A new semi-empirical model is proposed for determining the half lives of radioactive nuclei exhibiting cluster radioactivity. The parameters of the formula are obtained by making a least-square fit to the available experimental cluster decay data. The calculated half-life time for cluster decay is compared with the corresponding experimental values and with the values proposed by earlier scaling laws and with those predicted by the Coulomb and proximity potential model. The semi-empirical formula is applied to alpha decay of parents with Z = 85–102 and is compared with experimental data and with other semi-empirical formula predictions. The predicted alpha and cluster decay half-life time values are found to be in good agreement with the experimental data. The calculated alpha decay half-life time is also compared with the values predicted by Viola–Seaborg–Sobiczewski and Horoi systematics.

The cluster decay half lives for 122 isotopes are computed for various clusters ranging from an alpha particle to 70 Ni within the Coulomb and proximity potential model. The computed alpha decay half lives agree with the values calculated using the Viola-Seaborg-Sobiczewski (VSS) systematic formulas. The half lives for spontaneous fission of these isotopes are carried out using the formula of Ren et al. It is found that the alpha emission is the dominant mode of decay for isotopes with mass number A < 306, and for those with A > 306 spontaneous fission is found to be dominant. The demarcation between alpha decay and spontaneous fission is at 306 122, which shows the presence of a spherical neutron shell closure at N = 184.

Within our fission model, the Coulomb and proximity potential model (CPPM) cluster formation probabilities are calculated for different clusters ranging from carbon to silicon for the parents in the trans-tin and trans- lead regions. It is found that in trans-tin region the 12^C, 16^O, 20^Ne and 24^Mg clusters have maximum cluster formation probability and lowest half lives as compared to other clusters. In trans-lead region the 14^C, 18, 20^O, 23^F, 24,26^Ne, 28,30^Mg and 34^Si clusters have the maximum cluster formation probability and minimum half life, which show that alpha like clusters are most probable for emission from trans-tin region while non-alpha clusters are probable from trans-lead region. These results stress the role of neutron proton symmetry and asymmetry of daughter nuclei in these two cases.Comment: 20 pages, 6 figure

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Exotic decay of various Nd isotopes emitting4He, 8Be, 12 C, 20Ne, 24Mg, 28Si and 32S was studied taking the potential barrier as the sum of Coulomb and proximity potentials. The predicted half-lives are well within the present upper limit for measurements (T1/2< 1030  s). It is found that 16O and 20Ne emissions from 120Nd are the most favourable for measurements with T1/2 ≈ 1010  s. The predicted lowest half-life time for 20Ne emission from 120Nd, stresses the role of the doubly magic 100Sn daughter in the exotic decay process. The nuclear structure effect and shell effect are evident from the Geiger–Nuttall plots for different clusters. It is found that the presence of neutron excess in the parent nuclei slows down the exotic decay process.

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The competition between the alpha decay and spontaneous fission half-lives of even-even elements with Z = 100-122 is studied using the Coulomb and proximity potential model and the phenomenological formula for spontaneous fission. The isotopes situated within the spontaneous fission half-life parabola will have alpha decay as the dominant mode of decay. We have studied the Seaborg plots connecting the spontaneous fission half-lives with the fissionability parameter (Z 2 /A) in the superheavy region for isotopes with Z = 100-138. The role of relative neutron excess in spontaneous fission half-lives is also studied. The isotopes in the first quadrant of the plot for the ratio of spontaneous fission to alpha decay half-lives against relative neutron excess will survive fission and can be synthesized and detected through alpha decay. Our computed alpha decay half-lives for all isotopes agree with the values calculated by the Viola-Seaborg empirical formula and with the experimental data.

Based on the concept of cold valley in cold fission and fusion, we have investigated the cluster decay process in 248−254 Cf isotopes. In addition to alpha particle minima, other deep minima occur for S, Ar and Ca clusters. It is found that inclusion of proximity potential does not change the position of minima but minima become deeper. Taking Coulomb and proximity potential as interacting barrier for post-scission region, we computed half-lives and other characteristics for various clusters from these parents. Our study reveals that these parents are stable against light clusters and unstable against heavy clusters. Computed half-lives for alpha decay agree with experimental values within two orders of magnitude. The most probable clusters from these parents are predicted to be 46 Ar, 48,50 Ca which indicate the role of doubly or near doubly magic clusters in cluster radioactivity. Odd A clusters are found to be favorable for emission from odd A parents. Cluster decay model is extended to symmetric region and it is found that symmetric fission is also probable which stresses the role of doubly or near doubly magic 132 Sn nuclei. Geiger-Nuttal plots were studied for various clusters and are found to be linear with varying slopes and intercepts.