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Fragments' mass and energy characteristics in the spontaneous fission of 236Pu, 238Pu, 240Pu, 242Pu, and 244Pu
NUCLEAR PHYSICS A ELSEVIER
Nuclear Physics A 617 (1997) 331-346
Fragments' mass and energy characteristics in the spontaneous fission of 236pu, 238pu, 24°pu, 242pu, and 244pll "~" L. Dematt~ a, C. Wagemans b, R. Barthdl6my a, R D'hondt c, A. Deruytter a a CEC, JRC, Institute for Reference Materials and Measurements, B-2440 Geel, Belgium b Dept. of Subatomic and Radiation Physics, University of Gent, Proeftuinstraat 86, B-9000 Gent, Belgium c Studiecentrum voor Kernenergie, Boeretang 200, B-2400 Mol, Belgium
Received 17 December 1996
Abstract The results of a systematic study of the mass and energy of fission fragments emitted in the spontaneous fission of 236'138"24°'242'244puare reported. A comparison of the fragments' mass and energy distributions demonstrates the occurrence of different fission modes with varying relative probability. These results are discussed in terms of the random neck rupture model as well as in terms of the scission point model, showing the influence of the neutron number of the fissioning system. Finally an improved method of analysis allows the investigation of the cold fission region. (~) 1997 Elsevier Science B.V. Keywords: RADIOACTIVITY; Fission 236,238,24o,242,244Pu, measured complementary fragment kinetic energies; Deduced energy, mass distributions, mass-energy correlations; Performed fission mode analysis; Selected cold fission events PACS: 24.75.+i; 23.90.+w
1. Introduction D u r i n g the past decades, the fission fragments' charge mass and energy characteristics have been studied in detail for a large variety o f fissioning systems. A n excellent review was recently m a d e by G 6 n n e n w e i n [ 1 ]. Still, for several nuclides data are lacking or can * This work is part of the Ph.D. Thesis of L. Dematt~ presented at the University of Gent, Belgium. 0375-9474/97/$17.00 (~) 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 5 - 9 4 7 4 ( 9 7 ) 0 0 0 3 2 - 8
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L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
be improved, so the data base needed for a detailed systematic study of the dependence of the fission fragments' mass and energy characteristics as a function of the neutron (N) and proton ( Z ) number of the fissioning nucleus certainly needs to be completed. Important efforts have been made recently at Darmstadt [2] and FSU [3], however for fissioning systems at moderate excitation energy. In the present work, the results of a systematic study of the energy and mass characteristics of the fragments emitted in the spontaneous fission of a series of Pu isotopes (ranging from mass number A = 236 to A = 244) is reported. These isotopes make indeed an ideal field of investigation, having the same proton number, excitation energy, spin and parity, thus only differing by the number of neutrons. However, in order to allow a decent intercomparison of the results, all isotopes need to be studied under the same experimental conditions and using samples of comparable quality. For these reasons, a series of measurements was performed between 1982 and 1995 under very similar experimental conditions. Partial or preliminary results of these measurements were already reported previously [4-6]. Last year, the data taking was finalized and the whole set of results was analysed with an improved data reduction programme, which also enabled to look for fission modes and to select cold fission events. Detailed results of this analysis are now reported and discussed.
2. The experiment The kinetic energy and mass characteristics of the fission fragments were determined using the double energy method. A sample, consisting of a homogeneous mixture of the spontaneously fissioning isotope and 239pu, was sandwiched in between two silicon surface-barrier detectors cooled to a constant temperature of 4°C and mounted in the centre of a vacuum chamber. With such a setup, a geometry of almost 4 ~ can be reached, in order to compensate for the low counting rate of the spontaneous fission measurements. It was previously demonstrated that the results are quite independent from the geometry, provided that the quality of the samples is excellent [4]. Table 1 summarizes the characteristics of the samples used, all of them being prepared by the evaporation of the plutonium (under vacuum) on very thin backing foils, transparent for fission fragments. The experiments have been performed at the BR1 reactor of the SCK/CEN in Mol, Belgium, since 239pu(nth,f) is used for the calibration of the detection chain. This graphite-moderator reactor provides well-thermalized neutron beams with fluxes of a few 10 6 neutrons/cm2s and it was operated during the day and shutdown at night and during the weekend. Such an operation allows a regular, almost daily calibration, needed to verify the longterm stability of the setup. The pulseheights of coincident fission fragments were recorded event by event (list mode) in a 1024 x 1024 channels configuration and stored on a magnetic tape unit via a Hewlett Packard 1000E computer, that is also the terminal end of the data acquisition
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Table 1 Characteristics of the evaporated samples Sample
236pu-239pu 238pu-239pu 24°pu-239pu 242pu-239pa
Isot. comp. (atoms %) 98.1% 1.9% 54% 46% 24% 76% 18%
239pu 236pa 239pu 238pu 239pu 24°pu 239pu
Manufacturer
Thickness (/zg/cm 2)
Backing
AERE, HarweU
1.3
222/zg/cm 2 Ni
IRMM, Geel
1.18
200/zg/cm 2 Ni
IRMM, Geel
19
1RMM, Geel
5.5
IRMM, Geel
7
29/zg/cm 2 P.I. 32 ~g/cm 2 El.
82% 242pu 244pu-239pu
50% 44% 1.5% 4.5%
239pu 244Ptl 24°pu 242pu
200/.tg/cm 2 Ni
system. The data were afterwards transferred to disk files on an IBM 4341 main frame, and finally to a workstation IBM RS/6000, were they have been analysed.
3. Data analysis The conversion of the pulseheights into mass and energy has been carried out by means of an iterative procedure described by Schmitt et al. [7], and incorporating the massdependent Schmitt-Neiler calibration procedure, the mass and momentum conservation relations and a correction for prompt neutron emission of the fission fragments. The detector calibration constants were obtained from the 239pu(nth,f) measurements. For these constants, the values proposed by Neiler et al. [8] were adopted, instead of those revised by Weissenberger et al. [9], in order to facilitate a comparison with older data. Moreover, both procedures yield consistent results in the case of 239pu(nth,f) [ 1 ]. The correction for prompt neutron emission is a delicate problem which we have examined carefully. It was assumed that a dependence on the pre-neutron fragment mass m7 (i = 1,2 is the fragment index) and total kinetic energy E~ [ 10] holds
(v)(m*) (E~)(m~) - E~ v(m*,E~) = (v)(m~) + (v)(m*) + ( u ) ( m f - m*) En '
(1)
where (v)(m*) is the average number of emitted prompt neutrons as a function of the pre-neutron fragment mass, (E;,)(m T) the average pre-neutron total kinetic energy as a function of the pre-neutron fragment mass, mf the mass of the compound nucleus and E, (8.6 MeV) the mean energy needed to emit a neutron. For 239pu(nth,f) we have available neutron data of Milton and Fraser [ 11], Apalin et al. [ 12] and evaluated data of Wahl [ 13]. From a comparison of the post-neutron fragment mass distribution of 239pu(nth,f) calculated with the three different neutron multiplicity curves it was
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
334
10 - - Wahl
zx
o Millon and Fraser Adalin el af.
a
a o
--
zx
o Neutron data from Wahl Radiochemical data
8
3
o~ &A
g2
~
a o
2
9LU
]
6
o 4
L
1
2
0
o i 90 110 130 150 P R E - N E U T R O N MASS (U)
70
0
170
7O
....
