Energy dependence of νp for neutron-induced fission of 235U below 1·0 MeV

Journalof NuclearEnergy.

1967.

Vol.21.PP. 157to 169. PergamonPressLtd. Printedin NorthernIreland

ENERGY DEPENDENCE OF i& FOR NEUTRON-INDUCED FISSION OF “35U BELOW 1.0 MeV* J. W. MEADOWS and J. F. WHALEN Argonne National Laboratory, Argonne, Illinois (Received 12 Auglrst 1966) Abstract-The energy dependence of 1,, the average number of prompt neutrons per fission, has been measured over the incident neutron energy range 0.0~1.0 MeV by measuring the ratio of prompt neutrons from neutron-induced fission of *W to those from spontaneous fission of W2f. It is confirmed that G2,is not a monotonically increasing function of energy below 0.6 MeV. Above

0.6 MeV, dJddE,, N 0.14 MeV-1 and is in good agreement with the assumption that all the kinetic energy of the incident neutron appears as internal excitation of the fragments. 1. INTRODUCTION ALTHOUGH recent experimental work on the energy and angular distribution of neutrons from thermal neutron-induced fission of 235U (SKAKSVAG and BERGHEIM, 1963; KAPOOR et al., 1963) and from spontaneous fission of 252Cf (BOWMAN et al., 1962)

show that ~10 per cent are emitted before scission, the energy dependence of the number of neutrons per fission should still depend largely on the factors affecting neutron evaporation from the fragments. In the following discussion these ‘prescission’ neutrons are ignored, which is the same as assuming them to have the same energy dependence as the ones evaporated from the fragments. If it is assumed that there is no correlation between the various quantities, the relation of the number of prompt neutrons per fission to the total energy associated with them is given by I?*

where i?, is the average binding energy of a neutron to the fission fragments, d is the average kinetic energy of an evaporated neutron in the fragment system, and E,* is the average fragment excitation energy carried off by the neutrons. It is given by &,* = & + B, + E,, - 1x - Ey.

(2)

where EM is the average energy obtained from a hypothetical spontaneous fission of the compound nucleus with zero excitation energy, B, is the binding energy of a neutron to the fissioning nucleus, En is the energy of the incident neutron, EK is the average kinetic energy of the fission fragment and EYis the average total energy of the prompt y-rays. B,, and E,, are the excitation energy brought in by the incident neutron and are zero for true spontaneous fission. The averages are all made over the massyield distribution. However, B, must also be the result of an average over the number of neutrons emitted by each fragment. This work supported by the U.S. Atomic Energy Commission. 157

??

J. W. MEADOWS and J. F. WHALEN

158

It is often assumed that, for E,, less than a few MeV, the mass-yield distribution does not change and & and EY are constant. It is certain that B,, and g are not constant. In general, B,, is expected to increase slowly as additional neutrons are evaporated. B will also increase with increasing E,, since the higher excitation energy will result in a harder spectrum. In this case, the energy dependence of i), may be expressed by the first term of a MacLaurin’s Series. Its coefficient is dp, -=-=m) dE,*

1

It is possible to make fairly good approximations of all the quantities in equation (3). B,, flM and d&,/dp, may be obtained by making suitable averages over the massyield distribution (MILTONand FRASER,1962) of quantities calculated by an empirical mass formula (CAMERON,1957; MILTON, 1962). &,, fly, and g can be obtained from experimental information (TERRELL,1962). dc/di, can be calculated from a relation given by TERRELL(1959) : -5= 0.621(?, + 1)1’2. (4) The results are listed below for 235U. B, = 5-OMeV. dB, =0*12MeV. dit,

d = l-21 MeV. g= yz,

0.17 MeV.

E n* = 150MeV. If it is assumed that &.,, EYi,and the mass-yield distribution are constant, then d&,* may be replaced by dE,. Then d?,ldE,

= 0.14 MeV-l.

