Preformation Factor Research Articles

Alpha and cluster decay using Modified Generalized Liquid Drop Model with iso-spin dependent pre-formation factor

Cluster decay half-lives of actinides ranging from 221Fr to 242Cm are studied with a model where MGLDM (Modified Generalized Liquid Drop Model) includes pre-formation factor which depends on size of cluster and daughter nucleus and also on iso-spin parameter. Theoretical prediction could replicate experimental values with a standard deviation of about 0.569. Also we checked the applicability of our model in the case of alpha decay and obtained exactly matching results. Then we make prediction of half-lives of several clusters which are not detected experimentally so far so that this will be very helpful for future investigation in this field.

Theoretical predictions for $\alpha$-decay properties of 283-339Og using a shell-effect induced generalized liquid-drop model

The $ \alpha$-decay half-lives of synthesized superheavy nuclei (SHN) from seaborgium to oganesson are calculated by employing the generalized liquid-drop model (GLDM), the Royer formula and the universal decay law (UDL) with experimental $ \alpha$-decay energies $Q_{\alpha}$. For the GLDM, we consider the shell correction. The agreement between the experimental data and the calculations indicates that all the methods we used are successful to reproduce $\alpha$-decay half-lives of known SHN. The decay-modes of known nuclei on the 294Og decay-chain are also consistent with the experiments. For the unknown nuclei, the $ \alpha$-decay half-lives have been predicted by inputting $ Q_{\alpha}$ values extracted from the newest Weizsacker-Skyrme-4 (WS4) model. In the GLDM with shell correction, we adopt the constant $ \alpha$-preformation factor $ P_{\alpha}$ as well as $ P_{\alpha}$ extracted by Cluster Formation Model (CFM). To calculate CFM $ P_{\alpha}$ values, we use FRDM binding energies and WS4 mass excess values. The relationship of $ P_{\alpha}$ and $ Q_{\alpha}$ shows that 294, 296, 314, 316, 320Og isotopes are relatively stable. The competition between $ \alpha$-decay and spontaneous fission is discussed in detail for 283-339Og isotopes. The decay-chains of 290-300Og have also been presented. Since the $ \alpha$-decay half-lives of 283-303Og isotopes are obviously lower than their spontaneous fission half-lives by more than 6 orders, these isotopes would mainly have $ \alpha$-decay. The 306-334Og isotopes may undergo spontaneous fission. The nuclei 304, 305Og would have both $ \alpha$-decay and spontaneous fission. By the shell-effect included GLDM with CFM $ P_{\alpha}$, we predict 295Og undergoes $ \alpha$-decay and $ T_{\alpha}^{1/2} = 0.37$ ms. The 296Og is also $ \alpha$-decay and has $ T_{\alpha}^{1/2} = 0.40$ ms.

Across barrier fission analysis of At⁎ isotopes formed in 3,4,6,8He+209Bi reactions

The fission decay mechanism of various 212,213,215,217At⁎ isotopes formed in tightly (3,4He) and loosely bound (6,8He) projectile induced reactions on 209Bi target, is studied within the framework of dynamical cluster-decay model (DCM), over a wide range of excitation energies spread across the Coulomb barrier. By optimizing appropriate neck-length parameter ΔR, the fission cross-sections are calculated for 212,213,215At⁎ compound nuclei (CN) at above barrier energies, where some experimental data is available. The DCM calculations are extended at below barrier region for these nuclei, and for one more reaction 8He+209Bi→217At⁎, using the systematics of 212,213,215At⁎ isotopes. The magnitude of fission cross-sections increase with the addition of neutrons in the He-projectile (or say in the At compound nucleus since the target nucleus of each reaction is same). To obtain better description of fission dynamics involved for neutron-deficient and neutron-rich He-induced reactions, the fragmentation potential and prefromation probability P0 of decaying fragments are analyzed along with corresponding barrier tunneling probability P. The fission fragment mass distributions are explored for all ‘At’ isotopes, and most probable fission fragments are identified. It has been observed that asymmetric fission forms the predominant decay mode for all isotopes, although a minor hump with very small preformation factor appears around symmetric fragments for lighter 212,213At⁎ nuclei. Finally, the N/Z dependence of fission cross-sections and most probable decaying fragments is explored in view of fragmentation structure and related cross-sectional yields.

Predictions on the α-cluster structure in 104Te

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.

