IL NUOVO CIMENTO VOL. 110 A, N. 6 Giugno 1997 NOTE BREVI
On the second mode of spontaneous fission of
252Cf
G. MOUZE(1) and R. A. RICCI(2)
(1) Faculté des Sciences - 06108 Nice cedex 2, France
(2) INFN - Legnaro, Padova, Italy
(ricevuto il 10 Maggio 1997; approvato il 4 Giugno 1997)
Summary. — The second mode of fission of 152Cf could result from cluster
configurations in the Ba fragments. PACS 25.85 – Fission reactions.
PACS 21.20 – Properties of nuclei; nuclear energy levels.
1. – Introduction
Ter-Akopian et al. [1], in a study of correlated fragment pairs emitted in spontaneous fission of 252Cf, have measured the independent yields of 139 individual secondary fragment pairs of five charge splits, ZL/ZH4 46 /52 , 44 /54 , 42 /56 , 40 /58 and 38 /60 , by detecting coincidences between prompt gamma-rays. These authors have observed that 70% of the fission events where more than 7 neutrons are evaporated occur for the MoOBa charge split. The experimental data for this charge split can be fitted by assuming that a second mode of fission exists, characterized by a mean total kinetic energy of only 153 MeV, instead of 189 MeV for the normal mode. The possibility of the formation of hyperdeformed barium nuclei has been put forward [1].
2. – The spontaneous fission of252Cf from the point of view of a cluster model The cluster model of asymmetric fission [2] assumes that a primordial cluster can be formed from the valence nucleons present in a fissile nucleus. In 252Cf, the 44 valence nucleons of the underlying doubly magic core 208Pb can condense into a 44S cluster, according to 252 Cf K208 Pb 144 S 1QC1. (1)
Using the experimental mass data of Audi and Wapstra [3], it can be shown that this clusterization releases an energy QC14 108 .67 (0.61) MeV. This energy remains stored in the252Cf nucleus, probably as vibration energy of a208Pb-44S “molecule” [4].
The cluster model assumes that fission results from rearrangement reactions
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occurring in such a molecule. One of these rearrangement reactions is the process: 208 Pb 144 S K146 Ba 1106 Mo 1QC2, (2)
which has to be considered here, because Ter-Akopian et al. [1] report that one mass split,106Mo-146Ba, or 107Mo-145Ba, or 108Mo-144Ba, or a combination of these mass splits, could be responsible for the second mode of fission. The theoretical energy release of reaction (2) is QC24 108 .65 MeV (QC2is the difference between the binding energy of 62 nucleons dressing a44S cluster in 106Mo and the binding energy of 62 nucleons present around a 146Ba “core” within 208Pb). Thus, the total energy release of this particular split could amount to QC11 QC24 217 .32 MeV . But the cluster model assumes that, before scission, this energy is stored, principally as vibration energy, or vibration-rotation energy, in the new dicluster molecule, here, according to (2), in (146Ba-106Mo).
The fact that vibration energy is partly converted into rotation energy, as in chemical molecules, can explain how, quite generally, high angular momentum values of the fission fragments are observed, even in spontaneous fission [1].
3. – Hypothesis of the formation of a cluster in146Ba
The doubly magic core 132Sn plays a key role in the cluster model of asymmetric fission [2]. This is a consequence of its great cohesion and of the fragility of its valence shells, which can be easily detached in transfer reactions. As an example of such reactions, the process
208 Pb 144
S K132
Sn 1120Cd (3)
is the most energy-yielding transfer reaction, because all the valence nucleons of132Sn are transferred to the 44S cluster. The energy release amounts to 127.95 (0.65) MeV. The reaction (2) is a rearrangement reaction in which only a fraction of the valence nucleons are transferred
208 Pb 144 S K (132 Sn 16p18n )1 (44 S 126p136n ) 4146 Ba 1106Mo . (28)
As a doubly magic nucleus,132Sn can probably condense its valence nucleons into a cluster: a process
146
Ba K132
Sn 114C (4)
would be perfectly similar to reaction (1).
If this hypothesis (4) is correct, reaction (2) is in competition with the process: 208 Pb 144 S K (132 Sn 114 C ) 1106Mo . (5)
It is noteworthy that the energy release of reaction (5) is greater than that of reaction (2), because (5) is the sum of
208 Pb 144 S K146 Ba 1106Mo (QC 24 108 .65 MeV ) and of 146 Ba K132 Sn 114 C 1QC(14C ) .
It is easy to demonstrate that the clusterization energy of 14C in 146Ba is equal to 8561.5 (96) keV, according to the data of ref. [3]. Thus, the energy release of (5), QC82, is equal to 117.21 MeV; and the corresponding total energy release, QC11 QC82, is equal to 225.88 MeV, a value which does not differ very much from the highest total energy release, 236.62 MeV.
ON THE SECOND MODE OF SPONTANEOUS FISSION OF252Cf 667
However, the relatively small QCvalue of process (4) corresponds to the formation of a low-energy vibrator. A vibrating system such as 132Sn-14C has certainly to be considered as a deformed nucleus. Furthermore, due to its small binding energy of only 8.56 MeV, it can be easily destroyed in a collision.
More precisely, it is conceivable, in view of the great vibration energy stored in the system, that the “heavy system” (132Sn-14C), at the closest approach of the light partner 106Mo, could suffer a kind of collision leading to a great variety of destruction channels, for example: 106 Mo 1 (132Sn-14 C ) K106 Mo 1138 Ba 18n , (6) 106 Mo 1 (132Sn-14 C ) K104 Mo 1138 Ba 110n . (7)
Both examples correspond to observed correlated fragment pairs, according to table III of ref. [1].
