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The yield of fission neutrons per neutron absorbed for PU239 up to 60-eV incident energy
J.Nuclear Energy, 1956.VoL3,pp.33 to44. PergamonPress Lrd..London
THE YIELD OF FISSION NEUTRONS PER NEUTRON ABSORBED FOR Pu239 UP TO 60-eV INCIDENT ENERGY F. J. M. FARLEY* Atomic Energy Research Establishment, Harwell, Didcot, Berks (Received 9 February 1956)
Abstrac&---Theyield of fast neutrons from plutonium discs is measured with a high-pressure methane counter for incident neutron energies up to 60 eV, using the Harwell time-of-flight neutron spectrometer. By measuring the transmission of the samples under identical conditions, and correcting for scattering, the number of incident neutrons captured in the sample is obtained. The ratio 7 of the fast-neutron yield to the number of incident neutrons captured is then calculated as a function of incident energy, the calibration constant being obtained by fitting to known values in the region 0*03-0.3 eV. The values of r] fluctuate widely from resonance to resonance, but r] appears to be constant within each resonance, and to change smoothly between resonances. A curve of the fission cross-section of PuzJ8up to 60 eV is also presented. INTRODUCTION THE
yield of fast neutrons from a fissile material per incident neutron absorbed, usually called 11, is of interest in reactor design. It is related to v, the number of neutrons emitted per fission, and to the capture and fission cross-sections a, and a, by the equation 7 = V4(% + 0,) = v lXr, + F,) (1) where l?, and rr are the partial widths for fission and for gamma-ray emission. For thermal neutrons incident, 7 has been measured in several laboratories, chiefly with a pile oscillator. The measurements have been reviewed by HARVEYand SANDERS (1956), who adopt the value 2.08 for Pu239. This we shall call Q,. Measurements of the variation of 7 with incident neutron energy can be made directly by using a neutron detector in conjunction with some form of spectrometer for the incident neutrons. The results are then normalized to fit the value 2.08 at thermal energy. SANDERS, using a crystal spectrometer, has detected. the fission neutrons with boron trifluoride counters embedded in paraffin, and explored the region 0.025436 eV (EGELSTAFF and SANDERS, 1955). PALEVSKY (1955) used six Hornyak-type fast-neutron scintillators (HORNYAK, 1952), with the Brookhaven slow chopper in the region 0~0141 eV, and the results have since been extended to 0.5 eV (HARVEY and SANDERS, lot. cit.). Measurements with Hornyak detectors, using a pulsed cyclotron as neutron source, have been repoited by NIKITIN, SUHORUCHKIN, IGNATYEV, and GALANINA (1955), whose results extend, with very poor resolution, up to about 60 eV. Less detailed information on the variation of 7 with energy can be obtained from experiments on reactor systems. HORTON and MCCULLEN (1955) have analysed the temperature coefficient of the reactivity of plutonium-water systems, and shown that q decreases with increasing energy in the thermal region. KANNE, STEWART, and WHITE (1955) exposed samples of plutonium to neutrons from a reactor, filtered through various shields so that the mean energy of the incident flux was varied. * On leave from Auckland University College, Auckland, New Zealand. 33
34
F. J. M. FARLEY
After irradiation, the PuMo and the fission-product concentrations were determined, the ratio yielding a&,, and hence 7, over five broad-energy regions extending to 15 keV. NIICITIN,KRUPCHITSKY,and BELKIN (1955) carried out a rather similar experiment, using a boron-loaded moderator to increase the mean energy.of the neutrons derived from a reactor, and report results on IJ= only. Values of 7 can also be deduced from an analysis of total cross-section and fission cross-section data. At low energies, where the data is obtained under conditions of good energy resolution, the accuracy is good, and the results agree with the direct measurements (HARVEYand SANDERS, Ioc. cit.); at higher energies, however, analysis of resonances in terms of the partial widths for neutron emission F,, gamma-ray emission Pr, and for fission l?,, is necessary, and the results are less reliable; the values obtained are displayed in Fig. 4 (EGELSTAFFand HUGHES,1956). In the present experiments the Harwell 15-MeV linear electron accelerator is used as a pulsed source of neutrons for time-of-flight spectroscopy (W~LIN, 1955), and a high-pressure methane counter (FARLEY, 1956) is used to detect the fast neutrons emitted from the fissile material. The number of neutrons stopped in the sample is alsomeasured, by means of a transmission experiment made under identical conditions. The value of 7 is then obtained from the ratio of the fast-neutron yield to the number of incident neutrons stopped in the sample, independent of self-shielding effects or of the energy’resolution of the equipment. The results are normalized to agree with those of SANDERSat low energies, and these in turn have been adjusted to the value 2.08 for thermal neutrons. Detailed information on 7 is thus obtained from zero to 6O-eV incident-neutron energy. METHOD A 3-in. diameter disc of fissile material is mounted perpendicular to the slow-neutron beam from the Harwell I5-MeV linear electron accelerator. Fast neutrons emitted from fissions accurring in the disc are detected by a fast-neutron counter placed alongside it. This counter is an ionization chamber, 2 in. diam. and 84 in. long, containing methane at a pressure of 40 atm; the collection time is in the range 0.2-1.9 p, and the overall efficiency is 0.07% for detecting fissions occurring in the disc (FARLEY, 1956). The fast-neutron signals are registered in a time-of-flight selector with one hundred channels each 2 p in width. They thus indicate the time of flight of the incident slow-neutrons between the accelerator and the fissile disc. Flight paths of 10.5 m, 7.3 m, and 3 m are used to cover the incident-neutron energy ranges 6-60 eV, 0.249 eV, and 0.03-064 eV respectively, the latter being used’for calibration of the experiment in the thermal region (see Fig. 1). The measurements give the yield of neutrons from the fissile material as a function the incident-neutron energy. In a subsidiary experiment, the fissile disc is removed and replaced by a group of short boron trifluoride counters. These are used to measure the number of incident neutrons in the beam as a function of time of flight (or energy). The fissile sample is then inserted in front of the counters and the run repeated. The difference between the two runs gives, after a correction for scattering, the number of incident neutrons captured in the disc as a function of energy. The ratio of the fast neutron yield to the number of incident neutrons removed from the beam is then proportional to 7. It is important in these measurements that the fast-neutron yield and the absorption
The yield of fission neutrons per neutron absorbed for Pups9 up to 6O-eV incident energy
of the incident neutrons should be measured using the same under identical conditions of flight-path and resolution. immediately the fast-neutron yield per neutron absorbed, required for resolution, or for self-screening by the sample. be of any thickness, although in practice a sample which
{,Fz rnetres
7
35
sample of fissile material The ratio then gives and no corrections are Indeed, the sample may is nearly “black” in the ---j
Concrete
Target
Baron - pbraffin shield FIG. I.--Apparatus.
