Preformed Cluster Model Research Articles

Study of various ground state decay mechanisms of Actinide nuclei* *Financial support from the Department of Science and Technology (DST), New Delhi, India in the form of a research project grant (CRG/2021/001144) is gratefully acknowledged.

The special property of the actinide mass region is that nuclei belonging to this group are radioactive and undergo different ground state processes, such as alpha decay, cluster radioactivity (CR), heavy particle radioactivity (HPR), and spontaneous fission (SF). In this study, the probable radioactive decay modes of the heavy mass region (Z = 89−102) are studied within the framework of the preformed cluster model (PCM). In the PCM, the radioactive decay modes are explored in terms of the preformation probability () and penetration probability (P) at the turning point , where the penetration of fragments is initiated [R = R (touching state) + (neck length parameter)]. First, the alpha decay half-lives are calculated for light and heavy nuclei, and points are obtained by optimizing the neck length parameter. These points are further employed to fix the Q-value dependent turning point ((Q)). Then, using the ((Q)) relation, the decay half-lives are computed, and the calculated results are compared with the available theoretical and experimental data. The isotopical trend of and P is studied with respect to the mass number of the parent and daughter nucleus, respectively. The CR and HPR channels are also explored, and a comparison of calculated data is conducted with the available literature. Comparative analysis of the fragmentation potential and preformation probability is carried out for alpha decay and SF. The mass distribution of the nuclei is studied as a function of fragment mass (A ) by considering the spherical and hot-compact deformation of the decaying fragments. Finally, the most probable fission fragments are identified using the fragmentation structure, and the corresponding fission fragment total kinetic energy of the identified fragments is calculated and compared with available data, wherever applicable.

Role of Skyrme forces in cluster radioactivity of parent nuclei with even ( A,Z )

We investigate the role of different Skyrme forces (SIII, SkI4, and SAMi) in the ground state decay of various radioactive parent nuclei such as Ra, Th, U, and Pu. The daughters of these nuclei are either doubly magic $^{208}\mathrm{Pb}$ or a nearby isotope of Pb. Using spherical choice of cluster and daughter, calculations are performed within the framework of the preformed cluster model (PCM), where the preformation probability ${P}_{0}$ and penetration probability $P$ of decaying fragments are used to obtain the half-lives of cluster emission. The considered forces modify the barrier characteristics and consequently the penetration path, as the scattering potential at the first turning point of the barrier is lowest with the SkI4 force (lowest penetrability) and highest with the SIII force (highest penetrability). However, the preformation probability of decaying clusters is highest for the SkI4 force followed by SAMi and SIII Skyrme forces. To look for the possible role of the spin-orbit effect on the cluster radioactivity, the half-lives of emitted clusters are calculated with and without the inclusion of spin-orbit potential ${V}_{J}$. In addition, the $\ensuremath{\alpha}$-decay half live are also calculated to extract an inclusive picture of the dynamics involved.

αdecay of Po and Rn isotopes using different choices of impinging frequency

A comprehensive study of $\ensuremath{\alpha}$ particle emergence from $^{188\text{--}218}\mathrm{Po}$ isotopes is carried out within the framework of the preformed cluster model (PCM). The mass asymmetry coordinate and the interfragment separation play crucial roles in the identification of the most probable decay channel and the barrier penetration of decay fragments. First, the barrier characteristics are studied using two choices of radii [with surface diffuseness (${C}_{i}$) and without surface diffuseness (${R}_{i}$)]. The fragmentation behavior of $^{188}\mathrm{Po}$, $^{202}\mathrm{Po}$, and $^{218}\mathrm{Po}$ isotopes is explored for the identification of the most probable decay channel in view of the structure of the fragmentation potential. The $\ensuremath{\alpha}$ decay is found to be the most prominent decay mode in the chosen set of isotopes. The preformation and penetrative probability of the decay fragments is studied with respect to increase in the neutron number of the parent nucleus. The $\ensuremath{\alpha}$ decay half-lives of polonium isotopes are calculated using classical assault frequency (${\ensuremath{\nu}}_{c}$) and quantum mechanical assault frequency (${\ensuremath{\nu}}_{q}$) and a comparison is made with the experimental data. Here, the term assault frequency is basically the impinging frequency of an $\ensuremath{\alpha}$ particle near the surface of the parent nucleus. Further, the $\ensuremath{\alpha}$ decay half-lives of the $^{198\text{--}220}\mathrm{Rn}$ isotopes are calculated using the effective assault frequency (${\ensuremath{\nu}}_{e}$) parameter, and a comparison is made with the available experimental data.

