fulltext

Binary and ternary cold fission of

252

Cf

(  ) A. SANDULESCU( 1 )( 2 )( 3 )( 4 ), A. FLORESCU( 1 )( 2 )( 4 ), F. CARSTOIU( 1 ),A. V. RAMAYYA( 2 ), J. H. HAMILTON( 2 ), J.K. HWANG( 2 ), B. R. S. BABU( 2 )and W. GREINER( 2 )( 3 )( 3 ) ( 1

) Institute of Atomic Physics - Bucharest P.O.Box MG-6 (

2

) Physics Department, Vanderbilt University - Nashville TN 37235 (

3

) Institut f¨ur Theoretische Physik der J.W.Goethe Universit¨at - Frankfurt am Main (

4

) Joint Institute for Heavy Ion Research - Oak Ridge TN 37831

(ricevuto il 13 Giugno 1997; approvato il 15 Ottobre 1997)

Summary. — Experimental integral isotopic yields for the spontaneous cold

(neutron-less) binary and-ternary fission of 252

Cf were obtained by using triple - -

coin-cidence technique at Gammasphere facility. For the first time10

Be- and14

C-ternary fission isotopic yields were also measured. The results are interpreted within simple cluster model with binary and ternary potential barriers generated by M3Y effective interaction and ground-state deformation.

PACS 25.85.Ca – Spontaneous fission. PACS 23.60 –decay.

PACS 23.70 – Heavy-particle decay. PACS 01.30.Cc – Conference proceedings.

In recent times, many new experimental data concerning the spontaneous cold frag-mentations of nuclei have been obtained. These include exotic decays with emission of heavy clusters having masses fromA

L= 12 to 34 [1]. In addition the cold fission of many

actinide nuclei produce fragments with masses from70 to166 atomic mass units [2-6].

Subsequently, several cases of such heavy clusters emitted with nearly zero internal exci-tation energy are now experimentally observed. They all confirm the theoretical predic-tions based on the idea of the cold rearrangements of large groups of nucleons from the ground state of the initial nucleus to the ground states of the two final fragments [7, 8].

For the cold fission studies, the Cf and Cm isotopes constitute a transition region be-tween the lighter actinides such as Th, U and Pu, and the bimodal fission region of Fm and Md nuclei. In the lighter actinides, the highest yields are observed when the heavier fragment is in the vicinity of132

Sn and the lighter fragment is strongly deformed [6]. In-deed, the experimental data for252

Cf (SF) [2] and248

Cm (SF) [3] indicate a preference

( 

)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and

Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.

close to the corresponding binary or ternary decay energyQor even equal to it. In order

to achieve such large TKE values, the scission point configurations should correspond to very compact shapes and deformations for final fragments close to those of their ground states [12, 13].

Based on a simple cluster model, we calculated the relative isotopic yields for the spon-taneous cold (neutronless) binary [14] and-ternary fission of

252

Cf [15]. These isotopic yields are given by the ratio of the penetrability through the binary (or ternary) potential barrier between the two (respectively three) final fragments, over the sum of penetrabili-ties for all possible binary (or ternary) fragmentations. We evaluated [14, 15] the nuclear plus Coulomb interaction between two coaxial deformed fragments with the help of the double folding potential defined asV

M3Y (R )= R dr 1 dr 2  1 (r 1 ) 2 (r 2 )v(r 12 )which

con-tains the corresponding M3Y nucleon-nucleon interaction. The two final nuclei are viewed as coaxial spheroids (”nose-to-nose” configuration) [14].

In our simple cluster model, similar to the one-body model used for the description of cluster radioactivity [1, 8], no preformation factors for the fragments are taken into ac-count. An advantage of this model is that the barrier between the two heavy fragments (for binary fission) and the barrier between the cluster and the heavier fragments (for ternary fission) can be calculated quite accurately due to the fact that the touching config-urations are situated inside of the barriers. TheQ-values and the deformation parameters

contain all nuclear shell and pairing effects of the corresponding fragments. In the case of cold ternary fission, due to the fact that the barrier between the two heavier fragments is much thinner than the barrier between the cluster and the heavier fragments, in our model first the two heavier fragments penetrate the potential barrier between them and later an LCP is emitted. In such a model the mass distributions of the heavier frag-ments are not influenced by the cluster trajectories. Consequently these mass distribu-tions are very similar to that of the cold binary fission of the daughter nucleus, e.g.248

