## 2 Materials and Methods
### Detection Apparatus  
We present here an example of an arrangement of existing detectors, inspired by the correlations discussed above, to perform measurements aimed at highlighting the occurrence of DTF and STF. The apparatus is shown in Figure 12. It consists of 4 detection elements mounted in the horizontal plane (our reaction plane) and centered around the target. The polar angles with respect to the beam direction (the z-axis) are positive anticlockwise. The four elements are named as follows:  
1. A TOF arm at \(-70^{\circ}\pm 5^{\circ}\);
2. A TOF arm at \(70^{\circ}\pm 5^{\circ}\);
3. A string of 7 telescope detectors covering 50\({}^{\circ}\) and centered at 90\({}^{\circ}\);  
Figure 11: Angular correlations of BF events. The distributions of fragment 2 (\(\theta_{2}\)) vs. fragment 1 (\(\theta_{1}\)) for symmetric (blue line) and asymmetric fission (orange line). The green boxes represent the two angular ranges covered by the detection setup proposed in Section 2.4. 4. A system of a TOF arm combined with a squared array of telescope detectors at \(60^{\circ}\pm 5^{\circ}\). Each TOF arm consists of a start and a stop detector that is position sensitive and allows the ion to pass through with a relatively small energy loss. The telescope detector consists of two stages and is made by a thin (20 \(\upmu\)m) and a thick (300 \(\upmu\)m) Si detectors. A string of 7 telescopes, mounted in a single raw, would be used for the construction of the detection element (iii). The same telescopes are mounted in a squared array downstream the stop detector of arm (iv) which will be able to collect therefore TOF and residual energy of the particles passing through. Each telescope can be used to identify the charge of the lighter ion by exploiting the \(\Delta E-E\) technique. The use of several telescopes in a raw (element (iii)) allows accessing the angular distributions over a wide angular range centered at \(90^{\circ}\). Example of expected angular and energy distributions for the light fragment in STF events are shown in Figure 10. At the forward angles, the narrower angular distribution calculated for the DTF events, instead, can be measured by exploiting the high spatial resolution of the TOF detector mounted upstream in the element (iv). The TOF detectors, featuring the (i), (ii), and (iv) detection elements, can be realized by using two TOSCA units [71] coaxially mounted downstream and acting as start and stop detectors, respectively. The TOSCA units represent the core detection elements. These detectors, developed for a wide variety of experiments as those described in [72; 73], have been successfully adopted for the study of binary fission and quasifission in 2023 and of multinucleon transfer reactions in 2024 at JYFL and GSI, respectively. Each unit measures the time and the (x, y) position of charged particles passing through a thin layer mounted orthogonal to the reaction plane. The TOSCA units, represented with triangular prisms in Figure 12, offer state-of-the-art spatial and time resolutions. By performing coincidence measurements between the two TOSCA units of each TOF detector, the velocity vectors of particles can be determined. By crossing thin layers (few \(\upmu\)m) of plastic material, the variations of trajectories and energies of particles are minimal, so further independent measurements can be performed. Thus, by mounting the telescope array downstream the stop detector in element (iv) we can also measure the mass, charge, and energy of light fragments with a single detection element. To collect valuable data, an effective trigger scheme able to collect events produced by different decay processes should be arranged. A single event occurs when each sensitive part of a detection element produces a valid signal, i.e., the detectors of each element should be arranged in AND mode. Then, by considering the different number of products and  
Figure 12: Schematic drawing of the detection apparatus consisting of three different detector types.