Nuclear fission of heavy (actinide) nuclei results predominantly in asymmetric mass-splits. Without quantum shells, which can give extra binding energy to these mass-asymmetric shapes, the nuclei would fission symmetrically. The strongest shell effects are in spherical nuclei, so naturally the spherical "doubly-magic" ${^{132}}$Sn nucleus (${Z=50}$ protons), was expected to play a major role. However, a systematic study of fission has shown that the heavy fragments are distributed around ${Z=52}$ to 56, indicating that ${^{132}}$Sn is not the only driver. Reconciling the strong spherical shell effects at ${Z=50}$ with the different ${Z}$ values of fission fragments observed in nature has been a longstanding puzzle. Here, we show that the final mass asymmetry of the fragments is also determined by the extra stability of octupole (pear-shaped) deformations which have been recently confirmed experimentally around $^{144}$Ba (${Z=56}$), one of very few nuclei with shell-stabilized octupole deformation. Using a modern quantum many-body model of superfluid fission dynamics, we found that heavy fission fragments are produced predominantly with ${52-56}$ protons, associated with significant octupole deformation acquired on the way to fission. These octupole shapes favouring asymmetric fission are induced by deformed shells at ${Z=52}$ and 56. In contrast, spherical "magic" nuclei are very resistant to octupole deformation, which hinders their production as fission fragments. These findings may explain surprising observations of asymmetric fission of lighter than lead nuclei.
In this work, we present new experimental data on mass distribution of fission fragments from $^{241}$Am proton-induced fission at $660$ MeV measured at the LNR Phasotron (JINR). The systematic analysis of several measured fragment mass distributions from different fission reactions available in the literature is also presented. The proton-induced fission of $^{241}$Am, $^{237}$Np and $^{238}$U at 26.5, 62.9 and 660 MeV was studied. The proton-induced fission of $^{232}$Th was studied at 26.5, 62.9 and 190 MeV. The fission of $^{208}$Pb also by a proton was investigated at 190, 500 and 1000 Me…
The character and prevalence of third minima in actinide fission barriers
许多锕系裂变势垒的双峰结构在实验和理论上都得到了很好的证实。也有实验和理论的证据表明，一些锕系元素核的势垒具有第三个最小值，在第二个裂变同质异能素最小值之外。我们进行了大规模的，系统的计算锕系裂变势垒，以确定哪些锕系核表现出第三个极小。我们发现，只有相对较少的核实验中表现出第三个极小的障碍，大约与质子数$Z$的范围$88 \leq Z \leq 94$和核子数$A$的范围$230 \leq A \leq 236 $的核。我们发现，轻Th和U同位素的第三个最低值是小于1兆电子伏深。这与以前的一些实验和理论结果是一致的，但不同于其他一些。我们讨论这些不兼容的结果可能的起源，什么是最现实的预测，在第三个极小值是可观察的。
Ternary fission of actinides probes the state of the nucleus at scission. Light clusters are produced in space and time very close to the scission point. Within the nonequilibrium statistical operator method, a generalized Gibbs distribution is constructed from the information given by the observed yields of isotopes. Using this relevant statistical operator, yields are calculated taking excited states and continuum correlations into account, in accordance with the virial expansion of the equation of state. Clusters with mass number $A \le 10$ are well described using the nonequilibrium genera…
Fission barriers heights and excitation energies of superdeformed isomeric minima are calculated within the microscopic - macroscopic Woods - Saxon model for 75 actinide nuclei for which the experimental data are known. State - of - the - art methods were used: minimization over many deformation parameters for minima and the imaginary water flow on many - deformation energy grid for saddles, including nonaxial and reflection-asymmetric shapes. We obtain 0.82 - 0.94 MeV rms deviation between the calculated and experimental barriers and 0.53 MeV rms error in the excitation of superdeformed minim…
Isotope-Resolved Ba and Xe Yields in Actinide Fission and Correlated Heavy--Light Fragment Systematics
National Centre for Nuclear Research（国家核研究中心）；China Institute of Atomic Energy（中国原子能科学研究院）；Maria Curie-Skłodowska University（玛丽·居里-斯克沃多夫斯卡大学）；Tsinghua University（清华大学）
The empirical calculations of the prompt neutrons average number for photofission of the 232Th, 233U, 234U, 235U, 236U, 238U, 237Np, 239Pu and 241Am actinides has been done as a function of photon energy, mass and charge of the nuclei, which can be used to evaluate the average number for photo-fission of nuclides for which no or scarce data are available.
