原子核中的结团发射现象

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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.

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This study explores the cluster decay half-lives in both experimentally measured and undetected radioactive nuclei within the mass number range The investigation employs the recently proposed preformation probability formula, focusing on the systematic behaviours governing cluster emissions. Emphasis is placed on the contribution of the Q-value during both preformation and decay processes. Experimental binding energy data are used to estimate Q-values, and the cluster penetration process is discussed using the M3Y and R3Y nuclear potentials. The interaction potential between the cluster and the daughter nucleus is obtained by folding the relativistic mean-field (RMF) densities with R3Y NN potential using the NL3* parameter set and compared with the phenomenological M3Y NN potential. The penetration probabilities are calculated from the WKB approximation. The formula is found to be a useful tool for understanding cluster radioactivity in heavy actinides. The result provides valuable insights into the systematics of cluster decay half-lives, highlighting the influence of neutron magic shell closures and interaction potentials on different cluster decay properties.

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In this study, based on the Wentzel-Kramers-Brillouin (WKB) theory, by parameterizing the assault frequency as a function of the decay energy and charge radius of parent nucleus, with the decay preformation factor being calculated through the cluster-formation model (CFM), we systematically investigate the decay half-lives of 559 nuclei from the ground state, including 177 even-even, 277 odd-A, and 105 odd-odd nuclei. The calculated results indicate that our model can effectively reproduce the experimental data, with a corresponding standard deviation of 0.408. In addition, we use this model to predict the decay half-lives of 70 even-even, odd-A, and odd-odd nuclei with Z = 119 and 120. For comparison, we also use the universal decay law (UDL) proposed by Qi et al. [Phys. Rev. Lett 103, 072501 (2009)] and the unitary Royer formula (DZR) proposed by Deng et al. [Phys. Rev. C 101, 034307 (2020)]. The calculated results are in good agreement.

Systematical evaluation of half-lives of four decay modes (proton emission, α decay, cluster radioactivity and spontaneous fission) toward a unified description are performed through the Bayesian neural network (BNN) method. In the BNN training, the existing experimental half-lives of nuclei are adopted directly as the target values. As a result, all of the predicated half-lives of the four decay modes agree with the experimental data well, and the BNN approach is possibly useful for evaluations of half-lives of decay modes even if rare/insufficient experimental data are available. In addition, the angular momentum Ι plays an important role in the prediction.

In this study, we systematically investigate the α decay half-lives of 263 emitters in the region and clusters 14C, 20O, 23Fe, 24,25,26Ne, 28,30Mg, and 32,34Si in the presence of an extended form of the Sextic potential to describe the strong nuclear interaction between the daughter nucleus and cluster in the parent nucleus using the Wentzel-Kramers-Brillouin (WKB) method. We find nuclear potential parameters that explain the decay mechanism for each variety of cluster and show that this form of double-well potential provides an excellent description of the nuclear decay phenomenon. We highlight constraints between the potential parameters and experimental data. Moreover, we emphasize the importance of the coupling parameters of the nuclear potential in the nature of the preformed cluster. The obtained results are compared with experimental and literature data. Our results are in very good agreement with the experimental data.

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Using four representative nuclear mass models, namely, WS4, FRDM, DZ10, and KTUY, we perform a systematic investigation on how nuclear masses affect the α-decay properties of superheavy nuclei, including decay energies, α-cluster preformation factors, and corresponding half-lives. The α-cluster preformation factors are obtained from two types of cluster-formation model (CFM) and extracted from experimental decay half-life. All mass models reproduce the known α-decay energies with small root-mean-square errors, while WS4 and FRDM show the highest accuracy. Strong correlations among preformation factors from different mass models are identified in both CFM and extracted results, although the exponential dependence of half-lives on decay energy weakens correlations between the two approaches. For possible α-decay chains of superheavy nuclei, the decay energy systematically decreases and the predicted half-life increases with decreasing proton number. This trend is also observed from the calculations for superheavy isotopes with same proton number. These results indicate that isotopes of superheavy elements with more neutrons are expected to exhibit enhanced stability, thus providing theoretical reference for future synthesis of elements with Z=119 and 120.

The study of superheavy nuclei (SHN) and their decay properties is one of the rapidly growing fields in nuclear physics. Using the CYE model, we have already studied the decay properties of the alpha decay, cluster decay, and spontaneous fission of the heavy and superheavy nuclei. In the present work, we will examine the effects by incorporating hexacontatetrapole (β6) parameter in the parent nucleus along with the quadrupole (β2), and hexadecapole (β4) deformations of the decaying parent nucleus emitting clusters 84Be and 126C. These deformations lower the half-life values, because they reduce the height and width of the potential barrier. Additionally, the creation of the doubly magic daughter 298114 from different decaying nuclei is computed. The calculated half-lives are compared with other models and are found to be in a good agreement. The branching ratios relative to the alpha-decay have also been calculated.

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The unique opportunity presented by 10B + 10B reactions to study high-energy, high-spin states in the A=10 mass region is explored. Results from the measurement at 72 MeV are presented, the most important being new and rarely seen states in the 12C [1] and 13C [2], which motivate targeted future experiments. In particular, a new state of 12C at Ex = 24.4 MeV is strongly populated in the triple α-particle coincidences, while the rarely seen state at Ex = 30.3 MeV is found to be strong in the d+10B decay channel, reinforcing the previous suggestions that it has the exotic 2α+2d molecular structure [3]. Regarding the 13C nucleus, a potentially novel state at Ex = 19.0 MeV is prominently observed in α+ 9Be coincidences and demonstrates a well-defined cluster structure. Lastly, high-spin states in mirror nuclei pairs 9Be-9B, 10Be-10C and 11B-11C populated in the presented measurement are explored.

Introduction: The emission of a particles is a powerful probe for the α-cluster structure of heavy nuclei. The α-nucleus potential is a crucial ingredient in the a-decay calculation within the preformed cluster model. One of the most reliable ways to construct this potential is the double folding model, where an effective nucleon-nucleon interaction is folded with the nuclear densities. In the folding model calculation, there are many ambiguities in the choice of the nuclear densities of the daughter nucleus for α-decay. We propose to directly constrain the α-nucleus potential for α- decay and choose the daughter nuclear density using the nuclear rainbow scattering phenomenon. Methods: The refractive rainbow pattern in the elastic scattering cross section within the optical model can probe deep into the interior region of the α-nucleus potential. We apply this method to investigate the reliability of the nuclear potential used in the α-decay of the 212Po nucleus leading to the 208Pb daughter nucleus by examining the elastic a scattering on 208Pb. In such an approach, we perform the double-folding calculation to construct the α-nucleus potential using several common parametrizations of the daughter nuclear densities. These parametrizations include the mean-field Hartree-Fock-Bogoliubov calculations with the BSk14 and D1S interactions, the independent particle model, and the 2-parameter Fermi distributions. The obtained nuclear potentials are applied to the optical model to calculate the elastic α-208Pb scattering cross sections that are compared with the experimental data. These nuclear potentials are further used in the preformed cluster model to study thea-decay half-life of 212Po. Results: The nuclear densities from the Hartree-Fock-Bogoliubov calculations are shown to provide the best description for both the nuclear rainbow scattering anda-decay half-life. The results indicate a strong correspondence between the capabilities of the nuclear potential to reproduce the cross section ofa scattering and the α-decay half-life. The extracteda preformation factors from the semiclassical preformed cluster model with folding potentials are in good agreement with those from other studies. Conclusion: The nuclear rainbow scattering phenomenon can be used to provide reliable a-nucleus potential for α-decay studies within the preformed cluster model. The nuclear densities from the mean-field Hartree-Fock-Bogoliubov method with the BSk14 and D1S interactions are the appropriate choices for the DFM calculation used in the α-decay study.