resonances has the advantage of higher counting rates. The measurements give directly the number of fast neutrons emitted per neutron absorbed, i.e. 7, there being no need to analyse the data in terms of fission and capture cross-sections. Calibration of the experiment in the thermal region corrects atuomatically for any increase in the fast-neutron yield due to multiplication in the sample. EXPERIMENTAL
DETAIL
The arrangement of the apparatus is indicated in Fig. 1. Two independent boron trifluoride counters (not shown) were used to monitor the neutron output of the accelerator, and thus to enable successive runs to be compared. The two monitor readings were consistent to better than 1%. To cut out the very slow neutrons, which would otherwise be received from the previous pulse of the accelerator 25 msec earlier, a filter was placed in the beam. For the 10.5-m flight-path, delay-times 100-300 psec, the filter was cadmium, 05 mm thick. To study the lower-energy region, 0.03 to O-64 eV, it was necessary to reduce the flight-path to 3 m, so as to increase the ratio of velocities for the desired neutrons, delay 250-1150 psec, and the undesired neutrons, delay 2750-3650 psec. A 2-mm thick filter of Pyrex glass was used as a filter to attenuate the slower neutrons, but these were in any case few in number because their energy was less than OGO7eV, that is, well below thermal energy. To measure the effect of these “second trip” neutrons, the recurrence frequency of the accelerator was reduced from 400 c/s to 200 c/s and the spectrometer gates set to cover the range 2750-3650 ,usec. This count, to be subtracted from the normal runs at 400 c/s, was in many cases negligible, and never greater than 3 %. For’ the 7-3-m flight-path the same procedure was used; the filter was Pyrex glass 5 mm thick; the second-trip neutrons, now 25 % of the count, were measured in the same way. The background counting rate of the counters was measured for each run with the accelerator switched off, but with the sample, if any, in position. An ungated count
F. J. M. FARLEY
36
was taken, and the contribution to each gate during the run calculated. For the neutron counter this background was important because of the spontaneous fissions occurring in the sample, and in the case of the 5-mm plutonium sample amounted to 9 % of the maximum counting rate per gate. In the case of the boron trifluoride counters, however, it was verified that the counters did not detect neutrons from fissions in the sample, a necessary condition for this part of the experiment. In the case of the neutron counter there was also a background due to the accelerator when the fissile material was removed. It is not clear why fast-neutron counts should be recorded several hundred microseconds after the emission of a pulse from the machine. This background, which was measured and subtracted, was about 2%. To obtain a true value of 7, it is essential that the neutron counter shall be sensitive only to fissions occurring in the sample, and shall not detect gamma rays of neutron capture. To verify that the bias was set high enough to exclude gamma rays, runs were made with samples of h-in. silver, &in. natural uranium, and #-in. cadmium, the latter providing the most stringent test. There was no significant response in the positions of the capture resonances. To avoid errors due to the 100 msec dead time in the registers of the time-of-flight selector, the counting rate per gate was kept below 6/min. In the case of the runs at 3 m with the boron trifluoride counters, this meant that the output of the machine had to be reduced to about 1% of normal. At this level the background of the monitors becomes important. It was measured and subtracted, the correction being at most 29%. For the 10.5-m path, two runs were made in each case, the second with an extra delay of 1 psec in the signal path. In this way experimental points 1 ,usec apart were obtained from the 2qsec gates of the time-of-flight selector, at a resolution of 2 ,usec. Measurements were made on two samples of plutonium, both 3 in. in diameter. The first (5-mm sample) contained 418 g of plutonium metal, the second(l-mmsample) 77.77 g. REDUCTION
OF RESULTS
AND
DISCUSSION
The gate readings were corrected for the individually measured gate widths, and the backgrounds mentioned above were subtracted. Before comparing the fastneutron yield with the number of incident neutrons removed from the beam by the sample, it is necessary to correct for the loss of neutrons by scattering. Three types of scattering are considered separately: scattering by the copper can, potential scattering by the plutonium, and resonance scattering by the plutonium. (a) Scattering by the copper can. The thickness of copper on each face was 0.040 in. for the 5-mm plutonium sample and 0.020 in. for the l-mm sample. The scattering is calculated from the incident-neutron flux Z1 (first face), the transmittedneutron flux I, (second face), and the total cross-section of copper. This yields the total scattering by the copper, but some of the scattered neutrons go into the plutonium and are absorbed. The fraction of scattered neutrons which finally leave the sample depends on the blackness of the sample, as indicated by log Ii/Z,; it varies from 1 for I, = Z1 to 0.5 for I, = 0. This factor has been calculated for infinite slab geometry, with the results indicated in Fig. 2. It has been assumed that all scattered neutrons which interact with the plutonium are captured. The small fraction which are rescattered rather than captured introduces negligible error, because the scattering
The yield of fission neutrons per neutron absorbed for PuSso up to 60-eV incident energy
37
correction is itself already small. The curve is valid provided the resolution of the equipment is high, so that log I1/le gives a true measure of the blackness of the sample at each energy. This condition is not well satisfied for the highest energies in our range, and in this case the scattering by the copper will be slightly overestimated in the resonances leading to a value of 11which is slightly too high in the resonance. The correction for scattering by copper varied from a few per cent in the resonances to 20 % or more between resonances.
g 8
0.5 2 c Y f 0.2 6 ‘S P
0
05
1.5 2.0 fraction of scattered neutrons which escape from sample. 1.0
2.5
Log I,&
FIG.
2.-The
(b) Potential scattering by the plutonium. A constant potential scattering crosssection of 10 barns has been assumed. The amount of scattering is then proportional to the mean flux lin the sample which can be found from the ingoing flux I1 and the outgoing flux I,, I= (II - IJ(log Zl - log I&. (2) Again a correction is necessary, because some of the scattered neutrons are captured in the sample before they can escape. This has been calculated as a function of log IJl,, and is also shown in Fig. 2. Again multiple processes are neglected, and the calculation assumes infinite slab geometry and good resolution. This is justified, because in the resonances the scattering is small, and between resonances the sample is thin and the assumptions valid. This correction was ~1% in resonances and 20 y0 or more between resonances. (c) Resonance scattering by the plutonium. Throughout a particular resonance a constant fraction of the incident neutrons suffer resonance scattering instead of capture. The correction can therefore be applied at the end of the calculation to the value of q calculated for this resonance. The fraction of neutrons suffering resonancescattering is l?,/l?, but only a fraction of these will escape from the sample. Estimates of resonance parameters (HUGHES and EGELSTAFF, lot. cit.) indicate that r,/l? is less than 4 % for all significant plutonium resonances. The fraction of scattered neutrons escaping will be No-3 (see Fig. 2) and therefore the correction is 1 ‘A or less. It is neglected. The net boron trifluoride count C, indicating the number of neutrons stopped in the sample, after the scattered neutrons have been subtracted, must now be corrected for the I/U variation of the efficiency of the counters. The net count is 3A
38
F. J. M. FARLEY
therefore divided by the time of flight r. In the thermal region there is a further correction due to the self-shielding of the counter, which causes a departure from the true l/u relation. This is computed from the dimensions of the counter and filling pressure, and applied as a separate correction factor, E, which drops from 1 at high energies to 0.70 at 0.037 eV. The final expression for 7 is then Y
p=~XiXEX~,
(3)
where Y is the fast-neutron count and 1 is a constant of proportionality determined by fitting in the low-energy region.
which is
0.8 t 0 0~6 z 0.4
002
005
05 0’1 02 Neutron energy -
l.0
2.0
5.0
10c &
Fro. 3.-q relative to thermal r].