Early measurements (LEACHMAN,1958) of 1, for neutron fission of 23aU seemed to be in agreement with this value but later measurements (MEADOWSand WHALEN, 1962; HOPKINSand DIVEN, 1963 ; MATHERet al., 1964) of higher precision indicated that d+,/dE,, varied from N O-1MeV-l near En = 0 to -0.19 MeV-l at E,, = 6.0 MeV. However recent measurements of i, in the region below 1.0 MeV (BLYUMKINA et al., 1964) showed a maximum in the it, curve at E,, - 0.4 MeV. The results of Mather et al. can also be interpreted as showing a similar maximum but at E, - 0.2 MeV. The series of measurements reported here are the results of an attempt to reexamine with improved precision the energy dependence of 1, for neutron-induced fission of 235Uin the energy region below I.0 MeV. 2. EXPERIMENTAL METHOD The results reported here are all relative to i), for spontaneous fission of 252Cf. Basically, the method consisted of measuring the number of neutrons detected per fission for spontaneous fission of 252Cfand for neutron-induced fission of 235U. The ratio of these two values, except for a small correction, was equal to the ratio S,(2s5U)/~~(262Cf).In practice, the two measurements were made at the same time with a single neutron detector. This reduced the possibility of error due to time-dependent changes in the background, detector efficiency or in the electronic components.

Energy dependence of GIrfor neutron-induced

fission

159

The experimental arrangement is illustrated in Fig. 1. Two fission detectors, one containing 235Uand the other 252Cf,were surrounded by the neutron detector. Neutrons entered through the tapered collimator. A fission pulse started a time analyser which recorded the neutron time distribution in 1024 channels for 1200 psec after the fission. Two time distributions were recorded, one for fission pulses originating in the 235U detector and one for those originating in the 252Cfdetector. The time analyser used an ‘on-line’ computer for data storage and processing. This has been described in detail elsewhere (WHALEN et al., 1964).

n-

I

I

FIG. l.--Schematic diagram of the counter and shield: (1) H,O-filled shield tank; (2) partin wax collimator and shield; (3) neutron detector assembly inside Cd shield; (4) 252Cf ion chamber; (5) *W ion chamber; (6) l”BFs counters.

The neutron detector consisted of twenty-four r0BF3 counters arranged in two concentric rings of twelve each and embedded in a paraffin cylinder 46 cm long and 51 cm in diameter. A tube, 8.6 cm in diameter, passing through the centre of this cylinder contained the fission detectors. All surfaces of the paraffin cylinder were covered with 0.5 mm cadmium sheet. The measured efficiency of this detector for 252Cfneutrons was 9.42 f 0.07 per cent. The fission detectors were multiple plate ion chambers, each having ten plates and occupying a region 4 cm long. The two chambers were separated by a plate thick enough to prevent the passage of fission fragments. In each chamber, the fissionable material was spread uniformly over the plates. The 235U detector contained 187 mg of uranium enriched to 96 per cent; while the 252Cfdetector contained enough californium to give ~600 fissions per minute. In order to minimize the background in the neutron detector due to scattered neutrons, the plates were made of 2.5 p nickel foil and the angle of the collimator was adjusted so that the incident neutrons could not strike the walls of the tube or the foil support rings. The analysed proton beam from a Van de Graaff accelerator was used to produce neutrons by the ‘Li(p, n)‘Be reaction. The thickness of the lithium targets was adjusted so that the energy loss of a proton passing through them corresponded to a neutron energy spread of 0~04+06 MeV except at the two points near O-04 MeV.

160

J. W. MEADOWSand J. F. WHALEN 3. TREATMENT

OF

DATA

The data were accumulated by an ‘on-line’ computer operating as a 1024~channel time analyser (Whalen et al.). Measurements at each energy consisted of a series of runs of about one hour each. For each run two time spectra were obtained, one resulting from about 35,000 252Cffissions and the other from 300@-15,000 235Ufissions. Typical time spectra are shown in Fig. 2. Fission neutrons were counted for the first 170 psec after fission. After 860 psec, the number of fission neutrons remaining in the detector was negligible; so the background was counted for the next 340 ,usec.

FIG. 2.-Typical time distributions of neutrons detected after a fission pulse. The original distributions were recorded in 1024 channels but have been summed in groups of 16 for plotting.

