Spontaneous Fission Half-lives Research Articles

Microscopic description of spontaneous fission based on a Gogny energy density functional including tensor contributions

This paper extends previous studies on the impact of tensor forces in fission dynamics of neutron-deficient Thorium isotopes to other isotopic chains of heavy actinides and low-mass super-heavy nuclei. Calculations are carried out within a mean-field framework based on the Gogny-D1S parametrization supplemented with the D1ST2a perturbative tensor term as driving force. Fission barrier heights and spontaneous fission half-lives are used as benchmarks to analyze the impact of the tensor term. A significant reduction of fission barrier heights and half-lives is associated with the tensor component of the force.

Is there an abrupt fall of spontaneous fission half-lives in 248No and 252Rf?

Is there an abrupt fall of spontaneous fission half-lives in 248No and 252Rf?

Improved formulas of spontaneous fission half-lives for heavy and superheavy nuclei

Improved formulas of spontaneous fission half-lives for heavy and superheavy nuclei

Improved empirical formula for spontaneous fission half-lives

The spontaneous fission (SF) half-lives of all 96 experimentally accessible SF emitters were examined. The SF emitters are classified as even Z-even A, odd Z-even A, odd Z-odd A and even Z-odd A. A plot of [Formula: see text] versus [Formula: see text] demonstrates a straight line, where k is variable. The [Formula: see text] values produced in this study are compared to all other semi-empirical relations such as Ren et al., [Nucl. Phys. A 759, 64 (2005)], Xu et al., [Phys. Rev. C 78, 044329 (2008)], Santhosh et al., [Nucl. Phys. A 832, 220 (2010)] and Karpov et al., [Int. J. Mod. Phys. E 21, 1250013 (2012)] available in the literature. When compared to earlier semi-empirical equations accessible in the literature, the new formula shows reduced uncertainty in standard deviation in the case of Odd Z-even A and even Z-Odd A nuclei. When compared to other sets of combinations (even Z-even A, and odd Z-odd A nuclei), this study more accurately reproduces the experimental SF half-lives for even Z-odd A and odd Z-even A nuclei with smaller [Formula: see text] in the atomic number range 9[Formula: see text]12 and mass number range 23[Formula: see text]84.

Spontaneous fission half-life in Fm isotopes with nuclear energy density functional

A microscopic description of fission dynamics is important to understand the decay properties of neutron-rich heavy nuclei that are relevant to r-process nucleosynthesis. To provide a reliable and efficient method to evaluate the spontaneous fission half-life, we develop a method, called the constrained Hartree– Fock–Bogoliubov (CHFB) plus local quasiparticle random-phase approximation (LQRPA), to include dynamical residual effects in the collective inertia. With the CHFB + LQRPA, we evaluate the collective potential and the collective inertia along a mass-symmetric fission path in Fm isotopes with the neutron numbers N = 158–164. The obtained LQRPA inertia is much larger than the cranking one that ignores dynamical residual effects and shows a remarkable variation along the fission path. We estimate the fission half-life of the Fm isotopes using the action integral with the obtained collective potential and inertia. A large difference between the fission half-lives obtained with the LQRPA inertia and with the cranking inertia is observed. This indicates the importance of evaluating the collective inertia for estimating the fission half-life.

The competition between α-decay and spontaneous fission for even–even isotopes of superheavy nuclei in the range 106≤Z≤124

The [Formula: see text]-decay and spontaneous fission (SF) half-lives for even–even isotopes of superheavy nuclei in the range [Formula: see text] are predicted using nuclear double-folding and Coulomb potentials. The [Formula: see text]-decay half-lives are computed based on WKB approximation for tunneling probability through potential barrier. The half-lives of SF have also been calculated using a semi-empirical relation constructed by Santhosh et al. [Nucl. Phys. A 832, 220 (2009)]. Our calculated half-lives of cold SF and [Formula: see text]-decay are compared with the available experimental data. This comparison indicates that our obtained half-lives are in good agreement with the available experimental data. The competition between [Formula: see text]-decay and SF is also analyzed in detail and the decay modes are predicted for the unknown cases. Variation of [Formula: see text]-decay and SF half-lives with mass number of the parent isotopes for each nucleus revealed the major role played with shell effect.