The final figures for q are normalized separately for the l-mm and 5-mm pluutonium samples to give the best fit to the figures of SANDERS in the range 0.037 to O-36 eV, where the two sets of data overlap. The two normalizing constants differ by 10% owing to the greater effect of internal fast-neutron multiplication in the larger sample. Fig. 3 gives the combined results, together with the points of SANDERS. It shaws the well-known drop in value in the region of 0.3 eV, and this is followed by a rise to about 0.8 thermal value in the region of low cross-section around 5 eV. No results are obtained in the neighbourhood of 1 eV, because of the strong absorption due to PUN in the samples. The statistical accuracy of the points is f2-5 % up to O-21 eV, f3.5 % from 0.21 to 0.64 eV, and &IO% in the region 3-6 eV. In this region the scattering corrections are large, ~30”/~ of the net boron trifluoride count, and therefore there is some uncertainty in the values. Using the same norqalization constants, 7 has been evaluated for the two samples in the higher-energy band, with the results shown in Fig. 4. Also shown in Fig. 4 are the fast-neutron yield curves for each sample per slow-neutron incident; in this case no correction has been made for scattering either by the plutonium or by the
The yield of fission neutrons per neutron absorbed for PLP up to @-eV incident energy
l-!-A-A
-
quappu! uoJqnou -Iad pi+
uoJqnaN
39
40
F. J. M. FARLEY
copper can, and no account is taken of the incident neutrons which emerge through the sample, but the fast-neutron multiplication in the sample has been allowed for. The curves show the resonant nature of the response. The normalization is such that, for a resonance in which the sample is black, the neutron yield should rise to a value equal to the value of q for that resonance, apart from the small effects of scattering. The arrows mark the positions of the resonances in the total cross-section of plutonium. In the graphs for q, the readings for each microsecond interval have .usually been evaluated completely independently. In regions of poor statistics between resonances, however, the points have been grouped to maintain an overall statistical accuracy of at least f 10 % per point. The figures for the thinner sample have been grouped at least in pairs throughout. A feature of the results is that the values of q tend to group around a definite constant value in each resonance. This is particularly clear in the 10.95, 22.35, and 59-eV resonances. In other cases, overlapping resonances give rise to a complex variation. These will now be considered in order. The 7*85-eV resonance shows a sudden change in q-value in the centre of the resonance. This suggests the presence of two overlapping resonances very close together, and confirmation of this can be obtained from an analysis of the total cross-section in this region. Next to the 10.95-eV resonance (q/v,, = O-88), is the 11.95-eV resonance with a very low q-value, but the effect of the more fertile resonance is still felt at 11.95 eV, and the minimum value of ~7is displaced to about 12.2 eV. In the next group of resonances, starting at the highest energy, we notice a definite plateau at q/q0 = O-60, corresponding to the 17*7-eV resonance, with a steady rise to 0.96 for the 15*3-eV resonance, and a drop to 060 for the 14.7-eV resonance. This is followed by a rise to q/q0 = O-8at.13.9 eV, indicating a further unresolved resonance on this side, and this again can be detectedin the total cross-section data. In this group it is interesting to see the effect of sample thickness on the neutron yield curves. For the l-mm sample, the .14+7-eVresonance with its larger total cross-section is dominant, while for the 15.3-eV resonance the sample is still thin and the neutron yield is low. In going to the 5-mm sample, however, the yield at 14.7 eV increases only slightly, because the sample is already nearly black in this region, but the 15.3-eV resonance with its higher value of 7 and lower cross-section becomes dominant. We note that the transition in q-value between the 14.7 and 15*3-eV resonance is not at the centre of the interval, but is displaced towards higher energies. This corresponds to the higher total cross-section of the lower 14*7-eV resonance. A similar effect between the 10.95 and 11.95 resonances has already been noted. In the range above 18 eV, the curve for 7 dips down between the resonances in the neutron yield curve. This is due to the presence of resonances of small q-value which are seen in the total cross-section, but do not show on the neutron yield curve. For example, examination of the total cross-section curve at 54 eV shows a resonance in the total cross-section corresponding to the observed dip in the 11value. FISSION
CROSS-SECTION
From the measurements, the fission cross-section of PUN has been calculated in the following way. Let b, be the efficiency of the boron trifluoride counters for counting the incident beam, and let &‘, be the efficiency of the fast-neutron counter for counting fissions in the sample. The mean flux of neutrons within the sample is
The yield of fission neutrons per neutron absorbed for PcF
up to 60-eV incident energy
41
obtained from the boron trifluoride counts with and without the sample, Zr and Zz, using equation (2),
then
i/a,
mean flux =
Therefore the number of incident neutrons captured in the sample is:
where N is Avogadro’s number, A the atomic weight of the sample, p its density, and x its thickness. The defect in the boron trifluoride counts ascribed to neutrons captured in the sample is therefore
c = f(%+
NPX
0,) 7
Further, the fast-neutron count Y is
Dividing (5) by (4), we find
(6) and from (5) Y
A
8, (7)
a,=-jxNpxq
The fission cross-section can therefore be found by comparing the fast neutron counts with the mean flux in the sample as given by (2), the constant of proportionality 8,/G; in (7) being determined by comparing equation (6) with the expression (3) used above for calculating 17. We have, finally, o,=,~Xlogz~/z~X-~XIX&XyV. 1
2
NPX
In this expression we take v = 2.92 (SANDERSand HARVEY, lot. cit.), and use the value of 1 already allocated to each sample in computing 7. In this way the fission cross-section has been evaluated independently for each sample, but in the composite results presented in Fig. 5 a selection has been made. In the regions of low cross-section the thicker (5-mm) sample gives the most accurate values, but in the peaks of the resonances this sample becomes too black for an accurate measurement of log Z1/Z2to be obtained from our data. In these regions the l-mm sample gives the best results. The values have been corrected for the 38 % PuM content of the samples. It should be noted that the normalization of our results for the fission cross-section is different from that used by other workers. We have in effect normalized to a particular value of V/Yat thermal energy, while more usually the results are normalized to fit a particciar value of 0,. The results agree well with those of PRICE and RICHMOND (1955) (fission chamber measurements using the Harwell linear accelerator), in the 7.85-eV resonance, and give a more detailed picture of the fission cross-section up to 60 eV. Between resonances
42
F. J. M. FARLEY
-
c?mrn
I
rl
I
’
5
6
7
FIO. S.-Fission
8
9
-pls,
10 15 Neutron energy -
20
30
cross-section of F%P (uncorrected for resolution or Doppler broadening).