The predictions on the heavier cluster decays of superheavy nuclei

We have calculated the half-lives of the $ \alpha$ and heavy-cluster decays of superheavy nuclei in the framework of the Wentzel-Kramers-Brillouin (WKB) method. Good agreement with the present experimental data with the WKB method and Universal Decay Law (UDL) has been obtained for the $ \alpha$ -decay half-lives of superheavy nuclei having proton numbers with $ 107 \le Z \le 118$ . We have utilized the cluster preformation factor form proposed by Santhosh and Nithya [#!san!#] with new parameters sets produced by fitting of the results with the UDL formula in order to obtain the cluster decay half-lives. Reasonable results have been obtained by using the cluster preformation factor together with the WKB formalism for the cluster decays. Furthermore, ratio calculations have been performed to find out the candidates of possible cluster emitters. The predictions for cluster emitters are in agreement with estimates with the CPPM model by Santhosh and Nithya [#!san!#] and new additional estimates with the WKB and UDL are made. The present results and predictions would be important for both the theoretical and experimental studies in this field.

Half-lives of cluster radioactivity using the modified generalized liquid drop model with a new preformation factor

Half-lives of clusters emitted from radioactive nuclei is determined using modified generalized liquid drop model (MGLDM), where a new preformation factor is added to the existing generalized liquid drop theoretical model with proximity 77 potential. Half-lives for radioactive nuclei whose mass numbers vary from 221 to 242, emitting C, O, F, Ne, Mg, and Si clusters, are calculated theoretically considering deformation and orientation effects and the values are in exact agreement with experimental data. Standard deviation of logarithm of half-lives using present model is found to be 0.755, which is a much better result in comparison with those of GLDM1 and GLDM2 of Bao et al. [J. Phys. G: Nucl. Part. Phys. 39, 095103 (2012)], which are 1.84 and 1.114, respectively. Also, half-lives of various radioactive nuclei whose mass numbers vary from 220 to 250 are predicted. We hope that our present study on cluster half-lives may be helpful for future works in this field.

α-Cluster structure above double-shell closures and α-decay of 104Te

An analysis of the α+core properties of 104Te along with a global discussion on the α-cluster structure above the double-shell closures is presented from the viewpoint of the local potential model. The α+core interaction is described by a nuclear potential of (1 + Gaussian)×(W.S. + W.S.3) shape with two free parameters, which has been successfully tested in nuclei of different mass regions. The model produces Qα values and α-decay half-lives for 104Te in agreement with the 2018 experimental data of Auranen et al. in the energy range 5.13 MeV<Qα<5.3 MeV using an α preformation factor Pα=1. The comparison of the calculated reduced α-widths for the ground state bands of 104Te, 94Mo and 212Po indicates that 104Te has an α-cluster degree significantly higher than 94Mo and much higher than 212Po. These results point to 104Te as a preferential nucleus for α-clustering in the N,Z=50 region and corroborate the statement on the superallowed α-decay in 104Te.

Alpha particle preformation factor of spherical nuclei for 67 ≤Z ≤91

In this paper, alpha decay half-lives of spherical nuclei in the range [Formula: see text] are studied by considering the Coulomb and proximity potential model (CPPM) and calculating the alpha particle preformation factor. Comparisons are made to existing data in the literature. The half-lives are compared to the experimental values and also with the existing theoretical models, the analytical formula of Royer (R) and also within the modified analytical formula of Royer (MR) and New Akrawy–Poenaru Formula (AKRE) by Akrawy and Poenaru and the semi-empirical model based on fission theory (SemFIS) of Poenaru et al., the Universal Decay Law (UDL) of Qi et al., the Scaling Law of Brown (SLB), the Scaling Law of Horoi et al. (SLH). Compared with the experimental alpha half-lives, it can be found that the half-lives obtained using our formalism is in good agreement with the experimental data.

Fission Cross Sections and Fragment Mass Distribution of Actinide Nuclei Formed in n-Induced Reactions

The fission dynamics of odd mass actinide nuclei, 233Th∗ and 239U∗ formed in n-induced reactions, is studied in the framework of dynamical cluster-decay model (DCM). The analysis is carried out over a range of incident energies varying from En = 32.8 to 59.9 MeV. A description of deformation effects is provided by considering spherical as well as deformed choice of fragmentation and the fragment mass distribution is examined accordingly. The study is extended to two more actinide nuclei (233Pa∗ and 239Np∗) and the barrier characteristics are compared for chosen reactions and corresponding preformation factor is worked out to estimate the relative influence on fragment mass distribution. In addition to this, the relative role of sticking (IS) and non-sticking (INS) moment of inertia on the decay of 233Th∗ is explored. Finally, the comparative analysis of n-induced reaction with p-induced reactions is carried out for Th and U nuclei.