Cm foremission and, respectively,

242

Pu for10

Be emission from252

Cf. This mechanism is supported by the comparison between the experimental data concerning the fission mass distributions in binary and alpha-accompanied fission of235

U [16]. On the other hand, sequential emission of an alpha-particle or a heavier cluster from the already separated fragments is not possible due to the fact that these are very neutron-rich nuclei with neg-ativeQ

 values. In addition, the presence of a Coulomb barrier (with typical height of

12 – 18 MeV for alpha in this region) further hinders emission of clusters in comparison with the neutron evaporation process at excitation energies above 6 – 7 MeV. Also, it is known that for the mass distributions in asymmetric spontaneous fission of the lighter actinides compared to the heavier ones, the position of the heavy mass peak remains un-changed while the light mass peak moves to lowerA values [10]. Thus we conclude that

Fig. 1. – The potential barrier (in MeV) in the (x;y) plane between the 10

Be cluster and the two heavier fragments142

Xe and100

Zr for a fixed distanceRHL =12:6fm between the heavier

frag-ments.

the mass distribution of fission fragments in cold ternary fission is almost identical with the mass distribution for the cold binary fission of the daughter nucleus.

At the scission configuration the two heavier fragments were assumed to be coaxial spheroids in contact at their tips. In the laboratory frame of reference thex-axis was

taken as the initial fissioning axis of the two heavier fragments with the origin at their point of contact, and we assumed that the three bodies are moving in the (x;y) plane. The

potential barriersV HL

,Q

HLbetween the two fragments are high but rather thin with

a width of about 2 to 3 fm. The cluster is initially situated in the potential well which is created by the sum of the potentials between the cluster and the two heavier fragments (see fig. 1). As the distance between the two heavier fragments increases the cluster potential well is narrowing and its bottom rises, forcing the LCP to jump over the barrier and to be repelled along they-axis by the Coulomb field of the other two fragments. For

the two fragments, the exit point from their potential barrier is typically between 15 and 16 fm, which supports our cluster model. Evidently from the top of the cluster barrier we can compute classical trajectories of all fragments as a function of time.

We estimated the penetrabilitiesP(A;Z)through the double folded potential barrier

in the framework of the WKB approximation.

The accurate evaluation of theQ-values is very important since the WKB

penetrabili-ties are very sensitive to them. We obtained theQ-values from recent experimental mass

tables [17]. The deformation parameters which we used were taken from the tables of ref. [18], and for some isotopes we employed the deformation values deduced from cold fission data [12, 19] which are similar or slightly larger in some cases (e.g. 5%to8%larger for

the Sr, Zr and Mo isotopes) than those from ref. [18]. The calculated values of the pen-etrabilities are very sensitive to the assumed deformations of the final fragments, since a10%increase in the

2 values leads up to an order of magnitude increase of the

pen-etrabilities. Consequently our calculated penetrabilities should contain an uncertainty factor of about ten. Nevertheless, the relative yields should not change significantly. The higher multipoles like the octupole can also play an important role introducing some ad-ditional uncertainties. We stress again that our theoretical isotopic yields correspond to those neutronless fragmentations with all final nuclei emitted in their ground state and

Fig. 2. – Triple -coincidence spectrum for neutronless 10

Be ternary fission of252

Cf.

consequently these yields are computed for TXE=0. The theoretical yields were calculated asY(A

L ;Z L )=P(A L ;Z L )= P A L Z L P(A L ;Z L )

for the most frequent spontaneous cold neutronless fragmentations of252

Cf. The highest binary yields are predicted for fragment masses98  A

L

110 and142  A H

 154

and for fragment charges38  Z L

 44and54  Z H

 60, respectively.

In order to study the spontaneous fission of252

Cf, a source with a strength of610 4

fissions/s was placed at the center of the new implemented Gammasphere with 72 Comp-ton suppressed Ge detectors. Triple or higher-fold coincidence events were recorded. A

- - ”coincidence cube” was built using the RADWARE program [20]. In the fission of 252

Cf, about 100 different final fragments are produced. After the fission into two primary fragments, these primary fragments emit several neutrons until the excitation energy of the fragment is below the neutron binding energy (6 MeV). The resulting excited

frag-ments are too neutron-rich to emit charged particles such as protons or alpha particles. Then the secondary fragments decay to their ground states by the emission of -rays.