5c
“x .s 5
.ilC F
I
I
I
I
I
I
20
40
60
60
100
120
x-f -
Fro, 6.-Distribution
Iv’lnl
* 5mm sampk, 7.3m ??1 mm sampk, lo*Jm
Id
of fission widths for E’LI”.
I
1 mV
4050
I
6070 eV
The yield of fission neutrons per neutron absorbed for PunJ8 up to 6O-e.V incident energy
43
our values are lower than those of PRICEand RICHMOND,due to the improved energy resolution. In the resonances there is good agreement at 7.85 eV: at 10.95 and 14-7 eV our peak cross-section is lower, but the difference could be due to statistical errors. In the higher resonances, our peak values are the higher, due to our better resolution. The overall agreement with the fission-chamber data indicates that v is constant within fl5 ‘A over the range studied. DISTRIBUTION
OF
FISSION
WIDTHS
Using our results for 7, it is now possible to calculate the fission widths r, of the plutonium resonances. From the fundamental expression (1) for 7 we have r, = qJ/(v
-
7).
(9)
It is assumed that rr is constant from resonance to resonance. For the first three main resonances, l’Y is 34 f 14, 40 & 5, and 43 f 15 mV (EGELSTAFFand HUGHES, lot. cit.). We therefore adopt for the higher resonances the value 40 + 8 mV. Using equation (9) and reading v from Fig. 4, we deduce the following values for l?,: E, (ev) 0 & 0.02
rr (mv) 345 14
r, (mv) 66 58 71 32 103 10 90 37 160
+ 13 56 i 20 16 t 20 t 3 i 20 + 10 i 70 -
f 0.10 i. 0.3 h 0.10 &- 0.3
43 24 61 21
+ 8 & 4 t20 t4
26.1 28.1 29.9 31.8
k f 5 i
0.2 0.3 0.3 0.3
49 I 10 5+3 11 +4 23 & 9
32.8 35.0 37.8 39.5 41.4 44.1 48.0 49.2
h 0.3 i 0.3 + 0.3 * 0.5 & 0.4 * 0.4 L- 0.5 & 0.5
80 + 25 8&4 <5 43 & 20 14 & 3 7t3 130 * 60 45 i 25
0.296 7.1 7.85 10.95 11.95 14.3 14.8 15.6 16.5
i 5 + * I 5 i &
17.75 19.2 22.35 23.6
0.002 0.2 0.03 0.05 0.05 0.2 0.2 0.3
40 i 5 43 * I5 -
To study the distribution of fission widths, the results are displayed in Fig. 6, which shows the number of resonances with fission width greater than l?, plotted against r,. The linearity of the graph on a semilogarithmic plot is striking, and suggests an exponential distribution of fission widths of the form: probability of width lying in range l?, to l?, + dr, =
r;f.exp (-q/F,). dr,,
where Ff’,,the mean fission width, is a constant and has the value 46 & 12 mV.
44
F. J. M. FARLEY
This result does not accord with suggestion of BOHR (1955) that the fission widths of the resonances should tend to group around two distinct values corresponding to the two possible spin values of the compound nucleus. Acknowledgements-The analysis in terms of fission widths was carried ,out by Dr.P. A. EGELSTAFF. The author wishes to thank Mr. E. R. WIBLINand Dr..E. R. RAE for their advice, Mr. J. W. JAGGERfor his able assistance, and Dr. E. BRET~CHERfor his interest in the problem. APPENDIX The formulae used to calculate the curves of Fig. 2, showing the fraction F of scattered neutrons which escape from the sample are, for neutrons scattered by the copper can, ‘exp(-zly)dy, s0 where z = log, (&/J*), and for neutrons scattered by the plutonium, F(s)=f+
F(z)=*[l
-exp(-z)]-lJrd
t
(1 - u)- ‘[ exp (-2) - exp (-z/y) ] y 4
+t[l-exp(-z)]-l~(l+y)-L[l-exp(-z)exp(-z/~)]~d~ In the latter case the first term represents the scattered neutrons which emerge from the front face of the sample, and the second those which emerge from the back. REFERENCES ‘Bona A. (1955) Collective motion in atomic nuclei. International Conference on the Peaceful Uses of Atomic Energy, Paper 991. EGEUTAFFP.
A. and HUGHESD. J. (1956) Resonance structure of U***,I.Pas, and Pu***.Progress in
Nuclear Energy Vol. Z, Pergamon Press, London. EGEUTAFFP.
A. and SANDERSJ. E. (1955) Neutron yields from fissile nuclei, international Conference
on the Peaceful Uses of Atomic Energy, Paper 425. FARLEYF. WIBLIN E.
J. M. (1956) A high pressure methane ionization chamber. J. Sci. Znstrum. (in press). R. (1955) Neutron spectrometers based on pulsed sources. International Conference on
the Peaceful Uses of Atomic Energy, Paper 421.
HARVEY J. A. and SANDERSJ. E. (1956) Stmunary of results on o,, a,, a, Y and 7 of II***,II**6and Pu*8B,Progress in Nuclear Energy, Vol. Z, Pergamon Press, London. HORNYAK W. F. (1952) A fast neutron detector. Rev. Sci. Znstrum. 23, 246. HORTONC. C. and MCCULLENJ. D. (1955) Plutonium water critical assemblies. International Conference on the Peaceful Uses qf Atomic Energy, Paper 428. KANNEW. R., S~WART H. B., and WHITEF. A. (1955) Capture to fission ratio’of Purr@and LPa5for intermediate energy neutrons. International Conference on the Peaceful Uses of Atomic Energy, Paper 595. NWTIN S. J., K~JPCHII-~KYP. A., and BELKMV. F. (1955) Meeting of Academy of Sciences of U.S.S.R. for the Peaceful Uses of Atomic Energy, Conference of the Section qf Physical and Mathematical Sciences, Academy of Sciences of U.S.S.R., Moscow. Nm S. J., SIJHORUCHKIN S. I., IGNATYEV K. G., and GALANINA N. D. (1955) ibid. PALEVSKYH.
(1955) Measurements of capture to fission ratio of U**‘, LP= and Pu= by a new method. International Conference on the Peaceful Uses of Atomic Energy, Paper 587. RICHMONDR. and Pama B. T. (1956) The fission cross-sections of PuuO and Puul J. Nuclear Energy, (in press).