Improved evaluation of nuclear charge radii for superheavy nuclei

Although significant progress has been made in the synthesis of superheavy nuclei, the experimental knowledge of them is still very limited while the alpha decay chain is the main tool used to identify newly produced superheavy nuclei. Previously, we have extracted nuclear charge radii of superheavy nuclei via the experimental alpha decay data. As a further step, the density dependent cluster model is improved by introducing the difference between the density distributions of protons and neutrons. Besides, the important quantity, i.e., the alpha preformation factor, is connected with the microscopic correction of nuclear mass during this procedure, to perform a more reasonable description of the alpha decay process. It is found that the present deduced nuclear charge radii of heavy nuclei are in a better agreement with the measured values as compared to those in our previous evaluations. Subsequently, the nuclear radii of heavier even–even isotopes with Z = 98–116 are probed, accompanied by the consistency with the empirical evaluations. Moreover, the effect of the depressed density at the center of superheavy nucleus on the final extracted nuclear radius plus the decay lifetime is discussed, which appears to be different from the case of lighter nuclide.

α particle preformation and shell effect for heavy and superheavy nuclei**Supported by National Natural Science Foundation of China (11675066, 11475050), Fundamental Research Funds for the Central Universities (lzujbky-2017- ot04) and Feitian Scholar Project of Gansu Province

The α particle preformation factor is extracted within a generalized liquid drop model for Z = 84 - 92 isotopes and N = 126, 128, 152, 162, 176, 184 isotones. The calculated results show clearly that the shell effects play a key role in α particle preformation. The closer the proton and neutron numbers are to the magic numbers, the more difficult the formation of the α cluster inside the mother nucleus is. The preformation factors of the isotopes reflect that N = 126 is a magic number for Po, Rn, Ra, and Th isotopes, but for U isotopes the weakening of the influence of the N = 126 shell closure is evident. The trend of the factors for N = 126 and N = 128 isotones also support this conclusion. We extend the calculations for N = 152, 162, 176, 184 isotones to explore the magic numbers for heavy and superheavy nuclei, which are probably present near Z = 108 to N = 152, 162 isotones and Z = 116 to N = 176, 184 isotones. The results also show that another subshell closure may exist after Z = 124 in the superheavy nuclei. This is useful for future experiments.

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.

Systematic study of α decay of nuclei around the Z=82, N=126 shell closures within the cluster-formation model and proximity potential 1977 formalism

In the present work, we systematically study the $\mathcal{\alpha}$ decay preformation factors $P_{\alpha}$ within the cluster-formation model and $\mathcal{\alpha}$ decay half-lives by the proximity potential 1977 formalism for nuclei around $Z=82$, $N=126$ closed shells. The calculations show that the realistic $P_{\alpha}$ is linearly dependent on the product of valance protons (holes) and valance neutrons (holes) $N_pN_n$. It is consistent with our previous works [X.-D. Sun \textit{et al.}, \href{https://journals.aps.org/prc/abstract/10.1103/PhysRevC.94.024338}{ Phys. Rev. C 94, 024338 (2016)}, J.-G. Deng \textit{et al.}, \href{https://journals.aps.org/prc/abstract/10.1103/PhysRevC.96.024318}{Phys. Rev. C 96, 024318 (2017)}], which $P_{\alpha}$ are model-dependent and extracted from the ratios of calculated $\mathcal{\alpha}$ half-lives to experimental data. Combining with our previous works, we confirm that the valance proton-neutron interaction plays a key role in the $\mathcal{\alpha}$ preformation for nuclei around $Z=82$, $N=126$ shell closures whether the $P_{\alpha}$ is model-dependent or microcosmic. In addition, our calculated $\mathcal{\alpha}$ decay half-lives by using the proximity potential 1977 formalism taking $P_{\alpha}$ evaluated by the cluster-formation model can well reproduce the experimental data and significantly reduce the errors.

Systematics of α-decay fine structure in odd-mass nuclei based on a finite-range nucleon–nucleon interaction

A systematic study on α-decay fine structure is presented for odd-mass nuclei in the range 83≤Z≤92. The α-decay partial half-lives and branching ratios to the ground and excited states of daughter nuclei are calculated in the framework of the Wentzel–Kramers–Brillouin (WKB) approximation with the implementation of the Bohr–Sommerfeld quantization condition. The microscopic α-daughter potential is obtained using the double-folding model with a realistic M3Y-Paris nucleon–nucleon (NN) interaction. The exchange potential, which accounts for the knock-on exchange of nucleons between the interacting nuclei, is calculated using the finite-range exchange NN interaction which is essentially a much better approximation as compared to the zero-range pseudo-potential adopted in the usual double-folding calculations. Our calculations of α-decay fine structure have been improved by considering the preformation factor extracted from the recently proposed cluster formation model on basis of the binding energy difference. The computed partial half-lives and branching ratios are compared with the recent experimental data and they are in good agreement.