At the end of a run, corrections were made for dead-time losses and background. The principal source of dead-time was in the time analyser which required 16 psec to record an event. The counts per channel, corrected for dead time, were given by

where NF is the number of fissions and J is the dead-time. The correction in the total number of neutrons detected per fission was ~4 per cent, but the resulting correction in the final result was only ~1 per cent since a similar correction was required for both time spectra. After correcting both spectra, the background was subtracted and the computer printed the data for the run. This included the two time distributions which were reduced to 64 channels each, the number of fissions associated with each, the ratio of the number of neutrons detected per 2ssU fission to the number detected per 252Cffission and the statistical error. A minimum of 15 runs were made at each energy. For points near 0.3 MeV, where the neutron yield from the lithium target was a minimum, as many as 40 runs were required. A series of runs was considered acceptable only if the standard deviation calculated from the total counts agreed with that calculated from the scatter of the individual runs. At this point, the experimental data gave the ratio of the number of neutrons detected per 235Ufission to the number detected per 252Cffission. To obtain ?,(z35U)/

Energy dependence of ii, for neutron-induced

fission

161

+J2s2Cf) it was necessary to consider a number of sources of error and to make corrections where necessary. These are discussed below. 3.1 Geometrical asymmetry of the neutron detector The physical centre of the detector did not quite correspond to the centre of efficiency. As a result, the efficiency of the 252Cf section was greater than the 235U section by a factor of I.015 f 0.002. This was determined by measuring the count rate of a small radium-beryllium neutron source at various positions in the central tube then integrating over the volume occupied by the fission detectors.

FIG. 3.-Fraction

of fissions caused by thermal neutrons.

3.2 Fission by neutrolu of lower energy Since the number of neutrons per fission varies with energy, corrections were required for fissions induced by neutrons of lower energy. The principal source of such neutrons were thermal or near-thermal neutrons produced in the neutron detector and shield tank. The relative number of thermal fissions was measured by pulsing the proton beam on for 100 psec then off for 200 psec and counting the number of fissions occurring during the beam pulse and between the pulses. The fraction of thermal fissions is shown as a function of the neutron energy in Fig. 3. The data were corrected assuming the ratio be(23sU)/Fp(2s2Cf)was O-6383 f 04077 at thermal energies. The second principal source of low-energy neutrons came from the ‘Li(p, n)‘Be* reaction in the Van de Graaff target which left the product nucleus in an excited state. Above the threshold for this reaction a second group of neutrons is produced with an energy below that of the main group. Corrections were made using the data of BEVINGTONet al. (1961) for the relative yield, experimental fission cross-section data (STEHNet al., 1965), and values of ?,(235U)/F,(252Cf) from this experiment. 3.3 Angular and energy dependence of the neutron detector eficiency Since the 23sU fission neutron energy spectrum may vary with the energy of the incident neutrons and is different from that of 252Cf, there were errors in +,(23sU)/ 5,(252Cf) caused by a dependence of the neutron detector efficiency on energy. Also, neutrons are generally assumed to be evaporated isotropically in the fragment coordinate system but are peaked in the direction of fragment motion in the laboratory system. Because of this, there may be an anisotropic neutron distribution due to the fragment anisotropy. The neutron detector efficiency was not independent of neutron 4

162

J. W. MEADOWS and J. F. WHALEN

direction. This was due to its cylindrical symmetry and resulted in an error in +,(““W)/+,(Wf). Corrections for these effects were calculated using a Monte Carlo computer programme to follow 15,000 neutron histories through the detector until they either escaped or were captured. It was assumed that the neutron source was a fission fragment moving at angle OF with respect to the detector axis and emitting neutrons isotropically with an energy distribution given by P(E) =

i$lzi

exp (-c/Q.

The parameters Wi and Ti were chosen so that the resulting laboratory corresponded closely to

spectrum

(7) where E,, the average neutron energy in the laboratory, was given by TERRELL (1959) E, = 0.78 + 0.621(9, + 1)1’2.

