Fission Barrier Research Articles

β -delayed neutron-emission and fission calculations within relativistic quasiparticle random-phase approximation and a statistical model

Background: $\ensuremath{\beta}$-delayed neutron emission and fission are essential in $r$-process nucleosynthesis. Although the number of experimental studies covering $r$-process nuclei has recently increased, the uncertainties of $\ensuremath{\beta}$-delayed neutron emission and fission are still large for $r$-process simulations.Purpose: Our aim is to introduce a theoretical framework for the description of $\ensuremath{\beta}$-delayed neutron-emission and fission rates based on relativistic nuclear energy density-functional and statistical models and investigate their properties throughout the nuclide map.Methods: To obtain $\ensuremath{\beta}$ strength functions, the relativistic proton-neutron quasiparticle random-phase approximation is employed. Particle evaporations and fission from highly excited nuclear states are estimated by the Hauser-Feshbach statistical model. $\ensuremath{\beta}$-delayed neutron branching ratios ${P}_{n}$ are calculated and compared with experimental data, and the $\ensuremath{\beta}$-delayed fission branching ratio ${P}_{f}$ are also assessed by using different fission barrier data.Results: Calculated ${P}_{n}$ are in a good agreement with the experimental data and the root mean square deviation is comparable to results of preceding works. It is found that energy withdrawal by $\ensuremath{\beta}$-delayed neutron-emission sensitivity varies ${P}_{n}$, especially for nuclei near the neutron drip line. ${P}_{f}$ depend sensitively on fission barrier data. It is found that not only the barrier height but also the number of barrier humps is important to evaluate ${P}_{f}$.Conclusions: The framework introduced in this work provides an improved theoretical description of the $\ensuremath{\beta}$-delayed neutron emission and fission. Since ${P}_{f}$ as well as ${P}_{n}$ depend strongly on fission barrier information, four kinds of fission barrier data are used in this work to allow further sensitivity studies of the $r$-process nucleosynthesis on the nuclear fission. More studies on fission barrier are highly requested to assess the role of $\ensuremath{\beta}$-delayed fission in the $r$-process study. A complete set of calculated data for $\ensuremath{\beta}$-delayed neutron emission and fission are summarized as a table in supplemental material for its use in $r$-process studies as well as to complement a part of nuclear data in which no experimental data are available.

Systematics on production of superheavy nuclei $$Z = 119-122$$ in fusion-evaporation reactions

The fusion dynamics on the formation of superheavy nuclei is investigated thoroughly within the dinuclear system model. The Monte Carlo approach is implemented into the nucleon transfer process for including all possible orientations, at which the dinuclear system is assumed to be formed at the touching configuration of dinuclear fragments. The production cross sections of superheavy nuclei Cn, Fl, Lv, Ts and Og are calculated and compared with the available data from Dubna. The evaporation residue excitation functions in the channels of pure neutrons and charged particles are analyzed systematically. The combinations with $^{44}$Sc, $^{48,50}$Ti, $^{49,51}$V, $^{52,54}$Cr, $^{58,62}$Fe and $^{62,64}$Ni bombarding the actinide nuclides $^{238}$U, $^{244}$Pu, $^{248}$Cm, $^{247,249}$Bk, $^{249,251}$Cf, $^{252}$Es and $^{243}$Am are calculated for producing the superheavy elements with Z=119-122. It is found that the production cross sections sensitively depend on the neutron richness of reaction system. The structure of evaporation residue excitation function is related to the neutron separation energy and fission barrier of compound nucleus.

Essential role for paxillin tyrosine phosphorylation in LPS-induced mitochondrial fission, ROS generation and lung endothelial barrier loss

We have shown that both reactive oxygen species (ROS) and paxillin tyrosine phosphorylation regulate LPS-induced human lung endothelial permeability. Mitochondrial ROS (mtROS) is known to increase endothelial cell (EC) permeability which requires dynamic change in mitochondrial morphology, events that are likely to be regulated by paxillin. Here, we investigated the role of paxillin and its tyrosine phosphorylation in regulating LPS-induced mitochondrial dynamics, mtROS production and human lung microvascular EC (HLMVEC) dysfunction. LPS, in a time-dependent manner, induced higher levels of ROS generation in the mitochondria compared to cytoplasm or nucleus. Down-regulation of paxillin expression with siRNA or ecto-expression of paxillin Y31F or Y118F mutant plasmids attenuated LPS-induced mtROS in HLMVECs. Pre-treatment with MitoTEMPO, a scavenger of mtROS, attenuated LPS-induced mtROS, endothelial permeability and VE-cadherin phosphorylation. Further, LPS-induced mitochondrial fission in HLMVECs was attenuated by both a paxillin siRNA, and paxillin Y31F/Y118F mutant. LPS stimulated phosphorylation of dynamin-related protein (DRP1) at S616, which was also attenuated by paxillin siRNA, and paxillinY31/Y118 mutants. Inhibition of DRP1 phosphorylation by P110 attenuated LPS-induced mtROS and endothelial permeability. LPS challenge of HLMVECs enhanced interaction between paxillin, ERK, and DRP1, and inhibition of ERK1/2 activation with PD98059 blocked mitochondrial fission. Taken together, these results suggest a key role for paxillin tyrosine phosphorylation in LPS-induced mitochondrial fission, mtROS generation and EC barrier dysfunction.