At first sight, the fact that barium isotopes so neutron-deficient are present among these correlated pairs suggests an evaporation process. For the mass-split106Mo-146Ba, suspected by the authors of ref. [1] to be responsible for the new fission mode, the evaporation process within the correlated fragment pair106Mo-138Ba is
146
Ba K138Ba 18n; (8)
this process needs an energy equal to S8 n(146Ba ), i.e. S2 n(146Ba ) 1S2 n(144Ba ) 1 S2 n(142Ba ) 1S2 n(140Ba ) 441342 keV, a very great amount of energy; for another correlated fragment pair,104Mo-138Ba, the evaporation process involves both 106Mo and 146Ba, and releases 10 neutrons:
146 Ba K138 Ba 18n; 106 Mo K104 Mo 12n; (9)
this evaporation process needs an energy equal to S8 n(146
Ba ) 1S2 n(106Mo ) 4 53 412 keV , according to [3].
However, the concentration of so great an amount of energy only in the particular mass split 106Mo-146Ba, and almost only in the particular fragment 146Ba, leading, only there, to the emission of as many as 8 or even 10 neutrons, seems more than surprising, and certainly difficult to explain on the basis of the sole evaporation.
Something new has to happen in this 106Mo-146Ba mass split and in this particular 146Ba, but it cannot be the simple birth of a monstrously deformed nucleus. It is better to ask: “how can suddenly, and only in this nucleus146Ba, so great an amount of energy be devoted to the destruction of the nucleus?”.
Our answer is: the formation of an unstable dicluster system is an explanation. But “why is this cluster a 14C cluster?”; or “why is only the mass split 106Mo-146Ba responsible for the effect?”.
Let us consider the QC-values for the formation of a12C cluster in144Ba, of a13C cluster in145Ba, of a14C cluster in146Ba, and even of a16C cluster in 148Ba, listed in table I.
Only146Ba can lead to the formation, in the valence shells of the doubly magic132Sn, of a cluster with enough energy of formation for constituting a deformed vibrating sys-tem, which is able to perturb, before scission, the usual rearrangement reactions. TABLEI. – Formation energy of a cluster in144-146Ba and148Ba.
Nucleus 144Ba 145Ba 146Ba 148Ba
Q
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4. – Conclusion
The hypothesis formulated in sect. 3 provides an explanation for the most important observations reported by Ter-Akopian et al. [1].
An extremely great number of neutrons are emitted in the Mo-Ba charge split, 8 for the mass split 106Mo-138Ba, 9 for the mass split 105Mo-138Ba, and 10 for the mass split 104Mo-138Ba. The yield for the104Mo-138Ba mass split is remarkably high (cf. table III of ref. [1]).
Now a great deformation cannot be the sole cause of the emission of such a great number of neutrons. And it is difficult to explain, on this basis, why both barium and molybdenum isotopes have such a deformation, and only for certain A values.
On the contrary, an internal 106Mo[ (132
Sn 114C ), xn ] process is able to explain the emission of 8 neutrons, when106Mo remains unchanged, and of 10 neutrons, when106Mo is changed into104Mo, if the great amount of energy stored in the system106Mo-(132Sn 1 14C ) is taken into account.
The present interpretation of observations made by Ter-Akopian et al. [1] constitutes a new extension of the cluster model of asymmetric fission, because this interpretation is based on the assumption, not only that clusters can be formed from the valence nucleons of doubly magic nuclei—a truism since the discovery of cluster radioactivity—, but also that clusters can play a role in nuclear dynamics, and in particular in the dynamics of fission [2].
Thus, the present argumentation has to be placed by the side of other recent arguments in favour of this model and on an equal footing with them.
These recent arguments are:
– The Coulomb fission of238U observed at relativistic energies can result from an increase, due to the dipole giant resonance, of the vibration energy of the primordial dicluster30Ne-208Pb molecule [5].
– The emission of equatorial and polar a-particles in ternary spontaneous fission involves very high-energy processes such as giant resonances created by the fierce ionization of the valence shells of the deep132Sn-core of fissile nuclei [6].
– Even the emission of the so-called non-statistical g-ray component emitted in fission and in fusion-fission reactions [4] can be considered as echoing this fierce ioniz-ation postulated by the cluster model of asymmetric fission [2].
R E F E R E N C E S
[1] TER-AKOPIAN G. M., HAMILTON J. H., OGANESSIAN YU. TS., DANIEL A. V., KORMICKI J., RAMAYYAA. V., POPEKOG. S., BABUB. R. S., LUQ.-H., BUTLER-MOOREK., MAW.-C., JONES E. F., DENG J. K., SHI D., KLIMAN J., MORHA´Cˇ M., COLEJ. D., ARYAEINEJAD R., JOHNSON N. R., LEEI. Y. and MCGOWANF. K., Phys. Rev. C, 55 (1997) 1146.
[2] MOUZE G., Proceedings of the VII International Conference on Nuclear Reaction
Mechanisms, Varenna, Italy, June 6-11, 1994, edited by E. GADIOLI(Università degli Studi di Milano, Ricerca Scientifica ed Educazione Permanente), Suppl. No. 100 (1994), p. 476. [3] AUDIG. and WAPSTRAA. H., Nucl. Phys. A, 565 (1993) 1.
[4] MOUZEG., Nuovo Cimento A, 109 (1996) 445. [5] MOUZEG., Nuovo Cimento A, 106 (1993) 715.