Landscape of α preformation probability for even–even nuclei in medium mass region

The behavior of α cluster preformation probability, in α decay, is a rich source of the structural information, such as the clustering, pairing, and shell evolution in heavy nuclei. Meanwhile, the experimental α decay data have been very recently compiled in the newest table NUBASE2016. Through a least square fit to the available experimental data of nuclear charge radii plus the neutron skin thickness, we obtain a new set of parameters for the two-parameter Fermi nucleon density distributions in target nuclei. Subsequently, we make use of these refreshed inputs, involved in the density-dependent cluster model, to extract α preformation factor () for a large range of medium α emitters with N < 126 from the newest data table. Besides checking the supposed smooth pattern of Pα in the open-shell region, the special attention has been paid to those exotic α-decaying nuclei around the Z = 50 and N = 82 shell closures. Moreover, the correlation between the α preformation factor and the microscopic correction of nuclear mass, corresponding to the effect of shell and pairing plus deformation, is in particular investigated, to pursue the valuable knowledge of the Pα pattern over the nuclide chart. The feature of α preformation factor along with the neutron–proton asymmetry is then detected and discussed to some extent.

The predictive accuracy of analytical formulas and semiclassical approaches for α decay half-lives of superheavy nuclei

Systematic calculations on the α decay half-lives are performed by using three analytical formulas and two semiclassical approaches. For the three analytical formulas, the experimental α decay half-lives and values of the 66 reference nuclei have been used to obtain the coefficients. We get only four adjustable parameters to describe α decay half-lives for even–even, odd–A, and odd–odd nuclei. By comparison between the calculated values from ten analytical formulas and experimental data, it is shown that the new universal decay law (NUDL) foumula is the most accurate one to reproduce the experimental α decay half-lives of the superheavy nuclei (SHN). Meanwhile it is found that the experimental α decay half-lives of SHN are well reproduced by the Royer formula although many parameters are contained. The results show that the NUDL formula and the generalized liquid drop model (GLDM2) with consideration of the preformation factor can give fairly equivalent results for the superheavy nuclei.

New insight into α clustering of heavy nuclei via their α decay

Based on the available experimental data of nuclear charge radii and neutron skin thickness, we have renewed the two-parameter Fermi (2pF) form of nucleon density distributions in heavy nuclei. Subsequently, we focus on the α clustering phenomenon of heavy nuclei in terms of the preformation probability of α cluster before its penetration in α decay. Through the experimental decay data, the α preformation factor Pα is extracted for a large range of nuclei above the N=126 shell, leading to the interesting recognition on the behavior of α cluster formation factor. It is found that the present α preformation factor varies more smoothly towards the large neutron–proton ratio, as compared to those from the previous evaluations. This may be explained by the fact that we have separately considered proton and neutron density distributions of related nuclei, while they are treated as the same form in our previous studies. Meanwhile, the presence of the Z=92 subshell is somewhat revealed by the picture of α formation factor in this study. Moreover, the similarity between the Pα value and the pairing gap is clearly demonstrated, indicating the crucial role of pairing correlation involved in the α decay process.

Fine structure of α decay from the variational principle

Starting from the variational principle, the time-dependent pairing equations are generalized by including the Landau-Zener effect and the Coriolis coupling. A system of microscopic equations of motion for configuration mixing is deduced, allowing the determination of quantities that have the same meaning as the preformation factors of the $\ensuremath{\alpha}$ particle. These equations are solved in order to reproduce the hindrance factors of the $\ensuremath{\alpha}$ decay of an odd-$A$ mass nucleus. The $\ensuremath{\alpha}$ decay of $^{211}\mathrm{Po}$ is treated as a superasymmetric fission process, by following the rearrangement of the nuclear orbitals from the parent ground state up to the scission configuration. The probabilities of finding the excited states of the daughter at scission are obtained from the microscopic equations of motion. The intensities of the transitions to the excited states of the daughter were evaluated theoretically. The experimental data were compared with the theoretical findings. A very good agreement was obtained. A mean value of the tunneling velocity of about $2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ fm/fs was extracted.

Improved double-folding α -nucleus potential by including nuclear medium effects

The nuclear medium effect in $\ensuremath{\alpha}$ decay is introduced into the microscopic double-folding model to construct an improved $\ensuremath{\alpha}$-nucleus potential. Under the local density approximation, the $\ensuremath{\alpha}$-cluster density distribution is considered to vary with the surrounding matter density as a result of the medium effect. The density-dependence of the $\ensuremath{\alpha}$ cluster is incorporated by the width parameter of the Gaussian function and constrained by the critical features derived from previous microscopic studies. The influence of the medium effect to the geometry of the $\ensuremath{\alpha}$-nucleus potential is studied by comparing with the conventional double-folding potential. To examine the improved potential, the $\ensuremath{\alpha}$-decay half-lives and preformation factors of even-even spherical nuclei are calculated and compared with experimental data. With the $\ensuremath{\alpha}$-decay data being well explained, it is concluded that the inclusion of the nuclear medium effect contributes to an improved double-folding $\ensuremath{\alpha}$-nucleus potential, which incorporates more details of the $\ensuremath{\alpha}$-decay process.

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.