An attempt to construct semi-empirical formula for angular momentum-dependent fission barriers of actinides

In this paper, a simple semi-empirical formula is proposed for angular momentum-dependent fission barriers of actinides [Formula: see text]. This formula produces angular momentum-dependent fission barriers with the simple inputs of atomic number (Z), mass number (A) and angular momentum ([Formula: see text]). The fission barriers produced by the present formula are compared with that of experiments and other models. There is a good agreement between the present formula and experiments. The present formula could be used to evaluate the angular momentum-dependent fission barriers of actinides.

Exploring the fission barrier of U235

In this work we have reexamined the shape isomer in $^{235}\mathrm{U}$. Reanalyzing data from a previous experiment gave a half-life of ${T}_{1/2}=(11\ifmmode\pm\else\textpm\fi{}3)\phantom{\rule{4pt}{0ex}}\mathrm{ms}$ and a cross section for populating the isomer of ${\ensuremath{\sigma}}_{\mathrm{iso}}=(12\ifmmode\pm\else\textpm\fi{}1)\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{b}$. Combining these new results with measured properties of fission fragments from the reaction $^{234}\mathrm{U}(n,f)$ allowed extracting parameters describing the outer fission barrier. The deduced barrier parameters are ${E}_{B}=(5.7\ifmmode\pm\else\textpm\fi{}0.6)$ MeV and $\ensuremath{\hbar}{\ensuremath{\omega}}_{B}=(0.5\ifmmode\pm\else\textpm\fi{}0.1)$ MeV for the height and curvature, respectively, as well as the energy of the superdeformed ground state ${E}_{II}=(2.4\ifmmode\pm\else\textpm\fi{}0.6)$ MeV. Separate barrier parameters for the standard-1 and standard-2 fission modes have been estimated, too. Finally, the results obtained in this work have been successfully tested for their plausibility.

Novel semi-empirical formula and examination for fission barriers of super-heavy nuclei with Z ≥ 100

In this study, we developed a semi-empirical formula for predicting fission barriers of super-heavy nuclei (SHN), which have fissilities χ > 48.5428, based on a former formula proposed by Myers and Swiatecki [1999 Phys. Rev. C 60, 014 606]. We calculated fission barriers for isotopes with Z = 100–135 using our formula and the Lublin-Strasbourg Drop model. It was found that the macroscopic component of the fission barrier is less than 0.2 MeV, which is large enough to be considered with microscopic part for many SHN. These results were compared to each other and to those estimated using other approaches. Through evaluations of theoretical fission barriers, we found that there is a significant difference, up to a few MeV, between the results obtained from different models. In other words, recent fission barrier predictions are very uncertain. Finally, the results of this study are useful for estimating the spontaneous-fission lifetime and production cross sections of unknown super-heavy nuclei.

Description of the multidimensional potential-energy surface in fission of Cf252 and No258

Microscopic studies of nuclear fission require the evaluation of the potential-energy surface as a function of the collective coordinates. A reasonable choice of constraints on multipole moments should be made to describe the topography of the surface completely within a reasonable amount of computing time. We present a detailed analysis of fission barriers in the self-consistent Hartree-Fock-Bogoliubov approach with the D1S parametrization of the Gogny nucleon-nucleon interaction. Two heavy isotopes representing different spontaneous fission modes, $^{252}\mathrm{Cf}$ (asymmetric) and $^{258}\mathrm{No}$ (bimodal), have been chosen for the analysis. We have shown the existence of complicated structures on the energy surface that cannot be fully described in two-dimensional calculations. We analyze apparent problems that can be encountered in this type of calculations: multiple solutions for given constraints and transitions between various overlapping potential-energy surfaces. These issues may be partially solved by the analysis of the potential-energy surface spanned by triple constraints, but even in this case one may find multiple solutions and surface discontinuities. Analysis of the potential-energy surface in two dimensions is often very successful but it must be carried out with special attention to possible discontinuities.

