Outer Fission Barrier Research Articles

Microscopic analysis of induced nuclear fission dynamics

The dynamics of low-energy induced fission is explored using a consistent microscopic framework that combines the time-dependent generator coordinate method (TDGCM) and time-dependent nuclear density functional theory (TDDFT). While the former presents a fully quantum mechanical approach that describes the entire fission process as an adiabatic evolution of collective degrees of freedom, the latter models the dissipative dynamics of the final stage of fission by propagating the nucleons independently toward scission and beyond. By combining the two methods, based on the same nuclear energy density functional and pairing interaction, we perform an illustrative calculation of the charge distribution of yields and total kinetic energy for induced fission of $^{240}$Pu. For the saddle-to-scission phase a set of initial points for the TDDFT evolution is selected along an iso-energy curve beyond the outer fission barrier on the deformation energy surface, and the TDGCM is used to calculate the probability that the collective wave function reaches these points at different times. Fission observables are computed with both methods and compared with available data. The relative merits of including quantum fluctuations (TDGCM) and the one-body dissipation mechanism (TDDFT) are discussed.

Fission resonances observed in the ^{237}Np(d,pf) reaction and the fission barrier topology of ^{238}Np

The fission probability of ^{238}Np was measured as a function of the excitation energy in the energy range of E^* = 5.4 - 6.2 MeV in order to search for transmission fission resonances. A radioactive ^{237}Np target was bombarded with deuterons of E_d = 12 MeV, whereas the energy of the protons was analyzed with a superior resolution of varDelta E = 8 keV. The experiment was performed at the Tandem accelerator of the Maier-Leibnitz Laboratory in Garching employing the ^{237}Np(d,pf) reaction. A group of fission resonances has been observed at excitation energies between E^* = 5.5 - 5.8 MeV, which could be ordered into three (superdeformed) rotational bands with a rotational parameter of hbar ^2/2varTheta = 3.507 keV, and identified as the first direct observation of transition states composing rotational bands in an odd-odd nucleus as they appear above the top of the outer fission barrier. Nuclear reaction code (talys1.95) calculations were also performed to extract the multi-humped fission barrier parameters of ^{238}Np by fitting them to the experimental data of the present (d,pf) and previous (n,f) experiments. The extracted barrier parameters also support the above interpretation of the observed resonances.

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.

Fission barriers of two odd-neutron actinide nuclei taking into account the time-reversal symmetry breaking at the mean-field level

Background: Fission barriers of actinide nuclei have been mostly and for long been microscopi- cally calculated for even-even fissioning systems. Calculations in the case of odd nuclei have been performed merely within a so-called equal-filling approximation (EFA) as opposed to an approach taking explicitly into account the time reversal breaking properties at the mean field level- and for only one single-particle configuration. Purpose: We study the dependence of the fission barriers on various relevant configurations (e.g. to evaluate the so-called specialization energy). Besides, we want to assess the relevance as a func- tion of the deformation of the EFA approach which has been already found out at ground state deformation. Methods: Calculations within the Hartree-Fock plus BCS with self-consistent particle blocking have been performed using the SkM* Skyrme effective interaction in the particle-hole channel and a seniority force in the particle-particle channel. Axial symmetry has been imposed throughout the whole fission path while the intrinsic parity symmetry has been allowed to be broken in the outer fission barrier region. Results: Potential energy curves have been determined for six different configurations in U-235 and four in Pu-239. Inner and outer fission barriers have been calculated along with some spectroscopic properties in the fission isomeric well. These results have been compared with available data. The influence of time-reversal breaking mean fields on the solutions has been investigated. Conclusions: A sizeable configuration dependence of the fission barrier (width and height) has been demonstrated. A reasonable agreement with available systematic evaluations of fission barrier heights has been found. The EFA approach has been validated at the large elongations occurring at the outer barrier region.

Induced Fission of (240)Pu within a Real-Time Microscopic Framework.

