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Measurements of the energy dependence of the fission neutron yield per neutron absorbed in 239pu and 235u in the range 0·006–0·36 eV
J. NuclearEnergy,1958.Vol.6, pp. 212to 221. PergamonPressLtd..London
MEASUREMENTS OF THE ENERGY DEPENDENCE OF THE FISSION NEUTRON YIELD PER NEUTRON ABSORBED IN 23QPuAND 235U IN THE RANGE 0.006436 eV H. M. SKARSGARD and C. J. KENWARD Atomic Energy Research Establishment, Harwell, Berkshire (Received 20 May 1957) Abstract-The
energy dependence of 7, the fission neutron yield per neutron absorbed, has been measured for assPu over the energy range 0~0070-036 eV and for 2s6Uover the range 04060-0~050 eV, using a crystal spectrometer. For energies less than 0.050 eV a mechanical neutron-velocity selector was used in conjunction with the crystal spectrometer to eliminate higher order neutrons from the diffracted beam. For zssPu, at 0.3 eV, 7 is found to be 78.5 per cent of its value at 0.0253 eV. A theoretical expression for 7, based on single level parameters deduced from the published total cross-section values, is’fitted to the measured variation and gives a value for a,,,.2B,j, the ratio of radiative capture to fission in the 0.297 eV resonance, of 0.80 i 0.05. The temperature coefficient of the effective value of 77averaged over a Maxwellian flux distribution is -0.027 per cent per “C for temperatures in the vicinity of 20°C. Within experimental errors, q for zssU appears constant from 0.006 to 0.050 eV. 1. INTRODUCTION DIRECT measurements
of the energy dependence of 7, the fission neutron yield per neutron absorbed, have been made for 23gPuover the energy range 0*0070-0.36 eV and for 235Uover the range 0~00604050 eV. A mechanical neutron-velocity selector, used in conjunction with a crystal spectrometer, has enabled the measurements to be extended to lower energies than were reached in previous work. The low resolution velocity selector serves to eliminate the high order contamination of the diffracted beam which becomes especially troublesome at energies below the peak of the thermal flux distribution. Direct measurements of the energy dependence of q have been reported previously for 23gPu(PALEVSKY, 1955; PALEVSKY et al., 1956; EGELSTAFF and SANDERS, 1955; FARLEY, 1956; NIKITIN et al., 1955) and for 235U(PALEVSKY, 1955 ; PALEVSKYet al., 1956; SMITH and MAGLEBY, 1955; NIKITIN et al., 1955). Considering the low energy limit of the measurements for 23sPu, the work of PALEVSKYet al. with the Brookhaven slow-chopper extend to 0.017 eV, while the Harwell crystal spectrometer measurements by SANDERS reported at Geneva by EGELSTAFT;and SANDERS (1955) do not go below 0.025 eV. The U.S.S.R. pulsed cyclotron work of NIKITIN et al. extends to 0.011 eV, but the points between 0.01 and 0.02 eV show considerable scatter. The Brookhaven and Harwell data are in good agreement, within the experimental errors, up to 0.7 eV. They show a decrease in 7 with increasing energy up to about 0.3 eV, at which energy 7 is about 75 per cent of its value at O-025 eV. Beyond 0.3 eV the value rises again. 7 may also be inferred from the relationship q = ~(oJa,>, where Yis the number of fission neutrons per fission, assumed constant, and crf and o, are the fission and total absorption cross-sections respectively. (The values used are those quoted in HARVEY and SANDERS(1956). These are based on results presented 212
at the Geneva Conference.)
Measurements of the energy dependence of the fission neutron yield
213
When this is done, q is observed to decrease up to 0.3 eV to about 85 per cent of its value at O-025 eV. However, values of 7 inferred in this way are subject to consider-
able uncertainty and the discrepancy between this value and that measured directly is hardly outside the errors. A real discrepancy would imply that v was not constant over the energy range from O-025 to 0.3 eV. This possibility has been checked (AUCLAIR et al., 1955; SANDERSand KENWARD, 1956; PALEVSKYet al., 1956), and v .was found to be constant to within about 1 per cent over this range. The Russian data do not agree very well with the Brookhaven and Harwellresults and show a decrease in q up to 0.3 eV to about 85 per cent of the O-025 eV value, more in agreement with the variation of 7 inferred from the cross-section data. Because of these discrepancies it was decided to repeat the Harwell measurements, with improved accuracy, and to extend the measurements to lower energies. For 235U the measurements reported by PALEVSKYet al. (1956) together with those of SMITH (1955) agree well, within the errors, with the energy dependence of 7 inferred from the cross-section data. The measurements extend from 0.01 to I.0 eV. Over the energy range from 0.01 to 0.10 eV q appears to increase by about 1 per cent. The Russian data show rather poor agreement with the American data, a decrease of about 10 per cent being observed between 0.01 and 0.10 eV.
Aperture cadmium
in sheet
Diffracted
beam
Fast-
FIG. l.-Experimental
2. EXPERIMENTAL
arrangement.