THE YIELD OF FISSION NEUTRONS PER NEUTRON ABSORBED FOR Pu239 UP TO 60-eV INCIDENT ENERGY F. J. M. FARLEY* Atomic Energy Research Establishment, Harwell, Didcot, Berks (Received 9 February 1956)
Abstrac&---Theyield of fast neutrons from plutonium discs is measured with a high-pressure methane counter for incident neutron energies up to 60 eV, using the Harwell time-of-flight neutron spectrometer. By measuring the transmission of the samples under identical conditions, and correcting for scattering, the number of incident neutrons captured in the sample is obtained. The ratio 7 of the fast-neutron yield to the number of incident neutrons captured is then calculated as a function of incident energy, the calibration constant being obtained by fitting to known values in the region 0*03-0.3 eV. The values of r] fluctuate widely from resonance to resonance, but r] appears to be constant within each resonance, and to change smoothly between resonances. A curve of the fission cross-section of PuzJ8up to 60 eV is also presented. INTRODUCTION THE
yield of fast neutrons from a fissile material per incident neutron absorbed, usually called 11, is of interest in reactor design. It is related to v, the number of neutrons emitted per fission, and to the capture and fission cross-sections a, and a, by the equation 7 = V4(% + 0,) = v lXr, + F,) (1) where l?, and rr are the partial widths for fission and for gamma-ray emission. For thermal neutrons incident, 7 has been measured in several laboratories, chiefly with a pile oscillator. The measurements have been reviewed by HARVEYand SANDERS (1956), who adopt the value 2.08 for Pu239. This we shall call Q,. Measurements of the variation of 7 with incident neutron energy can be made directly by using a neutron detector in conjunction with some form of spectrometer for the incident neutrons. The results are then normalized to fit the value 2.08 at thermal energy. SANDERS, using a crystal spectrometer, has detected. the fission neutrons with boron trifluoride counters embedded in paraffin, and explored the region 0.025436 eV (EGELSTAFF and SANDERS, 1955). PALEVSKY (1955) used six Hornyak-type fast-neutron scintillators (HORNYAK, 1952), with the Brookhaven slow chopper in the region 0~0141 eV, and the results have since been extended to 0.5 eV (HARVEY and SANDERS, lot. cit.). Measurements with Hornyak detectors, using a pulsed cyclotron as neutron source, have been repoited by NIKITIN, SUHORUCHKIN, IGNATYEV, and GALANINA (1955), whose results extend, with very poor resolution, up to about 60 eV. Less detailed information on the variation of 7 with energy can be obtained from experiments on reactor systems. HORTON and MCCULLEN (1955) have analysed the temperature coefficient of the reactivity of plutonium-water systems, and shown that q decreases with increasing energy in the thermal region. KANNE, STEWART, and WHITE (1955) exposed samples of plutonium to neutrons from a reactor, filtered through various shields so that the mean energy of the incident flux was varied. * On leave from Auckland University College, Auckland, New Zealand. 33
34
F. J. M. FARLEY
After irradiation, the PuMo and the fission-product concentrations were determined, the ratio yielding a&,, and hence 7, over five broad-energy regions extending to 15 keV. NIICITIN,KRUPCHITSKY,and BELKIN (1955) carried out a rather similar experiment, using a boron-loaded moderator to increase the mean energy.of the neutrons derived from a reactor, and report results on IJ= only. Values of 7 can also be deduced from an analysis of total cross-section and fission cross-section data. At low energies, where the data is obtained under conditions of good energy resolution, the accuracy is good, and the results agree with the direct measurements (HARVEYand SANDERS, Ioc. cit.); at higher energies, however, analysis of resonances in terms of the partial widths for neutron emission F,, gamma-ray emission Pr, and for fission l?,, is necessary, and the results are less reliable; the values obtained are displayed in Fig. 4 (EGELSTAFFand HUGHES,1956). In the present experiments the Harwell 15-MeV linear electron accelerator is used as a pulsed source of neutrons for time-of-flight spectroscopy (W~LIN, 1955), and a high-pressure methane counter (FARLEY, 1956) is used to detect the fast neutrons emitted from the fissile material. The number of neutrons stopped in the sample is alsomeasured, by means of a transmission experiment made under identical conditions. The value of 7 is then obtained from the ratio of the fast-neutron yield to the number of incident neutrons stopped in the sample, independent of self-shielding effects or of the energy’resolution of the equipment. The results are normalized to agree with those of SANDERSat low energies, and these in turn have been adjusted to the value 2.08 for thermal neutrons. Detailed information on 7 is thus obtained from zero to 6O-eV incident-neutron energy. METHOD A 3-in. diameter disc of fissile material is mounted perpendicular to the slow-neutron beam from the Harwell I5-MeV linear electron accelerator. Fast neutrons emitted from fissions accurring in the disc are detected by a fast-neutron counter placed alongside it. This counter is an ionization chamber, 2 in. diam. and 84 in. long, containing methane at a pressure of 40 atm; the collection time is in the range 0.2-1.9 p, and the overall efficiency is 0.07% for detecting fissions occurring in the disc (FARLEY, 1956). The fast-neutron signals are registered in a time-of-flight selector with one hundred channels each 2 p in width. They thus indicate the time of flight of the incident slow-neutrons between the accelerator and the fissile disc. Flight paths of 10.5 m, 7.3 m, and 3 m are used to cover the incident-neutron energy ranges 6-60 eV, 0.249 eV, and 0.03-064 eV respectively, the latter being used’for calibration of the experiment in the thermal region (see Fig. 1). The measurements give the yield of neutrons from the fissile material as a function the incident-neutron energy. In a subsidiary experiment, the fissile disc is removed and replaced by a group of short boron trifluoride counters. These are used to measure the number of incident neutrons in the beam as a function of time of flight (or energy). The fissile sample is then inserted in front of the counters and the run repeated. The difference between the two runs gives, after a correction for scattering, the number of incident neutrons captured in the disc as a function of energy. The ratio of the fast neutron yield to the number of incident neutrons removed from the beam is then proportional to 7. It is important in these measurements that the fast-neutron yield and the absorption
The yield of fission neutrons per neutron absorbed for Pups9 up to 6O-eV incident energy
of the incident neutrons should be measured using the same under identical conditions of flight-path and resolution. immediately the fast-neutron yield per neutron absorbed, required for resolution, or for self-screening by the sample. be of any thickness, although in practice a sample which
{,Fz rnetres
7
35
sample of fissile material The ratio then gives and no corrections are Indeed, the sample may is nearly “black” in the ---j
Concrete
Target
Baron - pbraffin shield FIG. I.--Apparatus.
