Clustering in dissipative ternary processes induced
in medium-mass systems
(
)
L. VANNUCCI(1), P. BOCCACCIO(1), R. A. RICCI(2), G. VANNINI(3), R. DONA`(4)
I. MASSA(4), J. P. COFFIN(5), P. FINTZ(5), G. GIULLAUME(5), F. JUNDT(5)
F. RAMI(5)and P. WAGNER(5) (
1
) Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro
35020 Legnaro, Italy
( 2
) Dipartimento di Fisica dell’Universit`a di Padova - 35100 Padova, Italy (
3
) Dipartimento di Fisica dell’Universit`a di Trieste - 34100 Trieste, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Trieste - 34100 Trieste, Italy
( 4
) Dipartimento di Fisica dell’Universit`a di Bologna - 40100 Bologna, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Bologna - 40100 Bologna, Italy
( 5
) Centre de Recherches Nucleaires, Universit´e Louis Pasteur - Strasbourg, France
(ricevuto il 29 Luglio 1997; approvato il 15 Ottobre 1997)
Summary. — Ternary reactions, induced by low energy collisions (E'6AMeV), have
been studied in the32
S+45 Sc,76 Ge,89 Y,59 Co,63 Cu and19 F+63
Cu systems. Both, se-quential binary decay and fast disassembly of the system have been observed. Cluster-ing effects influence the system fragmentation.
PACS 25.70 – Low and intermediate energy heavy-ion reactions. PACS 01.30.Cc – Conference proceedings.
1. – Ternary processes in low-energy heavy-ion collisions
It is well established that in heavy-ion reactions, at low bombarding energy, clustering phenomena can contribute to the fragmentation of the system in more than two massive bodies [1]. Evidence of this, however, has been found only for light and medium-light sys-tems. This paper reports the presence of clustering effects in ternary reactions induced by dissipative collisions in a wide mass range aroundA=100u.
We studied six reactions (32S+45Sc,76Ge,89Y,59Co,63Cu and19F+63Cu) at bombard-ing energy of'6 AMeV. Pairs of fragments were detected in coincidence by means of
(
)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and
Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.
Fig. 1. – Scatter plots for pairs of coincident fragments detected in the32
S+63
Cu reaction.a)Total
measured energy vs. total measured atomic number. b)Total measured atomic number vs. the
relative angle in the c.m. system of the two detected fragments.
two ionization chambers having a large angular acceptance (50 < 1 ;cm < 115 ;45 < 2 ;cm <110
). Details on the experimental apparatus are reported elsewhere [2-5]. All the studied reactions show similar characteristics. In particular in the scatter plot (fig. 1a) of the total measured energy (E1+ E2) vs. the total measured atomic number (Z1+ Z2), three sets of events are distinguishable. The group A which comes from reactions
of the beam with target contaminants, the group B due to dissipative binary processes coupled with light particle emission and the group T characterized by a large missing-charge which roughly corresponds to a missing-mass varying between 16 and 70 u [2].
A so large number of undetected nucleons cannot be explained only by light particle emission. Therefore, at least a third massive body should be produced in the reaction (although undetected) and the group T of events should be due to ternary processes.
Several processes seem to contribute to the ternary fragmentation of the system. In fact the scatter plot (fig. 1b) of the total measured atomic number vs. the relative angle (12
;cm) in the c.m. system of the two detected fragments shows the presence of two
groups of events (T1and T2).
The first group of events (T1), peaked around12 ;cm
=140
, has been previously stud-ied and characterized as due to a sequential binary process. Preliminary results regard-ing all the six measured reactions are reported in ref. [2] and a more detailed analysis in ref. [5].
The second group of events (T2) for kinematical reasons was observed only in the
32S+59Co and32S+63Cu reactions. These events are differently characterized with
re-spect the ones of the T1group because the two detected fragments have a back-to-back relative motion (12
;cm
' 180
) in the c.m. system. Therefore, because of the linear momentum conservation, the break-up of the system in three bodies should occur in a collinear configuration. Moreover, at the scission, the three produced fragments are strongly interacting because the relative energy between two of them increases with the atomic number of the third one and then with its Coulomb repulsion (see fig. 2a).