Temperature dependence of cluster decay

A universal decay law (UDL) for light cluster decay of excited nuclei is formulated by fitting the UDL half-lives to those evaluated within an excitation energy-dependent double folding model (DFM). The half-lives are evaluated within a preformed cluster model. The excitation energy dependence is introduced both in the energy of the emitted cluster and in the interaction potential through the density distributions of the interacting nuclei. The half-lives are found to decrease when the difference between the excitation energies of the parent and daughter nuclei, ΔE⁎> 0, increases, with the reduction being a few orders of magnitude for higher values of ΔE⁎. This can be of importance for nucleosynthesis calculations of heavy elements formed in extremely hot environments, as well as in highly energetic heavy-ion collisions. The UDL for excited nuclei is used to provide an estimate of the enhancement in the cluster decay rates of thermally excited nuclei such as those produced in r-process nucleosynthesis.

Macroscopic–microscopic calculations of the ground state properties of Z = 120 isotopes and their α-decay chains

One of the substantial successes achieved in nuclear physics in the last two decades was the synthesis of dozens of isotopes of new elements up to [Formula: see text]Og, which closed the seventh row of the periodic table and inspired the ambition of adding more elements. This work aims to study extensively the ground state structure and decay properties of proposed [Formula: see text] isotopes. We employed Macroscopic–microscopic scheme based on the Skyrme energy density functional, the Woods–Saxon single-particle potential and Strutinsky’s method to find the structure properties, in a multidimensional deformation space. The same nucleon–nucleon potential is used to find the [Formula: see text]-decay half-life, within the Preformed Cluster Model. For 45 [Formula: see text]120 isotopes, the total energy surfaces, ground state masses, binding energy, deformations and fissionability are determined. The [Formula: see text]-values of the different competing decays and [Formula: see text]-decay half-lives are investigated based on the obtained structure. The results indicate the [Formula: see text]120 isotopes to be the most bound among the studied isotopes. The smallest fission barriers are indicated for the [Formula: see text]120 isotopes. The [Formula: see text]120 isotopes showed the longer half-lives against [Formula: see text]-decay, with an order of [Formula: see text]. The longest half-lives are estimated for the [Formula: see text]120 ([Formula: see text] and [Formula: see text]120 ([Formula: see text] isotopes. The longest full decay chain ending with the stable [Formula: see text]Pb nucleus is anticipated for the [Formula: see text]120 isotope. The shortest decay chain of [Formula: see text]120 terminates after three [Formula: see text]-decays by the spontaneous fission of [Formula: see text]Fl.

Systematic Analysis for Neck-Length and Q-Values on Cluster Decay from Ba Isotopes

The present study provides a detailed investigation of the neck-configuration and Q-values on the cluster decay of proton-rich even-even 124-128Ba isotopes using the relativistic mean-field (RMF) formalism with the NL3* parameter set. The densities of the interacting nuclei from the RMF approach are folded with the R3Y and M3Y interactions to obtain the nuclear potential via the double-folding technique. The preformed cluster model (PCM) based on the quantum mechanical fragmentation theory is employed for the calculation of the decay half-lives. The preformation probability P0 and the penetration probabilities are estimated by the phenomenological scaling factor of Blendowske & Walliser and the WKB approximation respectively. The present investigation reveals that the M3Y and R3Y are associated with different barrier characteristics which are significantly modified with a little variation in the neck-length parameter ΔR. From the Q-value analysis, we have demonstrated that α-decay may not be a favourable decay mode for proton-rich barium isotopes with A > 122.