This paper presents a systematic investigation of α-decay properties in even-even isotopic chains of Po ( ), Cm ( ), Hs ( ), and Fl ( ) using a semi-classical approach. Ground-state properties, including binding energies and nucleon density distributions, are calculated by minimizing a Skyrme-based energy density functional augmented with microscopic corrections. The derived nuclear densities and -values are used to construct the α decay potential through the double-folding model (DFM). The α-decay dynamics are treated quantum mechanically based on the preformed cluster model (PCM) within the Wentzel-Kramers-Brillouin (WKB) approximation. The analysis reveals distinct signatures of spherical shell closures at and , along with secondary anomalies near , , and , which are consistent with deformed sub-shell effects predicted by nuclear structure models. The signature of daughter nuclear stability is systematically observed through one or more of the following features: shortened α-decay half-lives, enhanced values, increased penetrabilities, and/or reduced assault frequencies. A new universal scaling relation, relating the decay half-lives and a scaled combination of nuclear charge and decay energy, is established, showing strong correlation across a wide mass range. Systematic comparisons demonstrate particular predictive advantages for superheavy nuclei, with the proposed method accurately reproducing observed half-life variations across all isotopic chains. The results confirm the sensitivity of α-decay observables to both spherical and deformed shell effects and reinforce the role of α-decay systematics as powerful tools for probing nuclear structure and guiding predictions in unexplored regions of the nuclear chart.

In the present work, based on a Gamow-like model, considering the deformation effect of Coulomb potential, where the effective nuclear radius constant is parameterized, we systematically investigate the cluster radioactivity half-lives of 25 trans-lead nuclei. For comparison, a universal decay law (UDL) proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and a scaling law proposed by Horoi [J. Phys. G: Nucl. Part. Phys. 30, 945 (2004)] are also used. The calculated results within the deformed Gamow-like model are in better agreement with the experimental half-lives. The deformation effect is also discussed within both the Gamow-like and deforemed Gamow-like models. Moreover, we extend this model to predict the cluster radioactivity half-lives of 49 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.

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Some regularities of cluster decays are revealed, which make it possible to predict the existence of a large number of medium, heavy and, possibly, superheavy f-active nuclei. The stability of the majority of non-magic nuclides (products of cluster radioactivity) is explained by the simultaneous action of the already known factors slowing (stabilizing) the radioactive decays of atomic nuclei and some additional factors. Among the additional factors, a weakly expressed effect of pairing of α-particles in light nuclei can be noted. In some cases, an additional particle (neutron, proton or light cluster) contributes to the stability of the nucleus by intensifying the forces of mutual nuclear attraction. Compact arrangement of α-clusters in another additional factor stabilizing the nuclei. One more factor is associated with compact placement of neutrons (possibly paired) between α-clusters within the of light nuclei.

The study of cluster structures in light nuclei has become a central direction in modern nuclear physics. Experimental and theoretical investigations have revealed that many light systems, such as $^6\text{He}$, $^8\text{Be}$, $^{12}\text{C}$, and others, exhibit pronounced cluster configurations that strongly influence reaction mechanisms. Particularly striking is the $\alpha\text{-cluster}$ structure of $^{12}\text{C}$ and its excited Hoyle state, which plays a key role in astrophysical nucleosynthesis. Among light nuclei, the stable yet weakly bound $^9\text{Be}$ nucleus is of special interest due to its Borromean character and competing cluster configurations, typically described as $(\alpha+\alpha+n)$ or $(^5\text{He}+\alpha)$. These structural features manifest themselves in decay channels, scattering processes, and transfer reactions, and they directly affect the cross sections relevant for astrophysical scenarios such as the $\text{triple-}\alpha$ process and the $r\text{-process}$. The paper provides a comprehensive overview of theoretical and experimental approaches to nuclear clustering, emphasizes recent advances, and examines outstanding questions concerning the structure of $^{9}\text{Be}$ and its significance in nuclear reactions and nucleosynthesis. 

In 1980 A. Sǎndulescu, D.N. Poenaru from Bucharest, Romania and Walter Greiner from Frankfurt am Main, Germany, published an article in which cluster radioactivity was predicted. For years latter (1984) H.J. Rose and J.A. Jones from Oxford University reported the first experimental evidence of 14 C radioactivity of 223 Ra. Extensive calculations have been published by D.N. Poenaru et al. in 1986 and 1991 in Atomic Data and Nuclear Data Tables. A very useful review of experimental results was published by R. Bonetti and A. Guglielmetti from Milano, Italy in Romanian Reports in Physics 59 (2007) 301-310. In this article we compare the measured Q-values and half-lives with predictions within the Analytical Super-Asymmetric Fission (ASAF) model. Cluster radioactivity (spontaneous emission of particles larger than 4 He) is a rare phenomenon in a large background of alpha decay. For some very heavy nuclei it is possible to observe cluster radioactivity comparable or even stronger than alpha decay.

In recent years, the synthesis and identification of Superheavy elements have been of a great interest in the area of both experimental and theoretical nuclear physics. Using the CYE model, the alpha decay, cluster decay, and spontaneous fission in the heavy and superheavy nuclei have been studied. In the current work, we will investigate the α decay and obtain cluster decay half lifetimes in the interval Z = 127–138 and the spontaneous fission half lifetimes using the two-sphere approximation and will compare the results with the other theoretical values and the semiempirical formula by Xu et al. We believe that the predicted decay half-lifetimes are valuable for future tests, because they are in a good agreement with other theoretical formalisms.

The search for heavy elements has yielded many surprises and enhanced our knowledge of nuclear synthesis and associated dynamical aspects. Although new elements and their associated isotopes have been synthesized, information concerning elements with , remains scarce. Further, concerning the transfermium elements, the nuclear shell structure is key to ensuring nuclear stability. Hence, the shell effects have key implications on such nuclei. Many experimental and theoretical investigations have been conducted to examine the reactions induced by heavy ions and the subsequent decay mechanisms in the superheavy mass region. In addition, the region of transfermium elements is of great interest because of the neutron/proton shell effects. Here, our objective is to analyze the decay mechanisms of nuclides having Z = 102 nuclei, i.e., 248No* and 250No*. An extensive study was conducted using the dynamical cluster-decay model (DCM) based on Quantum Mechanical Fragmentation Theory (QMFT). The focus was to investigate compound nucleus (CN) and non-compound nucleus (nCN) mechanisms, including fusion-fission (ff), quasi-fission (QF), and fast fission (FF). The specific isotopes of interest are 248No* and 250No*, with attention given to the role of the center-of-mass energy and angular momentum . The nuclear interaction potential was derived using the Skyrme energy density formalism (SEDF) with the GSkI force parameters. The capture cross-sections were calculated using the -summed Wong Model. The determination of the probability of compound nucleus formation (PCN) involved a function that is dependent upon the center-of-mass energy. The lifetimes of the ff and QF channels were also investigated. Here, CN and nCN decay mechanisms for two isotopes of Z = 102 nobelium were analyzed over the range of center-of-mass values considering the quadrupole deformation and optimum orientations of the decaying fragments. The fragmentation potential, preformation probability, neck length parameter, and reaction cross-sections were explored. Further, PCN was calculated to determine the mechanisms of decay of 248No* and 250No* isotopes. The obtained fusion–fission lifetimes and quasi-fission lifetimes are compared with the dinuclear system (DNS) approach. Among the considered isotopes having Z = 102, i. e., the 248No* formed in the 40Ca + 208Pb reaction and 250No* formed via two different entrance channels, 44Ca+206Pb and 64Ni+186W, show asymmetric fragmentation with the effect of deformation at the energies beyond the Coulomb barrier. Of note, the nCN (QF and FF) decay mechanisms compete with the CN fission channels. The calculations based on the DCM show a strong correlation with the experimental data. The most probable fragments, such as 122Sn and 128Te, were observed near the magic shell closure at Z = 50 and N = 82. Further, as the excitation energy increased, the fusion–fission and quasi-fission lifetimes decreased.

