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Low-energy γ-rays and spins of 235U neutron resonances
~
Nuclear Physics A203 (1973) 145-- 163; (~) North-Holland Publishiny Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
L O W - E N E R G Y 7-RAYS AND SPINS OF 23SU N E U T R O N RESONANCES F. C O R V I *, M. S T E F A N O N *, C. C O C E V A * a n d P. G I A C O B B E t
CBNM Euratom, Geel, Belgium, CNEN Centro di Calcolo, Bologna, Italy Received 29 September 1972 Abstract: Low-energy p r o m p t ~-ray spectra in the range 95-670 keV have been m e a s u r e d for forty-one 235U n e u t r o n resonances selected by time-of-flight in the n e u t r o n energy range 1.5-58 eV. D i s c r i m i n a t i o n against the natural 0-activity o f 235 U has been o b t a i n e d by m e a n s o f a coincidence technique. T h e spectra s h o w a very complicated structure owing to a few capture a n d m a n y fission ~-rays. T h e ratios o f the intensities o f the 160.3 keV a n d 642.4 keV capture 7-rays have been used for spin a s s i g n m e n t s o f fourteen resonances with small fission widths. Some conclusions are d r a w n a b o u t the spin dependence o f average fission widths, a n i s o t r o p y o f fission f r a g m e n t s a n d s y m m e t r i c fission yields. EI
NUCLEAR
t
REACTIONS
235U(n,~), ( n , f ) , E =
1.5-58 eV; m e a s u r e d E.I, 17.
236U deduced resonances, J. Enriched target. 1. Introduction
An extensive knowledge of the spin of 235 U neutron resonances would be an important step towards a better understanding of slow-neutron induced fission. In fact it would lead immediately to the spin dependence of all those quantities which have already been measured in 235U single resonances such as fission widths, angular distributions of fission fragments from aligned z35U nuclei 1, 2) and symmetric fission yields 3). It would be quite interesting to compare experimental results with the channel theory of fission 4, 5) even if effects due to the double-humped deformation potential 6) could strongly affect the results. Finally, from the point of view of applied physics, a knowledge of the spins is necessary for a satisfactory multi-level analysis of low-energy neutron cross sections. Many efforts have been made, with different methods, to assign a significant number of spins, but in spite of this there are only few and often discordant results. One method, which is the most direct, consists of measuring the transmission of polarized neutrons through a polarized target 7); however, up to now, it could only be applied to the three lowest resonances. A larger number of spin assignments was obtained by Poortmans 8) from measurements of scattering and transmission cross sections; the extensive application of such a method to 23SU is hampered by the smallness of the spin effect, due to the high target spin (I = -~), by the high level density, and by the very weak scattering yield of many resonances. Comitato Nazionale Energia Nucleare, Ispra, Italy. 145
146
F. CORVI et
aL
Measurements of the multiplicity of v-rays 9) and of the relative intensity of the 642 keV capture transition 1o) were also attempted. More recently, primary capture transitions leading to low-lying J = 2 states in the 236U compound nucleus were observed in order to identify a certain number of J = 3 resonances 11, 12): this method is obviously limited by the fact that when these y-rays are not detected it is impossible to decide whether this is due to the resonance spin being 4 or to the intensity of the dipole transition falling below the threshold of observation. The results of all these measurements are in many cases conflicting, so that the use of an independent method is highly desirable. This paper reports an attempt to apply to 235U the recently developed low-level population method of spin assignment, which has already proved very successful for non-fissile nuclei 13-15). In short, this method consists of measuring the low-energy v-ray spectra from capture in individual resonances and determining the relative intensities of at least two prominent v-rays. If these transitions de-excite two states of different spins, it can be shown that the ratio of their intensities depends significantly on the spin of the initial compound state. This method combines the following advantages: (i) it has been successfully applied to a variety of non-fissile target nuclei with different spins and parities, and no exception to its validity has yet been found; (ii) its results are qualitatively well understood in terms of a generally accepted statistical behaviour of the electromagnetic decay, and are also quantitatively confirmed by numerical simulations of the v-ray cascade 16, 17); (iii) the spin effect is large: in favourable cases the intensity ratios may differ by a factor two for the two initial spins; (iv) no normalization of the intensities to the capture yield of each resonance is necessary. 2. Description of the experiment
The application of the low-lying level population method to a fissile nucleus such as 235U has to cope with two major difficulties: (i) the presence of prompt and delayed fission v-rays, and (ii) natural v-activity following the s-decay o f 235U. The first effect highly complicates the structure of low-energy v-ray spectra emitted from 235 U resonances, while the natural activity is strong enough compared with the presently available sources of resonance neutrons to wipe out any other effect below about 250 keV. The success of the method depends then on the availability of at least two lowenergy capture v-rays, de-exciting two states of different spins, which are sufficiently resolved and intense to be measurable in many resonances. One of these v-rays, namely the 642 keV transition de-exciting a 2- level at 687 keV, has already been exploited by Weigmann et al. lo). More recently, in an accurate measurement of the 7-ray spectrum in the 4.84 eV resonance, Kane 11) found several capture v-rays above 400
23sU NEUTRON RESONANCES
147
keV; however, their intensities are too small to be measurable in many resonances. The only possibility left then is to look at a lower energy: a possible candidate is the 160 keV transition between the 6 + and 4 + members of the ground state rotational band. F r o m population systematics of other heavy nuclei with similar capture states and from the value of the theoretical internal conversion coefficient for E2 radiation, one should expect an intensity of 0.02-0.03 7-rays per captured neutron for this transition. The comparison between the intensities of the 160 and 642 keV lines would be very suitable for the spin assignment of neutron resonances since the population of a
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MONIT. UNIT
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Fig. 1. Experimentalset-up and block diagram of the electronics. 6 + relative to that of a 2 - level is expected to change by at least a factor of two as a function of the initial spin 13,23) ( j ~ = 3- or 4 - ) . However, in order to go down to the 100 keV region, it is mandatory to discriminate against the natural 7-activity: this can be accomplished by means of a coincidence technique. The experiment was performed at the Geel linac using the time-of-flight technique. The characteristics of the linac and the general lay-out of the neutron capture 7-ray facility have already been described in ref. 18); fig. 1 shows the detection system and the electronics used for this measurement. A metallic z35U disk (12 cm diameter, 0.1 g/cm 2 thick, 93 % enriched) is exposed to the neutron flux at a 13 m flight distance and is viewed by a 40 cm 3 coaxial Ge(Li) detector and a large 18 x 15 cm NaI(TI)
148
F. CORVI
et aL
crystal, both placed at right angles with respect to the beam. The NaI(Tl) crystal is shielded from fission and scattering neutrons, and from soft ?-radiation coming from the sample by about 3.5 cm of borated palyethylene, 2 g/cm 2 of 10B and 1 cm of lead. Pulses from the Ge(Li) detector are accepted only if in coincidence with pulses from the NaI(TI) detector corresponding to an energy higher than 0.7 MeV. In this way the low-energy natural ?-activity should be removed, except for random coincidences. Timing of Ge(Li) pulses is performed with an extrapolated-leading-edge timing discriminator, allowing a coincidence resolving time of 25 ns with 95 O//ocoincidence efficiency. This is done at the expense of the low-energy counting rate, since small pulses with longer rise times are unable to trigger the timing discriminator. The output of the coincidence unit is sent to a 4096-channel time coder with 0.125 Fls channel width. Pulses from the Ge(Li) detector are amplified and fed to a 4096-channel ADC: their amplitude analysis is enabled by the stop signal from the time coder. Drifts in zero and gain are compensated for by a digital stabilizer with windows set on two highly stable reference pulses placed at the lower and upper energy ends of the spectrum, respectively. The amplitude and time-of-flight addresses corresponding to each event are then stored in a 400-word buffer memory. Every time the memory is full, its content is recorded on magnetic tape in IBM compatible format. Each standard tape contains approximately 2.6 x 106 events; in the present measurements 13 tapes were recorded for a total measuring time of 250 h. The data sorting, consisting basically of building amplitude spectra corresponding to given time-of-flight intervals, was performed off-line by computer. The integral amplitude and time-of-flight spectra were continuously monitored throughout the whole measurement by a 4096channel analyser and display, connected in parallel with the bidimensional system. The time-of-flight spectrum of the coincidences is shown in fig. 2 for the neutron energy range 2-58 eV; the resonance energies in eV are indicated above the 41 intervals for which amplitude spectra were sorted out; in particular the time intervals corresponding to the 14 resonances to which spin was assigned and to two background regions are represented by shaded areas. Strong overlapping of two or more levels is present in many energy regions; however, only one resonance is associated with a given interval when its capture yield is at least a factor five larger than the cumulative yields of other superimposed resonances. This is the case for the levels at 41.90, 30.85, 24.32 and 23.40 eV. Two typical ?-ray spectra covering the energy range between 95 and 670 keV are shown in fig. 3. The spectrum in the upper half corresponds to a resonance with predominant capture. The peaks at 104, 160, 423 and 642 keV are due to capture 7-rays while the one at 185 keV is the main peak of the natural 235U activity, still important because of random coincidences. The relevant 236U level scheme is represented above. The remaining structure is mainly due to fission ?-rays, as appears from a comparison with the spectrum in the lower half, referring to a resonance with predominant fission. The decrease in counting rate below about 200 keV is due to the effect of the leading-edge timing discriminator, as explained above. The 160 keV transition has a fair intensity; however, it is only partially resolved from at least one
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Fig. 2. Time-of-flight spectrumof coincident7-rays following neutron interaction with 2asU. The resonance energies in eV are listed above the 41 intervals for w hi c h a m p l i t u d e s pe c t ra were sor ted out. The time intervals c o r r e s p o n d i n g to the 14 resonances to w hi c h spin was a s s i gne d a n d to two b a c k g r o u n d regions are represented by s h a d e d areas.