90 110 130 150 P O S T - N E U T R O N MASS (U)
170
10 --
o Neutron data from Milton & Fraser Radicchemical data
--
o Neutron data from Apalin et al, Radiochemical data
8
q tu
9uJ
6
==
2S 0 70
150 90 110 130 P O S T - N E U T R O N MASS (U)
170
0 - . 70
++
90 110 130 150 P O S T - N E U T R O N MASS (U)
170
1. Neutron emission data (top left) and corresponding 239pu(nth,f) post-neutron mass yields compared with the radiochemical data of Wahl [ 1 3 1 Fig.
concluded that the best results are obtained when using Wahl's evaluated neutron data [13] (see Fig. 1). However, since no detailed fission neutron data are available for the spontaneous fission decays, we used the 239pu(nm,f) data multiplied by the ratio F =
(ur(SF))
(2)
(/)T ( 239pu(nth, f) ) ) '
where v r are the total neutron multiplicities reported by Holden and Zucker [ 14]. This is a very acceptable approximation since it is well established that the shape of (v)(m*) is very similar for all fissioning systems in this mass region. In Table 2 the global characteristics of the fission fragments' mass and energy distributions of 239pu(nth,f) are summarized, showing a fairly good agreement with the data published in the literature.
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
335
Table 2 Main characteristics of the 239pu(nth,f) energy and mass distributions
(E~) erE* (m~) ~rm~
(MeV) (MeV) ( u) (u)
This work
Schillebeeckx et al. [61
Wagemans et al. [4]
Schmitt et al. [7]
Simon [15]
177.45 11.36 139.54 6.61
177.93 11.81 139.66 6.55
177.65 12.14 139.70 6.64
177.7 11.09 139.66 6,01
177.97 11.00 139.26 5.88
Table 3 Global characteristics of the fission fragments' mass and energy distributions of 236,238,240.242,244Pu(SF). The indicated errors are only statistical
236pu(SF) 238pu(SF) 24°Pu(SF) 242Pu (SF) 244pu(SF)
N
(E~) (MeV)
O'E; (MeV)
(M~I) (amu)
O'M~ (ainu)
1977 2051 11867 31722 17541
175.34-0.3 176.44-0.3 178.54-0.1 180.5 4 - 0 . 1 179.04-0.1
11.0 4-0.2 11.3 4-0.2 11.5 +0.1 11.524-0.04 I l.l 5:0.1
139.1 4-0.1 139.4 4-0.1 138.875:0.05 137.895:0.03 138.324-0.04
5.3:4-0.1 5.9 4-0.1 5.764-0.04 5.244-0.02 5.774-0.03
4. Results
The global characteristics of the fission fragments' mass and energy distributions of 236'238'24°'242'244pu(SF) are summarized in Table 3, N being the total number of events considered in the analysis. In Fig. 2 the average pre-neutron total kinetic energy (E~) is plotted as a function of the Z2/A 1/3 of the respective fissioning system, clearly showing a deviation from the linear trend suggested by Viola [ 16] and Unik [ 17]. This points to a local predominance of the microscopic corrections over the macroscopic behaviour. Fig. 3 shows the mass distributions of the 236'238'24°'242'244pu(SF) fragments. While one observes in Table 3 that the average heavy fragment mass (M~I) hardly varies, at least compared to the corresponding shifts in the light fragment mass, nevertheless important variations in the heavy fragment mass distributions arise when changing the mass of the fissioning system. In particular, it is apparent that for the two lighter systems, namely 236pu(SF) and 238pu(SF), the heavy fragment mass distributions peak around M~ = 141 while for the others the most probable mass fragmentation is around M~ = 136. This behaviour can be also observed in Figs. 4 and 5, where the two-dimensional energy and mass distributions and the corresponding contour plots are shown. The cold fission region was investigated by means of an improved method of selection of the fission events of interest. Instead of performing a selection on the basis of the light fragment energy, we kept those events satisfying the condition: Ek >~ m a x { Q - Sn} where Q - Sn is the Q-value of the fission reaction lowered with the neutron binding energy and the maximum is taken over all the possible charge splittings. This is equivalent to
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
336
182
.........
, .........
, .........
~Pu
, .........
, .........
• - - • This work
- -
Viola
-----
Unik
180
2,Opu
~i,~
~178 ~v
176
174 141'
1415
1420
1425
1430
1435
Z 2 / A ''a
Fig. 2. Average pre-neutron total kinetic energy release for 236,238,24°,242,244pu(SF) plotted versus Z2/A 1/3 of the fissioning system. Solid and long-dashed curves refer to Viola's [ 16] and Unik's [ 17] systematics, respectively. The indicated errors are only statistical.
10
. . . . . . . . .
, . . . . . . . . .
, . . . . . . . . .
~ . . 2"~Pu(SF) • • Z=Pu(SF)
• •" /
, . . . . . . . . .
A-..= 24°Pu(SF)
".
4 , ~ ~.
~,..2'~
.
. . o ...*
...
~.
244pu(SF )
ILl >LU
_>
~ 4 ._1
'si i s
"i
U!, i
i
I:I
LU rr
!
• i -I
'i t". '7
i~ '.
[y °
Yi::'=
• ,?_'. . i- ~ _ ' i ~
0 120
!:.,-~_ j. •
. . . . . . . . . . .
130
i . . . . . . . . .
140 PRE-NEUTRON
i
150 MASS
....
"ll~tl~tl;;l.~
160
(U)
Fig. 3. Pre-neutron heavy fragment mass distributions of 236'238'24°,242,244pu(SF).
337
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
23@Pu
~2tO
236Pu
x tso
170
tso
@
o
15o ~020
, .... ~3~ ~ .... ~40 ~.... 1~5 i .... i .... ~.... 125.... 130 ~50 ~ I~0 Heovy frogment moss (u)
.,i
2~IPu
~2oo l
o
-
~
~9o
a-
oleo
s 4.
/
16o
2. ~5~6o
,,~
o.
210 2OO 190
1~0135 ~
240Pu
~
15o
140120 125 ~Z,O
135
~,~o 145 1~ ~55 Heavy fragment moss
'~! (u)
2~Pu
~.21o
~.200 t, 190 180
zo
'°i ,
200 190 tSO
°
,3g,o ,z,*" 140,2 o
..,i
°
~
N
.... r .... i .... i .... i, , .~,. 125 13o ~35 14o 145 50
Heovy
°
,,i .... ls5 1so (u)
frogment mass
Fig. 4. Two-dimensional yield distributions Y( M~, E~ ) of 236,238,240PII(SF) (left) and corresponding contour plots (right).
338
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
242Pu
242Pu
~210 >
>,2O0
~ 190 N
~ laO 5
170
o
150
q
140120
244Pu
244Pu
~210 ~200 ~90
o 110
150
. , i
148120 "' ~Y (MeV)
. . . .
125
J
. . . .
130
t
. . . .
135
J . . . . i . . . . i .... ~ 140 145 150 155 160 Heovy frogment moss ( u )
Fig. 5. Two-dimensionalyield distributions Y(M~, E~) of 242'244pu(SF) (left) and correspondingcontour plots (right). calculate the Q-value of the reaction
Afzf
~ Auz H +
ALZL +
n.