DETAILS
Procedure
The experimental procedure which was followed is a modification of that used in previous measurements of the energy dependence of q by SANDERS (reported by EGELSTAFFand SANDERS,1955) and by SANDERSet al. (1957). A diagram of the apparatus is shown in Fig. 1. A collimated beam from the centre of BEPO is diffracted by a KC1 crystal to give a monoenergetic beam of neutrons. A mechanical neutronvelocity selector was used for energies up to 0.05 eV to prevent neutrons with energies corresponding to higher order reflections from reaching the crystal. Use of the neutron-velocity selector is the major modification of the experimental arrangement reported in the earlier work at Harwell. It is described in detail in an appendix to 3
214
H. M. SKARSGARD and C. J. KENWARD
this paper. The (200) planes of the KC1 crystal were employed and gave an energy resolution (width of half maximum of the energy distribution) of about 2 per cent at 0.01 eV. The diffracted neutron beam passes through a monitor counter before striking a disc of the fissile sample in which it is almost completely absorbed. The fissile sample is placed on the axis of a cylindrical fast-neutron detector which consists of sixteen 1°BF, proportional counters embedded in paraffin wax. It has an efficiency of about 3.0 per cent. The inside of the fast-neutron detector is lined with sufficient B,O, to absorb the slow neutrons scattered from the disc and canning material. The monitor counter used was either a l”B foil proportional counter or, at energies above 0.05 eV, a 1°BF, proportional counter. In the foil counter the l”B is coated on thin aluminium foils through which the beam is passed. The walls of the counter are of thin aluminium. The efficiency of this counter is about 2-O per cent for O-025 eV neutrons. The l”BF, counter has an efficiency about eight times as great. The walls are made of thin copper. The counters and fission sample are surrounded by a cadmium-lined paraffin wax shield to reduce the background. The assembly is mounted on a trolley which can be rotated about the crystal and aligned to receive the diffracted beam by means of a light, mirror, and photocell. The energy dependence of 11is then measured by observing the ratio of counts in the fast-neutron detector to those in the monitor counter for various settings of the crystal. Thus, if NF and NM are the counts recorded in the fast-neutron detector and monitor counter respectively, then N,
A W% Ells NM
where E”’ allows for the l/u dependence of the absorption cross-section of l0B at these neutron energies. A, is the product of several small corrections for effects which depend on the energy of the incident neutrons. These are: (a) The departure of the response of the monitor counter from that of a l/u counter. A correction was made for absorption and scattering effects in the l”B and materials making up the monitor counters. The correction was estimated for the l”B foil counter and varied by about l-8 per cent over the range of energies for which the counter was used. In the case of the 1°BF, monitor counter the correction was estimated and, as a check, was measured by placing both this counter and the l”B foil counter in the beam-the l”B foil counter behind the l”BF, counter-and observing the ratio of counts recorded in each as a function of the incident energy of the neutrons. Over the range from 0.05 to 0.36 eV, for which the 1°BF, monitor counter was used, the correction varied by 5.3 per cent. (The absolute value of the correction was less than 11 per cent over this range.) (b) Scattering and absorption by canning material and isotopic impurities of fissile samples. A 1 mm thick disc of 239Pu containing about 3.8 per cent 240Puwas used. It was enclosed in a double-walled copper can of thickness 0.020 in. The 235Usample was an untanned 5 mm thick disc. A correction which did not exceed 3.5 per cent was made for the absorption and scattering of the incident beam by the copper canning material surrounding the 23gPu sample. A correction was necessary for the varying competitive absorption of the 240Pu,which has a large resonance in the vicinity of 1-O
Measurements of the energy dependence of the fission neutron yield
215
eV. This correction amounted to less than 1.5 per cent for energies up to 0.36 eV. The cross-section of 240Pu was taken from recent work of EGELSTAFF et al. (1957). The corresponding correction for absorption in the 238U impurity present in the 235U sample was negligible. The fraction of incident neutrons which was scattered by the fissile sample was estimated as ,!?(cr.JaJ where /3is a function of the transmission of the fissile sample which approaches 0.15 as the transmission of the sample approaches zero. For the measurements reported in this paper ,/3remained very near this limit. The scattering cross-section cs for 23gPuwas taken as 11 barns. For the 235Usample an average value of 18*2 barns was used for as---estimated by taking into account the increase in potential scattering due to the 238Uimpurity in the sample and by including the contribution to the elastic scattering from the negative energy level in 235U at -1.4 eV, which has a large partial neutron width (SAILOR, 1955). The scattering correction applied was less than O-3 per cent for 23gPu and less than 0.6 per cent for 7J. (c) Transmission of the fissile samples. A correction not exceeding I.3 per cent was made for the finite transmission of the 23gPu disk. The correction was negligible for 235U. (d) Counting losses due to scaler dead times. This correction was less than I.0 per cent for 23gPu and’almost negligible for the 235Umeasurements. (e) Higher order contamination in the diffracted neutron beam. Normally the diffracted beam from a crystal spectrometer set at energy E contains neutrons with energies 4E, 9E etc., corresponding to higher order reflections. It is necessary to correct for the effect of these neutrons by considering the contribution which they make to the counts recorded in the monitor and fast-neutron counters. In order to do this accurately one must know the intensities of the higher order neutrons and the efficiencies with which they are detected in the monitor counter relative to the first order as well as their scattering and absorption cross-sections in the monitor counter and in the sample. Furthermore, one must know the value of 7 relative to that for the first order. Since some of these factors are not well known it is desirable to reduce the higher order effects to such proportions that the uncertainties become unimportant. In the energy range below 0.05 eV, use of the neutron-velocity selector reduced the corrections to almost negligible proportions. Estimates of the correction did not exceed 0.5 per cent. In the 23sPu measurements above 0.05 eV the correction was not greater than 2.0 per cent. Cadmium and indium filters were used above 0.133 eV in order to reduce the higher order effect. It was especially important to reduce the higher order effect in this energy region, as the 240Puimpurity, with a large resonance at 1 eV, competes significantly with the 23gPu for absorption of the higher orders; this gives rise to an added uncertainty because of the poorly known cross-section for 240Pu and the inaccurate knowledge of the isotopic composition of the sample. In addition to these effects, the variation of neutron multiplication in the fissile sample with incident neutron energy was examined. This effect depends on the variation, with energy, of the mean penetration depth of incident neutrons in the disk. It was found to be of negligible proportions in these measurements. Cross-section data compiled by HUGHES and HARVEY (1955) were used in making estimates of the various corrections.
216
H. M. SKARSGARD and C. J. KENWARD
In order to reduce the effects of drift in the counter sensitivities, the measurements at various energies were interspersed frequently with measurements at some fixed energy. The results were normalized to the value of q at this point. For 23gPu this point was 0.05 eV, at which energy the readings taken with the neutron-velocity selector overlap those taken without it. For 235Uthe reference energy was 0.025 eV. The results have been adjusted in absolute value so as to be consistent with pile oscillator measurements of the average effective thermal value of q (HARVEY and SANDERS, 1956). Errors quoted are the statistical standard deviations on the counts recorded. The high background count rate in the fast-neutron detector due to the 240Puimpurity in the sample made it difficult to obtain accurate results for 23gPu below about 04070 eV. 3. RESULTS
239Pu. The present measurements are plotted in Fig. 2. The dashed 7 = v (of/u,) which has been fitted to lized to a value of 2.08 at O-0253 eV.