(8)

The results of this calculation were used to calculate the detector efficiency as a function of E,, and 0,. The energy and angular dependence of the detector efficiency for typical situations are shown in Fig. 4. The reliablility of the calculations was checked by comparing the measured and calculated efficiencies for 252Cffission neutrons. The results are given in Table 1. The largest correction was due to the energy dependence of the neutron detector efficiency. For thermal fission, the correction factor for +,(235U)/G,(252Cf)was 0.975 f 0.002. However, over the energy range covered, the change in the 235U neutron spectrum was small. For isotropicjssion by 1.0 MeV neutrons, the factor increased to only O-977. The corrections for fragment angular distributions were made using the data of SIMMONSand HENKEL (1960). Again the largest correction was for fission by 1-OMeV neutrons but even so the correction factor only increased to O-979. 3.4 Fission counter backgrounds The bias settings of the pulse-height discriminators in the fission counter amplifiers were of necessity a compromise between rejecting a-particle pulses and noise and accepting the maximum number of fissions. The separation of cc and fission pulses in the 2s2Cf detector was quite good and permitted setting the bias level well above the cc-pulses. For this reason, we felt justified in assuming the 252Cfbackground to be negligible. In the 236Ucounter, the separation of c( and fission pulses was not as good due to the high u-rate from the 234U contamination and the thick deposit of U,O, on the plates. Consequently, it was necessary to set the bias at a somewhat lower level to avoid rejecting too many fission pulses. As a result, there was a small background count of about 4 cph which was primarily due to a pile-up. This was checked at frequent intervals and a correction was made by subtracting this number from the number

of 235U fissions counted

in each hour run.

Energy dependence of B, for neutron-induced

163

fission

1.2 --I.0

~-_:~~

(b)

0

IO

20

30

40

50

60

70

60

90

100

RF’ w

FIG. 4(a).-Dependence

of the neutron detector efficiency on energy for an isotropic source. FIG. 4(b).-Dependence of the neutron detector efficiency on OF, the fission fragment angle, for a fission neutron spectrum corresponding to *W thermal fission.

3.5 Undetectedjissions

Since the discriminator bias level had to be set high enough to exclude practically all non-fission pulses, some small-amplitude fission pulses were also excluded. The fission pulse height depended upon a number of factors, many of which had more connexion with the counter construction than with the fission mode. However, since certain fission modes may have been preferentially excluded, we felt that it was necessary to determine the effect of the bias setting on these measurements. Figure 5 shows the dependence of the number of neutrons detected per s5%f fission on the bias setting and the corresponding fraction of fissions detected. It is constant for efficiences between 80 and 98 per cent. At very low settings, corresponding to 98-99 per cent efficiency, the background began to be a problem; so all measurements were made at a setting corresponding to 96 per cent efficiency, For the 235Ucounter, the bias setting which kept the background less than 4 cph corresponded to an efficiency of 93 per cent. TABLE

I.-COMPARISON

NEUTRON

DETECTOR

OF THE MEASURED

EFF’ICIENCIES

FOR

*=Cf

AND

CALCULATED

FISSION

NEUTRONS

Efficiency Calculated (%>

Observed (%)

Inner counter ring

7.3 i 0.2

6.18 f 0.05

Outer counter ring

3.5 * 0.1

3.25 f 0.04

10.3 + 0.2

9.42 zb 0.07

Inner + outer

J. W. MEADOWSand J. F. WHALEN

164

Because of the small energy range covered and the small variation in it, encountered in these measurements, most of these corrections had little effect on the relative values, although they had quite large effects in the absolute values. The final values of F,(235U)/?D(252Cf),including all the above corrections, are listed in Table 2. The ?, values in Table 2 and Fig. 6 are based on i,(252Cf) = 3.782 f 0.020 (Mather et al.).

2.4

-

t1 0

I

III 0.2

I

I

I

I

0.4 NEUTRON

FIG.

I

I

II

II

0.6 ENERGY,

I”‘11

0-e

I.0

Mev

6.-Results of the measurementof G,(E,,)for **W. 4. DISCUSSION

The data plotted in Fig. 6 indicates that 1, for 236U is not a monotonically increasing function of energy below O-6 MeV. There is an initial rapid increase with dS,/dE,, - 0.25 MeV-l. As Blyumkina et al. has previously observed, there is at least one maximum at En ‘V O-4 MeV. For En > O-548 MeV the data is in good agreement with i, = 2.414 + 0.14 E, but within the standard deviations of the few points involved and the narrow range of energy covered, no real significance can be attached to these numbers. However, the low values of dG,/dE, previously reported (MEADOWS and WHALEN (1962); Hopkins and Diven; Mather et al.) may have been due to attempts to fit a first- or second-order polynomial to data in a region where the energy dependence is much more complex.

