Heavy Cluster Emission Research Articles

The phenomenology of particle and cluster emission

We review emission data for proton-, even–even α- and heavy cluster (HC) radioactivity in a unified model by using a realistic analytical approach for the barrier penetration and spectroscopic factor. The realistic fragment–core nuclear interaction is approximated by a parabolic dependence which is matched to the Coulomb potential at the barrier radius. Thus, the fragment dynamics inside the barrier can be described with analytical semiclassical solutions. The centrifugal and deformation effects within the Fröman approach are investigated. We present systematics of the spectroscopic factors and give universal laws for decay widths of proton, even–even α and heavy cluster emission processes. We make remarks on the main universal phenomenological features of these decays. Finally we describe the universal law for the even–even α-emission fine structure.

Empirical formula for heavy cluster decay in the superheavy region

In this paper, an empirical formula to describe the heavy cluster decay with [Formula: see text] ([Formula: see text] is the charge number of the emitted cluster) from superheavy elements is proposed. The predictions of our formula are compared with the predictions of Coulomb and Proximity Potential Model (CPPM), the predictions of Analytical Super Asymmetric Fission (ASAF) model and the predictions by UDL formula of Qi et al. Excellent agreement is found between the predictions of CPPM and ASAF models and those of the present formula. Using our formula, we have calculated the decay half-lives of various heavy cluster emission from superheavy elements leading to doubly magic [Formula: see text]Pb and compared with the predictions of CPPM. The predictions of UDL formula deviate considerably from the predictions of this formula, CPPM and ASAF model, giving much lower decay half-lives, as the order of decay half-life increases. Possible heavy cluster emissions from [Formula: see text] and 122 nuclei leading to [Formula: see text]Pb and [Formula: see text]Bi are also predicted.

Radioactive decay of Og288−296 via heavy cluster emission within a modified generalized liquid drop model with a Q -value-dependent preformation factor

A systematic study on radioactive decay of various isotopes of superheavy element oganesson $(Z=118)$ with mass numbers varying from 288 to 296 via heavy cluster emission is considered. The half-life of an emitted cluster is computed using the modified generalized liquid drop model with the Q value dependent preformation factor, for all possible splitting of each Og isotope. The heavy clusters with half-lives comparable to or less than the alpha half-life are probable for emission. From calculations, it is evident that for each Og isotope, the cluster emission with half-life comparable to alpha decay are indium and cadmium, which have nearly a proton magic number $(Z=50)$ and also the cluster emission with minimum half-lives among all splitting are $^{136}\mathrm{Xe}$ and $^{138}\mathrm{Ba}$, both having a magic neutron number $N=82$. The role of the magic number in the stability of heavy cluster decay is evident. Modes of decay of each isotope of Og is identified by comparing ${T}_{1/2}^{\ensuremath{\alpha}}$ values with corresponding ${T}_{1/2}^{\mathrm{SF}}$ values computed using the new mass inertia $({I}_{\mathrm{rigid}})$ dependent formula. The experimental alpha decay half-life of $^{294}\mathrm{Og}$ is 0.89 ms and the theoretically predicted value using our model is 0.395 ms. We were able to reproduce experimental alpha decay half-lives and decay modes in the case of $^{294}\mathrm{Og}$, thereby proving the reliability of our model, hence we believe that the predictions made in the case of other isotopes of Og would serve as a guiding tool for future studies in this field.

Prediction of α -decay chains and cluster radioactivity of 121300–304 and 122302–306 isotopes using the double-folding potential