(3)
As can be seen in Fig. 6, the two methods do not coincide especially near the symmetric and far asymmetric mass region. In Table 4 the main cold fission characteristics of the spontaneously fissioning isotopes as well as of 239pu(nth,f) are summarized. Again, the errors quoted are only statistical. It must be noted, however, that the main goal of the present experiments was not to investigate the cold fission phenomenon. So the experimental conditions were not optimized for such studies, which require a minimal amount of scattered fission fragments, hence samples of an extremely good quality are needed. In our case, instead of investigating the mass distribution of the cold fission events, we limit ourselves to check wether the proposed method gives consistent results. In Fig. 7 the relative cold fission
L. Dematt~ et aL/Nuclear Physics A 617 (1997) 331-346
339
240
NX
•
* Q
-----
S,
\
220
rr uJ Z uJ
-
EL > 117.16 MeV
200
180
.... 160 120
i .... 130
i ....
i ....
140 150 HEAVY FRAGMENT MASS (U)
i .... 160
170
Fig. 6. Comparison between the Q-value lowered by the neutron separation energy and the total kinetic energy corresponding to a fixed value of the light fragment energy for 239pu(nth,f). The mass excess data were taken from [18].
3,0 2~pu
7
v
q
2.5
LLI >.Z
24~pu
U) (/)
238pu
i'i- 2.0
9
24°pu
0 W "~ LU 1.5 112
1.0 2.10
244pu
2,15
2.20 NEUTRON MULTIPLICITY
2.25
Fig. 7. Relative cold fission yield plotted versus the average neutron multiplicity for 236,238,240,242,244Pu(SF).
340
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
Table 4 Main characteristics of the cold fission in 236'238'24°'242'244pu(SF) and 239pu(nth,f) N. of events 238pu(SF) 24°pu(SF) 242Pu(SF) 244pu(SF)
49 33 208 632 213
239Pu(nth,f)
2631
236 Pu(SF)
Rel. yield (%)
(Mh> (amu)
(El) (MeV)
2.36 4 - 0 . 3 4 1.58 4 - 0 . 2 8 1.73 :1:0.12 1.961 4-0.079 1.193 :t:0.082
140.79-4-1.21 139.534-0.88 136.994-0.40 136.844-0.20 139.844-0.39
199.40-t-1.68 197.734-1.03 200.634-0.44 201.54-1-0.24 197.804-0.43
0 . 1 9 0 0 4 - 0 . 0 0 3 7 136.414-0.14
205.944-0.14
0.6
--
0.5
Average=0.286 +/- 0.011
0.4
>-
0.3
0.2
0.1
f~
0'-234
I
I
I
I
236 238 240 242 MASS OF THE FISSIONING SYSTEM (U)
244
Fig. 8. Ratio between our results Yc and the neutronless fission probability P0 [ 14]. yield is plotted as a function of the average neutron multiplicity, which is a measure of the deformation of the spontaneously fissioning system. The expected correlation (the smaller the number of neutrons emitted, the higher the cold fission yield) clearly arises. Furthermore, we compared our results with the measurements of Po (the probability to have neutronless fission) for 236pu(SF), 238pu(SF), 24°pu(SF) and 242pu(SF) [14]. In Fig, 8 we see that the ratio Yc/Po is constant within the experimental uncertainties. Also this gives confidence to the selection criterion applied. The most striking observation to be made from Table 4 is the reduction of the cold fission yield by about one order o f magnitude between 24°pu(SF) and 239pu(nth,f). This points to a strong influence of the excitation energy on the cold fission yield, which is not surprising since the nuclear temperature of the fissioning system rises in the case of 239pu(nth,f) due to the binding of the neutron.
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
341
5. Discussion The problem of the interpretation of the fission fragments' energy and mass characteristics is one of the most challenging in the field of nuclear fission. Some years ago, the Random Neck Rupture model of Brosa et al. [ 19] received great attention because it gave a quantitative interpretation" of the mass and energy distributions of fission fragments in terms of fission modes (originally called fission "channels"). Despite the fact that the previous authors criticized the former Scission Point model [20], both models predict a strong influence of especially two nuclear configurations. In the terminology of the Random Neck Rupture model these are called Standard I and Standard II fission modes and they can be identified with the spherical N = 82 and the deformed N ~ 88 heavy fragment neutron shell closures of the Scission Point model, respectively. In Ref. [6] Schillebeeckx et al. performed a fission mode analysis of the spontaneous fission of 238pu, 24°pu and 242pu and of the thermal neutron induced fission of 239pu. Each fission mode was characterized by a Gaussian mass distribution around an average mass value, and a Gaussian conditional energy distribution around an average energy value according to the corresponding charge splitting:
Y ( E ' m ) ° c e x p [ - l ( m - (E- -m( )E),#)2(]Jme )x'p~[z-]l '(o v m
ore
/ J
(4)
Since for the Standard ! fission mode the two fragments are assumed to be spherical, (E) (m) has the following expression:
(E)l(m) = e 2 [ZH -- 0.5] [ZL + d
0.5]
'
(5)
where ZH, ZL are the heavy and light fragment charges, respectively, calculated within the Unchanged Charge Distribution (UCD), and d is a parameter representing the average distance between the two fragments. For the Standard II fission mode, in view of its higher deformation, a more general expression is proposed: (E)ll(m) = a0 +
aim + a2m2 ,
(6)
with a0, al, a2 being free parameters. In Ref. [21], Brosa and Knitter proposed a phenomenological conditional energy distribution curve that takes into account the asymmetries caused by the finite Q-value of the reaction:
Y(EIm) cx (2o0) - - 2exp
r [2
O-Zmtd
~'O" (LM -----L-"~ Lm)2 L---dd1.I '
(7)
with D = e2( Zu Z L ) / E and ZI4, ZL calculated by means of the UCD approximation. The parameters LM, Lm, Ld represent the fragment distance for which the yield is maximum (LM), the minimum distance (Lm) and the scale for the variation of Y(EIm) with D
(Ld).
342
L. DemattO et al./Nuclear Physics A 617 (1997) 331-346
Table 5 Characteristics of the fission modes in 236,238,24(I,242,244Pu (SF) W (%)
(M~I) (amu)
O'M* (amu)
(E,~) (MeV)
O'E* (MeV)
Standardl
236pu(SF) 238pu(sF) 24°pu(SF) 242pu(SF) 2~Pu (SF)
9.74-2.1 6.3-t-1.4 26.4±1.1 37.3±0.5 44.54- l.l
132.0 :t:0.3 133.5 ±0.2 134.604-0.06 134.68±0.03 134.91±0.05
2.7 ±0.4 1.6 ±0.2 2.67±0.06 2.69±0.02 3.41 ±0.04
191.3 4-1.0 193.1 ±0.6 190.6 4-0.2 190.3 4 - 0 . 1 187.0 ±0.2
6.5 -t-0.9 4.9 4-0.7 6.9 -4-0.1 6.81±0.06 7.34±0.09
Standardll
236pu(SF) 238pu(sF) 24°pu(SF) 242pu(SF) 244pu(sF)
90.3±2.1 93.7±1.4 73.6-t-1.1 62.74-0.5 55.5±1.1
140.3 ±0.2 140.1 4-0.2 140.37±0.10 139.654-0.05 140.88±0.13
5.2 ±0.1 5.8 i 0 . 2 5.734-0.05 5.344-0.03 5.85±0.05
173.3 ±0.3 175.0 4-0.3 174.53±0.13 174.844-0.08 172.854-0.12
9.9 ±0.2 11.0 4-0.2 9.564-0.09 9.184-0.05 8.99±0.07
A fission mode deconvolution of the five correlated energy and mass distributions has been applied. Since no reliable fission mode calculation for any Pu isotope is available, we kept all the parameters free. Moreover, the very low statistics of the symmetric and very asymmetric mass regions led us to consider only the Standard I and Standard II fission modes. We found, in agreement with [6], that in order to have good fits a spherical (Coulomb±an) expression for the energy must be used for the Standard I fission mode, while for the Standard II fission mode the fragment deformations are not negligible, and a simple Coulomb repulsion dependency leads to poor results. Consequently the conditional energy distribution described in Eq. (7) does not seem to work very well. In particular one has a systematic over-estimation of the average total kinetic energy for masses m* >~ 145 u. For this reason, in Ref. [22] a correction to the simple UCD approximation was proposed, linear with the mass m: ZH = ZUCD +
AZ
,
AZ
= ao + aim.