The present investigation explores the fusion-fission phenomena in the field of nuclear physics, focusing particularly on their significance in astrophysical research, namely in the nucleosynthesis process occurring in the stars. The present work intends to investigate into the formations and fragmentation mechanisms of 104Cd* system, populated in the interaction of 40Ca and 64Ni ions at energies spanning the mutual electrostatic repulsion. For analysing the formation processes in complete fusion of 40Ca+64Ni channel, the fusion excitation functions are estimated via statistical CCFULL approach along with the dynamical model named as EDWSP. The dynamical effects are included via energy dependence. The fusion models suggests that it is imperative to include energy dependence and coupling effects to harmonize the experimental data. Furthermore, the Dynamical Cluster-decay Model (DCM) framework is exploited to scrutinized the fragmentation mechanism defining the decay of 104Cd*. The decay model suggests that the structure for evaporation residues and fission fragments gets altered by the incorporation of various angular momentum states. Other parameters such as nuclear deformations and neck-length parameter also pose influence on the structural aspects of decay profiles.

We systematically study the competition between {\alpha}-decay and spontaneous fission in even-even superheavy nuclei with (Z=120) and 256 \leq A \leq 304 within the preformed cluster-decay model using microscopic inputs from relativistic mean-field calculations with the NL3 parameter set. The {\alpha}-decay half-lives are obtained from WKB barrier penetration with empirically determined preformation factors, self-consistent Q_{\alpha} values from RMF, and nuclear interaction potentials constructed using both M3Y and relativistic R3Y nucleon-nucleon forces, and are benchmarked against standard semi-empirical formulas. Our results predict reduced spontaneous fission probabilities and extended {\alpha}-decay chains toward the fermium region for isotopes with 296 \leq A \leq 304, with enhanced stability reflected in maxima of log_{10} T_{1/2} around neutron numbers N \approx 166-182. In particular, the nuclei 296,298,300,302,304_{120} are identified as the most favorable candidates for survival against fission, demonstrating the crucial role of shell effects, deformation, and pairing correlations and providing quantitative guidance for future experimental searches of Z=120 nuclei.

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In this study, based on the framework of the Coulomb and proximity potential model (CPPM), we systematically investigate the cluster radioactivity half-lives of 26 trans-lead nuclei by considering the cluster preformation probability, which possesses a simple mass dependence on the emitted cluster according to R. Blendowske and H. Walliser [Phys. Rev. Lett. 61, 1930 (1988)]. Moreover, we investigate 28 different versions of the proximity potential formalisms, which are the most complete known proximity potential formalisms proposed to describe proton radioactivity, two-proton radioactivity, α decay, heavy-ion radioactivity, quasi-elastic scattering, fusion reactions, and other applications. The calculated results show that the modified forms of proximity potential 1977, denoted as Prox.77-12, and proximity potential 1981, denoted as Prox.81, are the most appropriate proximity potential formalisms for the study of cluster radioactivity, as the root-mean-square deviation between experimental data and relevant theoretical results obtained is the least; both values are 0.681. For comparison, the universal decay law (UDL) proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], unified formula of half-lives for α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)], and scaling law (SL) in cluster radioactivity proposed by Horoi et al. [J. Phys. G 30, 945 (2004)] are also used. In addition, utilizing CPPM with Prox.77-12, Prox.77-1, Prox.77-2, and Prox.81, we predict the half-lives of 51 potential cluster radioactive candidates whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are in the same order of magnitude as those obtained using the compared semi-empirical and/or empirical formulae. At the same time, the competition between α decay and cluster radioactivity of these predicted nuclei is discussed. By comparing the half-lives, this study reveals that α decay predominates.

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Using the analytical super asymmetric fission model (ASAFM), we have studied the light ( Zc≤14 ), medium ( 14<Zc<28 ), and heavy ( Zc≥28 ) cluster emission from even–even isotopes of superheavy nuclei Z = 122 in the mass region A = 300–314. The predicted half-lives for alpha and light clusters are compared with the predictions using different formalisms, such as the universal decay law (UDL), universal (UNIV) curve, and improved universal (Imp UNIV) curve. It is observed that UDL predictions have the least deviation from ASAFM values. The dip observed in the plot of log10T1/2 versus mass number, for alpha decay, at mass number A = 308 highlights the stability of daughter nuclei 304120, which is due to the neutron shell closure at N = 184 and predicted proton shell closure at Z = 120. We have identified isotopes of Sr, Zr, Mo, Cd, In, Sn, etc are the heavy clusters with half-lives comparable to alpha half-lives. The heavy clusters 82Ge, 83As, 84Se, 85Br, 86Kr, etc are also probable for emission from 300–314122. The role of deformed and spherical proton shell closure Z = 38, 40, 50, 82 and spherical neutron shell closure N = 50, 82, 126 of emitted cluster and residual nuclei are evident in heavy cluster radioactivity. The modes of decay of isotopes 300–314122 are analysed by comparing α half-lives and corresponding spontaneous fission (SF) half-lives evaluated by using the improved formula of Yuan et al It is found that the isotopes 300122, 302122, 304122, 306122, and 308122 will survive spontaneous fission and decay via 8α chains, 5α chains, 2α chains, 3α chains, and 1α chain, respectively, which could be of great interest to the experimentalists.

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The effective liquid drop model (ELDM) is improved by introducing an accurate nuclear charge radius formula and an analytic expression for assaulting frequency. Within the improved effective liquid drop model (IMELDM), the experimental cluster radioactivity half-lives of the trans-lead region are calculated. It is shown that the accuracy of the IMELDM is improved compared with that of the ELDM. At last, the cluster radioactivity half-lives that are experimentally unavailable for the trans-lead nuclei are predicted by the IMELDM. These predictions may be useful for searching for new candidates for cluster radioactivity in future experiments.