Cluster properties of heavy nuclei predicted with the Barcelona-Catania-Paris-Madrid energy density functional

We study the cluster emission properties of 224\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{224}$$\\end{document}Ra and 238\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{238}$$\\end{document}Pu employing the Barcelona-Catania-Paris-Madrid (BCPM) energy density functional (EDF). Starting from two-dimensional potential energy surfaces, coexisting fission paths are identified. A fission valley located at large octupole deformations, corresponding to a highly-asymmetric mass distribution, is found in both nuclei. As the corresponding fragments are dominated by the presence of 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, we can relate this fission path to the emergence of cluster emission. Using the octupole moment as collective degree of freedom, we compute the cluster decay half-lives and study the impact of collective inertias, pairing strength and collective zero-point energy. The agreement with experimental data resembles the results obtained for spontaneous fission half-lives, indicating the capability of BCPM to consistently describe a large variety of fission phenomena, including cluster emission.

Spontaneous fission half-lives of actinides and superheavy elements

Spontaneous fission half-lives of actinides and superheavy elements

Theoretical predictions on the decay modes of 282−310Og

Possible decay modes of 282−310Og are studied within the framework of the Coulomb and Proximity Potential Model (CPPM), Universal Decay Law (UDL) and the Hatsukawa formula. A new diffusion parameter and a new preformation factor are included in the CPPM Model calculations. We have refitted the Hatsukawa formula to calculate the alpha and cluster decay half-lives in the superheavy region. The spontaneous fission (SF) half-lives are calculated using the shell correction energy-dependent formula of Santhosh et al. The predicted alpha decay half-lives are compared with the predictions of the UDL formula; and the predictions of Soumya et al. and Koyuncu et al. Possible heavy cluster decays from 284−297Og are also studied within the UDL formula and by using the empirical formula of Hatsukawa et al. with new fitting parameters, and a comparison is made with the predictions of Santhosh et al.

Radioactive decay properties of superheavy element Z = 119

Within the macroscopic approach, investigation of different decay modes such as alpha-decay, cluster-decay (12C to 40Ca), heavy particle radioactivity (HPR) (58Ni to 85Rb), and spontaneous fission (SF) half-lives are investigated in detail in the superheavy element (SHE), Z = 119. The decay energies, penetration probability, and different decay half-lives in the isotopes of synthesized superheavy nuclei (SHN) 290–303119 are evaluated. Both 12C and 40Ar cluster emissions reveal shorter half-lives when compared to other cluster emissions. Furthermore, 85Rb heavy particle emission from the SHN 290–303119 discloses shorter half-lives compared to other heavy particle emissions. From the comparison of different decay half-lives, it is observed that 85Rb HPR is dominant in the region 290–299119, alpha-decay is dominant for the 300–302119, and SF half-lives are predominant in 303119 nuclei. Hence, the prediction of decay modes and decay path in the SHE, Z = 119 are helpful in the identification of experimentally synthesized SHE.

Least action description of dynamic pairing correlations in the fission of curium and californium isotopes based on the Gogny energy density functional

