mm. The final fission fragment detection efficiency was 889/o,slightly less than * The spontaneous fission rate was confirmed with poorer precision using a neutron coincidence counter designed for safeguards applications (Lambert, 1977). ~"Fission fragments recoiling in the plane of the foil will not be detected. Neutrons emitted in the direction of fragment recoil will, on average, have higher energies. Furthermore, neutrons emitted in the direction of the BF 3 detector symmetry axis will escape along the through tube. The highest energy neutrons from fragment recoils parallel to the detector axis are therefore always lost. However, such fragment recoils are not detected when the foil is arranged parallel to the axis, and hence the average kinetic energy for detected neutrons is higher.
that expected from fission fragment ranges (James and de Saussure, 1981), but probably accounted for by irregularities in target deposition. An extrapolation to 100~o detection efficiency was made (see Section 2.3.3).
2.2.3. Fission chamber absorption Absorption by the materials comprising the fission chambers necessitates a correction to the neutron detection efficiency of the BF a counter assembly. These corrections, again computed by MONK, resulted in reductions of (0.59 + 0.11)~o for the 252Cf chamber and (1.01 + 0 . 1 4 ) ~ for the 242pu chamber. The final gated detection efficiencies es were : eg(252C0
=
0.3872 +_0.0025
eg(2*2pu) = 0.3914+_0.0030.
2.3. Consistency and Sensitivity Checks 2.3.1. Background correction To check the accuracy of the background correction procedure described in Method I, a measurement of for 252Cf was made with the background increased (using an Am/Be neutron source) by a factor of 20 over that occurring naturally. The value of f was unchanged within statistics.
2.3.2. Fission chamber orientation The design of the two fission chambers used was different. The 242pu chamber had its foil orientated perpendicular to the symmetry axis of the detector; the 2s 2Cfchamber, however, had its foil parallel to this axis. A check on the effect of orientation of the chambers with respect to the detector axis was carried out. When the foils were arranged perpendicular to the axis, the ring ratio, and hence the mean detected neutron energy, was lower than when the foils were parallel to the axis.t
130
G. EDWARDSet al. I
I
I
I
Variation of P with Fission Fragment Detection E f f i c i e n c y
I T
376
3 72
370 P
252Cf
354
352
36°
do
I0
9'o
5'
I~0
Fig. 2. Measured ~ as a function of fission-fragment detection efficiency ~/for the 252 Cf fission chamber. Errors shown are the statistical errors for each point appropriately increased to account for the very small fluctuations in neutron detector efficiency (Section 2.3.4). Appropriately correcting the efficiency for the small change in neutron mean energy with orientation (equation (1)) and for the slightly different position of the fission foils in the two orientations led to values of different by only 0.38+0.14% and to values of a 2 different by only 0.46+0.42%; these amounts were included as errors (see Table 5). The values of ~7and a 2 quoted in this paper are for the parallel orientation. I
2.3.3. Variation o f measured ~ and a 2 with fragment
detection efficiency Since the fission-fragment detection efficiency of the 242pu chamber was ~ 88%, an extrapolation to 100% efficiency was necessary. Therefore a study of the variation of measured ~and a 2 with fragment detection efficiency was made for both 242pu and 2s2Cf. The results for ¢ are illustrated in Figs 2 and 3.
I
[
I
I
I 90
l 100
Variahon of ~ with Fission Fragment Detection E f f i c i e n c y 216
2.15
214
213
212
211
242pu
210
209
I 60
I 70
I 80 n I°/o)
Fig. 3. Measured ~ as a function of fission-fragment detection efficiency ~ for the 242Pu fission chamber. Errors as in Fig. 2.
and a 2 for spontaneous fission of 252Cf and 242Pu I
i
I
I
Variation of 0.2 with Fission Fragment Defection Efficiency
131 I
rt
'1 ' 6 2
1 60
1 58
oz
1 56
1 5/*
1 52 252Cf 1.50
1 1.8
I 60
I 70
I 80 n i%)
i 90
1 100
Fig. 4. Measured o 2 as a function of fission-fragment detection efficiency ~/for the 252Cf fission chamber. Errors as in Fig. 2. i
I Variation of a 2 with Fission Fragment Detection Efficiency
i
I
I
I 90
1 100
r/
1 31
1 3C
12S
o 2 128
1 27
242 PH
12E
12~
I 60
I 70
I S0 n (%}
Fig~5~Measured~2asafuncti~n~ffissi~n-fragmentdetecti~nef~ciencyqf~rthe242Pufissi~nchamber~Err~rs as in Fig. 2. Reducing fission-fragment detection efficiency by increasing the discrimination threshold preferentially excludes those fragments of lowest kinetic energy. Since fission fragments with low kinetic energy tend to have high excitation energy, and high excitation energy leads to high emitted neutron multiplicity, a reduction in q is expected. Based on the general trend of the data points, th~ results for q were fitted by the straight lines
* This effect is analogous to the variation in measured ~with fission-foil thickness (Boldeman and Frehaut, 1980).