In this article, we modified the universal (UNIV) formula of Poenaru et al [Phys. Rev. C 83, 014601 (2011)] by including the disintegration energy-dependent formula as a preformation factor. The improved universal formula (Imp UNIV) is applied to α decay of 309 heavy nuclei in the region Z = 74–93 and found that the standard deviation, σ of decimal logarithmic half-life decreased from 0.64312 (UNIV) to 0.56467 (Imp UNIV). It is also observed that the σ value decreased from 0.70502 (UNIV) to 0.68189 (Imp UNIV) in the case of cluster radioactivity showing improvement of present formalism Imp UNIV over UNIV in reproducing experimental half-lives of α and cluster radioactivity of heavy nuclei. The α decay half-lives of 80 superheavy nuclei (SHN) with Z≥104 have also been investigated by UNIV and Imp UNIV formula and the σ value is found as 1.10681 and 0.69399 respectively, which shows that experimental α half-lives of SHN can be reproduced well by using Imp UNIV formula. The plot connecting the sum of the decimal logarithm of half-life and preformation factor, log10T1/2(s)+log10S versus the decimal logarithm of external penetrability, −log10Ps for Imp UNIV is found linear for both α and cluster radioactivity with the same slope and intercept showing the universal nature of the curve. The good agreement between our predictions on α decay of Og (Z = 118) isotopes with the generalized liquid drop model (GLDM) and Royer formula reveals our formalism's reliability. The neutron shell closure at N = 184 and N ≈ 200 are evident in our study. The prediction of the unobserved α and cluster radioactivity performed in this study will be helpful for future experiments.

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In the present work, derived from Balasubramaniam’s formula [Phys. Rev. C 70, 017301 (2004)], further considering the effects of parent nucleus mass, blocking effect and reduced mass on cluster radioactivity half-lives, we propose a new Geiger-Nuttall law which is model-independent for systematically evaluating the half-lives of this process for 10 even-even nuclei and 16 odd-A nuclei. For comparison, a single universal curve for cluster radioactivities and α decay proposed by D. N. Poenaru [Phys. Rev. C 83, 014601 (2011)], a scaling law proposed by M. Horoi [J. Phys. G: Nucl. Part. Phys. 30, 945 (2004)], an extension of Viola-Seaborg formula from α decay to cluster radioactivity proposed by Ren et al. [Phys. Rev. C 70, 034304 (2004)], a new semi-empirical formula for exotic cluster decay proposed by M. Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)] and a unified formula of half-lives for α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives with the least rms being 0.605 and are better than the compared ones. Moreover, we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energy are energetically allowed or observed but not yet quantified in NUBASE2020.

In this study, we investigate the cluster radioactivity (CR) of new superheavy elements with and 120 based on two successful theoretical methods with modified parameters: the density-dependent cluster model (DDCM) and unified decay formula (UDF). First, we employ the DDCM and UDF to accurately reproduce the experimental half-lives of cluster emissions, which demonstrates the high reliability of our theoretical methods. Then, we systematically predict the probable cluster modes of 293-311119 and 293-302120 as well as their corresponding decay energies and half-lives. The half-lives of cluster decay derived from the DDCM are consistent with those from the UDF. Therefore, our results reveal that the cluster emission of 8Be, emitted from the 119 and 120 isotopic chains, exhibits the minimum half-life for cluster emission, and hence, 8Be emission is considered the most probable cluster decay mode. Moreover, we explore the competition between α decay and CR and find that α decay may be the dominant decay mode against CR. Furthermore, the good linear relationship between the decay energy and the number of α particles within the emitted cluster is extended to the range of superheavy nuclei (SHN). We anticipate that our theoretical predictions for CR will provide valuable references for the experimental synthesis of new SHN.

In this study, considering the modified preformation probability to be , where and are the α-particle preformation probability and an adjustable parameter proposed by Wang et al. [Chin. Phys. C 45, 044111 (2021)], respectively, we extend a new simple model put forward by Bayrak [J. Phys. G 47, 025102 (2020)] to systematically study the cluster radioactivity half-lives of 28 trans-lead nuclei ranging from to , which is based on the Wentzel-Kramers-Brillouin approximation and Bohr–Sommerfeld quantization condition. For comparison, a universal decay law proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a three-parameter model-independent formula put forward by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and the semi-empirical model proposed by Tavares et al. [Eur. Phys. J. A 49, 1 (2013)] are used. Our calculated results reproduce the experimental data well, with a standard deviation of 0.818. Furthermore, we use this model to predict the cluster radioactivity half-lives of 51 possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in NUBASE2020.

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In this study, based on Wentzel-Kramers-Brillouin theory, we systematically investigate the cluster radioactivity half-lives of 22 nuclei ranging from to using a phenomenological model that considers the screened electrostatic effect of the Coulomb potential. In this model, there are two adjustable parameters, t and g, which are related to the screened electrostatic barrier and the strength of the spectroscopic factor, respectively. The calculated results indicate that this model can effectively reproduce the experimental data, with a corresponding root-mean-square deviation of 0.660. In addition, we extend this model to predict the half-lives of possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2020. The predicted results are consistent with those obtained using other theoretical models and/or empirical formulas, including the universal decay law proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh et al. [J. Phys. G 35, 085102 (2008)], and a unified formula for the half-lives of α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)].

A simple relation (aZc+b)(Zd/Q)1/2+(cZc+d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(aZ_{c} + b)(Z_{d}/Q)^{1/2} + (cZ_{c} + d)$$\end{document} of estimation of the half-life of cluster emission is further improved for cluster and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-decays, separately, by incorporating isospin of parent nucleus as well as angular momentum taken away by the emitted particle. This improved version is not only found robust in producing experimental half-lives belonging to the trans-tin and trans-lead regions but also elucidates cluster emission in superheavy nuclei over the usual α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-decay. Considering daughter nuclei around the doubly magic 100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{100}$$\end{document}Sn and 208\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{208}$$\end{document}Pb nuclei for trans-tin and trans-lead (including superheavy) parents, respectively, a systematic and extensive study of 56 ≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le $$\end{document} Z ≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le $$\end{document} 120 isotopes is performed for the light and heavy cluster emissions. A fair competition among cluster emission, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-decay, spontaneous fission, and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-decay is observed in this broad range resulting in a substantial probability of C to Sr clusters from several nuclei, which demonstrates the adequacy of shell effects. The present article proposes a single, improved, latest-fitted, and effective formula of cluster radioactivity that can be used to estimate precise half-lives for a wide range of the periodic chart from trans-tin to superheavy nuclei.

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Theoretical predictions of [Formula: see text]-decay properties of several isotopes of the superheavy nucleus of [Formula: see text] [Formula: see text] and their consecutive [Formula: see text]-decay chains are presented. Based on the double-folding model, the [Formula: see text]–daughter interaction potential is constructed microscopically using a realistic M3Y–Paris nucleon–nucleon (NN) interaction. The [Formula: see text]-decay half-lives are computed for both spherical and deformed shapes of daughter nuclei within the density-dependent cluster model. The effect of deformation is found to decrease the [Formula: see text]-decay half-lives compared to spherical shapes. The calculated [Formula: see text]-decay half-lives are in satisfactory agreement with their counterparts using other theoretical methods. The prediction of the dominant decay mode for the isotopes [Formula: see text], which have not yet been experimentally synthesized, is presented through the competition between [Formula: see text]-decay and spontaneous fission. We have found that the isotopes [Formula: see text] survive fission and have relatively long half-lives which span the order [Formula: see text]–[Formula: see text]. Moreover, the correlation between the logarithm of the preformation probability deduced from the cluster formation model and the fragmentation potential for even–even [Formula: see text] isotopes is elucidated showing a negative linear relation. The feasibility of cluster emission from the superheavy isotope [Formula: see text] is investigated using different theoretical approaches. The predictions can provide useful guidance for future experimental researches.