AND
DISCUSSION
of the variation curve represents the measurements. This normalization
with energy of 7 for 23gPu a theoretical expression for The data have been normais based upon the variation
t 1.90 q
1.80
E
-
eV
FIG. 2.-Present measurements of the variation of 7 for 239Puwith energy. Broken-line curve represents a theoretical expression for 7 = P X (u&r,), which was fitted to the measurements.
of q, and an effective thermal value of 2.02 (HARVEY and SANDERS, 1956); the value of 7 for 0.0253 eV neutrons is 1.030 times the effective value of Q for a thermal flux distribution at 20°C. Over the energy region where they overlap, from O-017 to 0.36 eV, the new measurements of the variation of q for 23gPu are in reasonably good agreement with the earlier Hat-well measurements of SANDERS reported by EGELSTAFF and SANDERS (1955) and FARLEY (1956) and the Brookhaven results of PALEVSKY et al. (1956). The present measurements show that, in the vicinity of O-3eV, 11is about 78.5 per cent of its value at O-0253 eV. This is intermediate to the figure of 75 per cent indicated by the earlier direct measurements and the value of about 85 per cent inferred from the averaged fission and absorption cross-section values given by
Measurements
of the energy dependence of the fission neutron yield
217
HARVEY and SANDERS (1956). It is not practicable to extend the range of the measurements by increasing the thickness of the sample, since this causes the fission neutron background, due to spontaneous fission of 240Puin the samples, to increase to such an extent that accurate measurements are not possible. Below 0.0253 eV the new measurements show a levelling-off which is in satisfactory agreement with the inferred behaviour of q. The theoretical fit is based upon the resonance parameters deduced from the averaged Geneva total cross-section for 23gPu by HARVEYand SANDERS(1956) and EGELSTAFFand HUGHES(1956). Their analyses show a weak resonance at approximately zero neutron energy and a strong resonance at 0.297 eV. For the energy range covered by the measurement of q the absorption cross-section in the denominator of the theoretical expression is therefore written as the sum of three terms-the singlelevel contribution from each of the 0.297 eV and zero energy levels and a l/u component due to resonances at higher energies. By fitting the theoretical expression for oa to the averaged Geneva absorption cross-section (a, - 10 barns) at O-0253eV, the parameters E,, g13z”,and I’ for the two resonances fixed the contribution of the I/v component. The corresponding terms for a, depend on the values of (1 + LX) for each of the three components, where CIis the ratio of radiative capture to fission. By assuming a constant value for v, the theoretical expression for 7 was made to fit the measured variation by adjusting the value of ct for each of the components. At about O-3eV the absorption is almost entirely due to the strong resonance at 0.297 eV. Consequently a fit between theory and experiment at this energy gives a value for K of the O-297 eV resonance which only depends on the value of v, taken to be 2.91 (HARVEYand SANDERS,1956) and on the absolute normalization of 7. A value of CI(o.29,J= 0.80 f 0.05 was obtained for the 0.297 eV resonance where the error quoted is due chiefly to the uncertainties in v and 7 for a thermal spectrum. This is in agreement, within errors, with the more uncertain value of tl (o.29,)deduced from the resonance parameters for the averaged Geneva fission and absorption cross-sections. Owing to the predominance of the O-297eV resonance it is not possible to make reliable individual estimates for a of the zero energy resonance and the l/v component. However, by arbitrarily assuming the same value of dcfor the zero energy resonance as for the l/2; component, adjustment of this value to 0.09 then gave satisfactory agreement between the theoretical and the measured variation of r] over the energy range 0.007-0.36 eV. The error for this combined value of 7 should not be in excess of about 0.08, indicating an upper limit of O-17,which seems somewhat lower than the estimate obtained using the resonance parameters deduced from the averaged Geneva fission and total cross-section. However, the uncertainty in this estimate is large. The theoretical expression, shown fitted to the normalized measurements of 7 in Fig. 2, can be written in the form 7 = vxE*a,/E*a, as follows:
Y/= 2.91
3918/[(E - 0*297)2 + 0*00235] + 0*1268/[(E - 0.02)2 + 0.003601 + 30.8 7*050/[(E - O.297)2 + 0*00235] + 0*1377/[(E - 0.02)2 + 0.003601 + 33.4
The resonance parameters used in the expression for a, were, for the zero energy level E, = 0*02 eV, F = 0.120 eV, gFn” = 0.00175 x lop3 eV, and for the strong resonance E, = 0.297 eV, F = O-097 eV, gI’n” = 0.111 x 1O-3eV. These values
H. M. SKAR~GARD and C. J. KENWARD
218
agree, within the quoted errors, with those deduced by HARVEYand SANDERSand by EGELSTAFFand HUGHES from the averaged Geneva total cross-section. The slight adjustment was made so that the theoretical expression, while fitting the experimental variation of r] well, should at the same time give an arbitrary compromise between fitting the Geneva absorption and fission cross-sections. The r.m.s. deviation of the theoretical expression was then about 33 per cent for the absorption crosssection and about 54 per cent for the fission cross-section. These deviations could be reduced somewhat by slight adjustments, within the errors concerned, of the absolute normalization of 7 to a higher value or the normalization of the world 400
300
% 600
500
0.90
0,025 FIG. 3.-The
0.030 . .
varlatlon
0.035
0.040
0045
0.050 CV
of qeff (ssaPu) with the energy Maxwellian flux distribution.
(temperature)
of a
average fission cross-section (729 f 15 barns at O-0253 eV) to a lower value. The corresponding small changes in the parameters used in the theoretical fit would not affect its form or the agreement between the theoretical and measured variation of 9. The variation of 7 for 23QPu measured in this experiment, has been used to redetermine the temperature coefficient of qeff, the effective value of 11 averaged over a Maxwellian neutron flux distribution. verr is defined for a “thin” fissile sample (one in which the absorption is proportional to a,) as follows: reff(Eo) = Sq(E) @)F(E, Eo) dE Sea(E) F(E, E,) dE In this expression F(E, E,) is the neutron flux distribution and is proportional to E exp (-E/E,), where E. is the energy corresponding to the temperature of the Maxwellian distribution. The theoretical expressions for q(E) and a,(E) were used and the effective value of 7 was computed for several different values of the temperature.* The results are shown in Fig. 3. The effective value of q relative to that for a temperature of 20°C is plotted as a function of temperature (abscissa at top of graph) and of the corresponding energy E, (abscissa at bottom of graph). The result is * We are grateful computations.