We describe the fissioning dynamics of ^{240}Pu from a configuration in the proximity of the outer fission barrier to full scission and the formation of the fragments within an implementation of density functional theory extended to superfluid systems and real-time dynamics. The fission fragments emerge with properties similar to those determined experimentally, while the fission dynamics appears to be quite complex, with many excited shape and pairing modes. The evolution is found to be much slower than previously expected, and the ultimate role of the collective inertia is found to be negligible in this fully nonadiabatic treatment of nuclear dynamics, where all collective degrees of freedom (CDOF) are included (unlike adiabatic treatments with a small number of CDOF).

Description of induced nuclear fission with Skyrme energy functionals. II. Finite temperature effects

Understanding the mechanisms of induced nuclear fission for a broad range of neutron energies could help resolve fundamental science issues, such as the formation of elements in the universe, but could have also a large impact on societal applications in energy production or nuclear waste management. The goal of this paper is to set up the foundations of a microscopic theory to study the static aspects of induced fission as a function of the excitation energy of the incident neutron, from thermal to fast neutrons. To account for the high excitation energy of the compound nucleus, we employ a statistical approach based on finite-temperature nuclear density functional theory with Skyrme energy densities, which we benchmark on the 239 Pu(n,f) reaction. We compute the evolution of the least-energy fission pathway across multidimensional potential energy surfaces with up to five collective variables as a function of the nuclear temperature, and predict the evolution of both the inner and outer fission barriers as a function of the excitation energy of the compound nucleus. We show that the coupling to the continuum induced by the finite temperature is negligible in the range of neutron energies relevant for many applications of neutron-induced fission. We prove that the concept of quantum localization introduced recently can be extended to T > 0, and we apply the method to study the interaction energy and total kinetic energy of fission fragments as a function of the temperature for the most probable fission. While large uncertainties in theoretical modeling remain, we conclude that finite-temperature nuclear density functional may provide a useful framework to obtain accurate predictions of fission fragment properties.

Estimations of fission barrier heights for Ra, Ac, Rf and Db nuclei by neural networks

Accurate information about the fission barrier is important for studying of the fission process. Fission barrier is needed for discovering the island of stability in superheavy region and searching of the superheavy elements. Furthermore, the astrophysical r-process is closely related to the fission barrier of the neutron-rich nuclei. In this study, by using artificial neural network (ANN) method, we have estimated the fission barrier heights of the Rf , Db , Ra and Ac nuclei covering 230 isotopes. For inner barrier calculation, we have used Rf and Db nuclei and the barrier heights have been determined between nearly 1 MeV and 7 MeV. The related mean square error value has been obtained as 0.108 MeV. For outer barrier calculation, we have used Ra and Ac nuclei and the heights have been determined between nearly 8 MeV and 28 MeV. The related mean square error has been obtained as 0.407. The results of this study indicate that ANN is capable for the estimations of inner and outer fission barrier heights.

Spontaneous Fission Barriers Based on a Generalized Liquid Drop Model

The barrier against the spontaneous fission has been determined within the Generalized Liquid Drop Model (GLDM) including the mass and charge asymmetry, and the proximity energy. The shell correction of the spherical parent nucleus is calculated by using the Strutinsky method, and the empirical shape-dependent shell correction is employed during the deformation process. A quasi-molecular shape sequence has been defined to describe the whole process from one-body shape to two-body shape system, and a two-touching-ellipsoid is adopted when the superdeformed one-body system reaches the rupture point. On these bases the spontaneous fission barriers are systematically studied for nuclei from 230Th to 249Cm for different possible exiting channels with the different mass and charge asymmetries. The double, and triple bumps are found in the fission potential energy in this region, which roughly agree with the experimental results. It is found that at around Sn-like fragment the outer fission barriers are lower, while the partner of the Sn-like fragment is in the range near 108Ru where the ground-state mass is lowered by allowing axially symmetric shapes. The preferable fission channels are distinctly pronounced, which should be corresponding to the fragment mass distributions.

Nuclear fission in covariant density functional theory

The current status of the application of covariant density functional theory to microscopic description of nuclear fission with main emphasis on superheavy nuclei (SHN) is reviewed. The softness of SHN in the triaxial plane leads to an emergence of several competing fission pathes in the region of the inner fission barrier in some of these nuclei. The outer fission barriers of SHN are considerably affected both by triaxiality and octupole deformation.