for 252Cf" 17(~]) =
(3.424_+0.017)+ 10 -3 (3.26+0.18)q
(2)
with a correlation coefficient of -0.989 for 2 4 2 p u " 17(?/) ~-~ (2.028+0.012)+ 10 - 3
(1.25 _+0.15)q
(3) with a correlation coefficient of --0.995 where r/is the fragment detection efficiency (~).* Similar plots were made for o 2 (Figs 4 and 5), and
G. EDWARDSet al.
132
Table 3. Summary of 252Cf data
a l t h o u g h a linear dependence is perhaps not quite so obvious now, the d a t a are represented by the lines for
Date of run
Fission rate (s - 1)
~
0.2
10.87 10.81 10.69 10.74 9.88 9.67 9.29
3.759 3.759 3.746 3.744 3.745 3.751 3.757
1.554 1.568 1.557 1.586 1.571 1.541 1.560
--
3.752
1.562
252Cf: tr2(q) = (1.494 _ 0.042) + 10- a (0.684 + 0.459)r/
(4) with a correlation coefficient of - 0 . 9 9 0 for
242pu • o"2(/1) ---~(1.200 ~ 0.018) q-- 10- 3 (0.983 + 0.218)r/
(5)
9 June 1980 10 June 1980 11 June 1980 26 June 1980 12 November 1980 24 November 1980 29 January 1981 Mean
with a correlation coefficient of - 0 . 9 9 6 This b e h a v i o u r m a y also be u n d e r s t o o d in terms of preferential exclusion of high multiplicity. A small but significant dependence of ring ratio with fission-fragment detection efficiency was noted. It is possible to interpret this as a slight variation of n e u t r o n average kinetic energy with n e u t r o n multiplicity.
in the b a c k g r o u n d gate is slightly higher t h a n that occurring d u r i n g the spectrum gate since fissions c a n n o t have occurred before the spectrum gate but m a y occur during a n d after the spectrum gate. The ratio of the b a c k g r o u n d s is given by the formula
2.3.4. Long-term consistency The present m e a s u r e m e n t s were carried out between J u n e 1980 a n d July 1981. Over this period the detector efficiency was checked m a n y times a n d was found to vary on average by only 0.17~o. T h e statistical errors on ~Tandtr 2 values from individual runs were appropriately increased to account for this variation. Table 3 shows the consistency between individual 252Cf runs over this period. 3. D A T A
Bb~'¢k = (1 +fz) Bspec
(6)
where Bspec is the effective b a c k g r o u n d d u r i n g the spectrum gate Bback is the m e a s u r e d b a c k g r o u n d in the b a c k g r o u n d gate f i s the unparalysed fission rate z is the m e a n lifetime of a n e u t r o n in the detector,
ANALYSIS
Several corrections to the raw d a t a are m a d e before a value of ~7is obtained.
F o r a m e a n n e u t r o n lifetime in our detector of 135/~s, the correction to ~ a n d a 2 is <0.0001 for 252Cf a n d completely negligible for 242pu.
3.1. Paralysis Correction to Background Most of the b a c k g r o u n d (82Voofor 252Cfand 65~o for 242pu) is due to n e u t r o n s from other fission events. As s h o w n by Colvin a n d Sowerby (1965), however, when a paralysis period is imposed the b a c k g r o u n d measured
3.2. Other Corrections to Data B a c k g r o u n d a n d dead time corrections are m a d e as described in M e t h o d I. The changes in ~ a n d tr 2 m a d e by including these corrections are given in Table 4, where
Table 4. Effect of the various corrections made to the data on the values of ~ and a2 Average change when correction is included 0-2
Nature of correction Background Deadtime Background paralysis q extrapolation + 6eg* change in eg Isotopic impurities Fission-chamber absorption
2~2Cf
242pu
252Cf
242pu
- 0.022 + 0.009 < 10- 4
- 0.011 + 0.003 <<10 - 4 + 0.014 - 0.017 Negligible + 0.022
- 0.057 + 0.038 < 10 - 4 -+ 0.004 Negligible - 0.004
- 0.020 + 0.014 <<10- 4 + 0.013 - 0.004 Negligible + 0.005
- 0.024 + 0.001 + 0.022
* 6eg = 0.0025 for 252Cf, 0.0030 for 2d'2pu.
