  The cluster dynamics of radioactive nuclei decaying to neighbouring daughter
nuclei of the double magic $^{132}$Sn and $^{208}$Pb is investigated using the
relativistic mean-field (RMF) approach with NL3$^*$ parameter set within the
preformed cluster-decay model (PCM). The novel feature of the present study is
the application of the newly derived preformation formula, laying the
groundwork for accessing the break-up of the Q-value: preformation energy,
cluster emission energy and the recoil energy of the daughters formed. The
energy associated with cluster preformation is theoretically quantified for the
first time. This treatment underscores the shell effect, pairing correlation as
well as the blocking of particular orbitals by unpaired nucleons. To ascertain
the applicability of the new formula, the PCM based calculations are carried
out with nuclear potential obtained using the phenomenological M3Y and
microscopic RMF-based R3Y nucleon-nucleon (NN) potentials along with
corresponding densities. We found a marginal variation that can be attributed
to the difference in their barrier properties, however, the predictions for the
case of both M3Y and R3Y potentials are found to agree well with the
experimental half-lives. Although none of the considered reaction systems
yields a double magic daughter nucleus, we found that the kinematics of their
cluster emissions is governed by their proximity to the shell closure. The
deduced systematic of the recoil energy in cluster decays can provide valuable
insight for the synthesis of elements in superheavy mass region in the future.