to Miss M. BOWLER of the Harwell
Computing
Group
for carrying
out these
Measurements of the energy dependence of the fission neutron yield
219
nearly a straight line. In the vicinity of O-025eV, over the temperature range from 290 to 250”K, the average temperature coefficient is -0*027 per cent per “K. In close agreement with this value, HORTONand MCCULLEN (1955) found that a coefficient of -0.028 per cent per “K was needed in order to explain the temperature effects in a plutonium-water critical system. Over the temperature range from 290 to 350”K, the average temperature coefficient is -0.030 per cent per “K. Over this same temperature range, HARVEYand SANDERS(1956) found a linear decrease in q of O-036per cent per “K by using the earlier Harwell and Brookhaven measurements of 7. Their somewhat higher value can be partly explained by the extrapolation of 7
2.20 I 2.10 P
200’ 0001
I
I
I
Illlll
I
I
E-
FIG. 4.-Present
I
I11111 0.10
0.01
eV
measurements of the variation of r] for assU with energy.
that was necessary toward low energies where direct measurements were not then available. 235U: The new 7 measurements for i35U are plotted in Fig. 4. They have been normalized to 2.08 at an energy of 0.0253 eV. (The normalization of HARVEYand SANDERS(1956) was adopted.) Over the energy range from 0.006 to O-050 eV q appears constant, within the errors on the measurements. This result is consistent with the directly measured variation of q reported by PALEVSKYet al. (1956) for energies down to 0.01 eV. The present measurements, together with those reported by PALEVSKY et al. (which include the Hanford measurements of LEONARDreported at the Geneva conference by PALEVSKY,1955) are in excellent agreement with the variation of q inferred from the most recent cross-section data, given in BNL-325. APPENDIX:
NEUTRON
VELOCITY
SELECTOR
A photograph of the neutron-velocity selector (Fig. 5), shows the essential features. (The safety cover has been removed to provide a better view.) Four equally-spaced slotted disks rotate on a common shaft 66 in. long. Each disk consists of a 0.030 in. thickness of cadmium sandwiched between aluminium retaining flanges. Slots in successive discs along the shaft are angularly displaced so that when the shaft is set into rotation and a collimated beam of neutrons enters a slot in the first disk, only those neutrons with a certain range of velocities pass through slots in successive disks. When the velocity selector is used in conjunction with the crystal spectrometer, as shown in Fig. 1, the rotation speed of the shaft is adjusted so that the neutrons transmitted cover a range of velocities centred about the velocity corresponding to the first order reflection from the crystal. This band is just narrow enough to exclude neutrons with energies corresponding to higher order reflections from striking the crystal. (In order to enhance the transmission efficiency and to extend the useful range
220
H.M.
SKARSGARD
and C.J.
KENWARD
of the velocity selector to as high energies as possible, the energy resolution was made no better than was required to provide satisfactory elimination of higher order neutrons.) The detailed dimensions of the slotted cadmium disks are given in Fig. 6. Also shown is the angular displacement between slots in successive disks, 0.106 radians. This displacement, together with the 22 in. separation between successive disks on where S is the the shaft, yield the relationship S(rev/min) = 2.50 x lo4 fi(eV), rotary speed of the shaft and E is the energy of neutrons for which the transmission of the velocity selector is a maximum. The speed of rotation is continuously variable Slot in subsequent disc. \ 38 equally
FIG.
spaced
6.-Detailed section of one of the rotating cadmium disks.
from 600 to 5650 rev/min, corresponding to an energy range of 0.00058 to 0.051 eV. The maximum speed is limited by the power necessary to overcome air drag on the rotating disks. A 14 h.p. synchronous motor drives a variable speed unit which is coupled to a pulley on the shaft by means of a vee-belt. The transmission efficiency of the velocity selector, for a perfectly collimated beam having a diameter smaller than the depth of the slot, is about 38 per cent (equal to the ratio of the slot width to the distance between adjacent slots in a disk). Tests were carried out to determine the completeness with which higher orders were eliminated by the velocity selector. These showed that second order neutrons were reduced in intensity by a factor of about 1-O x 103. Higher order neutrons than the second, that still fell within the cadmium high absorption limit, were reduced to undetectable intensities. Estimates show that the intensities, relative to the first order, of higher order neutrons with energies above the cadmium cut-off, are less than 0.5 per cent over the energy range up to O-05 eV. Acknowledgements-The authors are grateful to Dr. J. E. SANDERS for much helpful advice rendered during the course of this work. The pile operating staff assisted by taking readings during over-night runs. The work was carried out during the tenure by one of us (H. M. S.) of a National Research Council of Canada Overseas Fellowship. This aid is gratefully acknowledged.
FIG.
5.-Neut ron-velocity selector.
p. 220
Measurements
of the energy dependence of the fission neutron yield
221
REFERENCES AU~LAIR J. M., LONDON H. H. and JACOB M. (1955) CR. Acad. Sci. Paris 241, 1935. EGEL~TAFF P. A. and SANDERS, J. E. (1955) Geneva Conference Paper P/425. EGELSTAFF P. A. and HUGHES D. J. (1956) Progress in Nuclear Energy Vol. 1, Chap. 2. EGELSTAFF P. A., GAYTHER D. B. and NICHOLSONK. P. (1957) To be published. FARLEY F. J. M. (1956) J. Nucl. Energy 3, 33. HARVEY J. A. and SANDERS J. E. (1956) Progress in Nuclear Energy Vol. 1, Chap. 1. HORTON C. C. and MCCLJLLEN J. D. (1955) Geneva Conference Paper P/428. HUGHES D. J. and HARVEY J. A. (1955) Neutron Cross-Sections BNL 325. NIKITIN S. J., GALAMINA N. D., IGNATIEW J. G., OKOROKOW W. W. and SUCHORUTCHKINS. I. (1955) Geneva Conference Paper P/646. PALEVSKY H. (1955) Geneva Conference Paper P/587. PALEVSKY H., HUGHES D. J., ZIMMERMANR. L. and EISBERG R. M. (1956) J. Nucl. Energy 3, 177. SAILOR V. L. (1955) Geneva Conference Paper P/586. SANDERS J. E. and KENWARD C. J. (1956) J. Nucl. Energy 3,70. SANDERS J. E., SKARSGARD H. M. and KENWARD C. J. (1957) To be published. SMITH J. R. and MAGLEBY E. H. (1955) Bull. Amer. Phys. Sot. 30, 7-11.