(8)
Thus modified, and applied in fitting the Standard II fission mode, these functions give about the same results as Eqs. ( 4 ) - ( 6 ) . Our results are summarized in Table 5, the errors quoted being statistical. A graphical representation of the deconvolution is shown in Figs. 9 and 10. The results of the fission mode deconvolution are in good agreement with Ref. [6] for 238pu(SF) and 24°pu(SF) but there is a discrepancy concerning the fission mode ratio of 242pu(SF). Due to the much larger statistics of the present data, these new results are likely to be more reliable. At this point we should warn again that the indicated errors are only statistical and that they should be incremented by a systematical error depending on the hypotheses underlying the deconvolution methods. The systematics of the fission mode characteristics show a dramatic change of the fission mode ratio throughout the five fissioning systems. This could be correlated with
343
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
~Pu(SF) 4
8
='~Pu(SF) I
~
=
g~
4
13o 140 15o PRE-NEUTRONMASS(U)
,20
o
160
~Pu(SF)
140
4
160 180 TOTALKINETICENERGY(MeV)
'=Pu(SF)
200
Ih
8
E 8 LU 6
cl
N a: 1
%o
130 140 150 PRE-NEUTRONMASS(U)
160
40
2'°Pu(SF)
160 180 TOTALKINETICENERGY(MeV)
=~Pu(SF)
200
1
3
d= 120
130 140 150 PRE-NEUTRONMASS(U)
160
040
160 180 TOTALKINETICENERGY(MeV)
200
Fig. 9. Fission mode deconvolution of 236"23S'240ptI(SF), The indicated errors are only statistical. the difference in the charge density between the fissioning system and that of the Standard I fission mode. In fact, from a study of the fission mode characteristics of the 241pu(nth,f) charge distribution [23], one observes that the average Standard I charge splitting is about 52/42. Taking into account the narrow width of the Standard I charge distribution and the fact that the proton number is the same for all the systems under investigation, it seems reasonable to assume that 5 2 / 4 2 is the dominant charge splitting o f the Standard
344
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
4i ~Pu(SF) 8
LU
w
,~4 1
0120
130 140 150 PRE-NEUTRON MASS (U)
160
140
160 180 TOTAL KINETIC ENERGY(MeV)
200
160 180 TOTAL KINETIC ENERGY (MeV)
200
='*Pu(SF) 3 t~
1
120
130 140 150 PRE-NEUTRON MASS (U)
160
0 140
Fig. 10. Fission mode deconvolution of 242,2'UPu(SF). The indicated errors are only statistical. Table 6 Charge densities of the five fissioning systems, their Standard I values and fission mode yields
(Z/A) F (Z/A)st. I Yst.I( % )
236pu(SF)
238pu(SF)
240pu(SF)
242pu(SF)
244pu(SF)
0.3983 0.3939 9.7
0.3950 0.3895 6.3
0.3917 0.3863 26.4
0.3884 0.3861 37.3
0.3852 0.3854 44.5
I fission mode for all five spontaneously fissioning plutonium isotopes. With this assumption we can calculate the Standard I charge density and compare it to the corresponding charge density of the fissioning system (see Table 6). One can easily see that the highest St.I/St.II fission mode ratio is reached in the case of 244pu(SF), where the difference between the charge densities is minimal. This again points to the dominant role of the charge equilibration in fission, as already observed previously, e.g. for 243Am(nth,f) [24]. The idea behind is that during the scission process first the protons are distributed between both fission fragments, as a consequence of the Coulomb repulsion. A neutron adjustement is believed to take place afterwards around each group of protons in order to respect the Z/N ratio of the fissioning system. This adjustement
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
345
will be facilitated if this last value equals Z/N of the fission mode. The results given in Table 5 and Figs. 9 and 10 also explain the behaviour of (E~) versus Z2/A I/3 shown in Fig. 2. The observed decrease of (E~) with increasing Z2/A 1/3 indeed simply reflects the reduced importance of the Standard I fission mode (with an (E~)-value around 190 MeV) and the corresponding growth of the Standard II mode having a much lower (E~).
6. Conclusion In the present work we could demonstrate the great impact of the neutron number on the fission fragments' mass and energy characteristics for five spontaneously fissioning Pu-isotopes. Especially the yield ratio of the Standard I and Standard II fission modes decreases by one order of magnitude when going from 244pu(SF) to 236pu(SF). This leads to a corresponding decrease of the total kinetic energy versus Z2/A U3 and causes a local deviation of the systematic trend governed by the macroscopic behaviour.
Acknowledgements The authors are deeply indebted to Dr. H. M~ten for his helpful suggestions concerning the cold fission. They would like to thank also Dr. H. Weigmann and Dr. F.-J. Hambsch for a careful reading of the manuscript.
References [ 1] E G6nnenwein, in The Nuclear Fission Process, ed. C. Wagemans (CRC Press, Boca Raton, USA, 1991). [2] M. de Jong, C. B6ckstiegel, H.-G. Clerc, A. Grewe, A. Junghans, J. MOiler, S. Steinh~iuser, J. Benlliure, A. Heinz, K.-H. Schmidt, M. Pf'titzner, A. Ignatyuk and G. Kudyaev, Proc. 4th Int. Conf. on Rad. Nucl. Beams, Omiya (Japan) 1996, in print. [ 3 ] M. Itkis, S. Mulgin, V. Okolovich, A. Rusanov, G. Smirenkin, M. Subbotin and S. Zhdanov, Proc. 2nd Int. Conf. on Dynamical Aspects of Nuclear Fission, ed. J. Kristiak and B. Pustylnik, Smolenice 1993, JINR Dubna Report E7-94-19 (1994) p. 160. [4] C. Wagemans, E. Allaert, A. Deruytter, R. Barth616my and P. Schillebeeckx, Phys. Rev. C 30 (1984) 218. [5] C. Wagemans, P. Schillebeeckx and A. Deruytter, Nucl. Phys. A 502 (1989) 287c. [6] P. Schillebeeckx, C. Wagemans, A. Deruytter and R. Barth~16my, Nucl. Phys. A 545 (1992) 623. [7] H. Schmitt, J. Neiler and E Walter, Phys. Rev. 141 (1966) 1146. [8] J. Neiler, E Walter and H. Schmitt, Phys. Rev. 149 (1966) 894. [9] E. Weissenberger, P. Geltenbort, A. Oed and E G6nnenwein, Nucl. Instr. and Meth. A 248 (1986) 506. [ 10] G. Barreau, A. Sicre, F. Ca'ftucoli, M. Asghar, T. Doan, B. Leroux, G. Martinez and T. Benfoughal, Nucl. Phys. A 432 (1985) 411. [11] J. Milton and J. Fraser, Ann. Rev. Nucl. Sci. 16 (1966) 1146. [121 V. Apalin, Yu. Gritsuyk, I. Kutikov, V. Lebedev and L. Mikaelian, Nucl. Phys. 71 (1965) 553. [131 A. Wahl, At. Data Nuci. Data Tables 39 (1988) 1. [ 14] N. Holden and M. Zucker, Proc. Advisory Group Meeting on Nuclear Standard Reference Data, Geel 1984, Rep. IAEA-TECDOC-335 (IAEA Vienna, 1985) p. 248.