The $\ensuremath{\alpha}$- and cluster-decay half-lives for the two superheavy nuclei (SHN) with $Z=121$ and 122 have been calculated within the density-dependent cluster model. The $\ensuremath{\alpha}$-nucleus potential was constructed by employing the double-folding model with a realistic $NN$ interaction whose exchange part has a finite range. We considered five isotopes for each one of the two SHN, $Z=121$ and 122, and compared the calculated $\ensuremath{\alpha}$-decay half-lives with those obtained from three semiempirical formulas, namely, the Viola-Seaborg-Sobiczewski formula, the modified Brown formula, and the semiempirical formula based on fission theory. The calculated $\ensuremath{\alpha}$-decay half-lives are in good agreement with their counterparts. We studied the competition between $\ensuremath{\alpha}$-decay and spontaneous fission and predicted possible decay modes for the SHN $^{300--304}121$ and $^{302--306}122$. The cluster decays for $^{300}121$ and $^{302}122$ have been studied within the double folding model, the unified formula, the scaling law of Horoi, and the universal decay law (UDL). We found that the UDL model predicts the possibility of heavy cluster emission from $^{300}121$ and $^{302}122$. We found that the proton and neutron numbers in the emitted clusters and their residual daughter nuclei are magic or near to the magic numbers. We hope that the theoretical prediction of $\ensuremath{\alpha}$-decay chains and cluster radioactivity could be helpful for future investigation in this field.

α-decay chains and cluster radioactivity of 295−299119 and 298−302120 isotopes using zero- and finite-range NN interactions

The α-decay half-lives of the superheavy nuclei (SHN) with Z = 119 and 120 are investigated by employing the density dependent cluster model. Within the double-folding model, the α-nucleus interaction potential is calculated microscopically using a realistic nucleon–nucleon (NN) interaction. The exchange part of the interaction potential is evaluated within a local density formalism, using the finite-range as well as the ordinary zero-range exchange components of the NN interaction. The influence of nuclear deformation is presented. The calculated values of α-decay half-lives for five isotopes of each of the SHN with Z = 119 and 120 have been compared with those values evaluated using other theoretical models. It was found that our theoretical values are in good agreement with their counterparts. The competition between α-decay and spontaneous fission is investigated and predictions for possible decay modes for the unknown nuclei 295−299119 and 298−302120 are presented. The probable cluster decay half-lives of 295119 and 298120 have been studied within the previously mentioned double-folding model as well as the unified formula (UF) of half-lives for α decay and cluster radioactivity, the scaling law by Horoi (Horoi) and the universal decay law (UDL). The cluster decay half-lives derived from the former three models are too large compared to α-decay half-lives, but the UDL formula predicts the possibility of heavy cluster emission. The mass number variations of the microscopic shell correction energy for different α-decay chains of Z = 119 and 120 isotopes are presented. The possible correlations between the shell effect and each of α-decay and cluster decay half-lives are discussed. We hope that the proposed theoretical predictions for α-decay chains and cluster radioactivity provide a new perspective to experimentalists.

Nuclear surface energy coefficients in cluster decay

The influence of different nuclear surface energy coefficients of the proximity potential in cluster decay of heavy, unstable radioactive nuclei is studied using a fission model by incorporating the preformation probability as the penetration probability of the overlapping region. An expression for preformation probability is fitted for preformation values, for which best matching is noted between calculated and experimental half-lives and is used in further calculations of cluster decay of superheavy elements. Half-lives for heavy cluster emission such as Ar, Ca, Ti, Cr, Fe, Co, Ni, Zn, Ga, Ge and Se, from superheavy nuclei with mass number in the range $ 252 \leq A \leq 294$ are predicted using the fitted expression for preformation probability. Predicted half-lives of heavy particle decay of superheavy nuclei compare well with the other prediction for a few clusters. Alpha decay being the predominant decay mode of heavy and superheavy nuclei, half-lives of heavy and superheavy nuclei are also calculated. Calculated half-lives of alpha decay for superheavy nuclei better reproduce the experimental values.

Systematic studies of α and heavy-cluster emissions from superheavy nuclei

The probabilities of \ensuremath{\alpha} decay and heavy-cluster decay in the superheavy region are investigated. The preformation probabilities for \ensuremath{\alpha} and cluster emissions are evaluated with a new formula which depends on the $Q$ value of the decay. The formula shows a better agreement with the experimentally extracted cluster preformation probabilities in the heavy region. The \ensuremath{\alpha} half-lives using our model are compared with the experimental results and it is found that the present model can be employed successfully to predict \ensuremath{\alpha} half-lives in the superheavy region. The probable heavy-cluster radioactivity from superheavy nuclei is also studied using the same model. A comparison of the heavy-cluster half-lives using the present model, the half-lives given by Poenaru et al. [Eur. Phys. J. A 54, 14 (2018)] (analytical superasymmetric fission) and Zhang et al. [Phys. Rev. C 97, 014318 (2018)] are performed. The agreement between these three formalisms is evident from the study. A further study on the competition between \ensuremath{\alpha} decay and heavy-cluster radioactivity leading to $^{208}\mathrm{Pb}$ is performed. The study suggests that heavy-cluster radioactivity may be comparable to or even dominant over \ensuremath{\alpha} decay for some of the isotopes with $Z\ensuremath{\ge}118$. The study shows that the present model can be used effectively to obtain the \ensuremath{\alpha} as well as the heavier cluster decay half-lives in the superheavy region.