F. CORVI
150
e t al.
2
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Ff
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Fig. 3. Two examples ofT-ray spectra in the range 95-670 keV, belonging to the resonances at 6.39 eV and 8.79 eV, respectively. The peaks at 104, 160, 423 and 642 keV are capture ~'-rays while the one at 185 keV is the main peak of the natural 235U activity. The relevant 236U level scheme shown above is taken from ref. ~1). fission a n d o n e a c t i v i t y p e a k , as will be seen b e t t e r in the sect. 3. T h e effective e n e r g y r e s o l u t i o n o f the m e a s u r e m e n t was 2.1 k e V at 185 k e V a n d 2.7 k e V at 642 keV. 3. D a t a a n a l y s i s and results
3.1. SHAPE ANALYSIS T h e energies a n d intensities o f t h e 7-rays are o b t a i n e d f r o m the e x p e r i m e n t a l spectra by m e a n s o f a g e n e r a l i z e d l e a s t - s q u a r e fitting m e t h o d , p r o g r a m m e d for a n I B M
z3sU N E U T R O N
RESONANCES
151
360-75. The shape of the spectra is assumed to be given by the superposition of peaks and a smooth background. The shape of a peak corresponding to a transition of energy Eo is assumed to be a Gaussian matched to an exponential tail below E 0 - 5 . The background is described by a polynomial. The two parameters defining the shape of the peak, i.e. the standard deviation a of the Gaussian and the distance 6 at which the exponential sets in, are obtained preliminarily, for a given energy region, by fitting the larger and best resolved peaks; the dominant activity peak at 185 keV and the 642 keV capture line were used for this purpose at low and high energy respectively. The transition energies and their intensities are obtained by fitting with fixed ~ and 5 I KCI~ 9B~
Z31Th
!
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En = 8.79 eV
I
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L ,/ , 3 ,~ '!
I ~3~Th ,
A .':~
•
1000 0
50
100
150
200
250
CHANNELS
Fig. 4. Fit o f the s p e c t r u m o f the 8.79 eV resonance in the range 95-238 keV. Experimental data are represented by dots a n d the fit by a c o n t i n u o u s curve while the fitted b a c k g r o u n d is described by a d a s h e d line. Vertical bars indicate the position o f all peaks considered in the fit. T h e energy in keV is given above each well-defined peak. T h e region delimited by the d o t - a n d - d a s h rectangle is s h o w n in m o r e detail in fig. 5c.
many peaks in wide energy regions. The program can fit simultaneously up to 35 peaks. In the fitting procedure a priori information about the peak parameters or about relationships among them can be introduced in the form of non-rigid constraints; for instance, if we know from other measurements that the position of a peak is E = Eo 4 - A E , it is possible to introduce both E o and A E in the computation. In this case a Gaussian distribution centered around E 0 with variance A E 2 is assumed as the a priori probability of the peak energy E. In the present work the use of a priori information becomes important because many similar 7-ray spectra are to be fitted in the same energy range. The information one gets from the analysis of some spectra can then be fed into the fits of other ones. Another feature of the program is the automatic blocking of those parameters for which there is insufficient information to reach convergence. The fitting procedure was carried out in the channel intervals
152
F. CORVI et al.
1-250 and 970-1005 (see fig. 3). In fact, since the low-energy part shows a very complicated structure, it was necessary to extend the fit over a considerable energy range in order to get a reliable value o f the b a c k g r o u n d under the 160 keV line; in the case o f the 642 keV transition, which is well isolated and sits on a rather constant continuum, a smaller energy interval was sufficient. A n example o f a fit o f the low-energy part o f the spectrum in the 8.79 eV resonance is shown in fig. 4. The energy value in keV is indicated only over the most prominent and well-defined peaks. The energy calibration was performed using sources o f 7Be, 51Cr, 57C0, 58C0, 139Ce and Z°VBi: a)
16o3
]
[ c)
~-~-En = 11"67eV
J
l
,~ 160.3
1000
500-
250-
J I ~ 163.36
~
~
50
o
8
158.8 En= 8.79eV
b)
- -
En=19"3eV
En=25.~/25.55eV,
°
0~
0-
o
Fig. 5. Fitted spectra of 4- resonances with increasing values of the fission width in the energy region between 154 and 169 keV. The fitted background was subtracted. The height of the bar below each peak is proportional to its intensity. The Fr values are taken from ref. 21). the error is estimated to be less than 0.2 keV. The calibration was checked by comparing the energies deduced for the 23 5U activity lines (indicated as 231Th in fig. 4) with the very precise values o f reE 19). Also, the energies o f the capture 7-rays agree well with the 23 6 U level scheme recently proposed by Fogelberg et al. 2 o). It should be pointed out that the fit does not intend to represent in detail all the lines: the peaks considered are just those necessary to reproduce the main features o f the spectrum, whose actual structure is certainly much more complicated. To clarify the structure o f the h u m p in which the 6 + - 4 + transition is to be found, the region around 160 keV is represented (background subtracted) on an expanded energy scale in fig. 5, for
2ssU NEUTRON RESONANCES
153
four resonances with very different fission widths F r. The height of the bar below each peak is proportional to its intensity. The peak at higher energy is the known 23~Th transition at 163.36+__0.01 keV, as given in ref. ~9). The nature of the other peaks is deduced by looking at the variation of their relative intensities with Ff. In fig. 5a, referring to a resonance with predominant capture, the peak at 160.3 keV stands out very clearly above the others. Moreover, as can be seen in figs. 5b-d, the ratio of the 158.8 to the 160.3 keV peak increases with Ff : therefore the 160.3 keV line is really the capture y-ray which we are looking for, while the other one is a fission line. Besides, at least two smaller peaks at about 155 and 165 keV are present. A shape fit to this complicated structure was obtained by making use of the constraints in the following way: the position of the 160.3 keV line with respect to the well-defined 185.72 keV peak was deduced with good precision in resonances with dominant capture. Similarly, the relative position of the 158.8 keV peak was obtained f r o m resonances with large Ff, and that of the activity line from a background spectrum. The relative positions of such lines and their uncertainties, as obtained from these determinations, were introduced as a priori information in the analysis of the other spectra. In this way it was possible to resolve the multiplet and obtain a reliable set of values: initial attempts to fit without constraints failed, giving rise to a set of widely varying peak positions, since the spectra did not usually contain enough information (due also to the poor statistics) to define correctly and unambiguously all parameters. In order to make sure that the results are completely reliable, it is necessary to evaluate the extent to which the capture line may be contaminated by fission y-rays. At first glance, the line seems reasonably pure since no important fission contribution shows up at 160.3 keV, even for resonances with extremely large Ff (see fig. 5d). However, a correlation analysis performed on a sample of 41 resonances showed that the ratios of the intensities of the two capture lines r -- I~ (160.3)/I(642.4) which should depend only on the spin, are positively correlated with the fission widths, the correlation coefficient being p = 0.6, which falls below the 0.1 percentile in the case of the uncorrelated distribution. This effect could be due to: (i) the presence of one or more fission y-rays other than the 158.8 keV one, superposed on the peak at 160.3 keV; (ii) systematic errors introduced when fitting close doublets, so that some strength of the 158.8 keV peak contributes to the capture line. In fact, when the distance between two peaks is only a~ of the F W H M , as is the case, a slight mismatch in the line shape or errors in the peak positions can give rise to systematic errors in the intensities. A more quantitative estimate of the magnitude of the effect was deduced by considering the relative intensities of the 160.3 keV line obtained from the fits in the resonances at 52.30, 25.20-25.55 and 14.0 eV, all with Ff > 300 meV: it was found that an upper limit for a possible fission contribution to the 160.3 keV line is 20 o/ O / o f the intensity of the 158.8 keV peak. This means that, if an error of less than 20 ~o is required for the intensity of the capture line, this line should not be smaller than the 158.8 keV one. This is very roughly equivalent to limiting the analysis to those
F. C O R V I et al.
154
resonances with Ff ~ 60 meV for J = 4 (see fig. 5b) and F r < 30 meV for J = 3 levels. To make sure that the ratios r between the intensities o f the two capture lines are not significantly affected by this spurious fission contribution, one should take into account only those resonances with Ff < 30 meV. According to the F'f values o f ref. 2~) only 11 o f the measured resonances satisfy this condition. The correspond0.8-
shape 0.6-
0,/4"
........
+--t- ........
o
stripping
"
___+_+
+-It
....
. . . . . . . .
+l!: I!t
I_ 0.2-
o
- ...........