The alignment of the momenta of the three fragments and their evident mutual inter-action at the scission clearly indicate that the fragmentation of the system occurs infast break-upprocesses.
Fig. 2. – Ternary collinear fragmentation of the32
S+63
Cu system. a)Relative energy of the two
detected fragments, normalized to the values of the Viola systematic as a function of the atomic number of the third fragment.b)Scatter plot of the kinetic energy in the c.m. system of a fragment
vs. the kinetic energy of another.
together with events widely distributed in the plane (the majority), also two narrow bands (C1and C2) appear.
Such a topology indicates correlations between the produced fragments [6] and sug-gests that the groups C1and C2are due to a reaction mechanism different from the one that produces the majority of the events.
2. – Clustering in ternary events produced by the sequential binary process
In this process nucleons are tranferred from the target to the projectile (first stage of the reaction) to form an intermediate excited complex which decays into two secondary fragments (second stage). Therefore the reaction proceeds like a pick-up. Some peculiar characteristics, however, indicate that both stages of the reaction could be influenced by clustering.
2.1. First reaction step. – Some aspects indicate that, during the reaction, the part of the target not transferred to the projectile (Z3) behaves as a weekly interacting spectator.
This is unexpected in this energy regime and suggests a reaction mechanism different from the ones usually observed.
In fact the outgoing direction of the intermediate complex (Z
S) is close to the beam
direction before its decay [5]. This means that, during the interaction, the target does not significantly deflect the projectile and that the system does not rotate. Moreover, in spite of the large number of transferred nucleons ('24), only a small fraction (< 10%) of the
linear momentum is transferred to the remaining part of the target [5].
So the piece of the target transferred to the projectile should beeasydetachableas it
happens in clustered configurations.
The hypothesis of a clustered structure of the system is supported also by other ev-idences. It is remarkable in fact that the number of transferred protons (Z) is
quasi-constant and close to the atomic number of magnesium, except for the19F+63Cu reaction whereZ'14. Moreover the remaining part of the target (Z3) is a fragment similar to -like nuclei (see table I). Finally the relative energy of the two primary fragments (E
S3
in table I) is much lower than the Coulomb repulsion calculated for two touching nuclei and this indicates a deformed configuration of the system at scission.
E
S 1.06
0.13 1.050.11 1.130.12 1.100.14 1.100.17 1.170.18
2.2. Second reaction step. – The sequential binary process here studied is a very dis-sipative phenomenon (Q',50MeV) so that the primary fragment which decays is
pro-duced with high excitation energy (E
S
in table I). In spite of this the charge partition in the decay ofZ
Sis governed by structure effects.
Fig. 3. – Sequential binary process in the32
S+63
Cu reaction. Atomic number distributions (Z2) of
one of the secondary fragments for fixed atomic number (ZS) of its source.
In fact whenZ
S is even and when there are two decay modes, namely into two nuclei
with even atomic numbers or into two nuclei with odd atomic numbers, the first mode is preferred with respect to the second one. This can be seen in figs. 3a and 3c which show the atomic number distributions of one of the two secondary fragments for a fixed atomic number of its source (Z
S
= 26;28). The odd-odd charge partition is clearly depressed
with respect to the decay into a couple of fragments with even atomic numbers. WhenZ
S is odd and only one decay mode exists into a couple of fragments, one of
which has an even atomic number and the other an odd atomic number, although some
Z-partitions are preferred, no even-odd effect appears (see figs. 3b and 3d).
Therefore, also in these hot decaying systems, the production of fragments with even atomic numbers is clearly preferred.
3. – Clustering in ternary events produced by the fast break-up process
The final states produced by the collinear fragmentation of the system are differently characterizable. In particular the reaction producing the narrow bands of events in fig. 2b systematically yields Ca in the C1 events and S in the C2 events (see table II). Conse-quently, as the atomic number of one of the fragments is fixed, the other two fragments are stronglyZ-correlated. However, not all the possibleZ-partitions between these two
TABLEII. –Zi: atomic number of the three fragments produced in the collinear break-up of the
system32
S+63
Cu;v
i: c.m. fragment velocities in units of c.