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115] G. Simon, Ph.D. Thesis, Orsay, Nr. 3593 (1990). [16] V. Viola, K. Kwiatkowski and M. Walker, Phys. Rev. C 31 (1985) 1550. [17] J. Unik, J. Gindler, L. Glendenin, K. Flynn, A. Gorski and R. Sjoblom, Proc. 3rd IAEA Symp. on Physics and Chemistry of Fission, Rochester, 1973, vol. II (IAEA Vienna, 1974) p. 19. [ 181 1~ MGller, J. Nix, W. Myers and W. Swiatecki, At. Data and Nucl. Data Tables 59 (1995) 185. [19] U. Brosa, S. Grossmann and A. MUller, Phys. Rep. 197 (1990) 167. [20] B. Wilkins, E. Steinberg and R. Chasman, Phys. Rev. C 14 (1976) 1832. [21] U. Brosa and H.-H. Knitter, Proc. XVIII Int. Symp. on Nuclear Physics "Physics and Chemistry of Fission", Gaussig, H. M/irten and D. Seeliger eds., Report ZfK-732 (1988) p. 145. [22] L. Dematt6, C. Wagemans, P. D'hondt and A. Deruytter, Proc. Seminar on Fission "Pont D'Oye I11", ed. C. Wagemans, Report EUR 16295 EN (1995) p. 66. [23] P. Schillebeeckx, C. Wagemans, P. Geltenbort, F. G6nnenwein and A. Oed, Nuc. Phys. A 580 (1994) 15. [24] C. Wagemans, L. Dematt~, S. Potato6 and P. Schillebeeckx, Nucl. Phys. A 597 (1996) 188.
Nuclear Physics A 617 (1997) 331-346
Fragments' mass and energy characteristics in the spontaneous fission of 236pu, 238pu, 24°pu, 242pu, and 244pll "~" L. Dematt~ a, C. Wagemans b, R. Barthdl6my a, R D'hondt c, A. Deruytter a a CEC, JRC, Institute for Reference Materials and Measurements, B-2440 Geel, Belgium b Dept. of Subatomic and Radiation Physics, University of Gent, Proeftuinstraat 86, B-9000 Gent, Belgium c Studiecentrum voor Kernenergie, Boeretang 200, B-2400 Mol, Belgium
Received 17 December 1996
Abstract The results of a systematic study of the mass and energy of fission fragments emitted in the spontaneous fission of 236'138"24°'242'244puare reported. A comparison of the fragments' mass and energy distributions demonstrates the occurrence of different fission modes with varying relative probability. These results are discussed in terms of the random neck rupture model as well as in terms of the scission point model, showing the influence of the neutron number of the fissioning system. Finally an improved method of analysis allows the investigation of the cold fission region. (~) 1997 Elsevier Science B.V. Keywords: RADIOACTIVITY; Fission 236,238,24o,242,244Pu, measured complementary fragment kinetic energies; Deduced energy, mass distributions, mass-energy correlations; Performed fission mode analysis; Selected cold fission events PACS: 24.75.+i; 23.90.+w
1. Introduction D u r i n g the past decades, the fission fragments' charge mass and energy characteristics have been studied in detail for a large variety o f fissioning systems. A n excellent review was recently m a d e by G 6 n n e n w e i n [ 1 ]. Still, for several nuclides data are lacking or can * This work is part of the Ph.D. Thesis of L. Dematt~ presented at the University of Gent, Belgium. 0375-9474/97/$17.00 (~) 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 5 - 9 4 7 4 ( 9 7 ) 0 0 0 3 2 - 8
332
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
be improved, so the data base needed for a detailed systematic study of the dependence of the fission fragments' mass and energy characteristics as a function of the neutron (N) and proton ( Z ) number of the fissioning nucleus certainly needs to be completed. Important efforts have been made recently at Darmstadt [2] and FSU [3], however for fissioning systems at moderate excitation energy. In the present work, the results of a systematic study of the energy and mass characteristics of the fragments emitted in the spontaneous fission of a series of Pu isotopes (ranging from mass number A = 236 to A = 244) is reported. These isotopes make indeed an ideal field of investigation, having the same proton number, excitation energy, spin and parity, thus only differing by the number of neutrons. However, in order to allow a decent intercomparison of the results, all isotopes need to be studied under the same experimental conditions and using samples of comparable quality. For these reasons, a series of measurements was performed between 1982 and 1995 under very similar experimental conditions. Partial or preliminary results of these measurements were already reported previously [4-6]. Last year, the data taking was finalized and the whole set of results was analysed with an improved data reduction programme, which also enabled to look for fission modes and to select cold fission events. Detailed results of this analysis are now reported and discussed.
2. The experiment The kinetic energy and mass characteristics of the fission fragments were determined using the double energy method. A sample, consisting of a homogeneous mixture of the spontaneously fissioning isotope and 239pu, was sandwiched in between two silicon surface-barrier detectors cooled to a constant temperature of 4°C and mounted in the centre of a vacuum chamber. With such a setup, a geometry of almost 4 ~ can be reached, in order to compensate for the low counting rate of the spontaneous fission measurements. It was previously demonstrated that the results are quite independent from the geometry, provided that the quality of the samples is excellent [4]. Table 1 summarizes the characteristics of the samples used, all of them being prepared by the evaporation of the plutonium (under vacuum) on very thin backing foils, transparent for fission fragments. The experiments have been performed at the BR1 reactor of the SCK/CEN in Mol, Belgium, since 239pu(nth,f) is used for the calibration of the detection chain. This graphite-moderator reactor provides well-thermalized neutron beams with fluxes of a few 10 6 neutrons/cm2s and it was operated during the day and shutdown at night and during the weekend. Such an operation allows a regular, almost daily calibration, needed to verify the longterm stability of the setup. The pulseheights of coincident fission fragments were recorded event by event (list mode) in a 1024 x 1024 channels configuration and stored on a magnetic tape unit via a Hewlett Packard 1000E computer, that is also the terminal end of the data acquisition
L. Demattb et al./Nuclear Physics A 617 (1997) 331-346
333
Table 1 Characteristics of the evaporated samples Sample
236pu-239pu 238pu-239pu 24°pu-239pu 242pu-239pa
Isot. comp. (atoms %) 98.1% 1.9% 54% 46% 24% 76% 18%
239pu 236pa 239pu 238pu 239pu 24°pu 239pu
Manufacturer
Thickness (/zg/cm 2)
Backing
AERE, HarweU
1.3
222/zg/cm 2 Ni
IRMM, Geel
1.18
200/zg/cm 2 Ni
IRMM, Geel
19
1RMM, Geel
5.5
IRMM, Geel
7
29/zg/cm 2 P.I. 32 ~g/cm 2 El.
82% 242pu 244pu-239pu
50% 44% 1.5% 4.5%
239pu 244Ptl 24°pu 242pu
200/.tg/cm 2 Ni
system. The data were afterwards transferred to disk files on an IBM 4341 main frame, and finally to a workstation IBM RS/6000, were they have been analysed.