165

Energy dependence of 3, for neutron-induced fission TABLE 2.-SUMMARY

i;,(“%f)

OF fp MEASUREMENTS. AESOLUTE VALUES ARE BASED ON = 3.782 f 0.020 (MATHER et al., 1964)

Error in i,

Run No. 16 1 10 8 6 2 9 4 13 15 11 5 3 12 7 14

V9 0.039 4 0.046 & 0.150 & 0.225 * 0.265 + 0.298 f 0.325 & 0.358 f 0.375 f 0.405 f 0.425 & 0.476 & 0.548 f 0.675 5 O-785 & 1.000 f

0.050 0.050 0.032 0.030 0.028 0.027 0.027 0.025 0.025 0.025 0.025 0.024 0.021 0.018 0.021 0.020

0.6403 0.6404 06509 06557 0.6531 0.6537 0.6646 0.6440 0.6549 0.6526 @6700 06643 0.6582 0.6646 0.6682 0.6771

2.422 2.423 2.462 2.480 2.470 2.472 2.514 2.436 2.477 2.468 2.534 2.512 2.489 2.514 2.527 2.561

Relative

Total

10.017 kO.016 10.018 10.018 ho.022 *0.022 ho.018 kO.018 10.022 *to.022 50.017 30.019 10.017 *0.017 10.014 +0.016

ho.023 10.027 kO.024 10.024 iO.027 30.027 10.024 *0.024 ho.027 kO.027 ho.023 ho.024 10.023 10.023 10.021 10.023

There is evidence that the energy dependence of i, below O-5 MeV exhibits some additional structure. Measurements at 0.358, 0.375 and 0.405 MeV are substantially lower than would be expected from the positions of their neighbours. If a smooth curve is drawn through the remaining points, one observes that the O-358 MeV point is low by about 4 standard deviations while the other two are low by about 2.5 standard deviations. Although this behaviour may be attributed entirely to statistical fluctuations, the possibility that the low values of these points are due to the existence of a real minimum cannot be excluded. The results of this experiment and two others (Mather et al., Blyumkina et al.) which have points well distributed in the region below 1-OMeV are shown in Fig. 7. Agreement is very good for En < 0.3 MeV. At higher energies the results of this experiment are consistently high, although still within the experimental error. There is no confirmation of the possible minimum at 0.35 MeV. On the other hand, none of the data points in either of these measurements are located so as to definitely exclude it. One of the principal assumptions made in the calculation of d?,/dE, was that EK remains constant. Blyumkina et al. measured the ratio ,!?K(E,J/EK(thermal) over the energy range 0.08 < En < 5.0MeV for neutron-induced fission of 233U and 235U. For E,,= 0*08X)*4MeV they found that XXfor 235Uwas 0+0*7 MeV less than the thermal value but in the interval En = 04-0~7 MeV, EKreturned to the thermal value and then remained constant. They assumed that any variation in EN would result only in a corresponding change in _I!?,*and calculated 1, according to

CI,= 2.43 + 0*13(E, - A&),

(9)

where AZX = l$(E,)- &thermal) and 2.43 is it, for thermal fission. These values are shown in Fig. 7. While the qualitative agreement with the experimental values is very good, the observed values of 1, are consistently less than the calculated values. However, if the calculated values are based on F,(thermal) = 2.412 (Mather et al.) the agreement with the results of this experiment is greatly improved.

J. W. MEAWWS and J. F. WHALEN

166

Blyumkina et al. interpret their results in terms of the BOHR (1956) model but make two additional assumptions: (1) the nucleus at the saddle point does not have axial symmetry and (2) the nuclear rotational energy and the energy associated with the splitting of the saddle point ground state by inversion doubling does not go into excitation of the fragments but passes into the fragment kinetic energy. According to the Bohr postulate, a nucleus with an excitation energy only slightly greater than the fission barrier will pass over the saddle point in a state that is ‘cold’ as far as internal excitation is concerned. For even-even nuclei, the lower fission channels will have quantum numbers characterized by the spin and parity of the

,/o’

i.6 0 TiP

-

0 0

2.5

0

-0

-/

n/ ??