Z 1 Z 2 Z 3 v 1(c) v 2(c) v 3(c) C1events 20 12,13 12,13 0.030 0.061 0.020 C2events 11 – 13 16 16 – 18 0.061 0.024 0.022 others 6 – 26 6 – 22 10 – 30 0.037 0.046 0.019
fragments are observed but only some of them which produce at least one nucleus close to magnesium (table II).
In conclusion, while the majority of the events have fragments with atomic number dis-tributed in a wide range, the process producing the C1and C2events selectively populates final states in which the fragments are -like nuclei or are similar to them.
On the other hand, independently from the different final states, the collinear fragmen-tation of the system is characterized by prompt break-up and by full momentum transfer. Therefore, at the scission, the system could resemble to a three-body chain that recoils with the compound nucleus velocity. In this situation the fragment located in the middle of the chain should have, in the c.m. system, the smallest velocity because of the opposite repulsion exerted on it by the fragments located at the ends of the chain.
Systematically for all the three sets of collinear events (the widely spread and the two narrow bands C1 and C2 in fig. 2) the undetected fragment (Z3) has the lowest velocity
(table II) showing to be located in the center of the system.
This common characterization suggests that the dynamics of break-up could be the same for all the collinear events and could be understandable in the framework of the same model. So we try to reproduce the kinetic energy of the three outgoing fragments by a simple model simulating the ternary fission. As is visible in fig. 4, the calculated values agree fairly well with the data except for two narrow peaks, present in theE1
;cm
and in theE2
;cmhistograms, which are due to the C1and C2events. Therefore, these two
sets of events show both atomic number and energy correlations which are unpredictable with the simplestatisticalmodel that we used.
Fig. 4. – Center of mass energy of the three fragments produced in the collinear break-up of the system32
S+63
Cu. Solid lines correspond to experimental values (dark histograms are the contri-butions of the sets of events C1and C2), dashed lines correspond to calculated values.
Fig. 5. – Behaviour of theQ-value vs. theY
3parameter in the 32
S+63
Cu reaction. a)Full set of
events from the collinear fragmentations.b)C
1set of events. c)C
2set of events.
Additional information on the process producing the C1and C2events can be deduced from the analysis of the energy dissipation and of the centrality of the collision. The latter can be estimated by the dispersion of the relative velocities of the three fragments by using the parameterY3 =hvreli,(vrel)min. Indeed low values ofY3are correlated with
small impact parameters whereas highY3-values indicate peripheral collisions.
Figure 5 shows that the reaction is very dissipative because the Q-value decreases
from,40until,70MeV with the centrality of the collision. Moreover the process
pro-ducing the C1and C2events is clearly peripheral so that the preferential break-up of the system in fragments similar to -like nuclei could be favoured by the preformation of a
clustered configuration in a dynamics that does not permit the system to evolve in the mono-nuclear regime.
4. – Conclusion
Three-body processes due to fast break-up and to sequential binary decay can be in-duced in a wide range of medium-mass region (A'100u) by low-energy collisions. The
large inelasticity of the processes indicates that the reaction threshold is not much lower than 6AMeV.
In spite of the large energy dissipation structure effects and clustering phenomena are clearly present and influence the deexcitation of the system.
REFERENCES
[1] COSTANZOE. et al., Phys. Rev. C, 44 (111) 1991 and references quoted therein. [2] BOCCACCIOP. et al., Z. Phys. A, 354 (121) 1996.
[3] VANNUCCIL. et al., Proceedings of the International Symposium on Time Characteristics of
Nuclear Reactions, September 20-25, 1993, Moscow, Russia, p. 72.
[4] VANNUCCIL. et al., Proceedings of the International Symposium on Large-Scale Collective
Motion of Atomic Nuclei, October 15-19, 1996, Brolo, Italy.
[5] BOCCACCIOP. et al., submitted to Z. Phys. A.