3. Data analysis The conversion of the pulseheights into mass and energy has been carried out by means of an iterative procedure described by Schmitt et al. [7], and incorporating the massdependent Schmitt-Neiler calibration procedure, the mass and momentum conservation relations and a correction for prompt neutron emission of the fission fragments. The detector calibration constants were obtained from the 239pu(nth,f) measurements. For these constants, the values proposed by Neiler et al. [8] were adopted, instead of those revised by Weissenberger et al. [9], in order to facilitate a comparison with older data. Moreover, both procedures yield consistent results in the case of 239pu(nth,f) [ 1 ]. The correction for prompt neutron emission is a delicate problem which we have examined carefully. It was assumed that a dependence on the pre-neutron fragment mass m7 (i = 1,2 is the fragment index) and total kinetic energy E~ [ 10] holds
(v)(m*) (E~)(m~) - E~ v(m*,E~) = (v)(m~) + (v)(m*) + ( u ) ( m f - m*) En '
(1)
where (v)(m*) is the average number of emitted prompt neutrons as a function of the pre-neutron fragment mass, (E;,)(m T) the average pre-neutron total kinetic energy as a function of the pre-neutron fragment mass, mf the mass of the compound nucleus and E, (8.6 MeV) the mean energy needed to emit a neutron. For 239pu(nth,f) we have available neutron data of Milton and Fraser [ 11], Apalin et al. [ 12] and evaluated data of Wahl [ 13]. From a comparison of the post-neutron fragment mass distribution of 239pu(nth,f) calculated with the three different neutron multiplicity curves it was
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
334
10 - - Wahl
zx
o Millon and Fraser Adalin el af.
a
a o
--
zx
o Neutron data from Wahl Radiochemical data
8
3
o~ &A
g2
~
a o
2
9LU
]
6
o 4
L
1
2
0
o i 90 110 130 150 P R E - N E U T R O N MASS (U)
70
0
170
7O
....
90 110 130 150 P O S T - N E U T R O N MASS (U)
170
10 --
o Neutron data from Milton & Fraser Radicchemical data
--
o Neutron data from Apalin et al, Radiochemical data
8
q tu
9uJ
6
==
2S 0 70
150 90 110 130 P O S T - N E U T R O N MASS (U)
170
0 - . 70
++
90 110 130 150 P O S T - N E U T R O N MASS (U)
170
1. Neutron emission data (top left) and corresponding 239pu(nth,f) post-neutron mass yields compared with the radiochemical data of Wahl [ 1 3 1 Fig.
concluded that the best results are obtained when using Wahl's evaluated neutron data [13] (see Fig. 1). However, since no detailed fission neutron data are available for the spontaneous fission decays, we used the 239pu(nm,f) data multiplied by the ratio F =
(ur(SF))
(2)
(/)T ( 239pu(nth, f) ) ) '
where v r are the total neutron multiplicities reported by Holden and Zucker [ 14]. This is a very acceptable approximation since it is well established that the shape of (v)(m*) is very similar for all fissioning systems in this mass region. In Table 2 the global characteristics of the fission fragments' mass and energy distributions of 239pu(nth,f) are summarized, showing a fairly good agreement with the data published in the literature.
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
335
Table 2 Main characteristics of the 239pu(nth,f) energy and mass distributions
(E~) erE* (m~) ~rm~
(MeV) (MeV) ( u) (u)
This work
Schillebeeckx et al. [61
Wagemans et al. [4]
Schmitt et al. [7]
Simon [15]
177.45 11.36 139.54 6.61
177.93 11.81 139.66 6.55
177.65 12.14 139.70 6.64
177.7 11.09 139.66 6,01
177.97 11.00 139.26 5.88
Table 3 Global characteristics of the fission fragments' mass and energy distributions of 236,238,240.242,244Pu(SF). The indicated errors are only statistical
236pu(SF) 238pu(SF) 24°Pu(SF) 242Pu (SF) 244pu(SF)
N
(E~) (MeV)
O'E; (MeV)
(M~I) (amu)
O'M~ (ainu)
1977 2051 11867 31722 17541
175.34-0.3 176.44-0.3 178.54-0.1 180.5 4 - 0 . 1 179.04-0.1
11.0 4-0.2 11.3 4-0.2 11.5 +0.1 11.524-0.04 I l.l 5:0.1
139.1 4-0.1 139.4 4-0.1 138.875:0.05 137.895:0.03 138.324-0.04
5.3:4-0.1 5.9 4-0.1 5.764-0.04 5.244-0.02 5.774-0.03
4. Results
The global characteristics of the fission fragments' mass and energy distributions of 236'238'24°'242'244pu(SF) are summarized in Table 3, N being the total number of events considered in the analysis. In Fig. 2 the average pre-neutron total kinetic energy (E~) is plotted as a function of the Z2/A 1/3 of the respective fissioning system, clearly showing a deviation from the linear trend suggested by Viola [ 16] and Unik [ 17]. This points to a local predominance of the microscopic corrections over the macroscopic behaviour. Fig. 3 shows the mass distributions of the 236'238'24°'242'244pu(SF) fragments. While one observes in Table 3 that the average heavy fragment mass (M~I) hardly varies, at least compared to the corresponding shifts in the light fragment mass, nevertheless important variations in the heavy fragment mass distributions arise when changing the mass of the fissioning system. In particular, it is apparent that for the two lighter systems, namely 236pu(SF) and 238pu(SF), the heavy fragment mass distributions peak around M~ = 141 while for the others the most probable mass fragmentation is around M~ = 136. This behaviour can be also observed in Figs. 4 and 5, where the two-dimensional energy and mass distributions and the corresponding contour plots are shown. The cold fission region was investigated by means of an improved method of selection of the fission events of interest. Instead of performing a selection on the basis of the light fragment energy, we kept those events satisfying the condition: Ek >~ m a x { Q - Sn} where Q - Sn is the Q-value of the fission reaction lowered with the neutron binding energy and the maximum is taken over all the possible charge splittings. This is equivalent to
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
336
182
.........
, .........
, .........
~Pu
, .........
, .........
• - - • This work
- -
Viola
-----
Unik
180
2,Opu
~i,~
~178 ~v
176
174 141'
1415
1420
1425
1430
1435
Z 2 / A ''a
Fig. 2. Average pre-neutron total kinetic energy release for 236,238,24°,242,244pu(SF) plotted versus Z2/A 1/3 of the fissioning system. Solid and long-dashed curves refer to Viola's [ 16] and Unik's [ 17] systematics, respectively. The indicated errors are only statistical.
10
. . . . . . . . .
, . . . . . . . . .
, . . . . . . . . .
~ . . 2"~Pu(SF) • • Z=Pu(SF)
• •" /
, . . . . . . . . .
A-..= 24°Pu(SF)
".
4 , ~ ~.
~,..2'~
.
. . o ...*
...
~.
244pu(SF )
ILl >LU
_>
~ 4 ._1
'si i s
"i
U!, i
i
I:I
LU rr
!
• i -I
'i t". '7
i~ '.
[y °
Yi::'=
• ,?_'. . i- ~ _ ' i ~
0 120
!:.,-~_ j. •
. . . . . . . . . . .
130
i . . . . . . . . .
140 PRE-NEUTRON
i
150 MASS
....
"ll~tl~tl;;l.~
160
(U)
Fig. 3. Pre-neutron heavy fragment mass distributions of 236'238'24°,242,244pu(SF).