resonances has the advantage of higher counting rates. The measurements give directly the number of fast neutrons emitted per neutron absorbed, i.e. 7, there being no need to analyse the data in terms of fission and capture cross-sections. Calibration of the experiment in the thermal region corrects atuomatically for any increase in the fast-neutron yield due to multiplication in the sample. EXPERIMENTAL
DETAIL
The arrangement of the apparatus is indicated in Fig. 1. Two independent boron trifluoride counters (not shown) were used to monitor the neutron output of the accelerator, and thus to enable successive runs to be compared. The two monitor readings were consistent to better than 1%. To cut out the very slow neutrons, which would otherwise be received from the previous pulse of the accelerator 25 msec earlier, a filter was placed in the beam. For the 10.5-m flight-path, delay-times 100-300 psec, the filter was cadmium, 05 mm thick. To study the lower-energy region, 0.03 to O-64 eV, it was necessary to reduce the flight-path to 3 m, so as to increase the ratio of velocities for the desired neutrons, delay 250-1150 psec, and the undesired neutrons, delay 2750-3650 psec. A 2-mm thick filter of Pyrex glass was used as a filter to attenuate the slower neutrons, but these were in any case few in number because their energy was less than OGO7eV, that is, well below thermal energy. To measure the effect of these “second trip” neutrons, the recurrence frequency of the accelerator was reduced from 400 c/s to 200 c/s and the spectrometer gates set to cover the range 2750-3650 ,usec. This count, to be subtracted from the normal runs at 400 c/s, was in many cases negligible, and never greater than 3 %. For’ the 7-3-m flight-path the same procedure was used; the filter was Pyrex glass 5 mm thick; the second-trip neutrons, now 25 % of the count, were measured in the same way. The background counting rate of the counters was measured for each run with the accelerator switched off, but with the sample, if any, in position. An ungated count
F. J. M. FARLEY
36
was taken, and the contribution to each gate during the run calculated. For the neutron counter this background was important because of the spontaneous fissions occurring in the sample, and in the case of the 5-mm plutonium sample amounted to 9 % of the maximum counting rate per gate. In the case of the boron trifluoride counters, however, it was verified that the counters did not detect neutrons from fissions in the sample, a necessary condition for this part of the experiment. In the case of the neutron counter there was also a background due to the accelerator when the fissile material was removed. It is not clear why fast-neutron counts should be recorded several hundred microseconds after the emission of a pulse from the machine. This background, which was measured and subtracted, was about 2%. To obtain a true value of 7, it is essential that the neutron counter shall be sensitive only to fissions occurring in the sample, and shall not detect gamma rays of neutron capture. To verify that the bias was set high enough to exclude gamma rays, runs were made with samples of h-in. silver, &in. natural uranium, and #-in. cadmium, the latter providing the most stringent test. There was no significant response in the positions of the capture resonances. To avoid errors due to the 100 msec dead time in the registers of the time-of-flight selector, the counting rate per gate was kept below 6/min. In the case of the runs at 3 m with the boron trifluoride counters, this meant that the output of the machine had to be reduced to about 1% of normal. At this level the background of the monitors becomes important. It was measured and subtracted, the correction being at most 29%. For the 10.5-m path, two runs were made in each case, the second with an extra delay of 1 psec in the signal path. In this way experimental points 1 ,usec apart were obtained from the 2qsec gates of the time-of-flight selector, at a resolution of 2 ,usec. Measurements were made on two samples of plutonium, both 3 in. in diameter. The first (5-mm sample) contained 418 g of plutonium metal, the second(l-mmsample) 77.77 g. REDUCTION
OF RESULTS
AND
DISCUSSION
The gate readings were corrected for the individually measured gate widths, and the backgrounds mentioned above were subtracted. Before comparing the fastneutron yield with the number of incident neutrons removed from the beam by the sample, it is necessary to correct for the loss of neutrons by scattering. Three types of scattering are considered separately: scattering by the copper can, potential scattering by the plutonium, and resonance scattering by the plutonium. (a) Scattering by the copper can. The thickness of copper on each face was 0.040 in. for the 5-mm plutonium sample and 0.020 in. for the l-mm sample. The scattering is calculated from the incident-neutron flux Z1 (first face), the transmittedneutron flux I, (second face), and the total cross-section of copper. This yields the total scattering by the copper, but some of the scattered neutrons go into the plutonium and are absorbed. The fraction of scattered neutrons which finally leave the sample depends on the blackness of the sample, as indicated by log Ii/Z,; it varies from 1 for I, = Z1 to 0.5 for I, = 0. This factor has been calculated for infinite slab geometry, with the results indicated in Fig. 2. It has been assumed that all scattered neutrons which interact with the plutonium are captured. The small fraction which are rescattered rather than captured introduces negligible error, because the scattering
The yield of fission neutrons per neutron absorbed for PuSso up to 60-eV incident energy
37
correction is itself already small. The curve is valid provided the resolution of the equipment is high, so that log I1/le gives a true measure of the blackness of the sample at each energy. This condition is not well satisfied for the highest energies in our range, and in this case the scattering by the copper will be slightly overestimated in the resonances leading to a value of 11which is slightly too high in the resonance. The correction for scattering by copper varied from a few per cent in the resonances to 20 % or more between resonances.
g 8
0.5 2 c Y f 0.2 6 ‘S P
0
05
1.5 2.0 fraction of scattered neutrons which escape from sample. 1.0
2.5
Log I,&
FIG.
2.-The
(b) Potential scattering by the plutonium. A constant potential scattering crosssection of 10 barns has been assumed. The amount of scattering is then proportional to the mean flux lin the sample which can be found from the ingoing flux I1 and the outgoing flux I,, I= (II - IJ(log Zl - log I&. (2) Again a correction is necessary, because some of the scattered neutrons are captured in the sample before they can escape. This has been calculated as a function of log IJl,, and is also shown in Fig. 2. Again multiple processes are neglected, and the calculation assumes infinite slab geometry and good resolution. This is justified, because in the resonances the scattering is small, and between resonances the sample is thin and the assumptions valid. This correction was ~1% in resonances and 20 y0 or more between resonances. (c) Resonance scattering by the plutonium. Throughout a particular resonance a constant fraction of the incident neutrons suffer resonance scattering instead of capture. The correction can therefore be applied at the end of the calculation to the value of q calculated for this resonance. The fraction of neutrons suffering resonancescattering is l?,/l?, but only a fraction of these will escape from the sample. Estimates of resonance parameters (HUGHES and EGELSTAFF, lot. cit.) indicate that r,/l? is less than 4 % for all significant plutonium resonances. The fraction of scattered neutrons escaping will be No-3 (see Fig. 2) and therefore the correction is 1 ‘A or less. It is neglected. The net boron trifluoride count C, indicating the number of neutrons stopped in the sample, after the scattered neutrons have been subtracted, must now be corrected for the I/U variation of the efficiency of the counters. The net count is 3A
38
F. J. M. FARLEY
therefore divided by the time of flight r. In the thermal region there is a further correction due to the self-shielding of the counter, which causes a departure from the true l/u relation. This is computed from the dimensions of the counter and filling pressure, and applied as a separate correction factor, E, which drops from 1 at high energies to 0.70 at 0.037 eV. The final expression for 7 is then Y
p=~XiXEX~,
(3)
where Y is the fast-neutron count and 1 is a constant of proportionality determined by fitting in the low-energy region.
which is
0.8 t 0 0~6 z 0.4
002
005
05 0’1 02 Neutron energy -
l.0
2.0
5.0
10c &
Fro. 3.-q relative to thermal r].