Hidden systematics of fission channels

It is a common procedure to describe the fission-fragment mass distributions of fissioning systems in the actinide region by a sum of at least 5 Gaussian curves, one for the symmetric component and a few additional ones, together with their complementary parts, for the asymmetric components. These components have been attributed to the influence of fragment shells, e.g. in the statistical scission-point model of Wilkins, Steinberg and Chasman. They have also been associated with valleys in the potential-energy landscape between the outer saddle and the scission configuration in the multi-channel fission model of Brosa. When the relative yields, the widths and the mean mass-asymmetry values of these components are fitted to experimental data, the mass distributions can be very well reproduced. Moreover, these fission channels are characterised by specific values of charge polarisation, total kinetic energy and prompt-neutron yields. The present contribution investigates the systematic variation of the characteristic fission-channel properties as a function of the composition and the excitation energy of the fissioning system. The mean position of the asymmetric fission channels in the heavy fragment is almost constant in atomic number. The deformation of the nascent fragments at scission, which is the main source of excitation energy of the separated fission fragments ending up in prompt-neutron emission, is found to be a unique function of Z for the light and the heavy fragment of the asymmetric fission channels. A variation of the initial excitation energy of the fissioning system above the fission saddle is only seen in the neutron yield of the heavy fragment. The charge polarisation in the two most important asymmetric fission channels is found to be constant and to appreciably exceed the macroscopic value. The variation of the relative yields and of the positions of the fission channels as a function of the composition and excitation energy of the fissioning system obey a hidden systematics that can be explained by the number of states in the vicinity of the outer fission barrier as a function of mass asymmetry, if the potential is constructed as the sum of the macroscopic contribution of the compound nucleus and empirically determined fragment shells. This hidden systematics also explains the transition from asymmetric to symmetric fission around 226 Th and around 258 Fm.

Parity restoration in the highly truncated diagonalization approach: Application to the outer fission barrier of240Pu

The restoration of the parity symmetry has been performed in the framework of the Highly Truncated Diagonalization Approach suited to treat correlations in an explicitly particle-number conserving microscopic approach. To do so we have assumed axial symmetry and used a generalized Wick's theorem due to L\"owdin in a projection-after-variation scheme. We have chosen the Skyrme SkM$^*$ energy-density functional for the particle-hole channel and a density-independent delta force for the residual interaction. We have applied this approach in the region of the outer fission barrier of the $^{240}$Pu nucleus. As a result, we have shown that the $K^{\pi} = 0^+$ fission isomeric state is statically unstable against intrinsic-parity breaking modes, while the projection does not affect the energy at the top of the intrinsic outer fission barrier. Altogether, this leads to an increase of the height of the outer fission barrier--with respect to the fission isomeric state--by about 350 keV, affecting thus significantly the fission-decay lifetime of the considered fission isomer.

Nonuniform character of the population of spin projections K for a fissile nucleus at the scission point and anisotropies in the angular distributions of fragments originating from the induced fission of nuclei

It is shown that the emergence of anisotropies in the angular distributions of fragments originating from the spontaneous and induced fission of oriented actinide nuclei is possible only if nonuniformities in the population of the projectionsM (K) of the fissile-nucleus spin onto the z axis of the laboratory frame (fissile-nucleus symmetry axis) appear simultaneously in the vicinity of the scission point but not in the vicinity of the outer saddle point of the deformation potential. The possibilities for creating the orientation of fissile nuclei for spontaneous and induced fission and the effect of these orientations on the anisotropies under analysis are considered. The role of Coriolis interaction as a unique source of the mixing of different-K fissile-nucleus states at all stages of the fission process is studied with allowance for the dynamical enhancement of this interaction for excited thermalized states of the nucleus involved that is characterized by a high energy density. It is shown that the absence of thermalization of excited states of the fissile nucleus that appear because of the effect of nonadiabaticity of its collective deformation motion in the vicinity of the scission point is a condition of conservation of the influence that transition fission states formed at the inner and outer fission barriers exerts on the distribution of the spin projections K for lowenergy spontaneous nuclear fission. It is confirmed that anisotropies observed in the angular distributions of fragments originating from the fission of nuclei that is induced by fast light particles (multiply charged ions) are due to the appearance of strongly excited equilibrium(nonequilibrium) states of the fissile nucleus in the vicinity of its scission point that have a Gibbs (non-Gibbs) distribution of projections K.