337
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
23@Pu
~2tO
236Pu
x tso
170
tso
@
o
15o ~020
, .... ~3~ ~ .... ~40 ~.... 1~5 i .... i .... ~.... 125.... 130 ~50 ~ I~0 Heovy frogment moss (u)
.,i
2~IPu
~2oo l
o
-
~
~9o
a-
oleo
s 4.
/
16o
2. ~5~6o
,,~
o.
210 2OO 190
1~0135 ~
240Pu
~
15o
140120 125 ~Z,O
135
~,~o 145 1~ ~55 Heavy fragment moss
'~! (u)
2~Pu
~.21o
~.200 t, 190 180
zo
'°i ,
200 190 tSO
°
,3g,o ,z,*" 140,2 o
..,i
°
~
N
.... r .... i .... i .... i, , .~,. 125 13o ~35 14o 145 50
Heovy
°
,,i .... ls5 1so (u)
frogment mass
Fig. 4. Two-dimensional yield distributions Y( M~, E~ ) of 236,238,240PII(SF) (left) and corresponding contour plots (right).
338
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
242Pu
242Pu
~210 >
>,2O0
~ 190 N
~ laO 5
170
o
150
q
140120
244Pu
244Pu
~210 ~200 ~90
o 110
150
. , i
148120 "' ~Y (MeV)
. . . .
125
J
. . . .
130
t
. . . .
135
J . . . . i . . . . i .... ~ 140 145 150 155 160 Heovy frogment moss ( u )
Fig. 5. Two-dimensionalyield distributions Y(M~, E~) of 242'244pu(SF) (left) and correspondingcontour plots (right). calculate the Q-value of the reaction
Afzf
~ Auz H +
ALZL +
n.
(3)
As can be seen in Fig. 6, the two methods do not coincide especially near the symmetric and far asymmetric mass region. In Table 4 the main cold fission characteristics of the spontaneously fissioning isotopes as well as of 239pu(nth,f) are summarized. Again, the errors quoted are only statistical. It must be noted, however, that the main goal of the present experiments was not to investigate the cold fission phenomenon. So the experimental conditions were not optimized for such studies, which require a minimal amount of scattered fission fragments, hence samples of an extremely good quality are needed. In our case, instead of investigating the mass distribution of the cold fission events, we limit ourselves to check wether the proposed method gives consistent results. In Fig. 7 the relative cold fission
L. Dematt~ et aL/Nuclear Physics A 617 (1997) 331-346
339
240
NX
•
* Q
-----
S,
\
220
rr uJ Z uJ
-
EL > 117.16 MeV
200
180
.... 160 120
i .... 130
i ....
i ....
140 150 HEAVY FRAGMENT MASS (U)
i .... 160
170
Fig. 6. Comparison between the Q-value lowered by the neutron separation energy and the total kinetic energy corresponding to a fixed value of the light fragment energy for 239pu(nth,f). The mass excess data were taken from [18].
3,0 2~pu
7
v
q
2.5
LLI >.Z
24~pu
U) (/)
238pu
i'i- 2.0
9
24°pu
0 W "~ LU 1.5 112
1.0 2.10
244pu
2,15
2.20 NEUTRON MULTIPLICITY
2.25
Fig. 7. Relative cold fission yield plotted versus the average neutron multiplicity for 236,238,240,242,244Pu(SF).
340
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
Table 4 Main characteristics of the cold fission in 236'238'24°'242'244pu(SF) and 239pu(nth,f) N. of events 238pu(SF) 24°pu(SF) 242Pu(SF) 244pu(SF)
49 33 208 632 213
239Pu(nth,f)
2631
236 Pu(SF)
Rel. yield (%)
(Mh> (amu)
(El) (MeV)
2.36 4 - 0 . 3 4 1.58 4 - 0 . 2 8 1.73 :1:0.12 1.961 4-0.079 1.193 :t:0.082
140.79-4-1.21 139.534-0.88 136.994-0.40 136.844-0.20 139.844-0.39
199.40-t-1.68 197.734-1.03 200.634-0.44 201.54-1-0.24 197.804-0.43
0 . 1 9 0 0 4 - 0 . 0 0 3 7 136.414-0.14
205.944-0.14
0.6
--
0.5
Average=0.286 +/- 0.011
0.4
>-
0.3
0.2
0.1
f~
0'-234
I
I
I
I
236 238 240 242 MASS OF THE FISSIONING SYSTEM (U)
244
Fig. 8. Ratio between our results Yc and the neutronless fission probability P0 [ 14]. yield is plotted as a function of the average neutron multiplicity, which is a measure of the deformation of the spontaneously fissioning system. The expected correlation (the smaller the number of neutrons emitted, the higher the cold fission yield) clearly arises. Furthermore, we compared our results with the measurements of Po (the probability to have neutronless fission) for 236pu(SF), 238pu(SF), 24°pu(SF) and 242pu(SF) [14]. In Fig, 8 we see that the ratio Yc/Po is constant within the experimental uncertainties. Also this gives confidence to the selection criterion applied. The most striking observation to be made from Table 4 is the reduction of the cold fission yield by about one order o f magnitude between 24°pu(SF) and 239pu(nth,f). This points to a strong influence of the excitation energy on the cold fission yield, which is not surprising since the nuclear temperature of the fissioning system rises in the case of 239pu(nth,f) due to the binding of the neutron.
L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
341
5. Discussion The problem of the interpretation of the fission fragments' energy and mass characteristics is one of the most challenging in the field of nuclear fission. Some years ago, the Random Neck Rupture model of Brosa et al. [ 19] received great attention because it gave a quantitative interpretation" of the mass and energy distributions of fission fragments in terms of fission modes (originally called fission "channels"). Despite the fact that the previous authors criticized the former Scission Point model [20], both models predict a strong influence of especially two nuclear configurations. In the terminology of the Random Neck Rupture model these are called Standard I and Standard II fission modes and they can be identified with the spherical N = 82 and the deformed N ~ 88 heavy fragment neutron shell closures of the Scission Point model, respectively. In Ref. [6] Schillebeeckx et al. performed a fission mode analysis of the spontaneous fission of 238pu, 24°pu and 242pu and of the thermal neutron induced fission of 239pu. Each fission mode was characterized by a Gaussian mass distribution around an average mass value, and a Gaussian conditional energy distribution around an average energy value according to the corresponding charge splitting:
Y ( E ' m ) ° c e x p [ - l ( m - (E- -m( )E),#)2(]Jme )x'p~[z-]l '(o v m
ore
/ J
(4)
Since for the Standard ! fission mode the two fragments are assumed to be spherical, (E) (m) has the following expression:
(E)l(m) = e 2 [ZH -- 0.5] [ZL + d
0.5]
'
(5)
where ZH, ZL are the heavy and light fragment charges, respectively, calculated within the Unchanged Charge Distribution (UCD), and d is a parameter representing the average distance between the two fragments. For the Standard II fission mode, in view of its higher deformation, a more general expression is proposed: (E)ll(m) = a0 +
aim + a2m2 ,
(6)
with a0, al, a2 being free parameters. In Ref. [21], Brosa and Knitter proposed a phenomenological conditional energy distribution curve that takes into account the asymmetries caused by the finite Q-value of the reaction:
Y(EIm) cx (2o0) - - 2exp
r [2
O-Zmtd
~'O" (LM -----L-"~ Lm)2 L---dd1.I '
(7)
with D = e2( Zu Z L ) / E and ZI4, ZL calculated by means of the UCD approximation. The parameters LM, Lm, Ld represent the fragment distance for which the yield is maximum (LM), the minimum distance (Lm) and the scale for the variation of Y(EIm) with D
(Ld).