Alpha decay and cluster decay of some neutron-rich actinide nuclei

Nuclei in the actinide region are good in exhibiting cluster radioactivity. In the present work, the half-lives of α-decay and heavy cluster emission from certain actinide nuclei have been calculated using cubic plus Yukawa plus exponential model (CYEM). Our model has a cubic potential for the overlapping region which is smoothly connected by a Yukawa plus exponential potential for the region after separation. The computed half-lives are compared with those of other theoretical models and are found to be in good agreement with each other. In this work, we have also studied the deformation effects on half-lives of cluster decay. These deformation effects lower the half-life values and it is also found that the neutron-rich parent nuclei slow down the cluster decay process. Geiger–Nuttal plots for various clusters are found to be linear and most of the emitted clusters are α-like nuclei.

MCNP6 updated proton-induced fission cross section calculations at intermediate energies

MCNP6 has been Validated and Verified against intermediate- and high-energy fission cross-section experimental data. Recent improvements contained in CEM03.03F and MCNP6-F to consider precompound emission of heavy clusters up to 28 Mg has necessitated a re-calculation of fission cross sections. With our re-calculation, we find that CEM03.03F, which is used in MCNP6-F, predicts fission cross sections in good agreement with available experimental data for reactions induced by protons on both subactinide and actinide nuclei at incident energies from several tens of MeV to several GeV.

Decay of the compound nucleus118*297formed in the reactionCf249+Ca48using the dynamical cluster-decay model

The decay of the $Z=118$, $^{297}118^{*}$ compound system, formed in the $^{249}\mathrm{Cf}+^{48}\mathrm{Ca}$ reaction, is studied for $2n$, $3n$, and $4n$ emissions, by using the dynamical cluster-decay model (DCM) at compound-nucleus (CN) excitation energies ${E}_{\mathrm{CN}}^{*}=29.2$ and 34.4 MeV. A parallel attempt is made to analyze the $^{294}118$ residue nucleus synthesized in the $^{250}\mathrm{Cf}+^{48}\mathrm{Ca}$ reaction, subsequent to the $4n$ emission from the $^{298}118^{*}$ nucleus, to check the possibility of isotopic mixing in the $^{249}\mathrm{Cf}$ target used in the $^{249}\mathrm{Cf}+^{48}\mathrm{Ca}$ reaction. The possible role of deformations and orientations, together with different nuclear proximity potentials, is also investigated. In addition, an exclusive analysis of the mass distributions of $Z=113$ to 118 superheavy nuclei, formed in $^{48}\mathrm{Ca}$-induced reactions, is explored within the DCM. A comparative importance of Prox-1977 and Prox-2000 potentials on the $\ensuremath{\alpha}$-decay chains is also investigated, first by using the preformed cluster model (PCM) for spontaneous decays $(T=0)$, the $\mathrm{PCM}(T=0)$, and then analyzing the possible role of excitation energy in PCM, i.e., $\mathrm{PCM}(T\ensuremath{\ne}0)$, via the measured recoil energy of the residual $^{294}118$ nucleus left after $3n$ emission from $^{297}118^{*}$ CN. The branching of $\ensuremath{\alpha}$ decay to the most-probable clusters is also examined for $^{294}118^{*}$ and its subsequent $^{290}116^{*}$ and $^{286}114^{*}$ parents occurring in the $\ensuremath{\alpha}$-decay chain. Interestingly, the calculated decay half-lives for some clusters such as $^{86}\mathrm{Kr}$, $^{84}\mathrm{Se}$, and $^{80}\mathrm{Ge}$, referring to doubly magic $^{208}\mathrm{Pb}$ or its neighboring daughter nucleus, present themselves as exciting new possibilities, though to date difficult to observe, of heavy cluster emissions in superheavy mass region.