and a 2 for spontaneous fission of 2s2Cfand 242Pu the effects of all other corrections are also listed. In computing the neutron detector efficiency for 252Cfan d 242pu we have assumed that equation (1) is a true representation of the efficiency above the mean energy of the Am/Be source 4.2 MeV. We have performed sensitivity checks based on the following extremely unlikely two assumptions : if e = 0 for E > 7.5 MeV then the present ~ values would increase by 1.09/o; if below 0.3 MeV e rises rapidly towards e = 1 as E ~ 0 the present q values would decrease by 0.45%. However these two assumptions are highly improbable. Further support for our use of equation (1) is that the neutron spectrum from an Am/Be source extends up to 10.3 MeV and marked deviations of e from linearity would be expected to markedly lower the measured Am/Be efficiency.
133
3.4. Evaluation of Errors As mentioned in Section 2.3.4, the statistical errors on ~7 and a 2 values from individual runs were appropriately increased (in quadrature) to account for the very small fluctuations in neutron detector efficiency. A detailed list of the components of the final errors in ~7and a 2 are given in Table 5 ; all components are + l a and were added in quadrature to give the final errors quoted in the next section. 4. RESULTS AND DISCUSSION
4,1. Absolute Values of ~ and a2 for 252Cfand 242pu The values oflTand 172for 2 s2Cfwere obtained from a weighted mean of seven runs, and are ~7(2s2cf) = 3.752 +0.029
3.3. Direct Determination of ~ and 172
a2(2s2Cf) = 1.562+0.011.
Following Lazarev (1977), ~ and 172 have been determined directly from the data using the relations =
F o r 242pu 15 runs were used to define the linear extrapolation to 100% shown in Figs 3 and 5, and the final results are
(7)
--
~g :
~(242pu) = 2.153 +0.019
,~ )
=
a2(242pu) = 1.298_ 0.008.
(8)
4.2. f for 242pu Relative to 252Cf where 9
9
nQ(n), ~ = ~ n2Q(n),
~ =
n=O
n=O
the Q(n) are the measured neutron distribution probabilities, and e, is the efficiency of the neutron detector.
As explained in Section 1, the ratio ~(242pu/~(252C0 is more accurate than either absolute value. The error in the ratio was computed from the components given in Table 5 by omitting the errors due to source orientation (the two fission chambers had their fission foils in the same orientation) and by replacing the errors due to detector efficiency calibration and fission neutron/~ by
Table 5. Contributions to errors quoted on the final f and a 2 results in Section 4.1 tr2 Source
Background Deadtime Fission-chamber absorption Gating factor Detector eft. calibration* Fission neutron E Statistical error Statistical error in extrapolated value 1% in fission rate Fission chamber position error Source orientation Total
2s2Cf
2*2pu
2s2Cf
2'*2pu
0.001 0 0.004 0.002 0.022 0.009 0.003
0* 0 0.003 0.001 0.012 0.010
0.002 0.002 0.002 0.001 0.004 0.002 0.008
0 0.001 0.001 0 0.003 0.002
-0.003 0.002 0.014
0.003 0.001 0.001 0.008
0.001 0 0.006
0.004 0.001 0 0.006
0.029
0.019
0.011
0.008
* Contributions less than 0.001 are denoted 0. t Includes covariance terms (see Section 2.1).