The impact of dynamic pairing correlations and their interplay with Coulomb antipairing effects on the systematic of the spontaneous fission half-lives for the nuclei $^{240-250}$Cm and $^{240-250}$Cf is analyzed, using a hierarchy of approximations based on the parametrization D1M of the Gogny energy density functional (EDF). First, the constrained Hartree-Fock-Bogoliubov (HFB) approximation is used to compute deformed mean-field configurations, zero-point quantum corrections and collective inertias either by using the Slater approximation to Coulomb exchange and neglecting Coulomb antipairing or by fully considering the exchange and pairing channels of the Coulomb interaction. Next, the properties of the {\it{least action}} and {\it{least energy}} fission paths are compared. In the {\it{least action}} case, pairing is identified as the relevant degree of freedom in order to minimize the action entering the Wentzel-Kramers-Brillouin (WKB) approximation to the tunneling probability through the fission barrier. Irrespective of the treatment of Coulomb exchange and antipairing, it is shown that the {\it{least action}} path obtained taking into account the pairing degree of freedom leads to stronger pairing correlations that significantly reduce the spontaneous fission half-lives $t_{SF}$ improving thereby the comparison with the experiment by several orders of magnitude. It is also shown that the Coulomb antipairing effect is, to a large extent, washed out by the {\it{least action}} procedure and therefore the $t_{SF}$ values obtained by the two different treatments of the Coulomb exchange and pairing are of similar quality.

Isotopic yields and spontaneous fission half-lives of 279Ds and 281Ds superheavy isotopes

In this paper, Isotopic yield and half-lives of cold spontaneous fission for [Formula: see text] and [Formula: see text] superheavy isotopes are studied. The interacting potential between fragments includes mean field proximity and Coulomb potentials. Fission [Formula: see text]-value, driving potential, [Formula: see text] and partial penetration probability of each possible individual fragmentation are calculated using [Formula: see text] approximation. According to the tunneling effect, the most favored pair of fragments is produced for the highest [Formula: see text]-value or the lowest driving potential. A few fragmentation with higher [Formula: see text]-value are selected for each atomic number Z. It is found that for [Formula: see text] isotope, the highest relative yield belongs to the [Formula: see text]Te + [Formula: see text]Ce fragmentation while for [Formula: see text], the combination [Formula: see text]Te + [Formula: see text]Ce has lowest driving potential and highest yield due to presence of fragments with magic or near magic proton and neutron numbers ([Formula: see text] and [Formula: see text]). By calculating yield of each fragmentation, its partial fission decay constant and then by summing over all decay constants for possible fragmentation, the fission decay constant for each superheavy isotope is obtained. Furthermore, half-life of each superheavy isotope is also estimated. Finally, the calculated half-lives using this method are compared with the experimental data. Good agreement achieved between our calculated half-lives and the experimental data.

Fission Properties of Neutron-Rich Nuclei around the End Point of r-Process

We studied the fission properties of neutron-rich nuclei 278, 286Cf around the end point of r-process by microscopic self-consistent approaches. The fission barriers and potential energy surfaces are obtained by constrained static Skyrme Hartree–Fock-BCS calculations. Fission fragments are studied by dynamical time-dependent Hartree–Fock+BCS calculations. Results show that 286Cf has an octupole deformation at ground state, which can increase the fission barrier height by 1.1 MeV and enhance significantly the spontaneous fission half-life. To search possible fission channels, dynamical calculations with a broad coverage of initial deformations result in two slightly asymmetric peaks around A = 128 and 150 for 278Cf, and A = 133 and 153 for 286Cf. Very asymmetric fission channels as given by semi-empirical models are not found in our results.

Building surrogate models of nuclear density functional theory with Gaussian processes and autoencoders