+
j-a___
-+-........................... 16
2'0
ab
~'o
50
E n (eV)
Fig. 6. Ratios r = I~(160.3)/I~(642.4) obtained with shape analysis and spectrum stripping plotted against neutron energy for 14 resonances. Full circles refer to resonances with /'f < 30 meV, while the three open circles correspond to resonances with slightly higher fission widths. Dotted lines indicate the weighted averages for each spin group. The upper figure refers to the shape analysis o f subsect. 3.1, the lower one to the spectrum stripping method o f subsect. 3.2.
ing ratios r are indicated in the upper half o f fig. 6 by full circles. It is evident that the ratios fall into two widely separated groups. Since r is a measure o f the population o f a 6 + relative to a 2 - level, the higher values are obviously associated with J = 4 resonances. The average values o f r for each spin g r o u p are, ?(4) = 0.507 and ?(3) = 0.230, and are indicated by dotted lines. The magnitude o f the spin effect, given by the ratio ?(4)/?(3) = 2.2 is in agreement with expectation ~3).
zssu NEUTRON
RESONANCES
155
The spin was assigned to three more resonances with slightly higher fission widths: those at 15.45 eV (Ff = 48 meV) and 22.95 eV (Ff = 42 meV) were added because their capture line at 160.3 keV is more than one and a half times as intense as the nearby fission line; moreover, the resonance at 24.25 eV was also added because, in spite of having Ff = 52 meV, it still falls clearly in the lower group. The ratios r for these three levels are represented by open circles in fig. 6. The positive difference with re-
200
642.4 163.36 160.3 En = 2.04 eV
100-
160.3 158
J=4
250
163,36 /L_/
oj
En = 4 . 8 4 eV
8
En = 11.67 eV
500
"~o //
200-
642.4
En = 12.39 eV
J-3
j ~
400200-
100
0
0-
/
En=6.39eV
En = 14.53 eV
,500-
J=3
o
I
o [
400 o
200°o
0
/
0
o o
o
o o
/t
Fig. 7a. F i t t e d spectra for the 154-169 keV energy region p l o t t e d t oge t he r w i t h the 642.4 keV p e a k for 6 resonances to w h i c h spin was assigned. The vertical scale refers to the low-energy p a r t o f the spectra, while the 642.4 p e a k is r e d u c e d by a factor o f two for better c o m p a r i s o n . The bars be l ow the two capture 7-rays of interest are t h i c k e r t ha n the ot he r ones.
spect to the corresponding averages is consistent with the expected fission contribution to the 160.3 keV peak. The r-values and the spin assignments for the whole set of 14 resonances (9 with J = 4 and 5 with J = 3) are given in table 1. It should be noted that they do not represent the ratios of the true intensities because no correction was introduced for the energy dependence of the photopeak efficiency of the detector. The spin depen-
156
F. C O R V I et al.
dence of the relative intensities of the two capture lines can easily be seen in figs. 7a and b where the fitted spectra are plotted in the energy range 154-169 keV beside the peak at 642.4 keV for the 14 resonances to which the spin was assigned. I
160.3
158.8
En = 15.45 eV
642.4 En= 23,40eV l
158~
154.8~1%4/ /$O~l~°o '°°1 ~
100-
160.3
i
167.36
J=4
2ooj
642.4
I
I I
En = 16.10 eV
200-
I
En - 24.32 eV
J=4
~°I,~~~~o-°° J=3'~o
100-
0] 0%
_~ ol 8 o
o /
L
En z 21.10 eV
J=4
En = 30.85 W
J=4 0
200"
o
o
o
Oo
En = 22.95 eV
E n - 4 1 . 9 0 eV
J=4
J=3
o
O
o
o
o
/
(
o
0-
Fig. 7b. Fitted spectra as in fig. 7a for 8 more resonances to which spin was assigned. 3.2. S P E C T R U M S T R [ P P I N G
To check the results, a different analysis procedure was devised: the intensity of the capture line was obtained by subtracting from the unresolved doublet formed by the 158.8 and the 160.3 keV peaks a fission 7-ray contribution calculated from the inten-
235U NEUTRON RESONANCES
157
sities of higher-energy fission 7-rays. I n this way the p r o b l e m of fitting a close doublet was avoided, but other statistical a n d systematic errors were introduced. As reference lines three peaks were chosen at 199.1,204.0 a n d 212.6 keV respectively (see fig. 4). The n o r m a l i z a t i o n factor, i.e. the ratio between the sum of these three intensities a n d the fission c o n t r i b u t i o n to the 160 keV h u m p , was again determined f r o m the three resonances with Yf > 300 meV. This procedure is correct if one assumes the shape of the p r o m p t fission 7-ray spectrum to be i n d e p e n d e n t of the particular resonance, as is reasonable a n d consistent with the present experimental evidence. TABLE 1 Ratios r between the intensities of the 160.3 and 642.4 keV capture ~-rays E, (eV)
2.04 4.84 6.39 11.67 12.39 14.53 15.45" 16.10 21.10 22.95* 23.40 24.25* 30.85 41.90
r
J
shape
stripping
present
0.27,0.05 0.49 =c0.04 0.55,0.03 0.49,0.04 0.21 ±0.03 0.22-*-0.08 0.61 ::t-0.10 0.47 =c0.05 0.49,0.06 0.59,0.11 0.48,0.07 0.30,0.09 0.51 iO. 10 0.25,0.05
0.24±0.07 0.52-t-0.04 0.51,0.04 0.51,0.04 0.25=~0.05 0.284-0.11 0.46i0.12 0.48,0.07 0.52 i0.07 0.51 I0.12 0.50 JzO.07 0.33,0.12 0.55 +0.13 0.31 --0.07
3 4 4 4 3 3 4 4 4 4 4 3 4 3
previous 3 a.b) (4) a) 3 a.b) 4 ~) 3 b.c) 3 t.)
(4) c) (3) c)
Columns 2 and 3 give the ratios r obtained with the shape and with the stripping method respectively for 14 neutron resonances of energy En. The deduced spin assignments and the results of previous works are listed in columns 4 and 5. Resonances with/'f > 30 meV are marked with. an asterisk. a) Spin assignments of Kane 1l). b) Spin assignments of Graves et al. 12). ~) Spin assignments of Poortmans et al. 8). The results are given in c o l u m n 3 of table 1 a n d plotted in the lower half of fig. 6: there is complete qualitative agreement with the previous ones, each resonance b e l o n g i n g to the same spin group. The error bars, which also include a 10 % uncertainty in the n o r m a l i z a t i o n factor, are o n the whole larger t h a n those of the shape analysis, as is u n d e r s t a n d a b l e because the m e t h o d does n o t fully exploit the informat i o n on shape a n d peak positions. The weighted averages are ? ( J = 4) = 0.511 a n d ~ ( J = 3) = 0.264; their ratio is 1.94. 3.3. COMPARISON WITH PREVIOUS RESULTS The deduced spin determinations are listed in c o l u m n 4 of table 1, together with the results o b t a i n e d in recent works, namely the p r i m a r y 7-ray measurements of K a n e 11)
158
F. CORVI et aL
and Graves et al. 12) and the scattering data of Poortmans et al. s). There is a general agreement, except for the 6.39 eV level to which Kane and Graves et al. assigned spin 3. Since among the assigned resonances this is perhaps the one with the largest capture yield, it is interesting to look for possible reasons for such a disagreement. The spin assignment 3- was supported by two arguments. First, Kane saw a weak y-ray leading to the 2 - state at 687 keV. Under the assumption that only dipole radiation is visible, he concluded that the capture state should be 3-; however, the probability that the transition is E2 instead of M1 cannot be ruled out, since E2 primary radiation has often been seen in resonance neutron capture, particularly in heavy nuclei, as was also recently shown by Wasson et al. 22) in the case of 23SU. The other piece of evidence in favour of J = 3 was the observation of a high-energy transition leading to a doublet of states identified by Kane as the 2 + members of the fl- and 7vibrational bands; however the identification of these bands is not exempt from ambiguities and contradictions with more recent data 20), so that it seems that a straightforward interpretation of the high-energy data will be possible only when a more complete and reliable 236U level scheme is available. The agreement of our results with those of Poortmans, although limited to the only four common resonances, is important because the two methods can be used in a complementary way for the spin assignment of resonances of fissile nuclei. Finally it should be noted that the present data, as well as those of Graves et al. 12) and Poortmans et al. 8), disagree with the results of Asghar et al. 9) and of Weigmann e t al. lo). This can perhaps be explained if one remembers that in the y-ray multiplicity measurement performed by Asghar no attempt is made to distinguish between capture and fission 7-rays; Weigmann's results, on the other hand, rely on the intensity measurement of the 642 keV 7-ray in individual resonances, which is a very difficult task in the case of fissile nuclei, since it implies the normalization of peak counting rates to the capture yield of the corresponding resonances. 3.4. CONSIDERATIONS ON THE METHOD First o f all it should be pointed out that the measurement of the 6+-4 + transition was the essential step that allowed the application of the low-lying population method. In spite of the fact that we were dealing with a coincidence measurement, the counting rate in this line was sufficient, thanks to the large spin effect, to assign also weak resonances, as shown in fig. 2. The main drawback of the method is that the results are limited' to resonances with small fission widths, because of the overlapping of capture and fission y-rays: in this respect it should be remarked that the coincidence method, while necessary for removing the sample activity, worsens the capture-to-fission ratio because the 7-rays associated with a fission event have a multiplicity higher than that of capture 7-rays. A possible way of improving such a situation would consist of using a 4n fast-neutron detector operated in anti-coincidence with the Ge(Li) diode, so as to discard most of the fission events.
235U NEUTRON RESONANCES
159
4. Spin dependence of fission properties The number of spin assignments obtained in this work is such that it is now possible to obtain information on the spin dependence of some fission properties of the lowenergy neutron resonances of 235U. To this end it is convenient to increase our sample of 14 spin-assigned, resonances by including all other reliable spin determinations. The following resonances were considered: (i) those at 0.29 eV with J = 3 and at 1.135 eV with J = 4, assigned by Schermer et al. 7) with a polarized-beam-polarized-target experiment: their assignment of a third resonance at 2.04 eV is in agreement with our result; (ii) the 9 resonances assigned by Poortmans et al. 8), namely those at 8.79, 39.41 and 56.47 eV with spin J = 3, and those at 19.30, 32.05, 33.51, 34.35, 35.16 and 51.28 eV with spin J = 4. One may thus rely on a total sample of 25 levels, 9 with J = 3 and 16 with J = 4. The results given in subsects. 4.1-4.3 are all obtained making use of the whole sample of 25 spin assignments. 4.1. AVERAGE FISSION WIDTHS The estimate of the average fission widths fir(3) and fir(4) for J = 3 and J = 4 respectively is not straightforward because in our experiment only resonances with a small Ff value could be assigned. Taking into account simply the arithmetic means would then lead to results strongly biased towards low values. As both the average values and the number of degrees of freedom of the fission width distributions are expected to be different for the two spins, the ratio between the arithmetic means would also be an unreliable estimate of R = Ff(3)/fff(4). A maximum-likelihood calculation was then carried out in which both assigned and unassigned resonances were taken into account in such a way that the estimate is not affected by the bias. In fact, if one assumes that the distribution of the fission widths is chi-squared with v(3) and v(4) degrees of freedom for J = 3 and J = 4 respectively, and that the probability of assigning the spin of a resonance depends on Fe only and not explicitly on the spin, the likelihood function reads: L(Ff(3), Ff (4), v(3), v(4))
= ]71~P(3)p(rf~//~f (3); v ( 3 ) ) g ( F , ) × ~IjP(4)p(Ffj/fff (4); v(a))g(Frj) × 1-]k [P(3)p(Ff~/ff(3); v(3))+P(4)p(Ff~/Fr(4); v(4))][1 --g(Ffk)], where the index i runs over J = 3 resonances, j over J = 4 resonances and k over the unassigned ones. The function p(x; v) is the chi-squared with v degrees of freedom, P ( J ) is the a priori probability for a resonance to have a certain J, and ,q(Ff) is the probability of assigning the spin of a resonance with a given Ff. Factorizing the
F. CORVI et aL
160
quantities which do not depend on F r (3), F r (4), v(3), v(4), one gets:
L (F r
(4), v(3), v(4)) = const.