The final figures for q are normalized separately for the l-mm and 5-mm pluutonium samples to give the best fit to the figures of SANDERS in the range 0.037 to O-36 eV, where the two sets of data overlap. The two normalizing constants differ by 10% owing to the greater effect of internal fast-neutron multiplication in the larger sample. Fig. 3 gives the combined results, together with the points of SANDERS. It shaws the well-known drop in value in the region of 0.3 eV, and this is followed by a rise to about 0.8 thermal value in the region of low cross-section around 5 eV. No results are obtained in the neighbourhood of 1 eV, because of the strong absorption due to PUN in the samples. The statistical accuracy of the points is f2-5 % up to O-21 eV, f3.5 % from 0.21 to 0.64 eV, and &IO% in the region 3-6 eV. In this region the scattering corrections are large, ~30”/~ of the net boron trifluoride count, and therefore there is some uncertainty in the values. Using the same norqalization constants, 7 has been evaluated for the two samples in the higher-energy band, with the results shown in Fig. 4. Also shown in Fig. 4 are the fast-neutron yield curves for each sample per slow-neutron incident; in this case no correction has been made for scattering either by the plutonium or by the
The yield of fission neutrons per neutron absorbed for PLP up to @-eV incident energy
l-!-A-A
-
quappu! uoJqnou -Iad pi+
uoJqnaN
39
40
F. J. M. FARLEY
copper can, and no account is taken of the incident neutrons which emerge through the sample, but the fast-neutron multiplication in the sample has been allowed for. The curves show the resonant nature of the response. The normalization is such that, for a resonance in which the sample is black, the neutron yield should rise to a value equal to the value of q for that resonance, apart from the small effects of scattering. The arrows mark the positions of the resonances in the total cross-section of plutonium. In the graphs for q, the readings for each microsecond interval have .usually been evaluated completely independently. In regions of poor statistics between resonances, however, the points have been grouped to maintain an overall statistical accuracy of at least f 10 % per point. The figures for the thinner sample have been grouped at least in pairs throughout. A feature of the results is that the values of q tend to group around a definite constant value in each resonance. This is particularly clear in the 10.95, 22.35, and 59-eV resonances. In other cases, overlapping resonances give rise to a complex variation. These will now be considered in order. The 7*85-eV resonance shows a sudden change in q-value in the centre of the resonance. This suggests the presence of two overlapping resonances very close together, and confirmation of this can be obtained from an analysis of the total cross-section in this region. Next to the 10.95-eV resonance (q/v,, = O-88), is the 11.95-eV resonance with a very low q-value, but the effect of the more fertile resonance is still felt at 11.95 eV, and the minimum value of ~7is displaced to about 12.2 eV. In the next group of resonances, starting at the highest energy, we notice a definite plateau at q/q0 = O-60, corresponding to the 17*7-eV resonance, with a steady rise to 0.96 for the 15*3-eV resonance, and a drop to 060 for the 14.7-eV resonance. This is followed by a rise to q/q0 = O-8at.13.9 eV, indicating a further unresolved resonance on this side, and this again can be detectedin the total cross-section data. In this group it is interesting to see the effect of sample thickness on the neutron yield curves. For the l-mm sample, the .14+7-eVresonance with its larger total cross-section is dominant, while for the 15.3-eV resonance the sample is still thin and the neutron yield is low. In going to the 5-mm sample, however, the yield at 14.7 eV increases only slightly, because the sample is already nearly black in this region, but the 15.3-eV resonance with its higher value of 7 and lower cross-section becomes dominant. We note that the transition in q-value between the 14.7 and 15*3-eV resonance is not at the centre of the interval, but is displaced towards higher energies. This corresponds to the higher total cross-section of the lower 14*7-eV resonance. A similar effect between the 10.95 and 11.95 resonances has already been noted. In the range above 18 eV, the curve for 7 dips down between the resonances in the neutron yield curve. This is due to the presence of resonances of small q-value which are seen in the total cross-section, but do not show on the neutron yield curve. For example, examination of the total cross-section curve at 54 eV shows a resonance in the total cross-section corresponding to the observed dip in the 11value. FISSION
CROSS-SECTION
From the measurements, the fission cross-section of PUN has been calculated in the following way. Let b, be the efficiency of the boron trifluoride counters for counting the incident beam, and let &‘, be the efficiency of the fast-neutron counter for counting fissions in the sample. The mean flux of neutrons within the sample is
The yield of fission neutrons per neutron absorbed for PcF
up to 60-eV incident energy
41
obtained from the boron trifluoride counts with and without the sample, Zr and Zz, using equation (2),
then
i/a,
mean flux =
Therefore the number of incident neutrons captured in the sample is:
where N is Avogadro’s number, A the atomic weight of the sample, p its density, and x its thickness. The defect in the boron trifluoride counts ascribed to neutrons captured in the sample is therefore
c = f(%+
NPX
0,) 7
Further, the fast-neutron count Y is
Dividing (5) by (4), we find
(6) and from (5) Y
A
8, (7)
a,=-jxNpxq
The fission cross-section can therefore be found by comparing the fast neutron counts with the mean flux in the sample as given by (2), the constant of proportionality 8,/G; in (7) being determined by comparing equation (6) with the expression (3) used above for calculating 17. We have, finally, o,=,~Xlogz~/z~X-~XIX&XyV. 1
2
NPX
In this expression we take v = 2.92 (SANDERSand HARVEY, lot. cit.), and use the value of 1 already allocated to each sample in computing 7. In this way the fission cross-section has been evaluated independently for each sample, but in the composite results presented in Fig. 5 a selection has been made. In the regions of low cross-section the thicker (5-mm) sample gives the most accurate values, but in the peaks of the resonances this sample becomes too black for an accurate measurement of log Z1/Z2to be obtained from our data. In these regions the l-mm sample gives the best results. The values have been corrected for the 38 % PuM content of the samples. It should be noted that the normalization of our results for the fission cross-section is different from that used by other workers. We have in effect normalized to a particular value of V/Yat thermal energy, while more usually the results are normalized to fit a particciar value of 0,. The results agree well with those of PRICE and RICHMOND (1955) (fission chamber measurements using the Harwell linear accelerator), in the 7.85-eV resonance, and give a more detailed picture of the fission cross-section up to 60 eV. Between resonances
42
F. J. M. FARLEY
-
c?mrn
I
rl
I
’
5
6
7
FIO. S.-Fission
8
9
-pls,
10 15 Neutron energy -
20
30
cross-section of F%P (uncorrected for resolution or Doppler broadening).