4
MEASUREMENTS OF THE ENERGY DEPENDENCE OF THE FISSION NEUTRON YIELD PER NEUTRON ABSORBED IN 23QPuAND 235U IN THE RANGE 0.006436 eV H. M. SKARSGARD and C. J. KENWARD Atomic Energy Research Establishment, Harwell, Berkshire (Received 20 May 1957) Abstract-The
energy dependence of 7, the fission neutron yield per neutron absorbed, has been measured for assPu over the energy range 0~0070-036 eV and for 2s6Uover the range 04060-0~050 eV, using a crystal spectrometer. For energies less than 0.050 eV a mechanical neutron-velocity selector was used in conjunction with the crystal spectrometer to eliminate higher order neutrons from the diffracted beam. For zssPu, at 0.3 eV, 7 is found to be 78.5 per cent of its value at 0.0253 eV. A theoretical expression for 7, based on single level parameters deduced from the published total cross-section values, is’fitted to the measured variation and gives a value for a,,,.2B,j, the ratio of radiative capture to fission in the 0.297 eV resonance, of 0.80 i 0.05. The temperature coefficient of the effective value of 77averaged over a Maxwellian flux distribution is -0.027 per cent per “C for temperatures in the vicinity of 20°C. Within experimental errors, q for zssU appears constant from 0.006 to 0.050 eV. 1. INTRODUCTION DIRECT measurements
of the energy dependence of 7, the fission neutron yield per neutron absorbed, have been made for 23gPuover the energy range 0*0070-0.36 eV and for 235Uover the range 0~00604050 eV. A mechanical neutron-velocity selector, used in conjunction with a crystal spectrometer, has enabled the measurements to be extended to lower energies than were reached in previous work. The low resolution velocity selector serves to eliminate the high order contamination of the diffracted beam which becomes especially troublesome at energies below the peak of the thermal flux distribution. Direct measurements of the energy dependence of q have been reported previously for 23gPu(PALEVSKY, 1955; PALEVSKY et al., 1956; EGELSTAFF and SANDERS, 1955; FARLEY, 1956; NIKITIN et al., 1955) and for 235U(PALEVSKY, 1955 ; PALEVSKYet al., 1956; SMITH and MAGLEBY, 1955; NIKITIN et al., 1955). Considering the low energy limit of the measurements for 23sPu, the work of PALEVSKYet al. with the Brookhaven slow-chopper extend to 0.017 eV, while the Harwell crystal spectrometer measurements by SANDERS reported at Geneva by EGELSTAFT;and SANDERS (1955) do not go below 0.025 eV. The U.S.S.R. pulsed cyclotron work of NIKITIN et al. extends to 0.011 eV, but the points between 0.01 and 0.02 eV show considerable scatter. The Brookhaven and Harwell data are in good agreement, within the experimental errors, up to 0.7 eV. They show a decrease in 7 with increasing energy up to about 0.3 eV, at which energy 7 is about 75 per cent of its value at O-025 eV. Beyond 0.3 eV the value rises again. 7 may also be inferred from the relationship q = ~(oJa,>, where Yis the number of fission neutrons per fission, assumed constant, and crf and o, are the fission and total absorption cross-sections respectively. (The values used are those quoted in HARVEY and SANDERS(1956). These are based on results presented 212
at the Geneva Conference.)
Measurements of the energy dependence of the fission neutron yield
213
When this is done, q is observed to decrease up to 0.3 eV to about 85 per cent of its value at O-025 eV. However, values of 7 inferred in this way are subject to consider-
able uncertainty and the discrepancy between this value and that measured directly is hardly outside the errors. A real discrepancy would imply that v was not constant over the energy range from O-025 to 0.3 eV. This possibility has been checked (AUCLAIR et al., 1955; SANDERSand KENWARD, 1956; PALEVSKYet al., 1956), and v .was found to be constant to within about 1 per cent over this range. The Russian data do not agree very well with the Brookhaven and Harwellresults and show a decrease in q up to 0.3 eV to about 85 per cent of the O-025 eV value, more in agreement with the variation of 7 inferred from the cross-section data. Because of these discrepancies it was decided to repeat the Harwell measurements, with improved accuracy, and to extend the measurements to lower energies. For 235U the measurements reported by PALEVSKYet al. (1956) together with those of SMITH (1955) agree well, within the errors, with the energy dependence of 7 inferred from the cross-section data. The measurements extend from 0.01 to I.0 eV. Over the energy range from 0.01 to 0.10 eV q appears to increase by about 1 per cent. The Russian data show rather poor agreement with the American data, a decrease of about 10 per cent being observed between 0.01 and 0.10 eV.
Aperture cadmium
in sheet
Diffracted
beam
Fast-
FIG. l.-Experimental
2. EXPERIMENTAL
arrangement.