× I-[,P(3)p(r,,/Ff (3); v(3)) × [IjP(a)p(rfflFf (4); v(4))
× I-lk[e(3)p(rrk/Fr (3); v(3)) +P(4)p(FrdFf (4); v(4))]. It follows that the bias in assigning the spin enters only as a constant factor into the likelihood function and thus does not affect the results of the maximization procedure. As the more interesting quantity is the ratio R = F r (3)/Ff(4), it is convenient to write the likelihood function in terms of R and of the sum S = F f ( 3 ) + F f ( 4 ) of the average fission widths: S~(R, S, v(3), v(4)) = L(Ff (3), F r (4), v(3), v(4)). The use of S as second variable has the advantage that its value has a small uncertainty, being roughly twice the mean F r over both assigned and unassigned resonances. In the estimation of the most probable value of R there are two main sources of uncertainty: (i) the lack of knowledge about the values of v(3) and v(4); (ii) the uncertainty in the ratio P(3)/P(4), i.e. in the ratio between the level densities for the two spins, which corresponds to the uncertainty in the spin cut-off parameter a. As the information available on v(3), v(4) and a is weak, one should assume a rather large range of possible values of these quantities in order to define the range of probable R-values. A convenient way to proceed is to average the likelihood function over v(3), v(4) and S, assuming that they are a priori uniformly distributed in a sufficiently large range. The average likelihood function is then:
A(R) ~ ~ ~ ( R , S, v(3), v(a))dv(3)dv(4)dS. The computation of A(R) was performed taking into account the 25 assigned resonances and all the unassigned resonances in the energy range 0-42 eV. It was assumed that the possible v-values lie between 1 and 3.5. Furthermore the calculation was repeated for two extreme values of the spin cut-off parameter ~r = 3.5 and a = ~ , and for two different evaluations of resonance fission widths, namely those given by Krebs et al. 21) and by de Saussure et al. z4). The results are shown in fig. 8. It appears that the behaviour of the curves does not depend very much on the different evaluations of t h e / ' r values. For high values of a the likelihood function has two peaks; the smaller one, at R ~ 0.5, arises from v-pairs having a high ratio v(3)/v(4). For cr = 3.5 these particular v-pairs have small likelihood and the secondary peak at R ~ 0.5 nearly disappears.
23sU N E U T R O N
RESONANCES
161
In conclusion, the available data suggest that most probably Ff (3) is significantly higher than Ff(4), but the uncertainties are so large that the case Ff(3) < Ff(4) cannot be disregarded. The importance of new spin assignments and of a better knowledge of the spin dependence of the level density is evident. b)
a) 0"=3.5
<
,'/_ I", ', ,,/cr=o~
[,
0
1
2
5
3
6
1
2
3
4
5
6
R
R
Fig. 8. Likelihood o f R = ~ ( 3 ) / ~ r ( 4 ) for two different values o f the spin cut-off p a r a m e t e r cr = 3.5 (full line) a n d cr -- oo (dashed line). T h e curves (a) o n the left are obtained with the /'f values given by K r e b s et al. 2~); the curves (b) o n the right are obtained with t h e / ' f values given by De Saussure et al. 2,).
A2
jr~= 4-
jl"l: = 3-
+]-
(J,l<) 0-
(J,K)
(3~2)
-1-
(~,2) exp .......
-2-
/////.I/////. z..'.~.
////~j
exp y l / ~ >'/ll/
(3,1)
(A,I) -3-
(3~0)
Fig. 9. Values o f the A2 coefficient in the expression for the a n g u l a r distribution o f the fission fragm e n t s for J ~ = 3 - a n d 4 - . Full lines give t h e A2 values for the (J, K ) fission channels which are expected to be open; the average A2 are indicated by dotted lines. T h e lines m a r k e d with " e x p " give the experimental values; the c o r r e s p o n d i n g errors are indicated by s h a d e d areas.
162
F. C O R V I et al.
4.2. A N I S O T R O P Y O F F I S S I O N F R A G M E N T S
Pattenden and Postma z) have measured the anisotropy of fission fragments emitted from the neutron fission of aligned 235 U nuclei. For each resolved resonance, they gave the value of the second Legendre coefficient A2 appearing in the simplified expression for the angular distribution
W(O) = 1 + A 2 f 2 (I)P2 (cos 0), where 0 is the angle between the direction of emission and the orientation axis and J) (I) is the alignment parameter. Making use of the spin assignments, the following average values for each spin group are obtained: A2 (3) = - 1.69+0.10, A2 (4) = - 1.98 +_0.09, where the 10 ~o correction introduced in the "note added in p r o o f " of ref. 2) is taken into account. The errors are those due to the limited statistical samples and do not include systematic errors. There is no appreciable spin dependence of the A 2 coefficients; however, it is interesting to compare them with the predictions 5) deduced from Bohr channel theory. In fig. 9 we plot for J~ = 3- and 4 - separately the A 2 values (continuous lines) appropriate to the (J, K) fission channels which are expected to be open, namely (J, K ) = (3, 0), (3, 1) and (3, 2) for spin 3- fission, and (J, K ) = (4, 1) and (4, 2) for 4- fission. Dotted lines indicate the values J-z (3) and ,42 (4), calculated under the assumption of equal contributions from all these channels. This assumption was chosen just because it is the simplest one. Full lines indicated by "exp" are the experimental values and shaded areas correspond to their errors. The position of the two experimental averages confirms the hypothesis 2) that the two K = 2 channels, although energetically the least favoured, do still play a r61e in the slow-neutron fission of 235U. 4.3. S Y M M E T R I C F I S S I O N Y I E L D
Cowan et al. 3) have measured radiochemically the ratio of 115Cd to 99Mo fission fragment yields in individual resonances; this quantity, which can be considered proportional to the ratio of symmetric to asymmetric fission, was found to exhibit a double-peaked distribution. The results were interpreted by associating spin 3 with the group of levels with higher symmetry and spin 4 to the other group. The spin assignments for 14 common resonances generally confirm Cowan's interpretation except for three resonances which definitely disagree, i.e. those at 34.35, 35.16 and 56.47 eV, assigned by Poortmans. The fact that spin-3 fission has a higher symmetric yield is at first surprising, since the available 3- collective transition states should be on the average more asymmetric than 4 - states. We are greatly indebted to A. Mauri and F. Gasperini for technical assistance. We wish to thank M. Magnani and C. Cervini for writing the tape analysis computer code.
z3~U NEUTRON RESONANCES
163
References 1) J. W. T. Dabbs, C. Eggerman, B. Cauvin, A. Michaudon and S. Sanche, Proc. 2nd Symp. on physics and chemistry of fission, Vienna, 1969, p. 321 2) N. J. Pattenden and H. Postma, Nucl. Phys. A167 (1971) 225 3) G. A. Cowan, B. P. Bayhurst, T. J. Prestwood, J. S. Gilmore and G. W. Knobeloch,Phys. Rev. C2 (1970) 615 4) A. Bohr, Proc. 1st Conf. on peaceful uses of atomic energy, Geneva, vol. 2, 1956, p. 151 5) J. E. Lynn, Proc. Int. Conf. on nuclear data for reactors, Paris, vol. 2, (1966) p. 89 6) V. M. Strutinsky, Nucl. Phys. A95 (1967) 420; A122 (1968) 1 7) R. I. Schermer, L. Passell, G. Brunhart, C. A. Reynolds, V. L. Sailor and F. J. Shore, Phys. Rev. 167 (1968) 1121 8) F. Poortmans, H. Ceulemans, E. Migneco and J. P. Theobald, Proc. 2nd Int. Conf. on nuclear data for reactors, Helsinki, 1970, p. 449 9) M. Asghar, A. Michaudon and D. Paya, Phys. Lett. 26B (1968) 664 10) H. Weigmann, J. Winter and M. Heske, Nucl. Phys. A134 (1969) 535 11) W. R. Kane, Phys. Rev. Lett. 25 (1970) 953 12) R. G. Graves, D. 1. Garber and R. E. Chrien, Bull. Am. Phys. Soc. 16 (1971) 1181 13) K. J. Wetzel and G. E. Thomas, Phys. Rev. C1 (1970) 1501 14) W. P. Poenitz and J. R. Tatarczuk, Nucl. Phys. A151 (1970) 569 15) M. R. Bhat, R. E. Chrien, D. I. Garber and O. A. Wasson, Phys. Rev. C2 (1970) 2030 16) W. P. Poenitz, Z. Phys. 197 (1966) 262 17) D. Sperber and J. W. Mandler, Nucl. Phys. A l l 3 (1968) 689 18) C. Coceva, F. Corvi, P. Giacobbe and M. Stefanon, Nucl. Phys. A170 (1971) 153 19) J. E. Cline, IN-1448 (1970) 20) B. Fogelberg and A. B~icklin, Contr. Conf. on nuclear structure study with neutrons, Budapest, 1972, p. 6 21) J. Krebs, G. Le Coq, 3. P. L'Heriteau and P. Ribon, Proc. 3rd Conf. on neutron cross sections and technology, Knoxville, vol. 1, 1971, p. 410 22) O. A. Wasson, R. E. Chrien, G. G. Slaughter and J. A. Harvey, Phys. Rev. C4 (1971) 900 23) C. Coceva, F. Corvi, P. Giacobbe and M. Stefanon, Contr. Conf. on nuclear structure study with neutrons, Budapest, 1972, p. 12 24) G. de Saussure, R. B. Perez and W. Kolar, ORNL-TM-3707 (1972)
Nuclear Physics A203 (1973) 145-- 163; (~) North-Holland Publishiny Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
L O W - E N E R G Y 7-RAYS AND SPINS OF 23SU N E U T R O N RESONANCES F. C O R V I *, M. S T E F A N O N *, C. C O C E V A * a n d P. G I A C O B B E t
CBNM Euratom, Geel, Belgium, CNEN Centro di Calcolo, Bologna, Italy Received 29 September 1972 Abstract: Low-energy p r o m p t ~-ray spectra in the range 95-670 keV have been m e a s u r e d for forty-one 235U n e u t r o n resonances selected by time-of-flight in the n e u t r o n energy range 1.5-58 eV. D i s c r i m i n a t i o n against the natural 0-activity o f 235 U has been o b t a i n e d by m e a n s o f a coincidence technique. T h e spectra s h o w a very complicated structure owing to a few capture a n d m a n y fission ~-rays. T h e ratios o f the intensities o f the 160.3 keV a n d 642.4 keV capture 7-rays have been used for spin a s s i g n m e n t s o f fourteen resonances with small fission widths. Some conclusions are d r a w n a b o u t the spin dependence o f average fission widths, a n i s o t r o p y o f fission f r a g m e n t s a n d s y m m e t r i c fission yields. EI
NUCLEAR
t
REACTIONS
235U(n,~), ( n , f ) , E =
1.5-58 eV; m e a s u r e d E.I, 17.