5c
“x .s 5
.ilC F
I
I
I
I
I
I
20
40
60
60
100
120
x-f -
Fro, 6.-Distribution
Iv’lnl
* 5mm sampk, 7.3m ??1 mm sampk, lo*Jm
Id
of fission widths for E’LI”.
I
1 mV
4050
I
6070 eV
The yield of fission neutrons per neutron absorbed for PunJ8 up to 6O-e.V incident energy
43
our values are lower than those of PRICEand RICHMOND,due to the improved energy resolution. In the resonances there is good agreement at 7.85 eV: at 10.95 and 14-7 eV our peak cross-section is lower, but the difference could be due to statistical errors. In the higher resonances, our peak values are the higher, due to our better resolution. The overall agreement with the fission-chamber data indicates that v is constant within fl5 ‘A over the range studied. DISTRIBUTION
OF
FISSION
WIDTHS
Using our results for 7, it is now possible to calculate the fission widths r, of the plutonium resonances. From the fundamental expression (1) for 7 we have r, = qJ/(v
-
7).
(9)
It is assumed that rr is constant from resonance to resonance. For the first three main resonances, l’Y is 34 f 14, 40 & 5, and 43 f 15 mV (EGELSTAFFand HUGHES, lot. cit.). We therefore adopt for the higher resonances the value 40 + 8 mV. Using equation (9) and reading v from Fig. 4, we deduce the following values for l?,: E, (ev) 0 & 0.02
rr (mv) 345 14
r, (mv) 66 58 71 32 103 10 90 37 160
+ 13 56 i 20 16 t 20 t 3 i 20 + 10 i 70 -
f 0.10 i. 0.3 h 0.10 &- 0.3
43 24 61 21
+ 8 & 4 t20 t4
26.1 28.1 29.9 31.8
k f 5 i
0.2 0.3 0.3 0.3
49 I 10 5+3 11 +4 23 & 9
32.8 35.0 37.8 39.5 41.4 44.1 48.0 49.2
h 0.3 i 0.3 + 0.3 * 0.5 & 0.4 * 0.4 L- 0.5 & 0.5
80 + 25 8&4 <5 43 & 20 14 & 3 7t3 130 * 60 45 i 25
0.296 7.1 7.85 10.95 11.95 14.3 14.8 15.6 16.5
i 5 + * I 5 i &
17.75 19.2 22.35 23.6
0.002 0.2 0.03 0.05 0.05 0.2 0.2 0.3
40 i 5 43 * I5 -
To study the distribution of fission widths, the results are displayed in Fig. 6, which shows the number of resonances with fission width greater than l?, plotted against r,. The linearity of the graph on a semilogarithmic plot is striking, and suggests an exponential distribution of fission widths of the form: probability of width lying in range l?, to l?, + dr, =
r;f.exp (-q/F,). dr,,
where Ff’,,the mean fission width, is a constant and has the value 46 & 12 mV.
44
F. J. M. FARLEY
This result does not accord with suggestion of BOHR (1955) that the fission widths of the resonances should tend to group around two distinct values corresponding to the two possible spin values of the compound nucleus. Acknowledgements-The analysis in terms of fission widths was carried ,out by Dr.P. A. EGELSTAFF. The author wishes to thank Mr. E. R. WIBLINand Dr..E. R. RAE for their advice, Mr. J. W. JAGGERfor his able assistance, and Dr. E. BRET~CHERfor his interest in the problem. APPENDIX The formulae used to calculate the curves of Fig. 2, showing the fraction F of scattered neutrons which escape from the sample are, for neutrons scattered by the copper can, ‘exp(-zly)dy, s0 where z = log, (&/J*), and for neutrons scattered by the plutonium, F(s)=f+
F(z)=*[l
-exp(-z)]-lJrd
t
(1 - u)- ‘[ exp (-2) - exp (-z/y) ] y 4
+t[l-exp(-z)]-l~(l+y)-L[l-exp(-z)exp(-z/~)]~d~ In the latter case the first term represents the scattered neutrons which emerge from the front face of the sample, and the second those which emerge from the back. REFERENCES ‘Bona A. (1955) Collective motion in atomic nuclei. International Conference on the Peaceful Uses of Atomic Energy, Paper 991. EGEUTAFFP.
A. and HUGHESD. J. (1956) Resonance structure of U***,I.Pas, and Pu***.Progress in
Nuclear Energy Vol. Z, Pergamon Press, London. EGEUTAFFP.
A. and SANDERSJ. E. (1955) Neutron yields from fissile nuclei, international Conference
on the Peaceful Uses of Atomic Energy, Paper 425. FARLEYF. WIBLIN E.
J. M. (1956) A high pressure methane ionization chamber. J. Sci. Znstrum. (in press). R. (1955) Neutron spectrometers based on pulsed sources. International Conference on
the Peaceful Uses of Atomic Energy, Paper 421.
HARVEY J. A. and SANDERSJ. E. (1956) Stmunary of results on o,, a,, a, Y and 7 of II***,II**6and Pu*8B,Progress in Nuclear Energy, Vol. Z, Pergamon Press, London. HORNYAK W. F. (1952) A fast neutron detector. Rev. Sci. Znstrum. 23, 246. HORTONC. C. and MCCULLENJ. D. (1955) Plutonium water critical assemblies. International Conference on the Peaceful Uses qf Atomic Energy, Paper 428. KANNEW. R., S~WART H. B., and WHITEF. A. (1955) Capture to fission ratio’of Purr@and LPa5for intermediate energy neutrons. International Conference on the Peaceful Uses of Atomic Energy, Paper 595. NWTIN S. J., K~JPCHII-~KYP. A., and BELKMV. F. (1955) Meeting of Academy of Sciences of U.S.S.R. for the Peaceful Uses of Atomic Energy, Conference of the Section qf Physical and Mathematical Sciences, Academy of Sciences of U.S.S.R., Moscow. Nm S. J., SIJHORUCHKIN S. I., IGNATYEV K. G., and GALANINA N. D. (1955) ibid. PALEVSKYH.
(1955) Measurements of capture to fission ratio of U**‘, LP= and Pu= by a new method. International Conference on the Peaceful Uses of Atomic Energy, Paper 587. RICHMONDR. and Pama B. T. (1956) The fission cross-sections of PuuO and Puul J. Nuclear Energy, (in press).