DETAILS
Procedure
The experimental procedure which was followed is a modification of that used in previous measurements of the energy dependence of q by SANDERS (reported by EGELSTAFFand SANDERS,1955) and by SANDERSet al. (1957). A diagram of the apparatus is shown in Fig. 1. A collimated beam from the centre of BEPO is diffracted by a KC1 crystal to give a monoenergetic beam of neutrons. A mechanical neutronvelocity selector was used for energies up to 0.05 eV to prevent neutrons with energies corresponding to higher order reflections from reaching the crystal. Use of the neutron-velocity selector is the major modification of the experimental arrangement reported in the earlier work at Harwell. It is described in detail in an appendix to 3
214
H. M. SKARSGARD and C. J. KENWARD
this paper. The (200) planes of the KC1 crystal were employed and gave an energy resolution (width of half maximum of the energy distribution) of about 2 per cent at 0.01 eV. The diffracted neutron beam passes through a monitor counter before striking a disc of the fissile sample in which it is almost completely absorbed. The fissile sample is placed on the axis of a cylindrical fast-neutron detector which consists of sixteen 1°BF, proportional counters embedded in paraffin wax. It has an efficiency of about 3.0 per cent. The inside of the fast-neutron detector is lined with sufficient B,O, to absorb the slow neutrons scattered from the disc and canning material. The monitor counter used was either a l”B foil proportional counter or, at energies above 0.05 eV, a 1°BF, proportional counter. In the foil counter the l”B is coated on thin aluminium foils through which the beam is passed. The walls of the counter are of thin aluminium. The efficiency of this counter is about 2-O per cent for O-025 eV neutrons. The l”BF, counter has an efficiency about eight times as great. The walls are made of thin copper. The counters and fission sample are surrounded by a cadmium-lined paraffin wax shield to reduce the background. The assembly is mounted on a trolley which can be rotated about the crystal and aligned to receive the diffracted beam by means of a light, mirror, and photocell. The energy dependence of 11is then measured by observing the ratio of counts in the fast-neutron detector to those in the monitor counter for various settings of the crystal. Thus, if NF and NM are the counts recorded in the fast-neutron detector and monitor counter respectively, then N,
A W% Ells NM
where E”’ allows for the l/u dependence of the absorption cross-section of l0B at these neutron energies. A, is the product of several small corrections for effects which depend on the energy of the incident neutrons. These are: (a) The departure of the response of the monitor counter from that of a l/u counter. A correction was made for absorption and scattering effects in the l”B and materials making up the monitor counters. The correction was estimated for the l”B foil counter and varied by about l-8 per cent over the range of energies for which the counter was used. In the case of the 1°BF, monitor counter the correction was estimated and, as a check, was measured by placing both this counter and the l”B foil counter in the beam-the l”B foil counter behind the l”BF, counter-and observing the ratio of counts recorded in each as a function of the incident energy of the neutrons. Over the range from 0.05 to 0.36 eV, for which the 1°BF, monitor counter was used, the correction varied by 5.3 per cent. (The absolute value of the correction was less than 11 per cent over this range.) (b) Scattering and absorption by canning material and isotopic impurities of fissile samples. A 1 mm thick disc of 239Pu containing about 3.8 per cent 240Puwas used. It was enclosed in a double-walled copper can of thickness 0.020 in. The 235Usample was an untanned 5 mm thick disc. A correction which did not exceed 3.5 per cent was made for the absorption and scattering of the incident beam by the copper canning material surrounding the 23gPu sample. A correction was necessary for the varying competitive absorption of the 240Pu,which has a large resonance in the vicinity of 1-O
Measurements of the energy dependence of the fission neutron yield
215
eV. This correction amounted to less than 1.5 per cent for energies up to 0.36 eV. The cross-section of 240Pu was taken from recent work of EGELSTAFF et al. (1957). The corresponding correction for absorption in the 238U impurity present in the 235U sample was negligible. The fraction of incident neutrons which was scattered by the fissile sample was estimated as ,!?(cr.JaJ where /3is a function of the transmission of the fissile sample which approaches 0.15 as the transmission of the sample approaches zero. For the measurements reported in this paper ,/3remained very near this limit. The scattering cross-section cs for 23gPuwas taken as 11 barns. For the 235Usample an average value of 18*2 barns was used for as---estimated by taking into account the increase in potential scattering due to the 238Uimpurity in the sample and by including the contribution to the elastic scattering from the negative energy level in 235U at -1.4 eV, which has a large partial neutron width (SAILOR, 1955). The scattering correction applied was less than O-3 per cent for 23gPu and less than 0.6 per cent for 7J. (c) Transmission of the fissile samples. A correction not exceeding I.3 per cent was made for the finite transmission of the 23gPu disk. The correction was negligible for 235U. (d) Counting losses due to scaler dead times. This correction was less than I.0 per cent for 23gPu and’almost negligible for the 235Umeasurements. (e) Higher order contamination in the diffracted neutron beam. Normally the diffracted beam from a crystal spectrometer set at energy E contains neutrons with energies 4E, 9E etc., corresponding to higher order reflections. It is necessary to correct for the effect of these neutrons by considering the contribution which they make to the counts recorded in the monitor and fast-neutron counters. In order to do this accurately one must know the intensities of the higher order neutrons and the efficiencies with which they are detected in the monitor counter relative to the first order as well as their scattering and absorption cross-sections in the monitor counter and in the sample. Furthermore, one must know the value of 7 relative to that for the first order. Since some of these factors are not well known it is desirable to reduce the higher order effects to such proportions that the uncertainties become unimportant. In the energy range below 0.05 eV, use of the neutron-velocity selector reduced the corrections to almost negligible proportions. Estimates of the correction did not exceed 0.5 per cent. In the 23sPu measurements above 0.05 eV the correction was not greater than 2.0 per cent. Cadmium and indium filters were used above 0.133 eV in order to reduce the higher order effect. It was especially important to reduce the higher order effect in this energy region, as the 240Puimpurity, with a large resonance at 1 eV, competes significantly with the 23gPu for absorption of the higher orders; this gives rise to an added uncertainty because of the poorly known cross-section for 240Pu and the inaccurate knowledge of the isotopic composition of the sample. In addition to these effects, the variation of neutron multiplication in the fissile sample with incident neutron energy was examined. This effect depends on the variation, with energy, of the mean penetration depth of incident neutrons in the disk. It was found to be of negligible proportions in these measurements. Cross-section data compiled by HUGHES and HARVEY (1955) were used in making estimates of the various corrections.
216
H. M. SKARSGARD and C. J. KENWARD
In order to reduce the effects of drift in the counter sensitivities, the measurements at various energies were interspersed frequently with measurements at some fixed energy. The results were normalized to the value of q at this point. For 23gPu this point was 0.05 eV, at which energy the readings taken with the neutron-velocity selector overlap those taken without it. For 235Uthe reference energy was 0.025 eV. The results have been adjusted in absolute value so as to be consistent with pile oscillator measurements of the average effective thermal value of q (HARVEY and SANDERS, 1956). Errors quoted are the statistical standard deviations on the counts recorded. The high background count rate in the fast-neutron detector due to the 240Puimpurity in the sample made it difficult to obtain accurate results for 23gPu below about 04070 eV. 3. RESULTS
239Pu. The present measurements are plotted in Fig. 2. The dashed 7 = v (of/u,) which has been fitted to lized to a value of 2.08 at O-0253 eV.