342
L. DemattO et al./Nuclear Physics A 617 (1997) 331-346
Table 5 Characteristics of the fission modes in 236,238,24(I,242,244Pu (SF) W (%)
(M~I) (amu)
O'M* (amu)
(E,~) (MeV)
O'E* (MeV)
Standardl
236pu(SF) 238pu(sF) 24°pu(SF) 242pu(SF) 2~Pu (SF)
9.74-2.1 6.3-t-1.4 26.4±1.1 37.3±0.5 44.54- l.l
132.0 :t:0.3 133.5 ±0.2 134.604-0.06 134.68±0.03 134.91±0.05
2.7 ±0.4 1.6 ±0.2 2.67±0.06 2.69±0.02 3.41 ±0.04
191.3 4-1.0 193.1 ±0.6 190.6 4-0.2 190.3 4 - 0 . 1 187.0 ±0.2
6.5 -t-0.9 4.9 4-0.7 6.9 -4-0.1 6.81±0.06 7.34±0.09
Standardll
236pu(SF) 238pu(sF) 24°pu(SF) 242pu(SF) 244pu(sF)
90.3±2.1 93.7±1.4 73.6-t-1.1 62.74-0.5 55.5±1.1
140.3 ±0.2 140.1 4-0.2 140.37±0.10 139.654-0.05 140.88±0.13
5.2 ±0.1 5.8 i 0 . 2 5.734-0.05 5.344-0.03 5.85±0.05
173.3 ±0.3 175.0 4-0.3 174.53±0.13 174.844-0.08 172.854-0.12
9.9 ±0.2 11.0 4-0.2 9.564-0.09 9.184-0.05 8.99±0.07
A fission mode deconvolution of the five correlated energy and mass distributions has been applied. Since no reliable fission mode calculation for any Pu isotope is available, we kept all the parameters free. Moreover, the very low statistics of the symmetric and very asymmetric mass regions led us to consider only the Standard I and Standard II fission modes. We found, in agreement with [6], that in order to have good fits a spherical (Coulomb±an) expression for the energy must be used for the Standard I fission mode, while for the Standard II fission mode the fragment deformations are not negligible, and a simple Coulomb repulsion dependency leads to poor results. Consequently the conditional energy distribution described in Eq. (7) does not seem to work very well. In particular one has a systematic over-estimation of the average total kinetic energy for masses m* >~ 145 u. For this reason, in Ref. [22] a correction to the simple UCD approximation was proposed, linear with the mass m: ZH = ZUCD +
AZ
,
AZ
= ao + aim.
(8)
Thus modified, and applied in fitting the Standard II fission mode, these functions give about the same results as Eqs. ( 4 ) - ( 6 ) . Our results are summarized in Table 5, the errors quoted being statistical. A graphical representation of the deconvolution is shown in Figs. 9 and 10. The results of the fission mode deconvolution are in good agreement with Ref. [6] for 238pu(SF) and 24°pu(SF) but there is a discrepancy concerning the fission mode ratio of 242pu(SF). Due to the much larger statistics of the present data, these new results are likely to be more reliable. At this point we should warn again that the indicated errors are only statistical and that they should be incremented by a systematical error depending on the hypotheses underlying the deconvolution methods. The systematics of the fission mode characteristics show a dramatic change of the fission mode ratio throughout the five fissioning systems. This could be correlated with
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~Pu(SF) 4
8
='~Pu(SF) I
~
=
g~
4
13o 140 15o PRE-NEUTRONMASS(U)
,20
o
160
~Pu(SF)
140
4
160 180 TOTALKINETICENERGY(MeV)
'=Pu(SF)
200
Ih
8
E 8 LU 6
cl
N a: 1
%o
130 140 150 PRE-NEUTRONMASS(U)
160
40
2'°Pu(SF)
160 180 TOTALKINETICENERGY(MeV)
=~Pu(SF)
200
1
3
d= 120
130 140 150 PRE-NEUTRONMASS(U)
160
040
160 180 TOTALKINETICENERGY(MeV)
200
Fig. 9. Fission mode deconvolution of 236"23S'240ptI(SF), The indicated errors are only statistical. the difference in the charge density between the fissioning system and that of the Standard I fission mode. In fact, from a study of the fission mode characteristics of the 241pu(nth,f) charge distribution [23], one observes that the average Standard I charge splitting is about 52/42. Taking into account the narrow width of the Standard I charge distribution and the fact that the proton number is the same for all the systems under investigation, it seems reasonable to assume that 5 2 / 4 2 is the dominant charge splitting o f the Standard
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L. Demattd et al./Nuclear Physics A 617 (1997) 331-346
4i ~Pu(SF) 8
LU
w
,~4 1
0120
130 140 150 PRE-NEUTRON MASS (U)
160
140
160 180 TOTAL KINETIC ENERGY(MeV)
200
160 180 TOTAL KINETIC ENERGY (MeV)
200
='*Pu(SF) 3 t~
1
120
130 140 150 PRE-NEUTRON MASS (U)
160
0 140
Fig. 10. Fission mode deconvolution of 242,2'UPu(SF). The indicated errors are only statistical. Table 6 Charge densities of the five fissioning systems, their Standard I values and fission mode yields
(Z/A) F (Z/A)st. I Yst.I( % )
236pu(SF)
238pu(SF)
240pu(SF)
242pu(SF)
244pu(SF)
0.3983 0.3939 9.7
0.3950 0.3895 6.3
0.3917 0.3863 26.4
0.3884 0.3861 37.3
0.3852 0.3854 44.5
I fission mode for all five spontaneously fissioning plutonium isotopes. With this assumption we can calculate the Standard I charge density and compare it to the corresponding charge density of the fissioning system (see Table 6). One can easily see that the highest St.I/St.II fission mode ratio is reached in the case of 244pu(SF), where the difference between the charge densities is minimal. This again points to the dominant role of the charge equilibration in fission, as already observed previously, e.g. for 243Am(nth,f) [24]. The idea behind is that during the scission process first the protons are distributed between both fission fragments, as a consequence of the Coulomb repulsion. A neutron adjustement is believed to take place afterwards around each group of protons in order to respect the Z/N ratio of the fissioning system. This adjustement
L. Dematt~ et al./Nuclear Physics A 617 (1997) 331-346
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will be facilitated if this last value equals Z/N of the fission mode. The results given in Table 5 and Figs. 9 and 10 also explain the behaviour of (E~) versus Z2/A I/3 shown in Fig. 2. The observed decrease of (E~) with increasing Z2/A 1/3 indeed simply reflects the reduced importance of the Standard I fission mode (with an (E~)-value around 190 MeV) and the corresponding growth of the Standard II mode having a much lower (E~).
6. Conclusion In the present work we could demonstrate the great impact of the neutron number on the fission fragments' mass and energy characteristics for five spontaneously fissioning Pu-isotopes. Especially the yield ratio of the Standard I and Standard II fission modes decreases by one order of magnitude when going from 244pu(SF) to 236pu(SF). This leads to a corresponding decrease of the total kinetic energy versus Z2/A U3 and causes a local deviation of the systematic trend governed by the macroscopic behaviour.
Acknowledgements The authors are deeply indebted to Dr. H. M~ten for his helpful suggestions concerning the cold fission. They would like to thank also Dr. H. Weigmann and Dr. F.-J. Hambsch for a careful reading of the manuscript.
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