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.

In this paper, we systematically investigate the cluster decay half-lives of heavy nuclei using the Wentzel–Kramers–Brillouin method and Bohr–Sommerfeld quantization condition for the Morse molecular potential. We determine the optimal nuclear potential parameters that best fit the experimental data of known cluster decay half-lives. Subsequently, we theoretically calculate the cluster decay half-lives for the heavy nuclei lacking experimental decay half-lives. Our findings reveal that the Morse model is highly effective in explaining the decay half-lives of the heavy nuclei, particularly when utilizing two degrees of freedom. This approach produces results that match the accuracy of empirical models found in the existing literature. Theoretical determinations of cluster decay half-lives with optimally derived model parameters are expected to guide future experimental studies.

The DAMA project has obtained many competitive or new results in the search for various rare nuclear processes. Most of them have been obtained with the help of many different high purity crystal scintillators which have been measured in the low-background DAMA set-ups located in the Gran Sasso underground laboratory of INFN In this paper, the main results will be summarized.

A semiempirical formula with only three parameters for calculating the logarithm of half-lives of heavy particle emission from a radioactive nucleus is recently proposed. The constants in the formula were obtained by fitting the available data in the trans-actinide region. The suitability of the formula in trans-tin region is studied here. The present study reveals that the semiempirical formula with only three parameters is not agreeing well with other theoretical models in the trans-tin region. Hence, one of the constants proposed earlier which acts a scaling constant is suitably replaced by a quadratic equation. The results are compared with analytical superasymmetric fission model and Shanmugham and Kamalakaran model. The semiempirical formula with new set of constants are found to have a better agreement with the available theoretical results.

In this work, the logarithmic half-life [log₁₀(T_1/2)] values have been reported for the exotic decay of some neutron rich even–even parent nuclei (56≤Z≤64) accompanied by the emission of alpha-like and non-alpha-like clusters in the trans-tin region. These values were calculated by using the single line of universal curve (UNIV) for alpha and cluster radioactive decay as well as the universal decay law (UDL). The half-life values were also separately calculated by considering the interacting nuclear potential barrier as the sum of Coulomb and proximity potentials. The half-life values based on the three calculations mentioned above, were found to agree with one another within a few orders of magnitude. Possible conclusions are drawn based on the present study.

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.

We calculate the ground, first intrinsic excited states and density distribution for neutron-rich thorium and uranium isotopes, within the framework of relativistic mean field (RMF) approach using axially deformed basis. The total nucleon densities are calculated, from which the cluster-structures inside the parent nuclei are determined. The possible modes of decay, like $\alpha$-decay and $\beta$-decay are analyzed. We find the neutron-rich isotopes are stable against $\alpha$-decay, however they are very much unstable against $\beta$-decay. The life time of these nuclei predicted to be tens of second against $\beta$-decay.

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.

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.

We have studied systematically the alpha decay and cluster radioactivity half-life of heavy ${}^{245-260}$Mendelevium ($Z=101$) isotopes. The alpha decays from Md isotopes have been studied within the framework of Coulomb and proximity potential model using 14 different versions of nuclear potentials. Also, we have studied the half-lives of alpha decay of Md nuclei within the nuclear potentials generalized liquid drop model (GLDM) and also within GLDM with modified different nuclear potentials, namely proximity potential 2010, 1977, 1988, 2000 and 2002. Moreover, the half-lives of the $\alpha$-decay and cluster radioactivity calculated using the Universal formula for cluster decay (UNIV) of Poenaru et al., the Universal decay law (UDL) of Qi et al. and the Unified formula of half-lives for both the $\alpha$-decay and cluster radioactivity (UFADCR) of Ni et al. and found to be in good agreement. Our results have been compared with experimental data and demonstrate the acceptability of the approach. Among the different proximity potentials, GLDM with proximity 1977 version (GLDM$+$P77) ($\sigma =0.8509$) provides the best description for alpha decay studies with low deviation.

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).

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.

The cluster radioactivity of ${}^{222,224,226}$Ra, ${}^{223,225}$Ac, ${}^{232,234,235,236}$U, ${}^{236,238}$Pu, ${}^{234,236}$U, ${}^{232,233,234,235,236}$U and ${}^{230,232}$Th isotopes which emitted ${}^{14}$C, ${}^{24}$Ne, ${}^{28}$Mg, ${}^{26}$Ne, ${}^{28}$Mg, ${}^{24}$Ne, respectively, has been analyzed with the help of fractional calculus for investigating the connection between order of the fractional derivative and nuclear structure. When the neutron number of daughter nuclei is equal to magic number, order of the fractional derivative shows a maximum. It is shown that there is a relationship between the order of fractional derivative and shell effect. This order has a similar role to the preformation factor in cluster radioactivity.

The Coulomb and Proximity potential Model (CPPM) is improved by introducing an accurate empirical expression for the nuclear surface diffuseness parameter in the expression for the proximity potential. Within the improved CPPM, the decay half-lives of experimentally detected cluster emissions from heavy elements are calculated. The results of the calculations using the Universal Decay Law (UDL) [Qi et al., Phys. Rev. Lett. 103 (2009) 072501], the improved empirical formula of Sahu et al. (ImSahuB) [Wang et al., Chin. Phys. C 45 (2021) 044111], and the empirical formula of Horoi [J. Phys. G. Nucl. Part. Phys. 30 (2004) 945] are compared with the predictions of the improved CPPM. The lowest standard deviation is obtained for the predictions using the improved CPPM. The model’s predictive power increases significantly when the proximity potential is modified by including the diffuseness parameter. Furthermore, improved CPPM is employed to calculate the decay half-lives of undiscovered cluster emissions from heavy elements, a valuable information for upcoming experimental investigations. The calculated values are compared with the predictions of the UDL, Horoi formula and the improved empirical formula of Sahu et al. (ImSahuB). There is a high degree of agreement between the improved CPPM, UDL, and Horoi formula predictions. The ImSahuB formula predict decay half-life one or two order magnitudes lower than the predictions of the other models.

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 competition of cluster decay (CD) and α decay is investigated in the region of superheavy (SH) nuclei with atomic numbers Z = 104 – 124. Calculations of half-lives within analytical superasymmetric fission (ASAF) model are performed by using the newest AME12 mass table as well as different theoretical mass models to determine the energy released, Q. For α decay the calculations are made using semFIS (semi-empirical Fission) model. A trend toward shorter half-lives and larger branching ratios relative to alpha decay for heavier SHs is observed.

The cluster radioactivity of ^208–238Th was studied by using a fission-like model taking interacting potential as the sum of coulomb and proximity potentials. The emission of the particle is considered as a quantum tunneling penetration of the potential barrier in the semi-classical WKB approximation. The released energy is deduced from the new table of atomic mass evaluation (AME12) and from the Finite Range Droplet Model. The obtained decay half-lives are compared with the few available experimental values and those of the effective liquid drop model.