## 2 Materials and Methods
### DTF and STF Differences in Energy and Angular Distributions
#### 2.2.2 Angular Distributions
Thus, for planning an experimental investigation the limited angular coverage of the used detectors has to be taken into account. In Figure 7, the angular correlations between \({}^{48}\)Ca and \({}^{68}\)Zn fragments are shown. The angular correlations are presented for DTF and STF for fixed values of the \({}^{132}\)Sn emission angle. We note that for \({}^{132}\)Sn emitted at the forward direction (\(\theta_{1}\geq-90^{\circ}\)), the same term of angles does not correspond to both the DTF and STF events, i.e., they are separable simply by collecting coincidence events from detector placed at different angles. However, to define the mechanism responsible for the TF it is convenient to perform measurements in which we can collect products of both mechanisms simultaneously and exploit other observables to disentangle each contribution. Figure 6: Kinetic energies of the product of \({}^{132}\)Sn + \({}^{68}\)Zn + \({}^{48}\)Ca tripartition. The products of the DTF and STF mechanisms are shown in the left and right panels, respectively. The results shown in Figure 7, for a specific tripartition, reflect what has been previously shown in Figure 5, i.e., wider distributions correspond to DTF whereas, in STF, only very narrow regions are found for the \({}^{68}\)Zn and \({}^{48}\)Ca angles. This is a general trend except for the configurations in which \(\theta_{1}=-\theta_{2}\). Also, in this case, the \(\theta_{3}\) distribution of DTF is narrower, as shown in Figure 8. Thus, with detectors covering only a small section of the solid angle, it would be possible to measure the \(\theta_{3}\) distribution. Particularly interesting are the events collected in the two-coincidence mode from detectors in \(\theta_{1}=-\theta_{2}=-70^{\circ}\) configuration because they include middle and heavy fragments produced by both the DTF and STF mechanisms. The dynamics of the DTF and STF processes also affect the energy of the fragments. At the separation stages, indeed, the different Coulomb repulsion drives the trajectories and determines the observed kinetic energy distributions. In Figure 9, we present the energies \({}^{68}\)Zn and \({}^{48}\)Ca for fixed \({}^{132}\)Sn angles (same values considered in Figure 7). Being the angular distribution of DTF fragments broader a similar trend is expected for the kinetic energy intervals. Thus, we observe \({}^{68}\)Zn and \({}^{48}\)Ca kinetic energies distributed over a wide interval ranging from few MeV up to about 300 MeV and form 50 MeV up to 350 MeV (blue lines), respectively, whereas the narrower angular distributions of STF produce strong correlations between the Zn and Ca kinetic energies as indicated by the red lines. In Figure 9, we observe that the phase space of \({}^{68}\)Zn and \({}^{48}\)Ca energies for  
Figure 8: DTF angular correlations of the \({}^{132}\)Sn + \({}^{68}\)Zn + \({}^{48}\)Ca tripartition for \(\theta_{2}=-\theta_{1}\). Figure 7: Angular correlations of the \({}^{132}\)Sn + \({}^{68}\)Zn + \({}^{48}\)Ca tripartition. The DTF (blue) and STF (pink) angular correlations \(\theta_{2}\) vs. \(\theta_{3}\) are presented for the fixed heavy fragment angle \(\theta_{1}\) described at the top of each panel. the STF and DTF are not overlapping except for a few points corresponding to the \({}^{132}\)Sn emitted at \(\theta_{1}=-90^{\circ}\), where an overlap in the angular distributions is also observed. Consequently, the kinetic energies of fragments are observables sensitive to the tripartition mechanism. The indications of the competition among the two ternary mechanisms, obtained by performing measurements of angular distributions, can be confirmed by measuring the energy spectra of a single fragment in coincidence with \({}^{132}\)Sn measured at a fixed angle. The correlations presented so far allow us to identify guidelines for selecting observables and detector locations if exclusive measurements have to be planned to disentangle fragments from DTF or STF mechanisms.