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Background: The deformation of the nuclei involved in the cluster decay of heavy nuclei affect seriously their half-lives against the decay. Purpose: We investigate the description of the different decay stages in both the optimum orientation and the orientation-averaged pictures of the cluster decay process. Method: We consider the decays of 232,233,234U and 236,238Pu isotopes. The quantum mechanical knocking frequency and penetration probability based on the Wentzel-Kramers-Brillouin approximation are used to find the decay width. Results: We found that the orientation-averaged decay width is one or two orders of magnitude less than its value along the non-compact optimum orientation. The difference between the two values increases with decreasing the mass number of the emitted cluster. Correspondingly, the extracted preformation probability based on the averaged decay width increases with the same orders of magnitude compared to its value obtained considering the optimum orientation. The cluster preformation probabilities (Sc) obtained in the two considered schemes give more or less comparable agreement with the Blendowske-Walliser (BW) formula based on the preformation probability of Sa(ave.) obtained from the orientation-averaging scheme. All the obtained results, including those obtained in the optimum-orientation scheme, deviate substantially from the BW law based on Sa(opt.) obtained using the optimum-orientation scheme. Conclusion: In order to account for deformations of the participating nuclei, it is more relevant to calculate the decay width by averaging over the different possible orientations of the participating deformed nucleus, rather than considering the corresponding non-compact optimum orientation.

The ground-state spin and parity of a formed daughter in the radioactive Alpha-emitter is expected to influence the preformation probability of the Alpha and daughter clusters inside it. We investigate the Alpha and daughter preformation probability inside odd-A and doubly-odd radioactive nuclei when the daughter and parent are of different spin and/or parity. We consider only the ground-state to ground-state unfavored decays. This is to extract precise information about the effect of the difference in the ground states spin-parity of the involved nuclei far away any influences from the excitation energy if the decays are coming from isomeric states. The calculations are done for 161 Alpha-emitters, with Z=65-112 and N=84-173, in the framework of the extended cluster model, with WKB penetrability and assault frequency. We used a Hamiltonian energy density scheme based on Skyrme-SLy4 interaction to compute the interaction potential. The Alpha plus cluster preformation probability is extracted from the calculated decay width and the experimental half-life time. We discussed in detailed steps the effect of angular momentum of the emitted Alpha-particle on the various physical quantities involved in the unfavored decay process and how it is finally increases the half-life time. We found that if the ground states spin and/or parity of parent and daughter nuclei are different, then the preformation probability of the Alpha-cluster inside parent is less than it would be if they have similar spin-parity. We modified the formula that gives the Alpha preformation probability in terms of the numbers of protons and neutrons outside the shell closures of parent, to account for this hindrance in the preformation probability for the unfavored decays between ground states.