Considering Coulomb and proximity potentials as barriers, we have calculated the half lives for ¹²C emission from various Ba isotopes using different mass tables. The half life for ¹¹²Ba isotope calculated by us is 6.020×10³ s which is comparable with the experimental value 5.620×10³ s. From our study it is found that ¹¹⁴Ba is the good parent for ¹²C emission whose emission rate is favorable for measurement. The half lives predicted by us lie very close to those reported by Shanmugam et al using their cubic plus Yukawa plus exponential model. It is observed that inclusion of proximity potential does not produce significant deviation from the linear nature of the Geiger-Nuttall plots. Also it is found that the neutron excess in the parent nuclei slows down the exotic decay process.

Exotic decay of some heavy nuclei with Z≥100 formed in heavy ion ‘cold fusion’ reaction were studied taking interacting barrier consisting of Coulomb and proximity potential. Calculated half-life time shows that some modes of decay are well within the present upper limit for measurements (T_1/2<10³⁰ s). Cluster formation probabilities are calculated for different clusters within fission model. It is found that transition from cluster mode to fission mode take place at mass of the cluster, A₂=20 in exotic decay which is comparable with the value A₂=16 of Shanmugam et al based on cubic plus Yukawa plus exponential model (CYEM).

Taking Coulomb and proximity potential as interacting barrier for post-scission region we calculated half-life time for different modes of exotic decay treating parent and fragments as spheres and these values are compared with experimental data. We studied the effect of deformation of parent and daughter on half-life time treating emitted cluster as spherical. When deformations are included half-life time values are found to decrease, though slightly. It is found that parent deformation alone will not produce appreciable change in half-life time since it affects relatively small pre-scission part of the barrier.

The $\alpha$ decay half-lives of hyper and normal isotopes of Po nuclei are studied in the present work. The inclusion of $\Lambda–N$ interaction changes the half-life for $\alpha$ decay. The theoretical predictions on the $\alpha$ decay half-lives of normal Po isotopes are compared with experimental results and are seen to be matching well with each other. The neutron shell closure at $N = 126$ is found to be the same for both normal and hypernuclei. The Geiger–Nuttal (G–N) law for $\alpha$ decay is unaltered in the case of hypernuclei. The hypernuclei will decay into normal nuclei by mesonic or non-mesonic decay modes. Since the half-lives of normal Po nuclei are well within the experimental limits, our theoretical results suggest experimental verification of the $\alpha$ emission from hyper Po nuclei in a cascade process.

Using the recently proposed unified ternary fission model (UTFM), the tripartition of $^{236}\rm{U}$ isotope was studied for all possible fragmentations, in which the interacting potential barrier is taken as the sum of the Coulomb and proximity potentials with fragments in collinear configuration. The highest yield is obtained for the fragmentation $^{48}\rm{Ca}+^{58}\rm{Ti}+^{130}\rm{Sn}$ and next highest yield is found for $^{58}\rm{Cr}+^{46}\rm{Ar}+^{132}\rm{Sn}$,which stress the importance of doubly magic or near doubly magic nuclei in the tripartition of $^{236}\rm{U}$ isotope. The formation of $^{68}\rm{Ni}$ and $^{70}\rm{Ni}$ as the edge fragments linking the doubly magic nucleus $^{132}\rm{Sn}$ by the isotope of Si is in good agreement with experimental and theoretical studies, in the collinear cluster tripartition of $^{236}\rm{U}$ isotope which reveals the reliability of our model (UTFM) in ternary fission.

The halo structure of a nucleus is investigated on the basis of separation energy consideration and potential energy calculations. Most of the predictions on the existence of halo nuclei are found to agree with the available experimental studies. For the first time, the possibility of emitting proton halo (p-halo) nuclei from heavy nuclei within the range $82 \leq Z \leq 102$ has been studied by evaluating decay half-lives for the emission of 1p-halo nuclei $^{8}\rm{B}, ^{12}\rm{N}, ^{13}\rm{N}, ^{17}\rm{F}$ and 2p-halo nuclei $^{9}\rm{C}, ^{17}\rm{Ne}, ^{18}\rm{Ne}, ^{20}\rm{Mg}$ using Coulomb and proximity potential model (CPPM). Of these, the emissions of 1p-halo nuclei $^{8}\rm{B}, ^{12}\rm{N}, ^{13}\rm{N}$ and $^{17}\rm{F}$ are found to be probable from various heavy nuclei as the half-lives of the corresponding emissions are within the experimental upper limit $(T_{1/2} \leq 10^{30} s)$. When dealing with 2p-halo nuclei, its emission is observed to be less probable compared to 1p-halo nuclei, except $^{18}\rm{Ne}$. Compared to the probability of emission of a normal cluster, the probability of emission of a p-halo nucleus from a radioactive nuclide is found to be less but still, there is a finite probability of p-halo emissions from heavy nuclei.

Cluster decay of the superheavy nuclei $^{270-318}118$ has been studied taking Coulomb and proximity potentials as interacting barriers. This study is based on the concept of cold valley. Cluster decay half-lives and other characteristics are computed for various clusters. The predicted α decay half-life values are compared with other theoretical models and also with the sole experimental value. Plots connecting half-lives with the neutron number of the daughter nuclei as well as with the neutron number of the parent nuclei, strongly indicated neutron shell closure at $N = 184$. Also, we noted that proton shell closure occurs at $Z = 114$. From our studies, we noted that the nuclide $^{298}_{184}114$, which is doubly closed, is very stable and we could reach the inference that $^{298}_{184}114$ is the most probable nuclide to be the centre of island of stability.

Cluster decay half-lives of trans-lead nuclei emitting clusters like C, N, O, F, Ne, Mg and Si are studied by incorporating various cluster pre-formation probabilities to the modified generalised liquid drop model (MGLDM). MGLDM is a method in which generalised liquid drop model (GLDM) is modified using proximity 77 potential. In this approach, we make the assumption that the cluster is pre-born inside the parent nuclei and the pre-formation factor that depends on Q value, size of the cluster and product of atomic number of the cluster and the daughter nuclei are formulated and added to MGLDM. Calculated half-lives using three formulae are cross checked with experimentally detected values from various isotopes of Fr, Ra, Ac, Th, U, Pa, Np, Pu and Amparent nuclei and the results match exactly. Standard deviations of logarithmic half-lives using pre-formation factors which depend on Q values, cluster size and product of atomic number of the cluster and the daughter nuclei, are 1.08, 0.995 and 1.07 respectively. Hence, we formulate a pre-formation factor that depends on all the three parameters together in an equation and the standard deviation is found to be 0.885. Again, the four formulae proved its applicability in the case of alpha decay from the parent nuclei of atomic numbers 85–102.