Measurement of fission excitation function for 19F + 194, 196, 198Pt reactions

Experimental fission cross-sections are reported for the 19F + 194,196,198Pt reactions populating an isotopic chain of compound nuclei comprising both closed and non-closed shell nuclei. The fission cross-sections are obtained at near and above Coulomb barrier energies by measuring fission fragment angular distributions. The present work aims to estimate nuclear dissipation and find its isotopic and shell closure dependence from statistical model (SM) analysis of experimental data. Pre-scission neutron multiplicity data for the same systems is also included in the SM analysis. An updated version of SM is used in the present analysis, which includes shell corrections in level density and fission barrier as well as the effect of collective enhancement of level density and orientation effect of the compound nucleus along the symmetry axis. An isotopic dependence of the dissipation strength fitting the fission excitation functions is observed. The pre-scission neutron multiplicity, however, is underestimated by the SM.

Rate of decline of the production cross section of superheavy nuclei with Z=114–117 at high excitation energies

The production cross sections of superheavy nuclei with charge numbers $114-117$ are predicted in the $(5-9)n$-evaporation channels of the $^{48}$Ca-induced complete fusion reactions for future experiments. The estimates of synthesis capabilities are based on a uniform and consistent set of input nuclear data provided by the multidimensional macroscopic-microscopic approach. The contributions of various factors to the final production cross section are discussed. As shown, the specific interplay between survival and fusion probabilities unexpectedly leads to a relatively slow decline of the total cross-sections with increasing excitation energy. This effect is supported by a favorable arrangement of fission barriers protecting the compound nucleus against splitting concerning energetic thresholds for the emission of successive neutrons. In particular, the probabilities of the formation of superheavy nuclei in the $5n$-, $6n$-, and in some cases even in $7n$-evaporation channels are still promising. This may offer a new opportunity for the future synthesis of unknown neutron-deficient superheavy isotopes.

Fission fragment mass yields of Th to Rf even-even nuclei * *Supported by the Polish National Science Center (2018/30/Q/ST2/00185) and the National Natural Science Foundation of China (11961131010, 11790325)

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.

Reflating the nucleus: The pachydermous droplet model

It is shown that the excessive squeezing characteristic of the leptodermous droplet model can be eliminated by taking into account the finite thickness of the nuclear surface. The same objective was achieved in the finite-range droplet model by the introduction of an exponential correction term, but this model breaks down at the large deformations encountered in fission barriers. With this term now being seen to be superfluous, a unified droplet-model treatment of masses and fission barriers becomes possible.

Fusion and fission barrier heights and positions within the Generalized Liquid Drop Model

The fusion and fission barriers have been determined with a Generalized Liquid Drop Model taking into account the proximity forces acting between surfaces in regard, the charge and mass asymmetry, the shell and pairing effects and quasimolecular shapes. The heights and positions of these barriers have been compared with the empirical results deduced from the experimental data. There is an overall agreement for the fusion barrier heights for most of the reactions. These fusion barrier heights may also be calculated from a proposed analytic formula or other formulas. The empirical fission barrier heights lie always between the values given by the GLDM and neglecting the microscopic effects in the fragments and the values determined in including the deformation and shell and pairing effects of the fragments.

Quasifission and fusion-fission lifetime studies for the superheavy element Z=120

We study the quasifission and fusion-fission lifetimes for a number of fusion reactions used to synthesize the superheavy element $Z=120$ using a statistical method within the framework of the dinuclear system model. In particular, influence of the target orientation and angular momentum on such lifetimes have been investigated. The quasifission and fusion-fission lifetimes have been compared very well with that of available experiments on successful superheavy element synthesis. We notice further the predicted quasifission and fusion-fission lifetimes of the projectile-target combinations used for the synthesis of the superheavy element $Z=120$ also show the similar trend. Furthermore, the fusion-fission lifetime is seen to somewhat decrease with the increase of the angular momentum as well as beam energy. Little effect is seen on fusion barrier of the reaction and fission barrier of superheavy compound nucleus. Variation of quasifission lifetime is also not much with orientation angle, beam energy and fission barrier of the superheavy compound nuclei. Hence, this lifetime study does not provide any good reason why the attempted reactions have failed to synthesize the superheavy nuclei $Z=120$. Furthermore, consideration of the fusion barrier, fissility, mass asymmetry, deformation parameter, fission barrier, etc., leads us to reveal that optimal colliding energy is important to have the largest evaporation residue cross section for any chosen reaction so that it is well within the measurable limit for a specific experimental set up.

