Nuclei in the actinide region are good in exhibiting cluster radioactivity. In the present work, the half-lives of $\alpha$-decay and heavy cluster emission from certain actinide nuclei have been calculated using cubic plus Yukawa plus exponential model ($\bf{CYEM}$). Our model has a cubic potential for the overlapping region which is smoothly connected by a Yukawa plus exponential potential for the region after separation. The computed half-lives are compared with those of other theoretical models and are found to be in good agreement with each other. In this work, we have also studied the deformation effects on half-lives of cluster decay. These deformation effects lower the half-life values and it is also found that the neutron-rich parent nuclei slow down the cluster decay process. Geiger–Nuttal plots for various clusters are found to be linear and most of the emitted clusters are $\alpha$-like nuclei.

Using the cubic plus Yukawa plus exponential model (CYEM), half-lives of $\alpha$ decay from the ground state of the parent nuclei to the ground state of the daughter nuclei and from the ground state to an excited state of the daughter nuclei have been systematically investigated for even–odd and even–even isotopes of Cm, Cf, Fm and No nuclei by incorporating centrifugal potential term, rotational energy term, deformation effects ($\beta_{2}$ and $\beta_{4}$) of the parent and daughter nuclei and spin–parity effects.We have done our calculations by considering the Coulomb, centrifugal and Yukawa plus exponential potentials as an interacting barrier for separated fragments and the cubic potential for the overlapping region. The calculated half-lives are compared with the available data. Our results are found to be in good agreement with each other. The effect of the centrifugal potential on half-life was evaluated. The branching ratio, hindrance factor and standard deviation of half-lives from the ground state of the parent nuclei to the ground state of the daughter nuclei have been calculated.