Also cold (neutronless) fragmentations are possible.

By using the threefold coincidences, the binary and ternary fragmentations were stud-ied. The neutron multiplicities and the correlated yields of even-Zsecondary fragments

were determined by setting a double gate on the light fragment and measuring the gamma intensities in the heavy fragment with different numbers of evaporated neutrons. For the odd-odd fragmentations we considered the total intensities obtained from summing all the gamma transitions to the ground state. Correcting the number of counts for the detector efficiency and for internal conversion, we obtain the gamma transition relative yields for the different neutron channels. Then the sum of these ground-state transition yields is normalized for a given light fragment in the Wahl Tables which give the estimated total isotopic yields in the binary fission of252

Cf [14]. If one isotope from the heavy fragment is missing we evaluate its corresponding yield by interpolation from its neighbors with a

Fig. 3. – Triple -coincidence spectrum for neutronless 14

C ternary fission of252

Cf.

Gaussian. A cross-check is necessary by imposing a double gate on the heavy fragment and determining the gamma intensities of the corresponding correlated light fragments. Again the sum of these yields is normalized to the Wahl Tables [21] for the heavy fragment. The final isotopic yields must be quite similar. When large discrepancies are observed a new determination is necessary in order to account for the doublets which may appear because of transitions with practically identical energies. In cases where the background is large a third determination was made by introducing a gate on the light fragment and another gate on the heavy fragment. We should like to mention that presently the spec-tra of odd-Z nuclei are not known, which does not allow us to determine experimentally

odd-Zisotopic yields.

In the case of cold (neutronless) ternary fission of252

Cf accompanied by an emitted LCP with massA

c and charge Z

c, we look at triple

-coincidences between two even-Z

fragments with the sum of chargesZ=98,Z

cand sum of masses

A=252,A

c. In fig. 2

we present the triple -coincidence spectrum obtained in the neutronless 10

Be-ternary fission with136

Te and106

Mo as heavier fragments. The double gate is set on the 606.6 (2 + ! 0 + ) keV transition in136 Te and 510.5 (6 + ! 4 + ) keV transition in106 Mo. Other ground-state band transitions such as 352.4 (6

+ !4 + ) and 424.0 (4 + !2 + ) keV in136 Te, and respectively 350.5 (4 + ! 2 + ) and 171.6 (2 + ! 0 + ) keV in106

Mo are clearly seen as evidence for the cold (neutronless)10

Be-accompanied ternary fission of252

Cf. As another example we present in fig. 3 a triple -coincidence spectrum for the neutronless

14

C-ternary fission with the double gate set on the 457.4 (4

+ ! 2 + ) keV transition in140 Xe and 289.0 (4 + ! 2 + ) keV transition in98

Sr. The ground-state band transitions at 376.7 (2 + !0 + ) and 582.5 (6 + !4 + ) keV in140

Xe, and respectively 144.3 (2 +

!0 +

) keV in

98

Sr are again observed as evidence for the cold (neutronless)14

C-accompanied ternary fission of252

Cf.

In table I we present the experimental isotopic yields for the spontaneous cold (neu-tronless) binary and-ternary fission of

252

Cf. The highest yields are found for the Zr/Ce and Mo/Ba binary splittings as predicted by our calculation [14] and respectively for the

Zr Ce Ba 0.082 0.010 102 Zr 150 Ce 0.020.01 146 Ba 0.0100.004 103 Zr 149 Ce 0.100.01 145 Ba 0.0840.029 104 Zr 148 Ce 0.020.01 144 Ba 0.0170.008 104 Mo 148 Ba 0.020.01 144 Xe 105 Mo 147 Ba 0.200.07 143 Xe 106 Mo 146 Ba 0.080.05 142 Xe 0.0180.007 107 Mo 145 Ba 0.240.06 141 Xe 0.0300.014 108 Mo 144 Ba 0.150.06 140 Xe 0.0070.003 110 Ru 142 Xe 0.100.05 138 Te 111 Ru 141 Xe 0.140.06 137 Te 112 Ru 140 Xe 0.040.02 136 Te 0.0110.006 116 Pd 136 Te 0.050.02 132 Sn 0.0060.003

Sr/Ce and Zr/Ba-ternary splittings [15]. We should like to stress that all the

neutron-less binary and-ternary even-Z fragmentations of 252

Cf which have predicted relative isotopic yields larger than 0.1% (see refs. [14, 15]) and whose fragments have known low-energy -transitions, were experimentally identified in table I. In table II we present for

the first time the cold10

Be and14

C-ternary fission yields observed in the same experi-ment. Important yields exhibit here the Sr/Ba, Zr/Xe and Zr/Te ternary fragmentations.