?? ~4x3 Oo# / A/

9

o/

aAop’-/8 /

00

$

0,

/

’

0

0

5 0

A A

’

0

NEUTRON

ENERGY,

MBV

FIG. 7.--f, for assU: 0 refers to this investigation; 0 to MATHERet al. (1964) while A and 0 refer to measured and calculated values by BLYUMKINA et al. (1964). The points in the upper left indicate typical errors associated with each set of data. The dashed line has a slope of 0.14 MeV-l and is drawn only for comparison. rotational band associated with the saddle point ground state. Bohr further assumes that the saddle point deformation is pear-shaped. Since it does not have reflection symmetry at a centre, the ground state band now becomes an inversion doublet; the separation of which is determined by the tunnelling frequency through the barrier between the mirror shapes. If axial symmetry is maintained, the lower band will have spin and parity J” = Of, 2+, 4+ . . . while the upper band will have J” = l-, 3-, 5- . . . . However, if there is a sufficiently large departure from axial symmetry (DAVYDOV and FILIPPOV, 1958) the lower band will contain J” = 0+, 2+, 3+, 4f . . . while the upper band will contain J” = l-, 2-, 3-, 4-. . . . These two bands are identified with the two lowest fission thresholds found in the (d,pf) reaction on 233U, 235U and 23gPu (NORTHROP et al., 1959). For the 236U target nucleus, the positive parity band is at E,, cv -0.6 MeV while the negative parity band is at En N $0.2 MeV. Since the spin and parity of the 235U ground state is 7/2-, fission at low energies by s-wave neutrons can proceed only through the upper channel. However optical model transmission coefficients for neutrons incident on nuclei with mass ~235 (MOLDAUER, 1961; AUERBACH and PEREY, 1962) indicate that, for E,, = 0.1 MeV,p-wave neutrons account for ~75 per cent of the compound nucleus formation. Furthermore, incident

Energy dependenceof i, for neutron-inducedfission

167

neutrons of odd 1 continue to account for ~75 per cent of the compound nucleus formation to at least E,, = 3-OMeV. If such is the case, then according to assumption (2) the change in ,?$ in going from thermal energies to E, ‘u 0.1 MeV should be N -0.6 MeV, in good agreement with experiment. With increasing neutron energy additional fission channels become available and the exact values of ,??Xand cp are the result of an average over a number of channels. The rapid variation associated with a few widely spaced channels no longer occurs. Blyumkina et al. attribute the sudden increase of _/$ and the corresponding decrease of ti,, in the interval E, N 0+0*7 MeV to the opening of additional fission channels associated with nucleon excitation and suggest that the constant value of KKat higher energies is the result of averaging over many of these channels. However, GRIFFIN (1963) suggests that the gap found in even-even nuclei between the ground state and the first state involving nucleon excitation increases with deformation. For saddle point deformations he estimates the gap to be -2.6 MeV. Measurements of fission fragment angular distributions from the (d,pf) reaction on 23gPuand 233U(BRITTet al., 1963) confirm this value. For the 23jU target nucleus this would place the lowest fission channel associated with nucleon excitation at E,, N 2-O MeV. Therefore, any new fission channels appearing at En N 04-0.7 MeV are probably due to collective excitations. The exact number will depend on their width and the way the energy is partitioned but no great number should be required. For example, if one assumes that the probability of fission through any energetically available channel is determined only by its spin and parity and that all the energy of the collective excitation passes into EK,,then the presence of only two additional vibration-rotation bands of positive parity are needed to account for the experimental data. Other assumptions made in the calculation of di,/dE, were (i) a constant massyield distribution, (ii) a constant value of &, and (iii) the ‘pre-scission’ neutrons have the same dependence on incident neutron energy as those evaporated from the fragments. It is known that assumption (i) is not strictly true, but the mass-yield distribution varies so little over the energy range considered here that quantities which are obtained by averaging over it are not significantly changed. Even at En = 6.0 MeV the peak-to-valley ratio is still 23-4 (MEADOWSand WHALEN,1965). Therefore, if assumptions (ii) and (iii) remain valid, di,/dE, should return to ~0.14 MeV-l for En > O-6 MeV. The dashed line in Fig. 7 is drawn with this slope. For En > 0.6 MeV it represents the general trend of the data in Fig. 7 very well. However, it has been shown experimentally that & is constant for En N 0.6-5.0 MeV. Figure 8 shows the data in this energy range from this experiment (Blyumkina et al., Mather et al., COLVINand SOWERBY (1965) ; Hopkins and Diven ; MEADOWS and WHALEN,1962). The latter three sets of data were adjusted to agree with i,(252Cf) = 3.782. A least-squares fit gave 1, = (2.394 & 0.007) + (0.134 & 0.004) En.

