## 1 Introduction
In STF, the first step is an asymmetrical binary fission (AsymBF). It produces one light and one heavy fragment. If the heavy fragment excitation energy is sufficient to overcome its fission barrier it, in turn, splits into two fragments within a time scale of 10\({}^{-20}\) s [23]. The mixing of STF and DTF events is one of the major issues in the experimental observation of TTF. Experimental evidence of the TTF has been claimed since the 60s [25]. A review of early experimental results can be found in ref. [23]. The production of ternary fragments, such as F, Ne, Na, Mg, Al, and Si isotopes, up to A = 35, has been identified by [PERSON] et al. [26] in neutron-induced fission on \({}^{242}\)Am target. However, TTF probability turned out to be very low. Typical values are those observed in the thermal neutron induced fission of \({}^{235}\)U, where a TTF event occurs every 6.7(\(\pm\)3.0)10\({}^{6}\) BF [27]. The low excitation energy seems to be a hindering factor of the TTF probability that, in addition, decreases exponentially with the increase in ternary fragment mass [28; 29]. Because of this, TTF is still a poorly known process and its occurrence in superheavy nuclei (SHN) is not experimentally confirmed [21; 30; 31; 32]. Yet, it is worth mentioning that the search of TF was mainly performed in spontaneous and neutron-induced fission, which gives access to fissioning nuclei with a neutron to proton ratios nearly constant and with atomic numbers in the narrow region Z = 90-98 [33; 34; 35; 36; 37; 38; 39; 40]. The conditions favoring the breakup in more than two fragments were suggested by [PERSON] [8]. Within the framework of the liquid drop model, the probability of true ternary fission increases rapidly as \(Z^{2}\)/A increases [8]. Many models have been proposed, including shell effects in the calculation of the PES. According to [PERSON] et al. [9] TTF is hindered by a double saddle path where the second saddle is higher in energy. With the increase in the charge of the nucleus, the second saddle tends to vanish and eventually disappear, making TTF accessible. Theoretical studies on \({}^{252}\)Cf [41; 42], and the giant nuclear system \({}^{238}\)U + \({}^{238}\)U [29] also indicate similar shell effects for TTF. Minima for tripartitions, which is composed by magic nuclei, appear in the PES proposed in ref. [43; 44]. These indications are supported by recent observations of TTF in the spontaneous fission of \({}^{252}\)Cf and in neutron-induced fission of \({}^{235}\)U [43; 45; 46; 47; 48]. In both cases, the observation of TTF-producing nuclei with masses close to the magic \({}^{132}\)Sn, \({}^{70}\)Ni, and \({}^{48}\)Ca isotopes was claimed [45; 46]. Further experimental results can be found in [25; 49; 50]. Particularly interesting are the systematics on \({}^{40}\)Ar-induced reactions [49; 51] where one could expect a TTF/BF ratio up to 3% [51] and a cross section of about 0.5 mb for TTF, which has a ternary fragment with \(A>23\). By using heavy-ion-induced reactions, it would be possible to test the above conditions that are supposed to ignite TTF by changing the neutron to proton ratio of the fissioning nucleus and its excitation energy. However, any experiment devoted to the detection of the TTF has to deal with the overlap of DTF and STF fragments. Therefore, an analysis of the possible detector configurations has to be planned carefully. This article aims to establish the guidelines to disentangle the products of DTF and STF mechanisms by analyzing the angular correlations and energies expected for TTF fragments to be identified in mass and charge. The reaction \({}^{40}\)Ar + \({}^{208}\)Pb at the beam energy of 230 MeV, producing \({}^{248}\)Fm\({}^{*}\) (\(Z^{2}/\) A = 40.3), is chosen as a case study to search for TTF. The beam energy is chosen so to keep the excitation energy low enough to be able to be sensitive to shell effects. The same reaction was exploited by [PERSON] et al. [52] by using mica and glass as a solid material to detect heavy ion tracks and rebuild the kinematics.