Probing the decay mechanism of hot nuclei by Coulomb chronometry

In this contribution, we propose a new Coulomb chronometer suitable for three-fragment exit channels. We use this chronometer to extract the evolution of the fragment emission time in Xe+Sn central collisions from 12 to 25 MeV/A bombarding energy. The involved time scale becomes compatible with simultaneous threefragment break-up above E∗ = 4.0 ± 0.5 MeV/A, which can be interpreted as the energy required for the onset of multifragmentation.


Introduction
Recent data on 129 Xe+ cat Sn central collisions [1] show that at 8 MeV/A bombarding energy, almost all the reaction cross section is composed of events with two heavy fragments in the exit channel (see Fig. 1(a)).Above 12 MeV/A bombarding energy, the three-fragment exit channel becomes significant, overcoming the two-fragment production rate above 18 MeV/A.The decay mechanism responsible for these three-fragment events is not well established: Is it the continuation of low energy fission or the precursor of high energy simultaneous fragmentation?To answer this question, a dynamical characterization of the decay mechanism is needed.In particular, the estimation of the involved time scales may allow to disentangle sequences of two binary fission from simultaneous three-fragment break-up.
In this contribution, we propose a new Coulomb chronometer suitable for three-fragment exit channels.We use this chronometer to extract the evolution of the fragment emission time in

Experimental analysis
Collisions of 129 Xe+ cat Sn at 12, 15, 18, 20, and 25 MeV/A were measured using the INDRA 4π charged product array [2] at the GANIL accelerator facility.In this analysis, we considered only fusion-like events leading to three heavy fragments (Z > 10) in the exit channel.Fusion-like events were selected by requiring at least 90% of the total charge of the system to be detected.
We start from the hypothesis that fragments are produced sequentially.If two successive splittings occur, three possible sequences of splittings have to be considered.To identify the sequence of splittings event by event, we compare the relative velocity between each pair of fragments with that expected for fission, taken from the Viola systematics [3,4].The pair with the most Violalike relative velocity is considered to have been produced during the second splitting.We can therefore trivially deduce that the remaining fragment was emitted first.Once the sequence of splittings is known event by event, fragments can be sorted according to their order of production.Let us now call Z f 1 and Z f 2 , the two nuclei coming from the first splitting.The fragment Z f 2 breaks in Z s 1 and Z s 2 during the second step (see Fig.
To estimate the mean inter-splitting time, we used the correlation between the inter-splitting angle θ and the relative velocity of the second splitting: (see Fig. 2(a)).These correlations present a maximum at θ ∼ 90, which is more pronounced as the beam energy increases.We quantify this effect by the Coulomb distortion parameter δv = v s 12 (90) −v s 12 (0) which increases with increasing beam energy (Fig. 2 translate δv in terms of inter-splitting time δt, we performed Coulomb trajectory calculations for point charges, which simulate sequential break-ups using experimental mean charges.Finally, we obtained the evolution of the inter-splitting time as a function of the beam energy (Fig. 3).

Discussion
A clear decrease of the inter-splitting time with increasing beam energy is observed in Fig. 3.At 12 MeV/A, the inter-splitting time δt is of the order of 600 fm/c.It shows that, for the lower beam energies, fragments arise from IWM EC 2014 two successive splittings, validating our starting hypothesis.As the beam energy increases from 12 MeV/A to 20 MeV/A, δt decreases monotonically from 600 fm/c to about 100 fm/c.Above 20 MeV/A, δt becomes compatible with zero.Our trajectory calculations show that, below δt ∼ 100 fm/c, fragment emissions can not be treated independently, and it is no longer meaningful to speak of a sequential process.Therefore, Fig. 3 shows that the three-fragment exit channel is compatible with successive binary splittings on shorter and shorter time scales, becoming indistinguishable from simultaneous three-fragment break-up at bombarding energies above 20 MeV/A, which correspond to E * ∼ 4 ± 0.5 MeV/A.

Figure 1 :
Figure 1: (color online).(a) Evolution of different exit channel probabilities as a function of the beam energy for 129 Xe+ cat Sn central collisions.(b) Definition of the relevant kinematic observables for the three-fragment exit channel, in the rest frame of the intermediate system Z f 2 .
(b)), indicating that the second splitting occured closer and closer to the first emitted fragment.To EPJ Web of Conferences 01006-p.2 1).

Figure 2 :Figure 3 :
Figure 2: (a) Correlation between the inter-splitting angle θ and the relative velocity of the second splitting v s 12 , vertical error bars are smaller than the size of the points; (b) evolution of the Coulomb distortion parameter δv as a function of the beam energy for 129 Xe+ cat Sn central collisions.
129Xe+ cat Sn central collisions from 12 to 25 MeV/A bombarding energy.