Constraining the α-nucleus potential for α-decay calculation with nuclear rainbow scattering

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.

Effect of compact and elongated configurations on the spontaneous and induced fission of Fm isotopes

The spontaneous fission (SF) analysis of even mass $^{242\ensuremath{-}260}\mathrm{Fm}$ isotopes is carried out using a preformed cluster model based on quantum mechanical fragmentation theory. The deformation effects are included up to the quadrupole (${\ensuremath{\beta}}_{2}$) deformed nuclei with optimum orientations (${\ensuremath{\theta}}_{i}^{\mathrm{opt}.}$) leading to hot-compact (side-to-side) and cold-elongated (tip-to-tip) configurations. The spherical and hot-compact deformed configurations of decay fragments result in the symmetric fragment mass distributions for Fm isotopes; however, the symmetric peak gets sharper with an increase in the neutron ($N$) number of the parent nucleus. In the case of cold orientations, a transition from two-peaked (asymmetric fission) to three-peaked (multimodal fission) mass distribution is observed with an increase in the mass number of Fm. The SF half-lives (${T}_{1/2}^{\mathrm{SF}}$) are calculated using the neck-length parameter ($\mathrm{\ensuremath{\Delta}}R$) for $^{242\ensuremath{-}260}\mathrm{Fm}$ isotopes and compared with the experimental data. Besides this, the induced fission of Fm isotopes is studied within the dynamical cluster-decay model. The energy dependence of fission fragment mass distributions and the isotopic dependence is analyzed at energy range ${E}^{*}=5$--42 MeV. In addition, the role of temperature-dependent deformations in the fission dynamics is also explored.

Analysis of various competing binary and ternary decay processes of the Es253 nucleus

The ground state binary and ternary decays of the $^{253}\mathrm{Es}$ radioactive nucleus are investigated using the quantum mechanical fragmentation theory (QMFT) based cluster decay models. First, the relative fragmentation of $^{253}\mathrm{Es}$ is analyzed within the framework of the preformed cluster model (PCM). The PCM-calculated binary fragmentation structure is explored for two types of nuclear potential, i.e., Yukawa plus exponential and proximity potentials. The structure of the fragmentation potential and the location of potential minima are found to be independent of the choice of nuclear potential. It is observed from binary fragmentation structures that $\ensuremath{\alpha}$ $(^{4}\mathrm{He})$ decay, cluster $(^{46}\mathrm{Ar})$ emission, heavy particle $(^{82}\mathrm{Ge})$ radioactivity, and spontaneous fission fragmentation $(^{125}\mathrm{In})$ are the possible ground state decay modes of the $^{253}\mathrm{Es}$ nucleus. The competitive emergence of these decay channels is explored by studying the preformation probability ${P}_{0}$, penetrability $P$, and half-lives ${T}_{1/2}$. The calculated half-lives of $\ensuremath{\alpha}$ and spontaneous fission match nicely with the experimental measurements. Also, the half-lives are predicted for cluster and heavy particle radioactivity, for which experimental verification would be of further interest. Further, an effort is made to explore the possibility of ternary fission (particle accompanied fission) for the decay of the $^{253}\mathrm{Es}$ nucleus using the three-cluster model (TCM), where $^{4}\mathrm{He}$ is observed to be the third fragment along with two binary fission fragments. A comparison of relative yields of binary and ternary fission confirm that the probability of the binary fission decay mode is larger than that of ternary fission. Moreover, closed shell effects play a significant role in the symmetric and asymmetric fission of binary and ternary fission, respectively.