Fission barriers in covariant density functional theory: Extrapolation to superheavy nuclei

Systematic calculations of fission barriers allowing for triaxial deformation are performed for even-even superheavy nuclei with charge number $Z=112-120$ using three classes of covariant density functional models. The softness of nuclei in the triaxial plane leads to an emergence of several competing fission pathes in the region of the inner fission barrier in some of these nuclei. The outer fission barriers are considerably affected by triaxiality and octupole deformation. General trends of the evolution of the inner and the outer fission barrier heights are discussed as a function of the particle numbers.

Attosecond time delays in heavy-ion induced fission measured by crystal blocking

The time delays in fission induced by bombardment of W with 180 MeV $^{32}\mathrm{S}$, $240\text{\ensuremath{-}}255$ MeV $^{48}\mathrm{Ti}$, $330\text{\ensuremath{-}}375$ MeV $^{58}\mathrm{Ni}$, and 390 MeV $^{74}\mathrm{Ge}$ have been measured by observation of crystal blocking. Nearly all results are consistent with exponential decay with lifetimes of order ${10}^{\ensuremath{-}18}$ s which depend weakly on the atomic number of the composite nucleus. This is inconsistent with the Bohr-Wheeler model of fission from a compound nucleus in statistical equilibrium at each stage in a neutron evaporation cascade and supports a picture of strongly damped quasifission. A simple diffusion model with one-body dissipation reproduces roughly the observed time scale and the exponential decay. It suggests that the outer fission barrier could play a significant role in the observed, very slow decays.

Symmetric vs asymmetric nucleon-induced fission of thorium up to 200 MeV

The transition from asymmetric to symmetric fission as dependent on the excitation energy and nucleon composition of fissioning Th and Pa nuclei is investigated for the 232Th(n, F) and 232Th(p, F) reactions, respectively. Observed neutron-induced fission cross sections are described in a fission/evaporation approximation. A separate relatively high outer fission barrier EfBSL with significant curvature was assumed for the symmetric mode, while the inner one (EfASL(AS)) was assumed to be the same for symmetric (SL) and asymmetric (AS) modes. Axial asymmetry and mass symmetry is assumed for the outer saddle of the SL-mode, as distinct from the AS-mode. A drop of (EfASL−EfAAS)=3.5 MeV to ∼1–1.5 MeV for Th and Pa nuclei with A⩽226 is responsible for the increase of the symmetric fission contribution to 225,229,230,231,232Th(n, F) or 232Th(p, F) fission cross sections with nucleon energy up to En(p)=200 MeV. It is shown that with increase of the En(p) above ∼80 MeV the 229,230,231,232Th(n, F) fission cross sections are no longer dependent on the Th target nuclide fissility. The dependence of 232Th fission cross section on the incident particle (n or p) is predicted to be different than in case of 238U target nuclide.

Role of transitional levels inNp237(γ,f): Perspectives for studying highly deformed systems

The transition levels at the top of the two $^{237}\mathrm{Np}$ fission barriers were obtained for the first time by means of the so-called semimicroscopic combined method, which we have developed and implemented. To overcome the difficulties in dealing with large nuclear deformations, we used our developed BARRIER code, which calculates single-particle spectra in a deformed Woods-Saxon potential using a coordinate system based on Cassini ovaloids as nuclear shape parametrization. The results enabled us to describe the experimentally observed near-barrier photofission cross-section structures for $^{237}\mathrm{Np}$, as well as a subbarrier shelf, the latter being consistently interpreted in terms of the accumulation of levels at the top of the inner and outer double fission barrier of $^{237}\mathrm{Np}$.