Cluster decay analysis and related structure effects of fissionable heavy and superheavy nuclei

Collective clusterization approach of dynamical cluster decay model (DCM) has been applied to study the attributes of hot (T ≠ 0) and rotating (l ≠ 0) nuclei lying in heavy and superheavy mass regimes. We present here an overview of the characteristic fission decay properties such as shell effect, role of entrance channel, quadrupole (β2) deformations and impact of hot (equatorial) compact orientation degree of freedom in comparison to cold (polar) elongated configuration. The presence of non-compound nucleus process, i.e., quasifission, is also investigated. Apart from studying the decay of excited state nuclei, the dynamics of heavy particle cluster emission is also addressed using the preformed cluster model (PCM).

Clustering in atomic nuclei: a mean field perspective

In this paper the physics of clustering in atomic nucleus as seen from a mean field perspective will be discussed. Special attention is paid to phenomena involving octupole deformation like the α structure of 20Ne or the emission of heavy clusters. The stabilizing role of spin for cluster-like highly deformed states is also discussed in the case of 36 Ar.

Role of shape and quadrupole deformation of parents in the cluster emission of rare earth nuclei

The nuclear structure effects on α decay and cluster emission are investigated in the case of even–even rare earth nuclei150–160Dy ,150–160Er ,150–160Yb ,158,162,166–176Hf ,160,164–178W and162,166,170–180Os . The role of shape and deformation of parent nuclei in the decay rate is studied by taking the Coulomb and proximity potentials as the interacting barrier for the post scission configuration. The quadrupole deformation of parent nuclei causes a slight change in the half-life of α emissions, but it affects the rate of heavy cluster emissions significantly. Prolate deformation of parents enhances cluster emission, while an oblate deformation slows down the decay. Shape and deformation of parent nuclei causes change in the branching ratio also. A prolate deformation increases the branching ratio, whereas an oblate deformation reduces it. Highest branching ratio is predicted at N ~ 90.

Stability of 248–254Cf isotopes against alpha and cluster radioactivity

Stability of 248–254Cf nuclei against alpha and cluster emissions is studied within our Coulomb and proximity potential model (CPPM). It is found that these nuclei are stable against light clusters (except alpha particles) and unstable against heavy cluster (A2≥40) emissions. For heavy cluster emissions the daughter nuclei lead to doubly magic 208Pb or the neighbouring one. The effects of quadrupole and hexadecapole deformations of parent nuclei, daughter nuclei and emitted cluster on half lives are also studied. The computed alpha decay half life values (including quadrupole deformation β2) are in close agreement with experimental data. Inclusion of quadrupole deformation reduces the height and width of the barrier (increases the barrier penetrability) and hence half life decreases.

Study of Alpha Decay Chains of Superheavy Nuclei and Magic Number Beyond Z = 82 and N = 126

We study various $\alpha $ -decay chains on the basis of the preformed cluster decay model. Our work targets the superheavy elements, which are expected to show extra stability at shell closure. Our computations identify the following combinations of proton and neutron numbers as the most stable nuclei: $Z=112$ , $N=161, 163$ ; $Z=114$ , $N=171, 178, 179$ ; and $Z=124$ , $N=194$ . We also investigate the alternative of heavy cluster emissions in the decay chain of 301120, instead of $\alpha $ decay. Our study of cluster radioactivity shows that the half-life for 10Be decay in 289114 is larger, indicating enhanced stability at $Z=114$ , $N=175$ . Similar calculations concerning the emission of $\ ^{14}{\rm C}$ and $\ ^{34}{\rm Si}$ from 301120 find the more stable combinations $Z=114$ , $N=173$ , and $Z=106$ , $N=161$ , respectively. From the same parent, 301120, the emission of a $\ ^{49-51}{\rm Ca}$ cluster yielding a $Z=100$ , $N=152$ daughter is the most probable.