Bohr Quadrupole Collective Dynamics and the Inner Fission Barrier of Some Heavy Even–Even Nuclei Within the Highly Truncated Diagonalization Approach

Bohr Quadrupole Collective Dynamics and the Inner Fission Barrier of Some Heavy Even–Even Nuclei Within the Highly Truncated Diagonalization Approach

Evaluation for half-lives in α-decay chains of 309−312126 based on semi-empirical approaches

In this paper, we estimated half-lives using semi-empirical formulae for isotopes with Z = 100 − 126 in four α-decay chains, which can appear in the syntheses of the 309−312126 nuclei. The spontaneous fission half-lives were calculated using the Anghel, Karpov, and Xu models, whereas the α-decay ones were predicted using the Viola-Seaborg, Royer, Akrawy, Brown, modified formulae of Royer, Ni, and Qian approaches. We found that there are large differences among the spontaneous fission half-lives estimated using the Xu model and those calculated using the others, which are up to 50 orders of magnitude. The α-decay half-lives also have large uncertainties due to difference in either methods or uncertainties in nuclear mass and spin-parities. Subsequently, there is an argument in determination of α-emitters, especially for the 312126 isotope. On the other hand, the α-decay half-lives are in the range from a few microseconds (309−312126) to thousands of years (257−260Fm) in the decay chains. It was found that the half-lives are very sensitive to not only the shell closure but also the angular momentum in the α decay. For experiments, with relatively long half-lives (a few milliseconds), the 289−292Lv isotopes can be observed as evidences for syntheses of the unknown super-heavy 309−312126 nuclei. Furthermore, measurements for precise mass, fission barrier, and spin-parity are necessary to improve accuracy of half-life predictions for super-heavy nuclei.

Investigation of the cold valley paths for the synthesis of isotopes of Ubh in optimum orientations

Cold valley paths have been investigated for the synthesis of isotopes of superheavy element Unbihexium using quantum mechanical fragmentation theory, which suggests the fusion of fission fragments belonging to the cold valleys in the potential energy surfaces with at least one spherical closed shell nucleus as the reaction partner for the nuclear synthesis. For the suitability of the cold valley fission fragments for the synthesis of isotopes of Ubh, first the fragmentation potentials, preformation probabilities and fission barriers of the fission fragments of 314Ubh and 326Ubh compound systems in their ground states have been compared by keeping the fragments either in hot or cold optimum orientations. The comparison suggests 138Ba + 176Yb and 132Sn + 194Os reactions in hot optimum orientations for the synthesis of isotopes of Ubh due to their highest values of preformation probabilities, lowest values of the fragmentation potentials and relatively good values of the fission barriers. Also, the reactions 68Ni + 246Cf and 70Ni + 256Cf have been considered for the comparison with 138Ba + 176Yb and 132Sn + 194Os reactions due to their relatively smaller values of the Coulomb potential, higher mass-asymmetry and fission barrier, and shell closures next to 48Ca which has been used in most of the experiments for the synthesis of superheavy elements. Finally, the excitation functions for the neutron evaporation from the compound systems formed in these reactions, the probabilities of the formation and survival of the compound nuclei have been compared to suggest the suitable cold valley paths energies for the synthesis of the isotopes of Ubh.

Properties of heaviest nuclei with [formula omitted] and [formula omitted

We systematically determine ground-state and saddle-point shapes and masses for 1305 heavy and superheavy nuclei with Z=98–126 and N=134–192, including odd-A and odd–odd systems. From these we derive static fission barrier heights, one- and two-nucleon separation energies, and Qα values for g.s. to g.s. transitions. Our study is performed within the microscopic–macroscopic method with the deformed Woods–Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy taken as the smooth part. We use parameters of the model that were fitted previously to masses of even–even heavy nuclei. For systems with odd numbers of protons, neutrons, or both, we use a standard BCS method with blocking. Ground-state shapes and energies are found by the minimization over seven axially-symmetric deformations. A search for saddle-points was performed by using the ”imaginary water flow” method in three consecutive stages, using five- (for nonaxial shapes) and seven-dimensional (for reflection-asymmetric shapes) deformation spaces. Calculated ground-state mass excess, nucleon separation- and Qα energies, total, macroscopic (normalized to the macroscopic energy at the spherical shape) and shell corrections energies, and deformations are given for each nucleus in Table 1. Table 2 contains calculated properties of the saddle-point configurations and the fission barrier heights. In Tables 3-7, are given calculated ground-state, inner and outer saddle-point and superdeformed secondary minima characteristics for 75 actinide nuclei, from Ac to Cf, for which experimental estimates of fission barrier heights are known. These results are an additional test of our model.

