Sequential decay analysis of $^{235}$U(n$^{th}$,f) reaction using fragmentation approach

Numerous experimental and theoretical observations conclude that the probability of the three fragment emission (ternary fission) or the binary fission increases when one proceeds towards the heavy mass region of nuclear periodic table. The collinear cluster tripartition (CCT) channel of $^{235}$U(n$^{th}$,f) reaction is studied and it was observed that the CCT may be a sequential process or a simultaneous emission phenomena. Till now, different approaches are introduced to study the CCT process as a simultaneous process or sequential process, but the decay dynamics of these modes is not fully explored. It will be of interest to identify the three fragments of the sequential process and to explore their related dynamics using some excitation energy dependent approach. Hence, in present work, an attempt is made to study the sequential decay mechanism of $^{235}$U(n$^{th}$,f) reaction using quantum mechanical fragmentation theory (QMFT). The decay mechanism is considered in two steps, where initially the nucleus splits into an asymmetric channel. In the second step, the heavy fragment obtained in the first step divides into two fragments. Stage I analysis is done by calculating the fragmentation potential and the preformation probability for the spherical and deformed choice of the decaying fragments. The most probable fragment combination of stage I are identified in view the dips in the fragmentation structure, and the corresponding maxima's of the preformation probability ($P_0$). The excitation energy of the decay channel is calculated using an iteration process. The obtained excitation energy of the identified heavy fragments is further used for the fragmentation analysis, and the subsequent binary fragments of the sequential process are obtained. The identified three fragments of the sequential process are in agreement with the experimental observation and are found nearby the neutron or proton shell closure. Finally, the kinetic energy of the observed fragments is calculated and the middle fragment of the CCT mechanism is identified.