236U deduced resonances, J. Enriched target. 1. Introduction
An extensive knowledge of the spin of 235 U neutron resonances would be an important step towards a better understanding of slow-neutron induced fission. In fact it would lead immediately to the spin dependence of all those quantities which have already been measured in 235U single resonances such as fission widths, angular distributions of fission fragments from aligned z35U nuclei 1, 2) and symmetric fission yields 3). It would be quite interesting to compare experimental results with the channel theory of fission 4, 5) even if effects due to the double-humped deformation potential 6) could strongly affect the results. Finally, from the point of view of applied physics, a knowledge of the spins is necessary for a satisfactory multi-level analysis of low-energy neutron cross sections. Many efforts have been made, with different methods, to assign a significant number of spins, but in spite of this there are only few and often discordant results. One method, which is the most direct, consists of measuring the transmission of polarized neutrons through a polarized target 7); however, up to now, it could only be applied to the three lowest resonances. A larger number of spin assignments was obtained by Poortmans 8) from measurements of scattering and transmission cross sections; the extensive application of such a method to 23SU is hampered by the smallness of the spin effect, due to the high target spin (I = -~), by the high level density, and by the very weak scattering yield of many resonances. Comitato Nazionale Energia Nucleare, Ispra, Italy. 145
146
F. CORVI et
aL
Measurements of the multiplicity of v-rays 9) and of the relative intensity of the 642 keV capture transition 1o) were also attempted. More recently, primary capture transitions leading to low-lying J = 2 states in the 236U compound nucleus were observed in order to identify a certain number of J = 3 resonances 11, 12): this method is obviously limited by the fact that when these y-rays are not detected it is impossible to decide whether this is due to the resonance spin being 4 or to the intensity of the dipole transition falling below the threshold of observation. The results of all these measurements are in many cases conflicting, so that the use of an independent method is highly desirable. This paper reports an attempt to apply to 235U the recently developed low-level population method of spin assignment, which has already proved very successful for non-fissile nuclei 13-15). In short, this method consists of measuring the low-energy v-ray spectra from capture in individual resonances and determining the relative intensities of at least two prominent v-rays. If these transitions de-excite two states of different spins, it can be shown that the ratio of their intensities depends significantly on the spin of the initial compound state. This method combines the following advantages: (i) it has been successfully applied to a variety of non-fissile target nuclei with different spins and parities, and no exception to its validity has yet been found; (ii) its results are qualitatively well understood in terms of a generally accepted statistical behaviour of the electromagnetic decay, and are also quantitatively confirmed by numerical simulations of the v-ray cascade 16, 17); (iii) the spin effect is large: in favourable cases the intensity ratios may differ by a factor two for the two initial spins; (iv) no normalization of the intensities to the capture yield of each resonance is necessary. 2. Description of the experiment
The application of the low-lying level population method to a fissile nucleus such as 235U has to cope with two major difficulties: (i) the presence of prompt and delayed fission v-rays, and (ii) natural v-activity following the s-decay o f 235U. The first effect highly complicates the structure of low-energy v-ray spectra emitted from 235 U resonances, while the natural activity is strong enough compared with the presently available sources of resonance neutrons to wipe out any other effect below about 250 keV. The success of the method depends then on the availability of at least two lowenergy capture v-rays, de-exciting two states of different spins, which are sufficiently resolved and intense to be measurable in many resonances. One of these v-rays, namely the 642 keV transition de-exciting a 2- level at 687 keV, has already been exploited by Weigmann et al. lo). More recently, in an accurate measurement of the 7-ray spectrum in the 4.84 eV resonance, Kane 11) found several capture v-rays above 400
23sU NEUTRON RESONANCES
147
keV; however, their intensities are too small to be measurable in many resonances. The only possibility left then is to look at a lower energy: a possible candidate is the 160 keV transition between the 6 + and 4 + members of the ground state rotational band. F r o m population systematics of other heavy nuclei with similar capture states and from the value of the theoretical internal conversion coefficient for E2 radiation, one should expect an intensity of 0.02-0.03 7-rays per captured neutron for this transition. The comparison between the intensities of the 160 and 642 keV lines would be very suitable for the spin assignment of neutron resonances since the population of a
Nol (TL) 18xlfcm
MONIT. UNIT
Ge(Li)
[
~
C.R.T. DSPLAY I I 4096CH. ANALYSER I L . . . . . . . . . .e.
/
~3Su s~le/
\, ",
\ '~
I~ D,~IR,MI
CH. '
, L__ r---
.F.
/ AMPLI I
I °'sc~l
I ~"=!s'*]
IRE~CTO"I
0 10 20 30 cm
i RECORDER J
(2)
Fig. 1. Experimentalset-up and block diagram of the electronics. 6 + relative to that of a 2 - level is expected to change by at least a factor of two as a function of the initial spin 13,23) ( j ~ = 3- or 4 - ) . However, in order to go down to the 100 keV region, it is mandatory to discriminate against the natural 7-activity: this can be accomplished by means of a coincidence technique. The experiment was performed at the Geel linac using the time-of-flight technique. The characteristics of the linac and the general lay-out of the neutron capture 7-ray facility have already been described in ref. 18); fig. 1 shows the detection system and the electronics used for this measurement. A metallic z35U disk (12 cm diameter, 0.1 g/cm 2 thick, 93 % enriched) is exposed to the neutron flux at a 13 m flight distance and is viewed by a 40 cm 3 coaxial Ge(Li) detector and a large 18 x 15 cm NaI(TI)
148
F. CORVI
et aL
crystal, both placed at right angles with respect to the beam. The NaI(Tl) crystal is shielded from fission and scattering neutrons, and from soft ?-radiation coming from the sample by about 3.5 cm of borated palyethylene, 2 g/cm 2 of 10B and 1 cm of lead. Pulses from the Ge(Li) detector are accepted only if in coincidence with pulses from the NaI(TI) detector corresponding to an energy higher than 0.7 MeV. In this way the low-energy natural ?-activity should be removed, except for random coincidences. Timing of Ge(Li) pulses is performed with an extrapolated-leading-edge timing discriminator, allowing a coincidence resolving time of 25 ns with 95 O//ocoincidence efficiency. This is done at the expense of the low-energy counting rate, since small pulses with longer rise times are unable to trigger the timing discriminator. The output of the coincidence unit is sent to a 4096-channel time coder with 0.125 Fls channel width. Pulses from the Ge(Li) detector are amplified and fed to a 4096-channel ADC: their amplitude analysis is enabled by the stop signal from the time coder. Drifts in zero and gain are compensated for by a digital stabilizer with windows set on two highly stable reference pulses placed at the lower and upper energy ends of the spectrum, respectively. The amplitude and time-of-flight addresses corresponding to each event are then stored in a 400-word buffer memory. Every time the memory is full, its content is recorded on magnetic tape in IBM compatible format. Each standard tape contains approximately 2.6 x 106 events; in the present measurements 13 tapes were recorded for a total measuring time of 250 h. The data sorting, consisting basically of building amplitude spectra corresponding to given time-of-flight intervals, was performed off-line by computer. The integral amplitude and time-of-flight spectra were continuously monitored throughout the whole measurement by a 4096channel analyser and display, connected in parallel with the bidimensional system. The time-of-flight spectrum of the coincidences is shown in fig. 2 for the neutron energy range 2-58 eV; the resonance energies in eV are indicated above the 41 intervals for which amplitude spectra were sorted out; in particular the time intervals corresponding to the 14 resonances to which spin was assigned and to two background regions are represented by shaded areas. Strong overlapping of two or more levels is present in many energy regions; however, only one resonance is associated with a given interval when its capture yield is at least a factor five larger than the cumulative yields of other superimposed resonances. This is the case for the levels at 41.90, 30.85, 24.32 and 23.40 eV. Two typical ?-ray spectra covering the energy range between 95 and 670 keV are shown in fig. 3. The spectrum in the upper half corresponds to a resonance with predominant capture. The peaks at 104, 160, 423 and 642 keV are due to capture 7-rays while the one at 185 keV is the main peak of the natural 235U activity, still important because of random coincidences. The relevant 236U level scheme is represented above. The remaining structure is mainly due to fission ?-rays, as appears from a comparison with the spectrum in the lower half, referring to a resonance with predominant fission. The decrease in counting rate below about 200 keV is due to the effect of the leading-edge timing discriminator, as explained above. The 160 keV transition has a fair intensity; however, it is only partially resolved from at least one
235U + n x 10~
19.30 3.0
35.15 56.t,7 52.30
2.0
34.35
1~-51 28
39./,1
t
[~r~l+ 466o llJ, Id I
1.0
51 i
419o [
i~;III 1'-4651 ~I
2110
2555 2520
3205
23.40
264~, 23 (
°3085 2~84[I 12295
L
0 300
200
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400
ch.