From the lightest Hydrogen isotopes up to the recently synthesized Oganesson (Z = 118), it is estimated that as many as about 8,000 atomic nuclei could exist in nature. Most of these nuclei are too short-lived to be occurring on Earth, but they play an essential role in astrophysical events such as supernova explosions or neutron star mergers that are presumed to be at the origin of most heavy elements in the Universe. Understanding the structure, reactions, and decays of nuclei across the entire chart of nuclides is an enormous challenge because of the experimental difficulties in measuring properties of interest in such fleeting objects and the theoretical and computational issues of simulating strongly-interacting quantum many-body systems. Nuclear density functional theory (DFT) is a fully microscopic theoretical framework which has the potential of providing such a quantitatively accurate description of nuclear properties for every nucleus in the chart of nuclides. Thanks to high-performance computing facilities, it has already been successfully applied to predict nuclear masses, global patterns of radioactive decay like β or γ decay, and several aspects of the nuclear fission process such as, e.g., spontaneous fission half-lives. Yet, predictive simulations of nuclear spectroscopy—the low-lying excited states and transitions between them—or of nuclear fission, or the quantification of theoretical uncertainties and their propagation to basic or applied nuclear science applications, would require several orders of magnitude more calculations than currently possible. However, most of this computational effort would be spent into generating a suitable basis of DFT wavefunctions. Such a task could potentially be considerably accelerated by borrowing tools from the field of machine learning and artificial intelligence. In this paper, we review different approaches to applying supervised and unsupervised learning techniques to nuclear DFT.

Properties and synthesis of the superheavy nucleus Fl114298

The one-nucleon separation energy ${S}_{n}$, two-nucleon separation energy ${S}_{2n}$, one-proton separation energy ${S}_{p}$, two-proton separation energy ${S}_{2p}, \ensuremath{\alpha}$-decay energy ${Q}_{\ensuremath{\alpha}}, \ensuremath{\alpha}$-decay half-life and spontaneous fission half-life of $Z=114$ isotopes and $N=184$ isotones are calculated by the finite-range droplet model (FRDM2012). It is found that $N=184$ is a neutron magic number, and $Z=114$ is a proton magic number. The properties of $Z=114$ isotopes and $N=184$ isotones provide a vital signal that $_{114}^{298}\mathrm{Fl}$ may be a spherical double-magic nucleus and also the center of the stability island of superheavy nuclei. Based on this, we began to investigate the optimal conditions for the synthesis of superheavy nucleus $_{114}^{298}\mathrm{Fl}$ within the dinuclear system model. To produce such neutron-rich compound nucleus, we consider using the extremely neutron-rich radioactive beams to bombard actinide targets. The evaporation residue cross section of superheavy nuclei synthesized by radioactive beam is analyzed in detail. Finally, we suggest that for the synthesis of $_{114}^{298}\mathrm{Fl}$, the radioactive beam-induced fusion reaction $^{64}\mathrm{Ti}+^{238}\mathrm{U}$ in the $4n$ evaporation channel with an excitation energy of 43 MeV is optimal.

Role of dynamic pairing correlations in fission dynamics. II. Fermium and nobelium isotopes

The competition between the quenching of pairing due to the repulsive Coulomb interaction and dynamic pairing correlations added by particle number symmetry restoration has been studied in a selected set of Fermium and Nobelium isotopes by using a hierarchy of Hartree-Fock-Bogoliubov--based approximations and a restricted variation after particle number projection, all of them based on the $\mathrm{D}1{\mathrm{M}}^{*}$ parametrization of the Gogny force. It is found that Coulomb antipairing is partially compensated by beyond-mean-field pairing correlations. However, the compensation is not perfect and a modulation of the spontaneous fission half-lives, as functions of the neutron number, indicates that the combined effect on fission dynamics of Coulomb antipairing and restricted particle number symmetry restoration cannot be overlooked. Neither can it be accounted for by the Coulomb Slater approximation.