AND
DISCUSSION
of the variation curve represents the measurements. This normalization
with energy of 7 for 23gPu a theoretical expression for The data have been normais based upon the variation
t 1.90 q
1.80
E
-
eV
FIG. 2.-Present measurements of the variation of 7 for 239Puwith energy. Broken-line curve represents a theoretical expression for 7 = P X (u&r,), which was fitted to the measurements.
of q, and an effective thermal value of 2.02 (HARVEY and SANDERS, 1956); the value of 7 for 0.0253 eV neutrons is 1.030 times the effective value of Q for a thermal flux distribution at 20°C. Over the energy region where they overlap, from O-017 to 0.36 eV, the new measurements of the variation of q for 23gPu are in reasonably good agreement with the earlier Hat-well measurements of SANDERS reported by EGELSTAFF and SANDERS (1955) and FARLEY (1956) and the Brookhaven results of PALEVSKY et al. (1956). The present measurements show that, in the vicinity of O-3eV, 11is about 78.5 per cent of its value at O-0253 eV. This is intermediate to the figure of 75 per cent indicated by the earlier direct measurements and the value of about 85 per cent inferred from the averaged fission and absorption cross-section values given by
Measurements
of the energy dependence of the fission neutron yield
217
HARVEY and SANDERS (1956). It is not practicable to extend the range of the measurements by increasing the thickness of the sample, since this causes the fission neutron background, due to spontaneous fission of 240Puin the samples, to increase to such an extent that accurate measurements are not possible. Below 0.0253 eV the new measurements show a levelling-off which is in satisfactory agreement with the inferred behaviour of q. The theoretical fit is based upon the resonance parameters deduced from the averaged Geneva total cross-section for 23gPu by HARVEYand SANDERS(1956) and EGELSTAFFand HUGHES(1956). Their analyses show a weak resonance at approximately zero neutron energy and a strong resonance at 0.297 eV. For the energy range covered by the measurement of q the absorption cross-section in the denominator of the theoretical expression is therefore written as the sum of three terms-the singlelevel contribution from each of the 0.297 eV and zero energy levels and a l/u component due to resonances at higher energies. By fitting the theoretical expression for oa to the averaged Geneva absorption cross-section (a, - 10 barns) at O-0253eV, the parameters E,, g13z”,and I’ for the two resonances fixed the contribution of the I/v component. The corresponding terms for a, depend on the values of (1 + LX) for each of the three components, where CIis the ratio of radiative capture to fission. By assuming a constant value for v, the theoretical expression for 7 was made to fit the measured variation by adjusting the value of ct for each of the components. At about O-3eV the absorption is almost entirely due to the strong resonance at 0.297 eV. Consequently a fit between theory and experiment at this energy gives a value for K of the O-297 eV resonance which only depends on the value of v, taken to be 2.91 (HARVEYand SANDERS,1956) and on the absolute normalization of 7. A value of CI(o.29,J= 0.80 f 0.05 was obtained for the 0.297 eV resonance where the error quoted is due chiefly to the uncertainties in v and 7 for a thermal spectrum. This is in agreement, within errors, with the more uncertain value of tl (o.29,)deduced from the resonance parameters for the averaged Geneva fission and absorption cross-sections. Owing to the predominance of the O-297eV resonance it is not possible to make reliable individual estimates for a of the zero energy resonance and the l/v component. However, by arbitrarily assuming the same value of dcfor the zero energy resonance as for the l/2; component, adjustment of this value to 0.09 then gave satisfactory agreement between the theoretical and the measured variation of r] over the energy range 0.007-0.36 eV. The error for this combined value of 7 should not be in excess of about 0.08, indicating an upper limit of O-17,which seems somewhat lower than the estimate obtained using the resonance parameters deduced from the averaged Geneva fission and total cross-section. However, the uncertainty in this estimate is large. The theoretical expression, shown fitted to the normalized measurements of 7 in Fig. 2, can be written in the form 7 = vxE*a,/E*a, as follows:
Y/= 2.91
3918/[(E - 0*297)2 + 0*00235] + 0*1268/[(E - 0.02)2 + 0.003601 + 30.8 7*050/[(E - O.297)2 + 0*00235] + 0*1377/[(E - 0.02)2 + 0.003601 + 33.4
The resonance parameters used in the expression for a, were, for the zero energy level E, = 0*02 eV, F = 0.120 eV, gFn” = 0.00175 x lop3 eV, and for the strong resonance E, = 0.297 eV, F = O-097 eV, gI’n” = 0.111 x 1O-3eV. These values
H. M. SKAR~GARD and C. J. KENWARD
218
agree, within the quoted errors, with those deduced by HARVEYand SANDERSand by EGELSTAFFand HUGHES from the averaged Geneva total cross-section. The slight adjustment was made so that the theoretical expression, while fitting the experimental variation of r] well, should at the same time give an arbitrary compromise between fitting the Geneva absorption and fission cross-sections. The r.m.s. deviation of the theoretical expression was then about 33 per cent for the absorption crosssection and about 54 per cent for the fission cross-section. These deviations could be reduced somewhat by slight adjustments, within the errors concerned, of the absolute normalization of 7 to a higher value or the normalization of the world 400
300
% 600
500
0.90
0,025 FIG. 3.-The
0.030 . .
varlatlon
0.035
0.040
0045
0.050 CV
of qeff (ssaPu) with the energy Maxwellian flux distribution.
(temperature)
of a
average fission cross-section (729 f 15 barns at O-0253 eV) to a lower value. The corresponding small changes in the parameters used in the theoretical fit would not affect its form or the agreement between the theoretical and measured variation of 9. The variation of 7 for 23QPu measured in this experiment, has been used to redetermine the temperature coefficient of qeff, the effective value of 11 averaged over a Maxwellian neutron flux distribution. verr is defined for a “thin” fissile sample (one in which the absorption is proportional to a,) as follows: reff(Eo) = Sq(E) @)F(E, Eo) dE Sea(E) F(E, E,) dE In this expression F(E, E,) is the neutron flux distribution and is proportional to E exp (-E/E,), where E. is the energy corresponding to the temperature of the Maxwellian distribution. The theoretical expressions for q(E) and a,(E) were used and the effective value of 7 was computed for several different values of the temperature.* The results are shown in Fig. 3. The effective value of q relative to that for a temperature of 20°C is plotted as a function of temperature (abscissa at top of graph) and of the corresponding energy E, (abscissa at bottom of graph). The result is * We are grateful computations.