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12.39
x 10t'
1.01805
16.10
11.67
]
[
140
[16.671184~1
539
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708
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I 23~uA
600
1200 ch.
1000
800
3.61 x 103 2.0
4~5
234
I[
3.15
~ .
2040
10
0
i
I
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2000
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Fig. 2. Time-of-flight spectrumof coincident7-rays following neutron interaction with 2asU. The resonance energies in eV are listed above the 41 intervals for w hi c h a m p l i t u d e s pe c t ra were sor ted out. The time intervals c o r r e s p o n d i n g to the 14 resonances to w hi c h spin was a s s i gne d a n d to two b a c k g r o u n d regions are represented by s h a d e d areas.
F. CORVI
150
e t al.
2
687.7
E n =6.39 eV
Ff
231Th
185
x 10 3
~ r
2.o
~I
6"
104
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m
u
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309
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~ 2.0
OF
o
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400
,ooo channels
Fig. 3. Two examples ofT-ray spectra in the range 95-670 keV, belonging to the resonances at 6.39 eV and 8.79 eV, respectively. The peaks at 104, 160, 423 and 642 keV are capture ~'-rays while the one at 185 keV is the main peak of the natural 235U activity. The relevant 236U level scheme shown above is taken from ref. ~1). fission a n d o n e a c t i v i t y p e a k , as will be seen b e t t e r in the sect. 3. T h e effective e n e r g y r e s o l u t i o n o f the m e a s u r e m e n t was 2.1 k e V at 185 k e V a n d 2.7 k e V at 642 keV. 3. D a t a a n a l y s i s and results
3.1. SHAPE ANALYSIS T h e energies a n d intensities o f t h e 7-rays are o b t a i n e d f r o m the e x p e r i m e n t a l spectra by m e a n s o f a g e n e r a l i z e d l e a s t - s q u a r e fitting m e t h o d , p r o g r a m m e d for a n I B M
z3sU N E U T R O N
RESONANCES
151
360-75. The shape of the spectra is assumed to be given by the superposition of peaks and a smooth background. The shape of a peak corresponding to a transition of energy Eo is assumed to be a Gaussian matched to an exponential tail below E 0 - 5 . The background is described by a polynomial. The two parameters defining the shape of the peak, i.e. the standard deviation a of the Gaussian and the distance 6 at which the exponential sets in, are obtained preliminarily, for a given energy region, by fitting the larger and best resolved peaks; the dominant activity peak at 185 keV and the 642 keV capture line were used for this purpose at low and high energy respectively. The transition energies and their intensities are obtained by fitting with fixed ~ and 5 I KCI~ 9B~
Z31Th
!
~85 7
En = 8.79 eV
I
~eefg 5:
q/I
c~3000
'J
qH 2000
"~3a
....
lt.2 ~ i
,
'A //I .
I
!
, [
I~
!
iJt ]IAJl •
'
!
~
,
22~o
'
I ........ ! ~ ,: ~ t X :,," , t~,~, , , ,' , £~ L,7 , L_e./ y_ _~
L ,/ , 3 ,~ '!
I ~3~Th ,
A .':~
•
1000 0
50
100
150
200
250
CHANNELS
Fig. 4. Fit o f the s p e c t r u m o f the 8.79 eV resonance in the range 95-238 keV. Experimental data are represented by dots a n d the fit by a c o n t i n u o u s curve while the fitted b a c k g r o u n d is described by a d a s h e d line. Vertical bars indicate the position o f all peaks considered in the fit. T h e energy in keV is given above each well-defined peak. T h e region delimited by the d o t - a n d - d a s h rectangle is s h o w n in m o r e detail in fig. 5c.
many peaks in wide energy regions. The program can fit simultaneously up to 35 peaks. In the fitting procedure a priori information about the peak parameters or about relationships among them can be introduced in the form of non-rigid constraints; for instance, if we know from other measurements that the position of a peak is E = Eo 4 - A E , it is possible to introduce both E o and A E in the computation. In this case a Gaussian distribution centered around E 0 with variance A E 2 is assumed as the a priori probability of the peak energy E. In the present work the use of a priori information becomes important because many similar 7-ray spectra are to be fitted in the same energy range. The information one gets from the analysis of some spectra can then be fed into the fits of other ones. Another feature of the program is the automatic blocking of those parameters for which there is insufficient information to reach convergence. The fitting procedure was carried out in the channel intervals
152
F. CORVI et al.
1-250 and 970-1005 (see fig. 3). In fact, since the low-energy part shows a very complicated structure, it was necessary to extend the fit over a considerable energy range in order to get a reliable value o f the b a c k g r o u n d under the 160 keV line; in the case o f the 642 keV transition, which is well isolated and sits on a rather constant continuum, a smaller energy interval was sufficient. A n example o f a fit o f the low-energy part o f the spectrum in the 8.79 eV resonance is shown in fig. 4. The energy value in keV is indicated only over the most prominent and well-defined peaks. The energy calibration was performed using sources o f 7Be, 51Cr, 57C0, 58C0, 139Ce and Z°VBi: a)
16o3
]
[ c)
~-~-En = 11"67eV
J
l
,~ 160.3
1000
500-
250-
J I ~ 163.36
~
~
50
o
8
158.8 En= 8.79eV
b)
- -
En=19"3eV
En=25.~/25.55eV,
°
0~
0-
o
Fig. 5. Fitted spectra of 4- resonances with increasing values of the fission width in the energy region between 154 and 169 keV. The fitted background was subtracted. The height of the bar below each peak is proportional to its intensity. The Fr values are taken from ref. 21). the error is estimated to be less than 0.2 keV. The calibration was checked by comparing the energies deduced for the 23 5U activity lines (indicated as 231Th in fig. 4) with the very precise values o f reE 19). Also, the energies o f the capture 7-rays agree well with the 23 6 U level scheme recently proposed by Fogelberg et al. 2 o). It should be pointed out that the fit does not intend to represent in detail all the lines: the peaks considered are just those necessary to reproduce the main features o f the spectrum, whose actual structure is certainly much more complicated. To clarify the structure o f the h u m p in which the 6 + - 4 + transition is to be found, the region around 160 keV is represented (background subtracted) on an expanded energy scale in fig. 5, for
2ssU NEUTRON RESONANCES
153
four resonances with very different fission widths F r. The height of the bar below each peak is proportional to its intensity. The peak at higher energy is the known 23~Th transition at 163.36+__0.01 keV, as given in ref. ~9). The nature of the other peaks is deduced by looking at the variation of their relative intensities with Ff. In fig. 5a, referring to a resonance with predominant capture, the peak at 160.3 keV stands out very clearly above the others. Moreover, as can be seen in figs. 5b-d, the ratio of the 158.8 to the 160.3 keV peak increases with Ff : therefore the 160.3 keV line is really the capture y-ray which we are looking for, while the other one is a fission line. Besides, at least two smaller peaks at about 155 and 165 keV are present. A shape fit to this complicated structure was obtained by making use of the constraints in the following way: the position of the 160.3 keV line with respect to the well-defined 185.72 keV peak was deduced with good precision in resonances with dominant capture. Similarly, the relative position of the 158.8 keV peak was obtained f r o m resonances with large Ff, and that of the activity line from a background spectrum. The relative positions of such lines and their uncertainties, as obtained from these determinations, were introduced as a priori information in the analysis of the other spectra. In this way it was possible to resolve the multiplet and obtain a reliable set of values: initial attempts to fit without constraints failed, giving rise to a set of widely varying peak positions, since the spectra did not usually contain enough information (due also to the poor statistics) to define correctly and unambiguously all parameters. In order to make sure that the results are completely reliable, it is necessary to evaluate the extent to which the capture line may be contaminated by fission y-rays. At first glance, the line seems reasonably pure since no important fission contribution shows up at 160.3 keV, even for resonances with extremely large Ff (see fig. 5d). However, a correlation analysis performed on a sample of 41 resonances showed that the ratios of the intensities of the two capture lines r -- I~ (160.3)/I(642.4) which should depend only on the spin, are positively correlated with the fission widths, the correlation coefficient being p = 0.6, which falls below the 0.1 percentile in the case of the uncorrelated distribution. This effect could be due to: (i) the presence of one or more fission y-rays other than the 158.8 keV one, superposed on the peak at 160.3 keV; (ii) systematic errors introduced when fitting close doublets, so that some strength of the 158.8 keV peak contributes to the capture line. In fact, when the distance between two peaks is only a~ of the F W H M , as is the case, a slight mismatch in the line shape or errors in the peak positions can give rise to systematic errors in the intensities. A more quantitative estimate of the magnitude of the effect was deduced by considering the relative intensities of the 160.3 keV line obtained from the fits in the resonances at 52.30, 25.20-25.55 and 14.0 eV, all with Ff > 300 meV: it was found that an upper limit for a possible fission contribution to the 160.3 keV line is 20 o/ O / o f the intensity of the 158.8 keV peak. This means that, if an error of less than 20 ~o is required for the intensity of the capture line, this line should not be smaller than the 158.8 keV one. This is very roughly equivalent to limiting the analysis to those
F. C O R V I et al.
154
resonances with Ff ~ 60 meV for J = 4 (see fig. 5b) and F r < 30 meV for J = 3 levels. To make sure that the ratios r between the intensities o f the two capture lines are not significantly affected by this spurious fission contribution, one should take into account only those resonances with Ff < 30 meV. According to the F'f values o f ref. 2~) only 11 o f the measured resonances satisfy this condition. The correspond0.8-
shape 0.6-
0,/4"
........