(10)

A second-order polynomial was also fitted to the data, but gave no significant improvement. The present data, therefore, are consistent with a linear dependence of i, with incident neutron energy in this region, and the slope is in good agreement with the assumption that all the kinetic energy of the incident neutron reappears in the fragment excitation energy. Equation (10) does not agree with the results of Mather et al. for E,, > 5-OMeV nor with the results of Hopkins and Diven at 14.5 MeV although it does agree with

168

J. W. MEADOWSand J. F. WHALEN

FIG. 8.-Dependence of i, on the incident neutron energy for 0.6 < E, < 5.0: 0 refers to this experiment; 0 to BLYUMKINAet al. (1964); A to MATHERet al. (1964), 0 to COLVINand SOWERBY(1965); 0 to HOPKINS and D~VEN(1963) and A to MEADOWS and WHALEN(1962). The latter three sets of data have been adjusted to agree with I,(asaCf) = 3.782. The error bars represent typical absolute errors associated with each set of data. The line is given by equation (10).

the results of MOAT et al. (1961) at 14.2 MeV. However, it is in this energy region that the assumptions made in calculating dij,/dE,, may no longer apply. The (n,n’f) reaction begins to be significant at ~6.0 MeV. At 14 MeV the increased amount of symmetric fission has made the mass-yield distribution significantly different from the distribution at thermal energies (KATCOFF, 1960). Furthermore, OKOLOVICHand SMIRENKIN(1964) have found ,?$ at 15 MeV to be 1.74 f 0.40 MeV less than the thermal value. REFERENCES AUERBACH E. H. and PEREY F. G. J. (1962)BrookhavenNational Laboratory Report BNL-765. BEVINGTON P. R., ROLLAND W. W. and LEWLT H. W. (1961)Whys.Reo. 121,871. BLYUMKINAYu. A., BONDARENKOI. I., KUZNETSOVV. F., NESTEROVV. G., OKOLOVICHV. N., SMIRENKING. N. and USACHEVL. N. (1964) Nucl. Whys. 52,648. BOHR A. (1956) Proceedings of the First International Conference on the Peaceful Uses of Atomic Energy, Geneva, P/911, Vol. 2, p. 151. United Nations, New York. BOWMANH. R., THOMSONS. B., MILTONJ. C. D. and SWIATECKIW. J. (1962) Phys. Reo. 126,212O. Bm H. C., STOKES R. H., GIBBSW. R. and GRIFFIN J. J. (1963) Phys. Rev. Lett. 11,343. CAMERONA. G. W. (1957) Chalk River Project Report CRP-690. COLMND. W. and SOWERBYM. G. (1965) Physicsand Chemistry of Fission, Vol. II, p. 25, International Atomic Energy Agency, Vienna. DAVYDOVA. S. and F~IPPOV G. F. (1958) J. exp. theor. Phys. 35,440; English transl. Sooiet Phys. JETP 35, 303. GRIFFIN J. J. (1963) Phys. Reu. 132,2204. HOPKINSJ. C. and DIVEN B. C. (1963) Nucl. Phys. 48,433. KAPOOR S. S., RAMANNA R. and RAMA RAO P. N. (1963) Phys. Rev. 131,283. KATCOFFS. (1960) Nuckonics 18, (11) 201. LEACHMANR. B. (1958) Proceedings of the Second International Coqference on the Peaceful Uses of Atomic Energy, Geneva, P/2467, Vol. 15, p. 229. United Nations, New York. MATHERD. S., FIELDHOUSEP. and MOAT A. (1964) Phys. Rev. 133, B1403. MEADOWSJ. W. and WHALENJ. F. (1962) Phys. Rev. 126,197; (1965) Argonne National Laboratory Report ANL-7110, p. 21. MILTONJ. C. D. (1962) University of California Radiation Laboratory Report UCRL-9883. MILTONJ. C. D. and FRASERJ. S. (1962) Can. J. Phys. 40, 1626.

Energy dependence of ii, for neutron-induced

fission

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