Isotopic Ratio of Radionuclides in Natural Materials

In this work, the 235U/238U ratio and 235U concentration were discussed. 235,238 U isotopes were measured and calculated for uranium mines samples and reference material. The difference and deviation in experimental and calculated values for 235U were discussed. It can be concluded that the 235U/238U ratio was varied naturally with a range of 0.0442 to 0.0478. The measured ratio was deviated upon the reference value (0.0462) with a range of -0.02% to 1.5%, as we can conclude that the measured values were very accurate. While the values of the calculated ratio were varied from -0.089% up to 17%, which represents low accuracy. Isotopic uranium ratio changes over time depending on spontaneous fission half-life, radioactive decay rate and gamma-ray intensity for 235,238U. These fractions in uranium isotopic were discussed and here we assume a tool for correction and normalization. It can be concluded that the 235U/238U ratio and 235Uconcentration can be varied naturally with a slight deviation. The difference and reliability of 235,238U isotope on experimental results of uranium mines depend on several reasons such as decay rate of natural uranium, Spontaneous fission half-life and Gamma-ray intensity for 235,238U. Therefore, the experimental results for 235U are very accurate than the calculated results to improve the isotopes of U and 235U/238U ratio in Uranium mines.

Nudged elastic band approach to nuclear fission pathways

Background: The nuclear fission process is a dramatic example of the large-amplitude collective motion in which the nucleus undergoes a series of shape changes before splitting into distinct fragments. This motion can be represented by a pathway in the many-dimensional space of collective coordinates. Within a stationary framework rooted in a static collective Schr\"odinger equation, the collective action along the fission pathway determines the spontaneous fission half-lives as well as mass and charge distributions of fission fragments.Purpose: We study the performance and precision of various methods to determine the minimum-action and minimum-energy fission trajectories in the collective space.Methods: We apply the nudged elastic band method (NEB), grid-based methods, and the Euler-Lagrange approach to the collective action minimization in two- and three-dimensional collective spaces.Results: The performance of various approaches to the fission pathway problem is assessed by studying the collective motion along both analytic energy surfaces and realistic potential-energy surfaces obtained with the Skyrme-Hartree-Fock-Bogoliubov theory. The uniqueness and stability of the solutions is studied. The NEB method is capable of efficient determination of the exit points on the outer turning surface that characterize the most probable fission pathway and constitute the key input for fission studies. This method can also be used to accurately compute the critical points (i.e., local minima and saddle points) on the potential-energy surface of the fissioning nucleus that determine the static fission path. The dynamic programming method also performs quite well and it can be used in many-dimensional cases to provide initial conditions for the NEB calculations.Conclusions: The NEB method is the tool of choice for finding the least-action and minimum-energy fission trajectories. It will be particularly useful in large-scale static fission calculations of superheavy nuclei and neutron-rich fissioning nuclei contributing to the astrophysical $r$-process recycling.

Studies on the decay modes of superheavy nuclei with Z = 120

A study on the competition between alpha-decay and spontaneous fission (SF) of the Z = 120 isotopes with 283 ≤ A ≤ 350 is performed in this paper. The alpha-decay half-lives are evaluated using the modified generalized liquid drop model (MGLDM). The SF half-lives are calculated within the shell-effect-dependent formula. It is found that the dominant decay mode of 294,295,297,298,301-304,308120 is alpha-decay and the half-lives fall within the experimental limit (>1 μs). Then the decay properties of the alpha-decay chain of 294,295,297,298,301-304,308120 are predicted within the MGLDM and the shell-effect-dependent formula. These predictions are helpful for searching and identifying the new elements in future. Finally, the possibility of the cluster radioactivity of the Z = 120 isotopes is discussed within the MGLDM. By analyzing the competition between the cluster radioactivity and alpha-decay, it is found that the possibility of the cluster radioactivity is much smaller than the corresponding alpha-decay.

Alpha-gamma decay studies of ^{247}Md

Alpha decay and spontaneous fission of the ground-state and the isomeric state of ^{247}Md were investigated with specific emphasis to identify the ground-state of the daughter nucleus ^{243}Es. The decay studies were accompanied by measuring alpha -gamma coincidences. On the basis of the measured data an improved decay scheme of ^{247}Md is proposed. Spontaneous fission half-lives of ^{247g}Md and ^{247m}Md were determined and the fission hindrance of the high spin ground-state (7/2^{-}) relative to the low spin isomeric state (1/2^{-}) was estimated.