Covariant density functional theory input for r -process simulations in actinides and superheavy nuclei: The ground state and fission properties

The systematic investigation of the ground state and fission properties of even-even actinides and superheavy nuclei with $Z=90-120$ from the two-proton up to two-neutron drip lines with proper assessment of systematic theoretical uncertainties has been performed for the first time in the framework of covariant density functional theory (CDFT). These results provide a necessary theoretical input for the r-process modeling in heavy nuclei and, in particular, for the study of fission recycling. Four state-of-the-art globally tested covariant energy density functionals (CEDFs), namely, DD-PC1, DD-ME2, NL3* and PC-PK1, representing the major classes of the CDFT models are employed in the present study. Ground state deformations, binding energies, two neutron separation energies, $\alpha$-decay $Q_{\alpha}$ values and half-lives and the heights of fission barriers have been calculated for all these nuclei. Theoretical uncertainties in these physical observables and their evolution as a function of proton and neutron numbers have been quantified and their major sources have been identified. Spherical shell closures at $Z=120$, $N=184$ and $N=258$ and the structure of the single-particle (especially, high-$j$) states in their vicinities as well as nuclear matter properties of employed CEDFs are two major factors contributing into theoretical uncertainties. However, different physical observables are affected in a different way by these two factors. For example, theoretical uncertainties in calculated ground state deformations are affected mostly by former factor, while theoretical uncertainties in fission barriers depend on both of these factors.

Mass-asymmetric fission of Bi205,207,209 at energies close to the fission barrier using proton bombardment of Pb204,206,208

Background: Recent observation of mass-asymmetric fission in neutron-deficient Hg and Pt nuclei has reignited interest in fission fragment mass distributions close to Pb. Investigations at energies close to the fission barrier, where mass-asymmetric fission is expected to be most obvious and the sensitivity to shell effects is maximized, are limited in this mass region.Purpose: To measure fission mass distributions for $^{205,207,209}\mathrm{Bi}$ nuclei at the lowest possible excitation energies to determine how the mass distributions change with excitation energy and the neutron number of the compound nucleus.Method: Proton beams bombarding targets of $^{204,206,208}\mathrm{Pb}$ were used to study the fission of $^{205,207,209}\mathrm{Bi}$ at energies from just above to 10 MeV above their fission barriers. Fission fragments were measured using the CUBE fission spectrometer. Fission fragment mass distributions were determined using a newly developed time difference analysis method. Mass distributions were characterized by triple-Gaussian fits to determine the systematic trends across each isotope with excitation energy.Results: Measured mass distributions of all three Bi isotopes exhibit a component of mass-asymmetric fission at all energies studied. The probability of mass-asymmetric fission decreases significantly with increasing excitation energy, from $\ensuremath{\approx}70$ to $\ensuremath{\approx}40%$ over a 10-MeV range. Comparisons between the three Bi isotopes hint at an increase in the mass-symmetric fission yield with increasing neutron number, which could be due to a decrease in the difference between the symmetric and asymmetric fission barriers. The centroids of the mass-asymmetric peaks suggest that several deformed shell gaps in the fission fragments could be contributing to the presence of the mass-asymmetric fission mode with ${Z}_{\mathrm{light}}\ensuremath{\simeq}38$, ${Z}_{\mathrm{heavy}}\ensuremath{\simeq}45$, and ${N}_{\mathrm{light}}\ensuremath{\simeq}56$ all present in the fission fragments.Conclusions: Measurements of fission mass distributions at the lowest possible excitation energies above the fission barrier provide an excellent platform to investigate the origins of the mass-asymmetric fission mode. Further systematic measurements at these energies offer an opportunity to rigorously test new models of fission in this mass region.

Mass Distribution of the Fission Products of Plutonium Isotopes as Calculated by Using a Semi-empirical Model

The fission product yields (FPYs) of plutonium isotopes induced by thermal, 500-keV and 2-MeV neutrons are calculated by using a semi-empirical model recently developed and applied to uranium isotopes. In this model, the FPYs are assumed to be proportional to the level density of a compound nucleus at the fission barrier. The fission barrier height that determines the level density is modeled as a sum of a macroscopic term and four microscopic terms. The model has ten parameters, four of which are taken to be the same as those fixed for the uranium isotopes. The remaining six parameters are adjusted to reproduce the FPYs of plutonium isotopes. The resulting parameters for the plutonium isotopes are discussed in comparison with those for the uranium isotopes. The calculated FPYs are compared with experimental and evaluated data, as well as the calculation results from other fission models such as GEF and TALYS. Our semi-empirical model is shown to reproduce the overall features of the FPYs of plutonium isotopes.