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In this study, the B3Y-Fetal \(NN\) interaction, originating from the lowest order constrained variational approach (LOCV), is applied to investigate cluster radioactivity in energetically favoured trans-lead nuclei from \(^{221}\mathrm {Fr}\) to \(^{242}\mathrm {Cm}\) within the preformed cluster model, using the Wentzel–Kramers–Brillouin (WKB) theory. Five density-dependent parametrizations are considered to ascertain the most suitable one for cluster radioactivity. The statistical cluster preformation probability is employed and compared with the well-known empirical mass-dependent preformation factor. The predictive power of the BDB3Y1 and BDB3Y0 with the statistical probability is found to give the most accurate description of decay half-lives. These findings underscore the applicability of the B3Y-Fetal interaction in cluster radioactive decays and the reliability of statistical preformation probability in exploring similar decays within the uncharted region of the nuclear landscape. Furthermore, our results demonstrate that DDB3Y1 can aptly address the peculiarity and deviations known for \(^{14}\)C clusters, which is a strongly bound nucleus with \(N/Z = 1.33\). The extension of this study to the prediction of energetically favoured but unobserved cluster radioactive decays holds prospects for future experimental endeavours. Published by the Jagiellonian University 2026 authors

Cluster radioactivity has been successfully described as a super-asymmetric fission mode within the microscopic self-consistent Gogny Hartree-Fock-Bogoliubov approximation [Phys. Rev. C 84, 044608 (2011)]. For nuclei preserving the neutron-to-proton $N/Z$ ratio of the doubly magic $^{208}$Pb, a cluster radioactivity fission valley has been identified. Such a valley can also be found both in actinides and super-heavy nuclei. In this paper, chains of isotopes and isotones are examined to determine the limits of existence of the cluster radioactivity fission mode. It is shown that the super-asymmetric valley can be found in a wide range of the nuclear chart. Nevertheless, the valley flattens more and more when diverging from the isospin asymmetry of $^{208}$Pb. For neutron-deficient nuclei with $N/Z<$ 1.41, it is found that the valley diminishes before reaching the scission point, and cluster radioactivity can not be observed.

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The possibility of cluster radioactivity (CR) of the neutron-deficient nuclei in the trans-tin region is explored by using the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), and several sets of analytic formulas. It is found that the minimal half-lives are at N d  = 50 ( N d is the neutron number of the daughter nucleus) for the same kind cluster emission because of the Q value (released energy) shell effect at N d  = 50. Meanwhile, it is shown that the half-lives of α -like ( A e  = 4 n , Z e  =  N e . Z e and N e are the charge number and neutron number of the emitted cluster, respectively.) cluster emissions leading to the isotopes with Z d  = 50 ( Z d is the proton number of the daughter nucleus) are easier to measure than those of non- α -like ( A e  = 4 n  + 2) cases due to the large Q values in α-like cluster emission processes. Finally, some α -like CR half-lives of the N d  = 50 nuclei and their neighbours are predicted, which are useful for searching for the new CR in future experiments.

Using Cubic plus Yukawa plus Exponential (CYE) model, half lives of alpha decay and heavy cluster radioactivity of Superheavy nuclei have been systematically investigated for even-even, even-odd, odd-even and odd-odd nuclei with 100 ⩽ Z ⩽ 120. 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 predicted half life time values by including deformation effects on parent and parent cluster have been compared with theAnalytical Super Asymmetric Fission (ASAF) model of D.N.Poenaru et.al. In this work, we have compared the half life time values of alpha and heavy cluster radioactivity of Super heavy nuclei leading to 208Pb. This study suggests that heavy-cluster radioactivity may be comparable to or even dominant over a decay for some of the isotopes with Z ⩾ 118. Furthermore, branching ratio calculations have been performed to find out the probable cluster emitters. The predictions for cluster emitters are in agreement with CPPM model by Santhosh et. al.,and Wentzel-Kramers-Brillouin (WKB) method by A.Soylu et. al. We hope that this study will help in future measurements on α-decay and cluster radioactivity half-lives of SHN.

As an important decay model of unstable superheavy nuclei, the cluster radioactivity half-lives of the ^306-339 126 isotopes is calculated by using universal decay law (UDL formula) and the scaling law of Horoi (Horoi formula), which can describe cluster radioactivity very well. The result of the two formulas' calculation is compared and analyzed. it shows that there is a long half-life at N=200 and 206. And ^318 126 is extremely unstable in cluster radioactivity.

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A linear universal decay formula is presented starting from the microscopic mechanism of the charged-particle emission. It relates the half-lives of monopole radioactive decays with the Q values of the outgoing particles as well as the masses and charges of the nuclei involved in the decay. This relation is found to be a generalization of the Geiger-Nuttall law in alpha radioactivity and explains well all known cluster decays. Predictions on the most likely emissions of various clusters are presented.

The resonant 14N+α particle scattering was studied in the 18F excitation region from 6.5 to 9 MeV at Astana cyclotron using the TTIK approach. The excitation functions for the elastic 14N+α scattering were analyzed in the framework of R-matrix approach. The observed strong alpha cluster structure in 18F is compared with that in 18O.

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Can relativistic heavy-ion collisions only probe the global shape of colliding nuclei, or their detailed internal structure as well? Taking $^{20}$Ne as an example, we attempt to directly probe its internal $\alpha$-cluster structure, by comparing experimentally measured observables in collisions at relativistic energies from density distributions of $^{20}$Ne with and without $\alpha$-cluster structure. Since the two density distributions give the same nucleus size and deformation, they lead to similar mid-rapidity observables. However, the $\alpha$-cluster structure may considerably reduce the free spectator nucleon yield and enhance the spectator light nuclei yield, as a result of more compact initial phase-space distribution of nucleons inside $\alpha$ clusters. We propose to measure the scaled yield ratio of free spectator neutrons to charged particles with mass-to-charge ratio $A/Z = 3$, 3/2, and 2 in ultra-central $^{20}$Ne+$^{20}$Ne collisions, which is found to be reduced by about $25\%$ at $\sqrt{s_\mathrm{NN}} = 7$ TeV and about $20\%$ at $\sqrt{s_\mathrm{NN}} = 200$ GeV with $\alpha$-cluster structure in $^{20}$Ne. This scaled yield ratio thus serves as a robust and direct probe of the existence of $\alpha$-cluster structure in $^{20}$Ne free from the uncertainty of mid-rapidity dynamics.

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Preliminary results of a study on triton clustering in neutron-rich 10Be and 12Be isotopes through triton (p,α) and alpha (d,6Li) transfer are presented. The experiment was performed using the LISE fragmentation beam line of GANIL, making use of the MUGAST-EXOGAM-ZDD setup, which ensures accurate measurement of charged particles and gamma-rays. The experiment, currently under analysis, aims to compare the measured differential cross sections with DWBA calculations performed using microscopic and cluster wave functions derived from models such as AMD or THSR. This ongoing analysis aims to provide quantitative insights into triton clustering in neutron-rich beryllium isotopes. The detection setup used in this experiment is presented, along with preliminary results on the data analysis.