to Miss M. BOWLER of the Harwell
Computing
Group
for carrying
out these
Measurements of the energy dependence of the fission neutron yield
219
nearly a straight line. In the vicinity of O-025eV, over the temperature range from 290 to 250”K, the average temperature coefficient is -0*027 per cent per “K. In close agreement with this value, HORTONand MCCULLEN (1955) found that a coefficient of -0.028 per cent per “K was needed in order to explain the temperature effects in a plutonium-water critical system. Over the temperature range from 290 to 350”K, the average temperature coefficient is -0.030 per cent per “K. Over this same temperature range, HARVEYand SANDERS(1956) found a linear decrease in q of O-036per cent per “K by using the earlier Harwell and Brookhaven measurements of 7. Their somewhat higher value can be partly explained by the extrapolation of 7
2.20 I 2.10 P
200’ 0001
I
I
I
Illlll
I
I
E-
FIG. 4.-Present
I
I11111 0.10
0.01
eV
measurements of the variation of r] for assU with energy.
that was necessary toward low energies where direct measurements were not then available. 235U: The new 7 measurements for i35U are plotted in Fig. 4. They have been normalized to 2.08 at an energy of 0.0253 eV. (The normalization of HARVEYand SANDERS(1956) was adopted.) Over the energy range from 0.006 to O-050 eV q appears constant, within the errors on the measurements. This result is consistent with the directly measured variation of q reported by PALEVSKYet al. (1956) for energies down to 0.01 eV. The present measurements, together with those reported by PALEVSKY et al. (which include the Hanford measurements of LEONARDreported at the Geneva conference by PALEVSKY,1955) are in excellent agreement with the variation of q inferred from the most recent cross-section data, given in BNL-325. APPENDIX:
NEUTRON
VELOCITY
SELECTOR
A photograph of the neutron-velocity selector (Fig. 5), shows the essential features. (The safety cover has been removed to provide a better view.) Four equally-spaced slotted disks rotate on a common shaft 66 in. long. Each disk consists of a 0.030 in. thickness of cadmium sandwiched between aluminium retaining flanges. Slots in successive discs along the shaft are angularly displaced so that when the shaft is set into rotation and a collimated beam of neutrons enters a slot in the first disk, only those neutrons with a certain range of velocities pass through slots in successive disks. When the velocity selector is used in conjunction with the crystal spectrometer, as shown in Fig. 1, the rotation speed of the shaft is adjusted so that the neutrons transmitted cover a range of velocities centred about the velocity corresponding to the first order reflection from the crystal. This band is just narrow enough to exclude neutrons with energies corresponding to higher order reflections from striking the crystal. (In order to enhance the transmission efficiency and to extend the useful range
220
H.M.
SKARSGARD
and C.J.
KENWARD
of the velocity selector to as high energies as possible, the energy resolution was made no better than was required to provide satisfactory elimination of higher order neutrons.) The detailed dimensions of the slotted cadmium disks are given in Fig. 6. Also shown is the angular displacement between slots in successive disks, 0.106 radians. This displacement, together with the 22 in. separation between successive disks on where S is the the shaft, yield the relationship S(rev/min) = 2.50 x lo4 fi(eV), rotary speed of the shaft and E is the energy of neutrons for which the transmission of the velocity selector is a maximum. The speed of rotation is continuously variable Slot in subsequent disc. \ 38 equally
FIG.
spaced
6.-Detailed section of one of the rotating cadmium disks.
from 600 to 5650 rev/min, corresponding to an energy range of 0.00058 to 0.051 eV. The maximum speed is limited by the power necessary to overcome air drag on the rotating disks. A 14 h.p. synchronous motor drives a variable speed unit which is coupled to a pulley on the shaft by means of a vee-belt. The transmission efficiency of the velocity selector, for a perfectly collimated beam having a diameter smaller than the depth of the slot, is about 38 per cent (equal to the ratio of the slot width to the distance between adjacent slots in a disk). Tests were carried out to determine the completeness with which higher orders were eliminated by the velocity selector. These showed that second order neutrons were reduced in intensity by a factor of about 1-O x 103. Higher order neutrons than the second, that still fell within the cadmium high absorption limit, were reduced to undetectable intensities. Estimates show that the intensities, relative to the first order, of higher order neutrons with energies above the cadmium cut-off, are less than 0.5 per cent over the energy range up to O-05 eV. Acknowledgements-The authors are grateful to Dr. J. E. SANDERS for much helpful advice rendered during the course of this work. The pile operating staff assisted by taking readings during over-night runs. The work was carried out during the tenure by one of us (H. M. S.) of a National Research Council of Canada Overseas Fellowship. This aid is gratefully acknowledged.
FIG.
5.-Neut ron-velocity selector.
p. 220
Measurements
of the energy dependence of the fission neutron yield
221
REFERENCES AU~LAIR J. M., LONDON H. H. and JACOB M. (1955) CR. Acad. Sci. Paris 241, 1935. EGEL~TAFF P. A. and SANDERS, J. E. (1955) Geneva Conference Paper P/425. EGELSTAFF P. A. and HUGHES D. J. (1956) Progress in Nuclear Energy Vol. 1, Chap. 2. EGELSTAFF P. A., GAYTHER D. B. and NICHOLSONK. P. (1957) To be published. FARLEY F. J. M. (1956) J. Nucl. Energy 3, 33. HARVEY J. A. and SANDERS J. E. (1956) Progress in Nuclear Energy Vol. 1, Chap. 1. HORTON C. C. and MCCLJLLEN J. D. (1955) Geneva Conference Paper P/428. HUGHES D. J. and HARVEY J. A. (1955) Neutron Cross-Sections BNL 325. NIKITIN S. J., GALAMINA N. D., IGNATIEW J. G., OKOROKOW W. W. and SUCHORUTCHKINS. I. (1955) Geneva Conference Paper P/646. PALEVSKY H. (1955) Geneva Conference Paper P/587. PALEVSKY H., HUGHES D. J., ZIMMERMANR. L. and EISBERG R. M. (1956) J. Nucl. Energy 3, 177. SAILOR V. L. (1955) Geneva Conference Paper P/586. SANDERS J. E. and KENWARD C. J. (1956) J. Nucl. Energy 3,70. SANDERS J. E., SKARSGARD H. M. and KENWARD C. J. (1957) To be published. SMITH J. R. and MAGLEBY E. H. (1955) Bull. Amer. Phys. Sot. 30, 7-11.
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