Role of channel temperature and mass window in the binary breakup of U*236

The dynamical cluster-decay model (DCM), an extension of the preformed cluster model of Gupta and collaborators for the decay of hot and rotating compound nuclei (CN) formed in low-energy reactions, has been applied to study the mass distribution of $^{236}\mathrm{U}^{*}$ formed at an excitation energy corresponding to the capture of thermal neutrons by $^{235}\mathrm{U}$. The role of excitation energy of the compound nucleus, neck length parameter, and mass window (range of mass numbers) considered are also analyzed. The excitation energy of the compound nucleus is kept fixed for all channels, and the temperature for each channel is obtained iteratively to conserve the sum of excitation energies of two fragments to the excitation energy of the compound nucleus at a fixed distance, mimicking the saddle configuration. The obtained mass distributions and yields are compared with experimental yields.

Analysis of competing ground state channels observed in decay of Cm isotopes

The possible decay modes of even [Formula: see text] [Formula: see text]Cm parents have been analyzed to explore the relative emergence of various ground state emission mechanisms using the collective clusterization approach. Based on the collective availability of [Formula: see text], cluster and spontaneous fission (SF) experimental half-life data, we limit our study to isotopes of Cm. In view of this, the most probable decaying fragments from [Formula: see text]Cm are identified in different mass regions and a comprehensive analysis of the shell closure effect of the decay fragments corresponding to different mass domains is carried out within the methodology of Preformed Cluster Model (PCM). The isotopic analysis of the mass distributions and the related barrier characteristic quantities are investigated in view of ground state decay of [Formula: see text]Cm isotopes. The PCM calculated [Formula: see text] and SF half-lives compare nicely with the experimental data and the predictions are made on cluster and heavy-cluster decay of Cm isotopes, where experimental data is not available. It will of further interest to validate these predictions by performing corresponding experiments.

Fragmentation analysis and α-decay half-lives of trans-Sn nuclei

The triple α-decay chain 114Ba ⟶α110Xe ⟶α106Te ⟶α102Sn gives three new α-emitters 114Ba, 110Xe and 106Te. In order to explore the excited state α-decays, the dynamics of 58Ni(58Ni,2n) reaction forming 116Ba⁎ is studied at the beam energy ELab=210MeV. The half-lives of the nuclei formed in successive α-decay chain are calculated using Dynamical Cluster decay Model (DCM), an extension of the Preformed Cluster Model (PCM) with temperature T- and angular momentum ℓ-effects included. In addition to this, the α-decay half-lives of some trans-Sn Te, I, Xe, Cs and Ba isotopes, lying near the super-allowed region of α-decay, have been addressed in view of ground state α-radioactivity. The role of various proximity potentials having different isospin dependence is investigated in order to extract the useful information about the barrier characteristics in decay of trans-Sn region nuclei. The preformation probability distribution, which gives an account of potential energy surfaces, is analyzed for the relative comparison of spontaneous and induced α-emission processes.

Collective clusterization approach to investigate the relevance of deformation effects in Sn radioactivity

The role of deformations and orientations is studied in cluster decays of various radioactive nuclei leading to doubly magic 100Sn or 132Sn daughter nucleus, using the preformed cluster model (PCM). This model treats the cluster emission process via tunnelling across the potential barrier, the cluster/fragment being preformed with a relative probability $ P_0$. With the incorporation of deformation and orientation effects, the fragmentation potential, the penetration path and related barrier characteristics get significantly modified, due to which both the preformation probability $ P_0$ and penetrability P of the emitting cluster get influenced. The calculated half-lives of the decaying clusters calculated using PCM are found to be within the upper limits of the present experiments. The influence of deformations and orientations on Sn radioactivity is also seen in terms of various barrier characteristics such as barrier modification, barrier height, etc. Moreover, the role of different nuclear proximity potentials, i.e., Prox 77, Prox 88 and Prox 00, is analyzed in the context of potential energy surfaces (PES) in the ground-state decay of parent nucleus. The behavior of PES is explored including, as well as without including, the shell corrections in the binding energies, which in turn help to explore the importance of doubly magic closed shell configuration of daughter and cluster nuclei. The possible role of higher order multipole deformations (i.e., up to $ \beta_{4i}$) is also analyzed in view of the fragmentation path and barrier tunnelling characteristics.