TABLEII. – Experimental isotopic yields for the10

Be- and12

C-ternary fission of252

Cf. See

cap-tion to table I for details.

Y (10 Be-ternary) (%) Y (14 C-ternary) (%) 96 Sr 146 Ba 0.00430.0031 142 Xe 98 Sr 144 Ba 0.01280.0080 140 Xe 0.00730.0038 100 Sr 142 Ba 0.00130.0010 138 Xe 0.0005 100 Zr 142 Xe 0.01900.0070 138 Te 102 Zr 140 Xe 0.00500.0020 136 Te 0.00510.0019 104 Zr 138 Xe 0.00660.0022 134 Te 0.00340.0012 106 Mo 136 Te 0.02930.0218 132 Sn 0.02200.0170 108 Mo 134 Te 0.0016 130 Sn 0.00230.0011 110 Ru 132 Sn 0.00330.0009 128 Cd 112 Ru 130 Sn 0.01750.0050 126 Cd

We mention here that we found enhanced experimental yields for the cold binary and ternary fission in which heavier partners are Ba isotopes with masses ranging from 144 to 147. Their higher yields could be attributed to the static octupole deformation observed in this region [22], since octupole shapes at the scission configuration could significantly lower the Coulomb barrier and increase the penetrability between the final fragments.

A few of the cold binary and-ternary fragmentations presented in table I involve

odd-odd splittings, and one can observe that their corresponding experimental yields are comparable or even higher than the yields for the even-even neighbours. The predicted yields [14, 15] do not include differences in the level densities near the ground states of the even-even and odd-odd nuclei. This feature of cold fragmentations suggests that either the cold fission yields are influenced by the level density of the fragments [6, 23] or that the deformations of odd fragments are larger than those of the corresponding even ones.

We stress again that the experimentally determined isotopic yields are integrated yields. In the spontaneous fission experiment of252

Cf the majority of the binary and ternary splittings lead to highly excited final nuclei which after neutron evaporation are decaying to the lowest states by cascades. Less frequently, there are also cold

fragmen-tations which leave the final nuclei in their ground or first excited states. We define these cold fission experimental yields as integrated yields since they collect the contributions of all (neutronless) transitions over a whole range of TXEs from zero up to at least the neutron binding energy, from where the evaporation of a first neutron becomes possible.

We have shown here that a simple cluster model is able to predict correctly the most important cold fragmentations observed in the spontaneous cold binary and ternary fis-sion of the nucleus252

Cf. In this region both the light and heavy fragments have important ground-state deformations that give rise to potential barriers between the two final nuclei which are significantly lowered, leading to increased penetrabilities and yields. Neverthe-less the scission configurations for these cold fragmentations are still much more compact than in the case of usual ”hot” fission.

The cold ternary fission of a heavy nucleus (252

Cf) was experimentally observed for the first time by using the triple -coincidence techniques, as we have shown above. The

cold ternary fission events are characterized by very low TXEs of the final fragments and high TKEs tending to theQ

tvalue associated to those splittings. Thus the

configura-tion of the scission point should be described in these cases by very compact shapes, the fragments being deformed only as permitted by their ground-state deformations. It was already shown that for cold binary fragmentations, the ground-state deformations are a key ingredient for the correct prediction of the most favoured splittings and of the isotopic yields [12-14, 19].

Finally we remark that for cold ternary fission the initial scission configurations are rather well known: the fragment deformations should be essentially that of the ground-state deformations. Only the initial position and velocity distributions of the LCPs have to be determined from their final kinetic energy and angular distributions. Presently the spontaneous cold fission of three nuclides, namely252

Cf,248

Cm and242

Pu, is under study using the triple gamma coincidence technique. The same set of deformation parameters should also explain the cold binary fission yields in all three cases so that we expect to extract new experimental information over different nuclear deformation regions. In ad-dition the cold alpha ternary fission yields of252

Cf should be similar with the cold binary fission yields of248

Cm and the cold10

Be -ternary fission yields of the same parent nu-cleus should be similar to the cold binary fission yields of242

Pu [24]. Consequently many cross-checks are possible.

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