Using the improved string-melting version of a Multi-Phase Transport model, we investigated the impact of nuclear geometry of $^{16}$O on anisotropic flows in O+O collisions at $\sqrt{s_{\rm NN}} = 200$ GeV. To evaluate the influence of nuclear structure and potential alpha clustering, we implemented four candidate configurations: Woods-Saxon, tetrahedron, square, and Nuclear Lattice Effective Field Theory. Initial-state geometry is quantified via the eccentricity cumulant ratio $\varepsilon_{2}\{4\}/\varepsilon_{2}\{2\}$, which provides a robust and evolution-independent measure sensitive to configuration differences. The model reproduces $v_{2}(p_{\rm T})$ at low $p_{\rm T}$ and $v_{3}(p_{\rm T})$ across the full $p_{\rm T}$ range, with integrated $v_{2}\{2\}$ and $v_{3}\{2\}$ matching the STAR data, demonstrating that transport dynamics captures the essential collectivity in this intermediate-size system. These findings establish a baseline for extending nuclear-structure studies in O+O collisions to other energies and differential observables within a unified transport model framework.

Helium(4He, or α)is the second most abundant element in the observable Universe. The α-particle induced reactions such as(α, γ), (α, n) and (α, p) play a crucial role in nuclear astrophysics, especially for understanding stellar heliumburning. Because of the strong Coulomb repulsion, it is greatly hindered to directly measure the cross sections for these α-capture reactions at stellar energies. Alpha-cluster transfer reaction is a powerful tool for investigation of astrophysical(α, γ), (α, n)and(α, p)reactions since it can preferentially populate the natural-parity states with an α-cluster structure which dominantly contribute to these astrophysical α-capture reactions during stellar heliumburning. In this paper, we reviewthe theoretical scheme, theexperimental technique, astrophysical applications and the future perspectives of such approach based on α-cluster transfer reactions.

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The intricate tapestry of the universe is woven from the interplay of elementary particles and the fundamental forces governing their interactions. Phenomena at all scales, from the subatomic realm of quarks and leptons to the grand structures of galaxies, are ultimately manifestations of these interactions. While the Standard Model of particle physics offers a robust framework for describing the most basic processes, the pathways from these elementary interactions to the emergence of stable nuclei, complex elements, and ultimately, life, remains a profound and unresolved challenge. Pivotal to bridging this gap is the development of effective theoretical models that can accurately characterize the forces between composite particles, such as atomic nuclei, which are themselves complex, many-body quantum systems. This paper rigorously examines the Ali-Bodmer potential—a seminal, phenomenological model introduced in 1965 to describe the interaction between alpha particles. By systematically analyzing its mathematical structure and success in reproducing experimental scattering data, we elucidate the model’s central role as a "folding model," which conceptually simplifies complex many-body interactions into a more tractable two-body potential. The enduring impact of the Ali-Bodmer potential is further highlighted through its diverse applications in the study of nuclear systems and astrophysical processes, such as the triple-alpha process responsible for forging carbon in stars. By tracing the legacy of this foundational model, we connect the historical evolution of theoretical nuclear physics to contemporary frontiers in quantum science, demonstrating the profound and far-reaching consequences of elementary particle interactions, from the formation of matter to the very principles of quantum entanglement that underpin the rapidly developing field of quantum computing.

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We explore the connection between the appearance of quasi-stable structures in mean-field type calculations, which arise as a result of the evolution of the underlying shell structure as a function of deformation, and $\alpha$-clustering in light even-even nuclei. The Nilsson-Strutinsky mean-field approach employs a macroscopic liquid-drop whose energy is modified by a shell correction term derived using the Strutinsky method. This method reflects the variations in the energies of the single-particle states with deformation. As such, there is no obvious connection to clustering. Here we use the changing level scheme of the deformed harmonic oscillator as a function of triaxial deformation to fully explore the variation in stability of $\alpha$-cluster structures in light even-even nuclei. The energies of the harmonic oscillator levels are used to deduce the energy required to disrupt the $\alpha$-cluster as a function of the triaxial deformation. We find that there is good agreement between variations in the shell correction energy in the mean-field method and the energy required to disrupt the $\alpha$-cluster. This provides a necessary link between understanding of the appearance of quasi-stable $\alpha$-cluster structures and quasi-stable shapes appearing in mean-field calculations.

It is important to understand whether $$\alpha $$ α -clustering structures can leave traces in ultra-relativistic heavy ion collisions. Using the modified AMPT model, we simulate three $$\alpha $$ α + core configurations of $$^{44}$$ 44 Ti in $$^{44}$$ 44 Ti $$ +^{44}$$ + 44 Ti collisions at $$\sqrt{s_{NN}}=5.02$$ s NN = 5.02 TeV as well as other systems with Woods-Saxon structures. One of these configurations has no additional constraint, but the other two have the Mott density edge $$r_{\textrm{Mott}}$$ r Mott set as either a lower or upper bound on the cluster position $$r_{\alpha }$$ r α to check the influence of $$\alpha $$ α dissolution. This is the first time that the initial stage of the geometric properties in heavy-ion collisions has been configured using the traditional treatment of the nuclear structure. We compare the radial nucleon density, multiplicity distribution, transverse momentum spectra, eccentricity, triangularity, elliptic flow and triangular flow of these six systems. $$\alpha +$$ α + core structures can alter all these observations especially in the most-central collisions, among which elliptic flow is the most hopeful as a probe of such structures.

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In a phenomenological approach, the $$\alpha $$ α + core structure is investigated in the $$^{20}$$ 20 Ne, $$^{44}$$ 44 Ti, $$^{94}$$ 94 Mo, $$^{104}$$ 104 Te, and $$^{212}$$ 212 Po nuclei through the local potential model using a double-folding nuclear potential with effective nucleon-nucleon interaction of M3Y + $$c_{\textrm{sat}}\delta (s)$$ c sat δ ( s ) type, where the term $$c_{\textrm{sat}}\delta (s)$$ c sat δ ( s ) acts only between the saturation regions of $$\alpha $$ α -cluster and core. Properties such as energy levels, $$\alpha $$ α -widths, B ( E 2) transition rates, and half-lives are calculated, and good level of agreement with experimental data is obtained in general. It is shown the inclusion of the term $$c_{\textrm{sat}}\delta (s)$$ c sat δ ( s ) is determinant for a better description of the experimental energy levels compared to the ground state bands produced with the simple M3Y interaction. The properties calculated for $$^{104}$$ 104 Te reinforce the superallowed $$\alpha $$ α -decay feature for this nucleus, as indicated in previous studies.

We calculated the energy spectra of the neutron-rich He $\Lambda$ hypernuclei with $A=6$ to 9 within the framework of an $\alpha + \Lambda +Xn$ ($X=1$--4) cluster model using the cluster orbital shell model. The employed constituent particles reproduce their observed properties. For resonant states of core nuclei such as $^5$He, $^6$He, and $^7$He, the complex scaling method is employed to obtain energies and decay widths. The calculated ground states of $^6_{\Lambda}$He and $^7_{\Lambda}$He are in good agreement with published data. The energy levels of $^8_{\Lambda}$He and $^9_{\Lambda}$He are predicted. In $^9_{\Lambda}$He, we find one deeply bound state and two excited resonant states, which are proposed to be produced at the Japan proton accelerator research complex (J-PARC) by the double-charge-exchange reaction $(\pi^-, K^+)$ using a $^9$Be target.

