Narrow Results

The cluster decay process is studied in the WKB approximation based on the unified fission model. The cluster is considered to be emitted by tunneling through a potential barrier taken as the sum of the Coulomb potential, the centrifugal potential and the modified Woods–Saxon (MWS) nuclear potential. The results of our calculations are compared to those obtained by other theoretical models as well as experimental data. It is shown that the unified fission model with the MWS nuclear potential can be successfully used to evaluate the cluster decay half-lives of heavy nuclei.

Empirical relations for the preformation probability of cluster decay process in terms of the Q-value, mass asymmetry (η), mass number of the emitted cluster A₂ is analyzed based on the discrepancy between the calculated and experimental half-lives of the cluster emitters. For the different empirical expressions considered corresponding to different physical quantities the preformation probability for the complete binary breakup of ²²⁶Ra is calculated and the obtained results are compared with the preformed cluster model calculation (P₀(PCM)) and another calculation in which the overlapping penetration probability is treated as the preformation probability (P₀(μ)). Our empirical results for the use of Q-value compare well with P₀(μ). Results due to the use of Q and its powers along with the combination of mass number A₂ of the cluster emitted, and mass asymmetry η, reveal that preformation factor depends strongly on Q-value rather than A₂ and η. Calculated half-lives of different cluster decays for the use of empirical P₀ values are found to be in good agreement with the experimental values.

The Coulomb and proximity potential model (CPPM), which comes under the class of fission models, has been used for the extensive study on the cluster decay process in ^298–336126 superheavy nuclei, and thus the probable cluster decays from the various isotopes of Z = 126 have been investigated and predicted. The Universal formula for cluster decay (UNIV) of Poenaru et al., the Universal Decay Law (UDL) of Qi et al., and the Scaling Law of Horoi et al., have also been used for evaluating the cluster decay half lives of these nuclei, and a comparison of the predicted decay half lives with the values evaluated using CPPM reveals that our predicted values matches well with these theoretical values. The behaviour of the cluster half lives with the neutron number of the daughter nuclei can be clearly seen from the plots for log₁₀(T_1/2) against the neutron number of the daughter nuclei in the corresponding decay, and these plots depicts that for most of the decays, the half life are the minimum for the decay leading to a daughter with N = 184. The odd-even staggering (OES) could be seen to be more prominent in the emission of heavy odd-mass clusters. The Geiger-Nuttall plots of log₁₀(T_1/2) versus Q^-1/2 and the Universal curve between -lnP and log₁₀(T_1/2) for various clusters ranging from ¹⁴C to ³⁰Mg from ^288–339126 isotopes have also been studied, and are found to be linear. Our study also reveals fact that, in cluster decays of SHN, the role of neutron shell closure is crucial than proton shell closure. Also, most of the predicted half lives are well within the present experimental upper limit (10³⁰s) and lower limit (10^-6s) for measurements and hence these predictions may be of great use for further experimental investigation on alpha and cluster decay in the superheavy region.

The one-proton emission, alpha decay and cluster decay using a Cubic Plus Proximity model with improved transfer-matrix method are executed for the first time for the study of decay properties of 368 isotopes of nuclei, far from the beta stability line and beyond the islands of stability $Z=130\text{–}144$ superheavy nuclei are studied within the range $290\le A\le 380$. The calculated decay half-lives are in good agreement with other theoretical approaches. The signature of neutron shell closure at $N=172,184,198,228,238$ and proton shell closure at $Z=138$ obtained from half-life curves for emission of different clusters pronounces the previous predictions. Investigation of competition between various decay modes brings out the dominant decay mode associated with an isotope; for a given $Z$ with increasing $A$ the dominant decay mode is seen to shift from proton decay to alpha decay and finally spontaneous fission. The decay modes and half-lives which are within the limit of experimental detection $10^{-6}s\le T_{1/2}\le 10^{30}s$ are presented.

The decay characteristics of various clusters and neutron halo nuclei from heavy elements $Z=92-102$ are studied within the framework of the Coulomb and Proximity Potential Model for Deformed Nuclei (CPPMDN) and using a new empirical formula proposed by us. The predictive power of our formula is verified by comparing the predictions with the available experimental data and with the predictions of other models such as CPPM, Universal Decay Law of Qi et al. (UDL), Unified Description formula (UD) of Ni et al. Using the present formula and CPPMDN, decay half-lives of various light clusters from heavy elements are calculated, and the results are compared with the predictions of UDL, UD, and predictions made by Santhosh et al. based on the Modified Generalized Liquid Drop Model (MGLDM). The decay half-lives of halo nuclei from heavy elements are also calculated using the new formula and CPPMDN and compared with the predictions of UDL, UD, and the predictions made by Santhosh et al. based on the Coulomb and Proximity Potential Model (CPPM).

The half-lives of the cluster decay (CD) from the isotopes having the known experimental values, the half-lives of the $\alpha$-decay (AD) of same nuclei and also the branching ratios are obtained, within the framework of two-potential approach with cosh potential including with and without the isospin effects. Using two-potential approach and taking into account the isospin effects in the calculations decrease the rms values and they improve the results. The obtained branching ratios are in good agreement with the experimental ones for some isotopes. It is obtained that the isospin-dependent potentials have an influence on the half-lives of the cluster decays of nuclei. Present calculations would be important for predicting the experimental half-lives and branching ratios for the cluster decays of different types of isotopes.

Using the Hartree–Fock–Bogoliubov mean-field theory, the ground-state structural and decay properties of Nd isotopes are investigated from the proton-rich side up to the neutron drip-line. Quantities such as binding energies per nucleon, one and two-neutron separation energies, rms charge radii, and quadrupole deformation parameters have been calculated. Compared with the relativistic mean-field results, the present calculations are in better agreement with the available experimental data. The results show clearly the signature of a shape transition at $N=90$ and an abrupt increase in the deformation near the neutron drip-line. Further, the possible decay modes like alpha, cluster and $\beta$-decay are analyzed in a unified fission model and phenomenological formulas. Overall, a good agreement is achieved between the calculated and experimental $Q$-values and half-lives wherever available. The most likely decay modes are thus identified throughout the isotopic chain.

Based on the Unified Fission Model with a Woods–Saxon potential (UFMWS), we have investigated alpha decay and cluster radioactivity of actinide nuclei. To ensure accuracy, we determined the most precise $Q$-values by comparing the results of four nuclear mass models: the liquid drop model (LDM), the DZ28 model, the WS4 model, and the finite range droplet model (FRDM), which were recently improved using a machine learning algorithm. Among these models, it is found that the improved WS4 (IWS4) provides the most accurate $Q$-values, enabling the UFMWS model to effectively reproduce experimental alpha and cluster decay half-lives. Consequently, the UFMWS model using IWS4 $Q$-values was employed to explore various combinations of parent nuclei and alpha particle as well as even–even emitted clusters ranging from Be to Si. The obtained results are consistent with previous study that identified minima in half-lives near corresponding to the doubly magic ${}^{208}$Pb daughter nucleus or its neighboring nuclei. It is found that neutron-deficient parent nuclei generally displayed the shortest half-lives, most of which are within the experimental range. Considering the experimental limitations, cluster decays favorable for measurement in the actinide region were identified. Interestingly, these decays did not involve the most neutron-deficient nuclei.