+--t- ........
o
stripping
"
___+_+
+-It
....
. . . . . . . .
+l!: I!t
I_ 0.2-
o
- ...........
+
j-a___
-+-........................... 16
2'0
ab
~'o
50
E n (eV)
Fig. 6. Ratios r = I~(160.3)/I~(642.4) obtained with shape analysis and spectrum stripping plotted against neutron energy for 14 resonances. Full circles refer to resonances with /'f < 30 meV, while the three open circles correspond to resonances with slightly higher fission widths. Dotted lines indicate the weighted averages for each spin group. The upper figure refers to the shape analysis o f subsect. 3.1, the lower one to the spectrum stripping method o f subsect. 3.2.
ing ratios r are indicated in the upper half o f fig. 6 by full circles. It is evident that the ratios fall into two widely separated groups. Since r is a measure o f the population o f a 6 + relative to a 2 - level, the higher values are obviously associated with J = 4 resonances. The average values o f r for each spin g r o u p are, ?(4) = 0.507 and ?(3) = 0.230, and are indicated by dotted lines. The magnitude o f the spin effect, given by the ratio ?(4)/?(3) = 2.2 is in agreement with expectation ~3).
zssu NEUTRON
RESONANCES
155
The spin was assigned to three more resonances with slightly higher fission widths: those at 15.45 eV (Ff = 48 meV) and 22.95 eV (Ff = 42 meV) were added because their capture line at 160.3 keV is more than one and a half times as intense as the nearby fission line; moreover, the resonance at 24.25 eV was also added because, in spite of having Ff = 52 meV, it still falls clearly in the lower group. The ratios r for these three levels are represented by open circles in fig. 6. The positive difference with re-
200
642.4 163.36 160.3 En = 2.04 eV
100-
160.3 158
J=4
250
163,36 /L_/
oj
En = 4 . 8 4 eV
8
En = 11.67 eV
500
"~o //
200-
642.4
En = 12.39 eV
J-3
j ~
400200-
100
0
0-
/
En=6.39eV
En = 14.53 eV
,500-
J=3
o
I
o [
400 o
200°o
0
/
0
o o
o
o o
/t
Fig. 7a. F i t t e d spectra for the 154-169 keV energy region p l o t t e d t oge t he r w i t h the 642.4 keV p e a k for 6 resonances to w h i c h spin was assigned. The vertical scale refers to the low-energy p a r t o f the spectra, while the 642.4 p e a k is r e d u c e d by a factor o f two for better c o m p a r i s o n . The bars be l ow the two capture 7-rays of interest are t h i c k e r t ha n the ot he r ones.
spect to the corresponding averages is consistent with the expected fission contribution to the 160.3 keV peak. The r-values and the spin assignments for the whole set of 14 resonances (9 with J = 4 and 5 with J = 3) are given in table 1. It should be noted that they do not represent the ratios of the true intensities because no correction was introduced for the energy dependence of the photopeak efficiency of the detector. The spin depen-
156
F. C O R V I et al.
dence of the relative intensities of the two capture lines can easily be seen in figs. 7a and b where the fitted spectra are plotted in the energy range 154-169 keV beside the peak at 642.4 keV for the 14 resonances to which the spin was assigned. I
160.3
158.8
En = 15.45 eV
642.4 En= 23,40eV l
158~
154.8~1%4/ /$O~l~°o '°°1 ~
100-
160.3
i
167.36
J=4
2ooj
642.4
I
I I
En = 16.10 eV
200-
I
En - 24.32 eV
J=4
~°I,~~~~o-°° J=3'~o
100-
0] 0%
_~ ol 8 o
o /
L
En z 21.10 eV
J=4
En = 30.85 W
J=4 0
200"
o
o
o
Oo
En = 22.95 eV
E n - 4 1 . 9 0 eV
J=4
J=3
o
O
o
o
o
/
(
o
0-
Fig. 7b. Fitted spectra as in fig. 7a for 8 more resonances to which spin was assigned. 3.2. S P E C T R U M S T R [ P P I N G
To check the results, a different analysis procedure was devised: the intensity of the capture line was obtained by subtracting from the unresolved doublet formed by the 158.8 and the 160.3 keV peaks a fission 7-ray contribution calculated from the inten-
235U NEUTRON RESONANCES
157
sities of higher-energy fission 7-rays. I n this way the p r o b l e m of fitting a close doublet was avoided, but other statistical a n d systematic errors were introduced. As reference lines three peaks were chosen at 199.1,204.0 a n d 212.6 keV respectively (see fig. 4). The n o r m a l i z a t i o n factor, i.e. the ratio between the sum of these three intensities a n d the fission c o n t r i b u t i o n to the 160 keV h u m p , was again determined f r o m the three resonances with Yf > 300 meV. This procedure is correct if one assumes the shape of the p r o m p t fission 7-ray spectrum to be i n d e p e n d e n t of the particular resonance, as is reasonable a n d consistent with the present experimental evidence. TABLE 1 Ratios r between the intensities of the 160.3 and 642.4 keV capture ~-rays E, (eV)
2.04 4.84 6.39 11.67 12.39 14.53 15.45" 16.10 21.10 22.95* 23.40 24.25* 30.85 41.90
r
J
shape
stripping
present
0.27,0.05 0.49 =c0.04 0.55,0.03 0.49,0.04 0.21 ±0.03 0.22-*-0.08 0.61 ::t-0.10 0.47 =c0.05 0.49,0.06 0.59,0.11 0.48,0.07 0.30,0.09 0.51 iO. 10 0.25,0.05
0.24±0.07 0.52-t-0.04 0.51,0.04 0.51,0.04 0.25=~0.05 0.284-0.11 0.46i0.12 0.48,0.07 0.52 i0.07 0.51 I0.12 0.50 JzO.07 0.33,0.12 0.55 +0.13 0.31 --0.07
3 4 4 4 3 3 4 4 4 4 4 3 4 3
previous 3 a.b) (4) a) 3 a.b) 4 ~) 3 b.c) 3 t.)
(4) c) (3) c)
Columns 2 and 3 give the ratios r obtained with the shape and with the stripping method respectively for 14 neutron resonances of energy En. The deduced spin assignments and the results of previous works are listed in columns 4 and 5. Resonances with/'f > 30 meV are marked with. an asterisk. a) Spin assignments of Kane 1l). b) Spin assignments of Graves et al. 12). ~) Spin assignments of Poortmans et al. 8). The results are given in c o l u m n 3 of table 1 a n d plotted in the lower half of fig. 6: there is complete qualitative agreement with the previous ones, each resonance b e l o n g i n g to the same spin group. The error bars, which also include a 10 % uncertainty in the n o r m a l i z a t i o n factor, are o n the whole larger t h a n those of the shape analysis, as is u n d e r s t a n d a b l e because the m e t h o d does n o t fully exploit the informat i o n on shape a n d peak positions. The weighted averages are ? ( J = 4) = 0.511 a n d ~ ( J = 3) = 0.264; their ratio is 1.94. 3.3. COMPARISON WITH PREVIOUS RESULTS The deduced spin determinations are listed in c o l u m n 4 of table 1, together with the results o b t a i n e d in recent works, namely the p r i m a r y 7-ray measurements of K a n e 11)
158
F. CORVI et aL
and Graves et al. 12) and the scattering data of Poortmans et al. s). There is a general agreement, except for the 6.39 eV level to which Kane and Graves et al. assigned spin 3. Since among the assigned resonances this is perhaps the one with the largest capture yield, it is interesting to look for possible reasons for such a disagreement. The spin assignment 3- was supported by two arguments. First, Kane saw a weak y-ray leading to the 2 - state at 687 keV. Under the assumption that only dipole radiation is visible, he concluded that the capture state should be 3-; however, the probability that the transition is E2 instead of M1 cannot be ruled out, since E2 primary radiation has often been seen in resonance neutron capture, particularly in heavy nuclei, as was also recently shown by Wasson et al. 22) in the case of 23SU. The other piece of evidence in favour of J = 3 was the observation of a high-energy transition leading to a doublet of states identified by Kane as the 2 + members of the fl- and 7vibrational bands; however the identification of these bands is not exempt from ambiguities and contradictions with more recent data 20), so that it seems that a straightforward interpretation of the high-energy data will be possible only when a more complete and reliable 236U level scheme is available. The agreement of our results with those of Poortmans, although limited to the only four common resonances, is important because the two methods can be used in a complementary way for the spin assignment of resonances of fissile nuclei. Finally it should be noted that the present data, as well as those of Graves et al. 12) and Poortmans et al. 8), disagree with the results of Asghar et al. 9) and of Weigmann e t al. lo). This can perhaps be explained if one remembers that in the y-ray multiplicity measurement performed by Asghar no attempt is made to distinguish between capture and fission 7-rays; Weigmann's results, on the other hand, rely on the intensity measurement of the 642 keV 7-ray in individual resonances, which is a very difficult task in the case of fissile nuclei, since it implies the normalization of peak counting rates to the capture yield of the corresponding resonances. 3.4. CONSIDERATIONS ON THE METHOD First o f all it should be pointed out that the measurement of the 6+-4 + transition was the essential step that allowed the application of the low-lying population method. In spite of the fact that we were dealing with a coincidence measurement, the counting rate in this line was sufficient, thanks to the large spin effect, to assign also weak resonances, as shown in fig. 2. The main drawback of the method is that the results are limited' to resonances with small fission widths, because of the overlapping of capture and fission y-rays: in this respect it should be remarked that the coincidence method, while necessary for removing the sample activity, worsens the capture-to-fission ratio because the 7-rays associated with a fission event have a multiplicity higher than that of capture 7-rays. A possible way of improving such a situation would consist of using a 4n fast-neutron detector operated in anti-coincidence with the Ge(Li) diode, so as to discard most of the fission events.