The nuclear clustering, as a quantum phase transition phenomenon governed by strong interactions, exhibits characteristics that are highly sensitive to the specific features of nuclear forces. Here, we examine how nuclear deformation and tensor forces influence $\alpha$-cluster formation in light nuclei. The axially deformed relativistic Hartree-Fock-Bogoliubov model is utilized to investigate the clustering structure of the $^{20}$Ne nucleus, at both the ground state and the excited state with a superdeformed prolate. The nuclear binding energies and the canonical single particle levels are obtained at different quadruple deformation, and the role of tensor force embedded in the Fock diagram of $\pi$-pseudovector ($\pi$-PV) coupling is revealed. It is shown that the level branches from the degenerated spherical orbits at the deformed prolate case are enlarged due to the extra contribution from pion-exchanged tensor force. Correspondingly, the excitation energy in this superdeformed prolate state is reduced due to the noncentral tensor interaction, leading to a predicted value which is much closer to the referred threshold for the $2\alpha$ decay mode of $^{20}$Ne. Possible $\alpha$-clustering configurations in $^{20}$Ne are then characterized by examining the nucleonic localization function. Although the contribution to the ground state is relatively small, the density profile and nucleonic localization are significantly changed by the pion tensor force for the superdeformed prolate excited state, as further evidenced by characterising the level mixing in the spherical basis components. The results reveal the extra role of the tensor force, correlated to the evolved single-particle levels with nuclear deformation, in the formation and stability of nuclear clustering.

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We investigate the impacts of nuclear $\alpha$-clustering structures and nucleon--nucleon cross-section on nuclear stopping power for ${}^{16}\text{O}$ + ${}^{40}\text{Ca}$ collisions below 300 MeV/nucleon using an extended quantum molecular dynamics (EQMD) model. Our results show that the specific $\alpha$-clustering configurations of ${}^{16}\text{O}$--including chain, square, kite, and tetrahedron--have a significant effect on collision dynamics. Among them, the tightly bound tetrahedral structure exhibits the highest stopping power. Moreover, the repulsive Coulomb interaction is found to reduce the stopping power of protons in the Fermi-energy domain. At higher energies, the decreasing trend is influenced by both the nucleon--nucleon cross-section and the mean field.

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Bijker and Iachello’s algebraic cluster model (ACM) and its extension to the cluster shell model (CSM), provides a new theoretical platform for the study of alpha-clustering in light nuclei. It led to the discovery of the D3h symmetry in 12C and 20Ne, with the discovery in 12C of a new g.s. rotational band with the spin sequence of, 0+, 2+, 3-, 4+/4- and 5-, including the predicted 4+ and 4- parity doublet. Applications of the CSM shell model to particle molecular orbits in 9Be and 13C (C2’ and D3h’ particle symmetries, respectively), lead us to conjecture molecular hole states in 7Be and 19F. We observe in these nuclei the predicted phenomenological structure. And we further consider conjectured p-h states in 8Be with the predicted phenomenological p-h structure of rotational band at high excitations of approximately 20 MeV. A search for these rotational band in 8Be was performed at ISOLDE.

We investigate medium-energy angular distributions data of proton elastic scattering on $^{12}$C, with the aim to probe the existence of cluster distributions in the ground state of $^{12}$C. In our approach, we exploit Coupled-Channel calculations to describe the scattering from a spheroidal-like structure, and we include a further contribution, based on a diffraction scattering formula, to explicitly take into account a possible triangular $\alpha$-cluster structure of the target. From the present analysis, we find a quite small cluster component in $^{12}$C ground state (with an upper limit on the occurrence probability of $1\%$, $99.75\%$ confidence level) and an inter-cluster distance of $\simeq 3.9$ fm. These values are compared with several theoretical predictions reported in the literature.

In the present work, we use the complex-energy shell model formalism to describe the alpha decay of the 212Po nucleus. Single-particle bases constructed from Woods-Saxon potentials are used to build many-body basis. Spin-isospinGaussian effective interaction between all pairs of nucleons is considered. Four-body spectroscopic factor and single-particle width are calculated. The stability of the spectroscopic factor renormalization protocol is demonstrated, thus ensuring its physical significance, and its influence on the calculated alpha decay is presented. It is observed that the renormalization modifies the calculated half-life by∼40 %, which is a value three times larger than the experimental. Still, without appealing to any cluster structure from the beginning, i.e., all calculations were carried out using single nucleon degree of freedom.

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Elastic scattering cross sections are a fundamental aspect of nuclear physics research, and studying the cross sections of various nuclei can provide important insights into the behavior of nuclei. In this study, the elastic scattering cross sections of 10C projectile by 27Al, 58Ni, and 208Pb target nuclei are analyzed. The aim of this study is to investigate the cluster structure of 10C and the sensitivity of the elastic scattering cross sections to different potentials. To achieve this objective, the double folding optical model and a simple cluster approach are used to analyze the cross sections. The real part of the optical potential is obtained by folding two different effective interactions, Michigan-3-Yukawa (M3Y) and JeukenneLejeune-Mahaux (JLM), with four different cluster density distributions of the 10C nucleus: 6Be + \alpha, 9B + p, 8Be + p + p, and \alpha + \alpha + p + p. The imaginary part is taken to be a Woods-Saxon phenomenological form. The sensitivity of the elastic scattering cross sections to different potentials is assessed by comparing the results obtained using different potentials. The cluster structure of 10C is validated by comparing the theoretical results with experimental data. The results show that the cross sections are sensitive to the choice of potential used and that the cluster structure of 10C is validated. The theoretical results show reasonable agreement with the experimental data.

Neutron-rich light nuclei are pivotal contributors in the nucleosynthesis process and the degree of alpha ( α ) clustering exerts significant influence on astrophysical reaction rates. Therefore, it is imperative to investigate the α -clustering in the isotopic chain of light mass nuclei. In this study, we have examined the evolution of the probability of α -cluster preformation in 41 , 45 , 49 Ca ∗ nuclei formed through neutron-induced reactions within the quantum mechanical fragmentation theory (QMFT). The results indicate a monotonous decrease in the α -cluster preformation factor as one moves from 41 Ca ∗ toward the neutron-rich 49 Ca ∗ nuclear system. Further, we have incorporated within QMFT, for the first time, the microscopic nuclear potential derived from folding the Fermi form fitted cluster densities from relativistic mean field theory and M3Y nucleon–nucleon interaction. We have varied the neutron skin thickness of the Ar cluster, which is complementary to the α -cluster, and its subsequent impact on the nuclear interaction potential and α -cluster preformation factor has been analyzed. The results demonstrate that, with the growth of neutron skin of the Ar cluster, the α -cluster preformation factor decreases. It highlights a relationship between neutron skin thickness and α -cluster preformation factor in these light mass 41 , 45 , 49 Ca ∗ nuclei.

The understanding structure and composition of compound nuclei provide valuable insights into nuclear reaction mechanisms, including decay modes and cross sections. The compound nucleus is a transient state where the nucleons from the projectile and the target nuclei combine, leading to a complex system. The interpretation of the intricate structure of the nucleus necessitates a crucial factor that facilitates its construction. This knowledge enables the calculation for cross sections of every decay particle in a nuclear reaction on individual basis. This factor is incorporated in the Dynamical cluster-decay model (DCM), known as the preformation probability, often denoted as P 0 . This is the key factor in determining the outcomes of nuclear reactions. Preformation probability refers to the plausibility of a specific configuration or state occurring in a system before a particular event or measurement. In theoretical models the preformation probability aid in predicting fission fragment yields. One of the notable advantages of the DCM is its incorporation of preformation probability, making it a more comprehensive framework compared to other fission models. This study explores the significance of P 0 , paving the way for breakthroughs in nuclear research and applications.