Clustering features in decay processes

Decay widths in emission processes are described within the stationary scattering theory. We use a pocket-like potential between emitted fragments, centered on the nuclear surface. This picture predicts a linear dependence between the logaritm of the reduced width and fragmentation potential. It turns out that this law is satisfied by proton emission, alpha-decay and heavy cluster emission processes. In particular, we show that, by using surface Gaussian-like components in single particle orbitals mocking four body correlations, it becomes possible to enhance both electromagnetic and α transition probabilities up to the experimental values in 212Po.

A fission model approach to alpha decay and cluster radioactivity of Dy, Er and Yb isotopes

Rare earth nuclei are probable candidates for exhibiting cluster radioactivity. In the present work, a theoretical study of alpha decay and heavy cluster emission from Dy, Er, and Yb nuclei in the mass range 150 < A < 190 has been carried out in a fission model approach. Some of the proton-rich isotopes of these nuclei are found to have long half-lives, but within the measurable range. Many of the neutron-rich isotopes under consideration are far from beta stability and the most probable light clusters predicted are highly exotic in nature and the corresponding half-lives are extremely short. However, the decays of most probable heavy clusters predicted have half-lives in the measurable range. The calculations on neutron-rich isotopes indicate the emergence of new magic numbers for protons and neutrons. The centrifugal barrier effect on decay rate of some proton-rich Er isotopes is also investigated.

Emission of heavy clusters in nuclear reactions at low collision energies

A survey of theoretical and experimental investigations of the process involving the emission of heavy clusters from excited nuclear systems produced in heavy-ion reactions at low collision energies is given. The dinuclear system (DNS) model for calculating cross sections for the formation of heavy clusters in complete-fusion and quasifission reactions is described in detail. The results of respective calculations are compared with relevant experimental data and with the results obtained on the basis of different models. The role of the angular momentum, the asymmetry of the entrance channel, the N/Z ratio, and the excitation energy in the formation of final reaction products is studied within the proposed approach. A method is developed for calculating cross sections for evaporation-residue formation. This method takes into account both channels of light-particle emission and channels of heavy-cluster emission. The possibility for the formation of Rn, Fr, and Ra isotopes in channels of heavy-cluster emission from the excited compound nucleus of Pu is demonstrated for the first time. The calculated cross sections and isotopic distributions for residual nuclei arising upon the emission of heavy clusters from an excited compound nucleus of Pu are in good agreement with experimental data. The model developed in the present study permits finding optimum experimental conditions (projectile-target combination and bombarding energy) for studying processes involving the emission of specific complex fragments.

Systematic study of heavy cluster emission from 210–226Ra isotopes

The half lives for various clusters lying in the cold reaction valleys of {210-226}^Ra isotopes are computed using our Coulomb and proximity potential model (CPPM). The computed half lives of 4^He and 14^C clusters from {210-226}^Ra isotopes are in good agreement with experimental data. Half lives are also computed using the Universal formula for cluster decay (UNIV) of Poenaru et al., and are found to be in agreement with CPPM values. Our study reveals the role of doubly magic 208^Pb daughter in cluster decay process. Geiger - Nuttall plots for all clusters up to 62^Fe are studied and are found to be linear with different slopes and intercepts. {12,14}^C emission from 220^Ra; 14^C emission from {222,224}^Ra; 14^C and 20^O emission from 226^Ra are found to be most favourable for measurement and this observation will serve as a guide to the future experiments.

Microscopic cold fission yields ofCf252

We show that the sharp maximum corresponding to $^{107}\mathrm{Mo}$ in the fragment distribution of the $^{252}\mathrm{Cf}$ cold fission is actually a Sn-like radioactivity, similar to other decay processes in which magic nuclei are involved, namely $\ensuremath{\alpha}$ decay and heavy cluster emission, also called Pb-like radioactivity. It turns out that the mass asymmetry degree of freedom has a key role in connecting initial Sn with the final Mo isotopes along the fission path. We investigate the cold rearrangement of nucleons within the framework of the two-center shell model in order to compute the cold valleys in the charge equilibrated fragmentation potential. The fission yields are estimated by using the semiclassical penetration approach. We consider 5 degrees of freedom, namely the interfragment distance, the shapes of fragments, the neck parameter, and mass asymmetry. We found an isomeric minimum between the internal and external barriers. It turns out that the inner cold valley of the total potential energy is connected to the doubly magic isotope $^{132}\mathrm{Sn}$.