Microscopic HFB Fission Barriers for r-Process Nucleosynthesis Calculations

New systematic calculations of fission barriers are performed in the 3-dimensional deformation space using the constrained Skyrme-Hartree-Fock-Bogoliubov (SHFB) plus Particle-Number Projection method. The BSk8 Skyrme force, fitted to the full set of more than 2000 experimentally known masses, is used. The energy surfaces are analysed using the flooding method, a necessary tool if more than two dimensions are spanned. The SHFB outer fission barriers are compared with experimental data. The reflection asymmetry is shown to play a significant role in the Z ≈ 94 open-shell region. Extrapolations in the neutron-rich region can differ with the previous compilations of fission barriers.

Uranium symmetric/asymmetric neutron-induced fission up to 200 MeV

The symmetric SL-mode and asymmetric lumped (S1 + S2)-mode fission cross-sections of 235U(n,F) and 233U(n,F) reactions are calculated up to $E_{\rm {n}} = 200$ MeV within a statistical model. For each U nuclide, emerging in $(\rm {n},x\rm {nf})$ reactions a separate triaxial outer fission barrier is assumed for the SL-mode. To reproduce the measured branching ratio of symmetric and asymmetric fission events for the 238U(n,F) reaction, more fissions coming from neutron-deficient nuclei were assumed. The damping of the triaxial collective modes contribution to the level density at the SL-mode outer saddle was essential for the branching ratio description. These assumptions allow to reproduce observed fission cross-sections of 235U(n,F) and 233U(n,F) reactions. The calculated branching ratio sensitivity to the target nuclide fissility is investigated.

Actinide symmetric/asymmetric nucleon-induced fission up to 200 MeV

The fission cross sections of the symmetric SL-mode and the asymmetric lumped (S1+S2)-mode of the 235U(n,F), 237Np(n,F) and 238U(p,F) reactions are calculated up to En=200 MeV within a statistical model. For each fissioning nuclide, emerging in (n,xnf) reactions, a separate triaxial outer fission barrier is assumed for the SL-mode. To reproduce the measured branching ratio of symmetric and asymmetric fission events, strong contribution of fission from neutron-deficient nuclei is assumed. Damping of the contribution of triaxial collective modes to the level density at the SL-mode outer saddle seems to be essential for the description of the branching ratio. The sensitivity of the calculated branching ratio to the fissility of the target nuclide and the incident particle is investigated.

Symmetric/asymmetric [formula omitted] neutron-induced fission up to 200 MeV

The symmetric SL-mode and lumped asymmetric (S1+S2)-mode fission cross sections of 238 U (n, f) reaction are calculated up to incident neutron energy of 200 MeV within a Hauser–Feshbach statistical model. For each U nuclide, contributing to the observed fission cross section via 238 U (n, xnf) reaction separate outer fission barrier is assumed for the SL-mode fission, while the inner one is assumed to be the same either for the symmetric SL- and lumped asymmetric (S1+S2)-mode fission. Inner saddle is axial asymmetric and mass-symmetric for fissioning U nuclei with number of neutrons N>144, for lower N values axial symmetry is assumed to persist. Axial asymmetry and mass-symmetry are assumed for the outer saddle of the SL-mode, as distinct from asymmetric fission modes, for which axial symmetry and mass-asymmetry are assumed. The SL-mode fission cross section up to emissive threshold is controlled by a rather high outer fission barrier with significant transparency. Damping of collective modes contribution to the level density at intrinsic excitation energies higher than 20–30 MeV for axial symmetric saddle and equilibrium deformations seems to be essential for the 238 U (n, F) observed fission cross section description. Ratio of symmetric to all 238 U neutron-induced fission events is described assuming damping of triaxial collective modes contribution to the level densities at outer saddles relevant for the SL-mode. High sensitivity of the ratio of symmetric and asymmetric fission cross sections to the relative contributions of emissive fission chances with high and low number of pre-fission (n, xnf) neutrons is observed.