Spontaneous fission of the end product in α-decay chain of recoiled superheavy nucleus: A theoretical study

The temperature-dependent preformed cluster model [PCM[Formula: see text]] is employed to extend our recent work [Niyti, G. Sawhney, M. K. Sharma and R. K. Gupta, Phys. Rev. C 91 (2015) 054606] on [Formula: see text]-decay chains of various isotopes of [Formula: see text]–118 superheavy nuclei (SHN), to spontaneous fissioning nuclei [Formula: see text]Lr, [Formula: see text]Rf, [Formula: see text]Db, [Formula: see text]Rg, and [Formula: see text]Cn occurring as end products of these [Formula: see text]-decay chains. The behavior of fragment mass distribution and competitive emergence of the dominant decay mode, i.e., the [Formula: see text]-emission versus spontaneous fission (SF), are studied for identifying the most probable heavy fission fragments, along with the estimation of SF half-life times T[Formula: see text] and total kinetic energy (TKE) of the above noted isotopes of [Formula: see text]–112 nuclei decaying via the SF process. The mass distributions of chosen nuclei are clearly symmetric, independent of mass and temperature. The most preferred decay fragment is found to lie in the neighborhood of doubly magic shell closures of [Formula: see text] and [Formula: see text], with largest preformation factor [Formula: see text]. In addition, a comparative study of the “hot compact” and “cold elongated” configurations of [Formula: see text]-deformed and [Formula: see text]-oriented nuclei indicates significantly different behaviors of the two mass fragmentation yields, favoring “hot compact” configuration.

Constraints on the nuclear symmetry energy and its density slope from the decay process

We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process. Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state (EOS). Each EOS is characterized by a particular symmetryenergy coefficient (asym) and a corresponding density-slope parameter L. The stepwise trends of the neutron (proton) skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life Tα with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value asym=32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay, yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.

Preformation probability of two-proton emitters

Within the cluster-core model picture using the preformed cluster model, proton rich, 2-proton emitting nuclei are studied. The experimentally established [Formula: see text]Fe, [Formula: see text]Ni, [Formula: see text]Zn and [Formula: see text]Kr are investigated in terms of simple potential energy surfaces for all possible cluster plus core configurations of the 2-proton emitting nuclei. The calculated potential energy surfaces reveal a strong minimum for 2-proton-cluster plus core configuration. In addition, the calculations are carried out for the theoretically studied 2-proton emitters such as [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which also reveal 2-proton cluster plus core configuration as the favorable one possessing strong minimum in the potential energy surface. Furthermore, the calculated potential energies are used to calculate the preformation probability by solving the stationary Schrödinger equation of motion in mass asymmetry coordinate. The formation yield also clearly reveals a larger formation probability for the 2-proton cluster plus core configuration for all the nuclei studied. The Q-value systematic of 1-proton, 2-proton, 4-proton and 4He is also analyzed.

Decay of Plutonium isotopes via spontaneous and heavy-ion induced fission paths

Based on the collective clusterization approach, we have extended our earlier study on α-decay, exotic cluster-decay, and heavy particle radioactivity, to the phenomenon of spontaneous fission (SF) in the ground-state (g.s.) decays of even mass 234−246Pu parents. The calculations for the SF half-lives of these Pu-isotopes have been made within the framework of preformed cluster model (PCM), both for spherical as well as β2-deformed choices of shapes, and a comparison is made with the relevant available experimental data, which prefer spherical shapes. The importance of the orientation degree of freedom (hot compact or cold elongated configurations) is also explored. Next, in order to look for the exclusive role of heavy-ion induced fission, the dynamics of 6He + 238U reaction forming 244Pu⁎ is studied over the center of mass energy range of Ec.m.=15.0–28.8MeV, using the dynamical cluster-decay model (DCM), an extension of the PCM with temperature T- and angular momentum ℓ-effects included. The β2-deformed fragments of 244Pu⁎ in the mass range A2=106–113 (plus their complementary heavy fragments), corresponding to asymmetric fission peaks, are found contributing towards the fission cross-section. Finally, the potential energy surfaces and barrier modification effects are presented for the relative comparison of spontaneous and the heavy-ion induced fission processes. Both are found to behave similar with respect to the probable emission of fragments and hence point out to the shell closure property of the decay fragments.

