For the first time, we apply the temperature dependent relativistic mean field (TRMF) model to study the ternary fission of heavy nucleus using level density approach. The probability of yields of a particular fragment is obtained by evaluating the convolution integrals which employ the excitation energy and the level density parameter for a given temperature calculated within the TRMF formalism. To illustrate, we have considered the ternary fissions in 252Cf, 242Pu and 236U with fixed third fragment A3 = 48Ca, 20O and 16O respectively. The relative yields are studied for the temperatures T = 1, 2 and 3 MeV. For the comparison, the relative yields are also calculated from the single particle energies of the finite range droplet model (FRDM). In general, the larger phase space for the ternary fragmentation is observed indicating that such fragmentations are most probable ones. For T = 2 and 3 MeV, the Sn + Ni + Ca is the most probable combination for the nucleus 252Cf. However, for the nuclei 242Pu and 236U, the maximum fragmentation yields at T = 2 MeV differ from those at T = 3 MeV. For T = 3 MeV, the closed shell (Z = 8) light mass fragments with its corresponding partners has larger yield values. But, at T = 2 MeV Si/P/S are favorable fragments with the corresponding partners. It is noticed that the symmetric binary fragmentation along with the fixed third fragment for 242Pu and 236U are also favored at T = 1 MeV. The temperature dependence of the nuclear shape and the single particle energies are also discussed.
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