134
G. EDWARDSet al. Table 6. Experimental values of ~ and a 2 for the spontaneous fission of 242pu
the error in the efficiency difference arising from the two different neutron mean energies/~ of 242pu and 252Cf. The ratio is
Author
~(242pu) - = 0.5738+0.0033. 1~(25 2Ct)
Hicks et al. ( 1 9 5 6 ) Crane et al. ( 1 9 5 6 ) Prokhorova et al. (1969) Boldeman (1974) Present work
4.3. Comparisons with Previous Measurements of ~ Smith (1980) summarizes the various measurements of ~ for 252Cf, pointing out the discrepancies between manganese bath and liquid scintillator measurements, and attempting to reduce the discrepancies by improved data corrections. The weighted average of the manganese bath measurements for ~7T, the total number of neutrons emitted per fission, is 3.750; removing the delayed neutron fraction of 0.009 per fission (Lemmel, 1975) gives a value of 3.741_+0.009 prompt neutrons per fission. Smith's evaluation of the group average of liquid scintillator measurements is 3.771_+0.009 (prompt). However a recent liquid scintillator measurement by Zhang and Liu (1979), published since the Smith review, gives a value of 3.743_+0.018, in excellent agreement with the weighted mean of the manganese bath measurements. The value from our experiment of 3.752_+ 0.029 agrees very well with both the manganese bath and most recent liquid scintillator measurements. As we mentioned previously the present measurements are tied to the N P L manganese bath through the neutron detector efficiency. However, manganese bath measurements of ~involve very precise measurements of the spontaneous fission rate, whereas our measurements of neutron multiplicity per fission event are not nearly so sensitive to absolute fission rates (see Section 2.3.3). The good agreement between our value of ~7and the N P L value of 3.734-+ 0.019 validates the N P L fission counting technique. Of the previous 242pu measurements (see Table 6), only Boldeman has good statistical precision. Our value of 2.153_+0.019 is slightly higher than Boldeman's value of 2.120-+ 0.007. The only previous measurement of the ratio V(242pu)/v(252Cf) was by Boldeman (1968, 1974). His revised value of 0.5663 _+0.0028 is not inconsistent with the value of 0.5738_+0.0033 obtained in the present work. However Boldeman's result has not been
~
a2
2.07___0.09 2.46+0.16
1.20+0.10 --
2.11 +0.05 2.120 + 0.007 2.153__+0.019
1.31 + 0.01 1.298+0.008
Results measured relative to 252Cfhave been renormalized to ~ (2 s2Cf) = 3.744 (the weighted mean of all measurements excluding the recent tentative value of Spencer (see Smith, 1980; Spencer, 1980)); otherwise the data of Lazarev (1977) are used for renormalization. corrected for fission-foil thickness (Boldeman and Frehaut, 1980), and this would increase his ratio and his absolute value of ~for 242pu. In addition it may be that a further revision of the effects of delayed 7-rays to which his results are sensitive (Boldeman, 1968, 1974) would bring the two measured ratios into closer agreement. 4.4. Comparisons with Other Measurements oft& The evaluation of Lazarev (1977) lists a 2 for 2s2cf as 1.57+0.01, in excellent agreement with the present value of 1.562+0.011. Previous experimental measurements o f a 2 for 242pu are shown in Table 6, and are in excellent agreement with the present value of 1.298 + 0.008. 4.5. Comparisons with Neutron Multiplicity Distribution Formulae The measured multiplicities have been fitted with two models : (1) Terrell's (1965) model (2) The Truncated Renormalized Double-Gaussian (TRDG) distribution of Edwards et al. (1981). Comparisons are presented in Table 7 between the ~7 and a 2 as determined directly, and as fitted by Terrell's model and the T R D G . In all cases the T R D G provides a more accurate description, particularly for the low distribution of 242pu, providing further validation of Edwards et al. (1981).
Table 7. Comparison between predictions of Terrell and TRDG fits and direct determination of ~Tanda 2 from equations (7) and (8), AffTerreU = 100 ((l~Tetr¢ll-- Vdirect)/Vdirect) etc. Fissioning nucleus
Fission-fragment det. eft. t/(~o)
f Direct
Terrell At7(~)
TRDG Af (~)
0-2 Direct
Terrell A°'2 (~oo)
TRDG A 0"2 (~o)
242Pu 2s 2Cf
88 100
2.139 3.751
-- 4.14 - 0.55
0.04 - 0.34
1.289 1.541
17.15 4.58
-- 0.25 2.66
and ~r2 for spontaneous fission of 252Cf and 242pu 5. CONCLUSIONS Absolute determinations of the prompt ~and a 2 have been obtained for the spontaneous fission of 252Cf and 242pu to <0.9~o precision. The importance of correcting 9 and a 2 for fission-fragment detection efficiency has been emphasized; for 242pu this increase amounts to 0.68~o for f and 1.04~o for tr 2. For 252Cf, the values of ~ and tr 2 agree within experimental error with those of previous workers. For 242pu, our ~ measurement is consistent with the only other precise measurement ; and our value of tr 2, deduced with greater precision, is also in agreement. The ratio ~(242pu) : ~7(252Ci) has been measured with greater accuracy than either absolute measurement. This value is not inconsistent with the only comparable measurement (Boldeman, 1974) and agreement would probably be improved if the Boldeman value were corrected for foil thickness. Acknowledgements--We are grateful to our colleagues in Chemistry Division and Instrumentation and Applied Physics Division for producing the fission foils and ionization chambers. We are indebted to Dr M. G. Sowerby for invaluable discussions throughout the project and to Dr M. S. Coates for a critical reading of the manuscript. REFERENCES
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