235U NEUTRON RESONANCES
159
4. Spin dependence of fission properties The number of spin assignments obtained in this work is such that it is now possible to obtain information on the spin dependence of some fission properties of the lowenergy neutron resonances of 235U. To this end it is convenient to increase our sample of 14 spin-assigned, resonances by including all other reliable spin determinations. The following resonances were considered: (i) those at 0.29 eV with J = 3 and at 1.135 eV with J = 4, assigned by Schermer et al. 7) with a polarized-beam-polarized-target experiment: their assignment of a third resonance at 2.04 eV is in agreement with our result; (ii) the 9 resonances assigned by Poortmans et al. 8), namely those at 8.79, 39.41 and 56.47 eV with spin J = 3, and those at 19.30, 32.05, 33.51, 34.35, 35.16 and 51.28 eV with spin J = 4. One may thus rely on a total sample of 25 levels, 9 with J = 3 and 16 with J = 4. The results given in subsects. 4.1-4.3 are all obtained making use of the whole sample of 25 spin assignments. 4.1. AVERAGE FISSION WIDTHS The estimate of the average fission widths fir(3) and fir(4) for J = 3 and J = 4 respectively is not straightforward because in our experiment only resonances with a small Ff value could be assigned. Taking into account simply the arithmetic means would then lead to results strongly biased towards low values. As both the average values and the number of degrees of freedom of the fission width distributions are expected to be different for the two spins, the ratio between the arithmetic means would also be an unreliable estimate of R = Ff(3)/fff(4). A maximum-likelihood calculation was then carried out in which both assigned and unassigned resonances were taken into account in such a way that the estimate is not affected by the bias. In fact, if one assumes that the distribution of the fission widths is chi-squared with v(3) and v(4) degrees of freedom for J = 3 and J = 4 respectively, and that the probability of assigning the spin of a resonance depends on Fe only and not explicitly on the spin, the likelihood function reads: L(Ff(3), Ff (4), v(3), v(4))
= ]71~P(3)p(rf~//~f (3); v ( 3 ) ) g ( F , ) × ~IjP(4)p(Ffj/fff (4); v(a))g(Frj) × 1-]k [P(3)p(Ff~/ff(3); v(3))+P(4)p(Ff~/Fr(4); v(4))][1 --g(Ffk)], where the index i runs over J = 3 resonances, j over J = 4 resonances and k over the unassigned ones. The function p(x; v) is the chi-squared with v degrees of freedom, P ( J ) is the a priori probability for a resonance to have a certain J, and ,q(Ff) is the probability of assigning the spin of a resonance with a given Ff. Factorizing the
F. CORVI et aL
160
quantities which do not depend on F r (3), F r (4), v(3), v(4), one gets:
L (F r
(4), v(3), v(4)) = const.
× I-[,P(3)p(r,,/Ff (3); v(3)) × [IjP(a)p(rfflFf (4); v(4))
× I-lk[e(3)p(rrk/Fr (3); v(3)) +P(4)p(FrdFf (4); v(4))]. It follows that the bias in assigning the spin enters only as a constant factor into the likelihood function and thus does not affect the results of the maximization procedure. As the more interesting quantity is the ratio R = F r (3)/Ff(4), it is convenient to write the likelihood function in terms of R and of the sum S = F f ( 3 ) + F f ( 4 ) of the average fission widths: S~(R, S, v(3), v(4)) = L(Ff (3), F r (4), v(3), v(4)). The use of S as second variable has the advantage that its value has a small uncertainty, being roughly twice the mean F r over both assigned and unassigned resonances. In the estimation of the most probable value of R there are two main sources of uncertainty: (i) the lack of knowledge about the values of v(3) and v(4); (ii) the uncertainty in the ratio P(3)/P(4), i.e. in the ratio between the level densities for the two spins, which corresponds to the uncertainty in the spin cut-off parameter a. As the information available on v(3), v(4) and a is weak, one should assume a rather large range of possible values of these quantities in order to define the range of probable R-values. A convenient way to proceed is to average the likelihood function over v(3), v(4) and S, assuming that they are a priori uniformly distributed in a sufficiently large range. The average likelihood function is then:
A(R) ~ ~ ~ ( R , S, v(3), v(a))dv(3)dv(4)dS. The computation of A(R) was performed taking into account the 25 assigned resonances and all the unassigned resonances in the energy range 0-42 eV. It was assumed that the possible v-values lie between 1 and 3.5. Furthermore the calculation was repeated for two extreme values of the spin cut-off parameter ~r = 3.5 and a = ~ , and for two different evaluations of resonance fission widths, namely those given by Krebs et al. 21) and by de Saussure et al. z4). The results are shown in fig. 8. It appears that the behaviour of the curves does not depend very much on the different evaluations of t h e / ' r values. For high values of a the likelihood function has two peaks; the smaller one, at R ~ 0.5, arises from v-pairs having a high ratio v(3)/v(4). For cr = 3.5 these particular v-pairs have small likelihood and the secondary peak at R ~ 0.5 nearly disappears.
23sU N E U T R O N
RESONANCES
161
In conclusion, the available data suggest that most probably Ff (3) is significantly higher than Ff(4), but the uncertainties are so large that the case Ff(3) < Ff(4) cannot be disregarded. The importance of new spin assignments and of a better knowledge of the spin dependence of the level density is evident. b)
a) 0"=3.5
<
,'/_ I", ', ,,/cr=o~
[,
0
1
2
5
3
6
1
2
3
4
5
6
R
R
Fig. 8. Likelihood o f R = ~ ( 3 ) / ~ r ( 4 ) for two different values o f the spin cut-off p a r a m e t e r cr = 3.5 (full line) a n d cr -- oo (dashed line). T h e curves (a) o n the left are obtained with the /'f values given by K r e b s et al. 2~); the curves (b) o n the right are obtained with t h e / ' f values given by De Saussure et al. 2,).
A2
jr~= 4-
jl"l: = 3-
+]-
(J,l<) 0-
(J,K)
(3~2)
-1-
(~,2) exp .......
-2-
/////.I/////. z..'.~.
////~j
exp y l / ~ >'/ll/
(3,1)
(A,I) -3-
(3~0)
Fig. 9. Values o f the A2 coefficient in the expression for the a n g u l a r distribution o f the fission fragm e n t s for J ~ = 3 - a n d 4 - . Full lines give t h e A2 values for the (J, K ) fission channels which are expected to be open; the average A2 are indicated by dotted lines. T h e lines m a r k e d with " e x p " give the experimental values; the c o r r e s p o n d i n g errors are indicated by s h a d e d areas.
162
F. C O R V I et al.
4.2. A N I S O T R O P Y O F F I S S I O N F R A G M E N T S
Pattenden and Postma z) have measured the anisotropy of fission fragments emitted from the neutron fission of aligned 235 U nuclei. For each resolved resonance, they gave the value of the second Legendre coefficient A2 appearing in the simplified expression for the angular distribution
W(O) = 1 + A 2 f 2 (I)P2 (cos 0), where 0 is the angle between the direction of emission and the orientation axis and J) (I) is the alignment parameter. Making use of the spin assignments, the following average values for each spin group are obtained: A2 (3) = - 1.69+0.10, A2 (4) = - 1.98 +_0.09, where the 10 ~o correction introduced in the "note added in p r o o f " of ref. 2) is taken into account. The errors are those due to the limited statistical samples and do not include systematic errors. There is no appreciable spin dependence of the A 2 coefficients; however, it is interesting to compare them with the predictions 5) deduced from Bohr channel theory. In fig. 9 we plot for J~ = 3- and 4 - separately the A 2 values (continuous lines) appropriate to the (J, K) fission channels which are expected to be open, namely (J, K ) = (3, 0), (3, 1) and (3, 2) for spin 3- fission, and (J, K ) = (4, 1) and (4, 2) for 4- fission. Dotted lines indicate the values J-z (3) and ,42 (4), calculated under the assumption of equal contributions from all these channels. This assumption was chosen just because it is the simplest one. Full lines indicated by "exp" are the experimental values and shaded areas correspond to their errors. The position of the two experimental averages confirms the hypothesis 2) that the two K = 2 channels, although energetically the least favoured, do still play a r61e in the slow-neutron fission of 235U. 4.3. S Y M M E T R I C F I S S I O N Y I E L D
Cowan et al. 3) have measured radiochemically the ratio of 115Cd to 99Mo fission fragment yields in individual resonances; this quantity, which can be considered proportional to the ratio of symmetric to asymmetric fission, was found to exhibit a double-peaked distribution. The results were interpreted by associating spin 3 with the group of levels with higher symmetry and spin 4 to the other group. The spin assignments for 14 common resonances generally confirm Cowan's interpretation except for three resonances which definitely disagree, i.e. those at 34.35, 35.16 and 56.47 eV, assigned by Poortmans. The fact that spin-3 fission has a higher symmetric yield is at first surprising, since the available 3- collective transition states should be on the average more asymmetric than 4 - states. We are greatly indebted to A. Mauri and F. Gasperini for technical assistance. We wish to thank M. Magnani and C. Cervini for writing the tape analysis computer code.
z3~U NEUTRON RESONANCES
163
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