The present work analyzes the α + core structure in 104Te using the local potential model. The α + core interaction is described by a nuclear potential of (1 + Gaussian)×(W.S. + W.S.3) shape. The energy levels, total α widths and rms intercluster separations are determined for the ground state band and compared with a previous calculation which uses a double-folding potential. The two potential forms produce similar spectra between the 0+ and 14+ states. The antistretching effect is predicted for the 104Te ground state band, as is observed in previous α + core calculations in intermediate mass nuclei. An α-decay half-life T1/2,α ≈ 3 ns is predicted for 104Te in the α-decay energy Qα ≈ 5.36 MeV using an α preformation factor P = 1. The calculated T1/2,α value is compatible with the recently reported experimental result on α-decay of 104Te.

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The light neutron-rich nuclei play a vital role in nucleosynthesis process and the extent of alpha (α) clustering significantly influence the astrophysical rates. Thus, it is significant to explore the α clustering in these nuclei and in the present work, we have studied the α clustering in 41,45,49Ca* nuclei formed in neutron induced reactions within the dynamical cluster decay model (DCM). The results present that with progression towards neutron-rich 45Ca* and 49Ca* nuclei, there is a significant decrease in the α-cluster preformation factor P0. The inclusion of relativistic mean field theory (RMFT) based microscopic temperature-dependent binding energies (T.B.E.) within DCM, give relatively enhanced α-cluster preformation factor for 41,45,49Ca* nuclei compared to the case of macroscopic T.B.E. based upon Davidson mass formula. The cross-section associated with α-cluster emission depicts strong isospin dependence and falls off significantly with increasing neutron number of Ca* nuclei. Further, for the first time, we inculcate the microscopic nuclear potential constructed via folding the standard Fermi form fitted RMFT cluster densities and M3Y nucleon-nucleon interaction within the DCM. The neutron skin thickness of the Ar cluster, complementary to α-cluster, is varied and its effect upon the nuclear interaction potential and α-cluster preformation factor is analysed. The results present that with growing neutron skin of Ar cluster, the α-cluster preformation factor decreases. It explores a strong correlation among the neutron skin thickness and α-cluster preformation factor in light mass 41,45,49Ca* nuclear systems.

The preformation factor quantifies the probability of {\alpha} particles preforming on the surface of the parent nucleus in decay theory and is closely related to the study of {\alpha} clustering structure. In this work, a multilayer perceptron and autoencoder (MLP + AE) hybrid neural network method is introduced to extract preformation factors within the generalized liquid drop model and experimental data. A K-fold cross validation method is also adopted. The accuracy of the preformation factor calculated by this improved neural network is comparable to the results of the empirical formula. MLP + AE can effectively capture the linear relationship between the logarithm of the preformation factor and the square root of the ratio of the decay energy, further verifying that Geiger-Nuttall law can deal with preformation factor. The extracted preformation probability of isotope and isotone chains show different trends near the magic number, and in addition, an odd-even staggering effect appears. This means that the preformation factors are affected by closed shells and unpaired nucleons. Therefore the preformation factors can provide nuclear structure information. Furthermore, for 41 new nuclides, the half-lives introduced with the preformation factors reproduce the experimental values as expected. Finally, the preformation factors and {\alpha}-decay half-lives of Z = 119 and 120 superheavy nuclei are predicted.

In this study, we propose a novel Bayesian inference framework combined with the two-potential approach (TPA) to systematically investigate the α-particle preformation factors and decay properties of heavy and superheavy nuclei. By employing Markov chain Monte Carlo (MCMC) sampling, we globally calibrate the adjustable parameters of phenomenological α preformation factors, while incorporating experimental uncertainties in decay energies and half-lives. Our results reveal a significant correlation between the parameters, and the nuclear shell effects near neutron magic numbers N=126, 152, and 162 play a key role. The 95% posterior confidence levels provided by the Bayesian method significantly enhance the reliability of parameter estimation, which is superior to traditional least-squares optimization. Notably, the derived preformation factors exhibit systematic deviations near shell closures, highlighting the necessity of explicitly incorporating nuclear structure effects. This work not only advances the precision of α-decay predictions but also offers a deeper understanding of shell evolution and collective effects in superheavy nuclei.

This study presents a holistic picture of the preformation of nuclear clusters with credence to the kinematics of their emissions. Besides the fitting of the preformation formula to reproduce the experimental half-lives, we have investigated the interrelationship between the parameters involved in the cluster decay process for medium, heavy and superheavy nuclei. Based on the established conceptual findings, we propose a new cluster preformation probability (P 0) formula that incorporates all influential parameters of the cluster radioactivity and thus has an edge over the existing formulae in the literature. Further, we hypothesize that a fraction of the decay energy is needed for cluster formation within the parent nucleus. The proposed formula opens a new paradigm to separately estimate the energy contributed during the cluster formation from its emission and thus shows that the contribution of the Q-value splits into three major parts accounting for the energy contributed during the cluster preformation, its emission and recoil of the daughter nucleus. Moreover, the expression P 0 is adept at accommodating the theorized concept of heavy particle radioactivity (HPR). The result reveals that, like α-decay, a proper estimation of the P 0- and Q-value in the cluster studies is enriched with qualitative information about the nuclear structure. However, from the analysis, the Geiger-Nuttall law is not the best compromise in the clustering due to the non-linearity between log10 T 1/2 and , unlike in α-decay. We have demonstrated that with the inclusion of the proposed formula, the half-life predictions from both microscopic R3Y and phenomenological M3Y NN potentials closely agree with the available experimental data and that the slight variation can be traced to their peculiar barrier characteristics.

In the present paper changes of cluster preformation probabilities (Pc’s) with different quantities like the size of the cluster (Ac), proton number of the cluster and daughter nuclei (ZcZd), and the decay energy (Q) have been studied. Three different formulae are suggested corresponding to each of these variables taking into account of the odd–even effects. The decay half-lives for various cluster emissions have been predicted in the trans-lead region with preformation probabilities using these three formulae. The theoretical estimates are compared with the experimental results and are found to go hand in hand with experimental data. The relation that connects the decay energy (Q) with cluster preformation demonstrates better alignment with experimental data compared to the other two models. The cluster preformation probability (Pc) is also calculated using the NpNn scheme for the effective number of valance particles. The decay half-lives are then calculated with the preformation factors obtained using the NpNn scheme. The comparison with experimental half-lives suggests the applicability of NpNn scheme for the cluster decays in trans-lead region.

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In this study, α-particle preformation factors in heavy and superheavy nuclei from 220Th to 294Og are investigated. By combing experimental α decay energies and half-lives, the α-particle preformation factors are extracted from the ratios between theoretical α decay half-lives calculated using the Two-Potential Approach (TPA) and experimental data. We find that the α-particle preformation factors exhibit a noticeable odd-even staggering behavior, and unpaired nucleons inhibit α-particle preformation. Moreover, we find that both the α decay energy and mass number of parent nucleus exhibit considerable regularity with the extracted experimental α-particle preformation factors. After considering the major physical factors, we propose a local phenomenological formula with only five valid parameters for α-particle preformation factors . This analytic expression has a clear physical meaning as well as good precision. As an application, this analytic formula is extended to estimate the α-particle preformation factors and further predict the α decay half-lives for unknown even-even nuclei with Z = 118 and 120.