Influence of proton-skin thickness on the decays of heavy nuclei

We investigate the effect of proton-skin thickness on the α decay process. We consider 188 neutron-deficient nuclei belonging to the isotopic chains from Te (Z = 52) to Pb (Z = 82). The calculations of the half-life are carried out in the framework of the preformed cluster model, with the Wentzel-Kramers-Brillouin penetration probability and assault frequency. It is shown that the proton-skin thickness ( of the daughter nucleus gives rise to a total α- daughter nucleus interaction potential of relatively wide deep internal pocket and a thinner Coulomb barrier of less height. This increases the penetration probability but decreases the assault frequency. The overall impact of the proton-skin thickness appears as a decrease in the decay half-life. The proton-skin thickness decreases the stability of the nucleus. The half-lives of the proton-skinned isotopes along the isotopic chain decrease exponentially with increasing the proton-skin thickness, whereas the -value increases with . α-decay manifests itself as the second favorite decay mode of neutron-deficient nuclei, next to the -decay and before proton-decay. It is indicated as main, competing, and minor decay mode, at 21%, 7%, and 57%, respectively, of the investigated nuclei.

Spontaneous fission and competing ground state decay modes of actinide and transactinide nuclei

Based on the preformed cluster model, we have carried out a comprehensive theoretical study on the decay paths of ground state actinide and transactinide nuclei, specifically from $^{232}\mathrm{U}$ to $^{264}\mathrm{Hs}$ exhibiting the phenomenon of spontaneous fission (SF). This is an extension of our earlier studies on $\ensuremath{\alpha}$ decay, exotic cluster emission, and heavy particle radioactivity, where an effort is made to identify the most probable fragments in the SF process. These observations in turn, could provide a testing ground for future SF half-life measurements. To obtain a clear picture of the dynamics involved, the variations of fragmentation potential, preformation factor, and decay barrier height have been examined. The calculated potential energy surfaces show a change from a predominantly asymmetric fission to a symmetric fragmentation with the increase in the N/Z ratio of parent nuclei. In addition, an exclusive analysis of SF with $\ensuremath{\alpha}$ and other possible cluster emissions for the $^{232,234,236,238}\mathrm{U}$ parents was made to have better insight of nuclear structure information. In other words, the comparative nature of $\ensuremath{\alpha}$, cluster, heavy fragment, and SF decay paths is analyzed in view of shell closure property of the decay fragments. Interestingly, the calculated decay half-lives for the $^{82}\mathrm{Ge}$ heavy cluster are in fact shown to lie within the limits of experiments, thereby presenting themselves as exciting new possibilities which may be validated via future experiments.

Cluster preformation law for heavy and superheavy nuclei

The concept of cluster radioactivity has been extended to allow emitted particles with ${Z}_{C}g28$ for superheavy nuclei by nuclear theory [Poenaru et al., Phys. Rev. Lett. 107, 062503 (2011)]. The preformation and emission mechanics of heavy-ion particles must be examined again before the fascinating radioactivity is observed for superheavy nuclei in laboratory. We extract the cluster preformation factor for heavy and superheavy nuclei within a preformed cluster model, in which the decay constant is the product of the preformation factor, assault frequency, and penetration probability. The calculated results show that the cluster penetration probability for superheavy nuclei is larger than that for actinide elements. The preformation factor depends on the nuclear structures of the emitted cluster and mother nucleus, and the well-known cluster preformation law $S({A}_{C})=S{(\ensuremath{\alpha})}^{({A}_{C}\ensuremath{-}1)/3}$ [Blendowske and Walliser, Phys. Rev. Lett. 61, 1930 (1988)] will break down when the mass number of the emitted cluster ${A}_{c}g28$, and new preformation formulas are proposed to estimate the preformation factor for heavy and superheavy nuclei.