We review recent work examining the influence of fission in rapid neutron capture ($r$-process) nucleosynthesis which can take place in astrophysical environments. We briefly discuss the impact of uncertain fission barriers and fission rates on the population of heavy actinide species. We demonstrate the influence of the fission fragment distributions for neutron-rich nuclei and discuss currently available treatments, including recent macroscopic-microscopic calculations. We conclude by comparing our nucleosynthesis results directly with stellar data for metal-poor stars rich in $r$-process el…
A new, rapidly convergent Fourier over spheroid parametrization is developed to describe the shape of a fissioning nucleus: its elongation, non-axiality and left-right asymmetry and neck formation. The 4D Potential Energy Surfaces (PES) of even-even actinide nuclei are evaluated within the macro-micro model. The Langevin trajectories generated on such PESs allow for obtaining the fission fragments' mass and kinetic energy yields. The charge equilibration at the scission configuration and the post-scission neutron emission are also discussed.
We employ density-dependent relativistic mean-field theory to study how the triaxiality and pairing interaction affect the inner fission barriers of actinide nuclei. It was found that triaxiality reduced the inner fission barriers and improved agreement with experimental values for many actinides. However, about 1-2 MeV discrepancy to the experimental values still remained for some of the considered nuclei. Such a discrepancy could be made further smaller by increasing the BCS pairing strength parameter. In this work, we demonstrated that adjusting the paring strength was effective to reproduc…
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…
We have studied strength in the BCS pairing force, used as a residual interaction to the relativistic mean-field to reproduce the height of the inner fission barriers for actinide nuclei. It was found that increasing the pairing strength by about 13% makes reproduce the inner fission barriers better over a wide range of actinide nuclei. This result was verified by using the moment-of-inertia of pairing rotational energy, which was introduced to avoid mean-field and odd-mass effects in the pairing interaction to deduce purely the pairing strength. The pairing interaction thus determined could s…
We propose an efficient approach to describe the fission-fragment charge yields for actinides based on the driving potential of fissioning system. Considering the properties of primary fission fragments at their ground states, the driving potential, which represents the potential energies of the system around scission configuration and closely relates to the yields of fragments, can be unambiguously and quickly obtained from the Skyrme energy-density functional together with the Weizsaecker-Skyrme mass model. The fission-fragment charge distributions for thermal-neutroninduced fission and spon…
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…
Low-energy positive and negative parity collective states in the equilibrium minimum, and the dynamics of induced fission of actinide nuclei are investigated in a unified theoretical framework based on the generator coordinate method (GCM) with the Gaussian overlap approximation (GOA). The collective potential and inertia tensor, both at zero and finite temperature, are computed using the self-consistent multidimensionally constrained relativistic mean field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separabl…
The first solids that form as a cooling white dwarf (WD) starts to crystallize are expected to be greatly enriched in actinides. This is because the melting points of WD matter scale as $Z^{5/3}$ and actinides have the largest charge $Z$. We estimate that the solids may be so enriched in actinides that they could support a fission chain reaction. This reaction could ignite carbon burning and lead to the explosion of an isolated WD in a thermonuclear supernova (SN Ia). Our mechanism could potentially explain SN Ia with sub-Chandrasekhar ejecta masses and short delay times.
Fission at low excitation energy is an ideal playground to probe the impact of nuclear structure on nuclear dynamics. While the importance of structural effects in the nascent fragments is well-established in the (trans-)actinide region, the observation of asymmetric fission in several neutron-deficient pre-actinides can be explained by various mechanisms. To deepen our insight into that puzzle, an innovative approach based on inverse kinematics and an enhanced version of the VAMOS++ heavy-ion spectrometer was implemented at the GANIL facility, Caen. Fission of $^{178}$Hg was induced by fusion…
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-…
The possibilities of the proposed statistical approach are shown in the task of investigating the post-scission transformation of mass and charge yields of fission fragments with considering the emission of different length of chains of elementary particles as the beta particles and neutrons fission. Using as the example the 232 Th isotope, which is located on the border between pre-actinide and actinides nuclei, the changes in the topology of fission fragments yields, the role of emission of nuclear particles in the competition of symmetric and asymmetric modes in fission processes are invest…
Comprehensive calculations of cross sections of photon induced reactions on $^{233-238}$U targets for incident photon energies from 3 up to 30 MeV are undertaken with the statistical model code EMPIRE-3.2 Malta. Results are compared with the experimental data from EXFOR and with the current evaluations. The differences and the similarities between the models and parameters used in calculations of photon- and neutron-induced reactions on the same nuclei are discussed with focus on fission. The role of the extended optical model for fission in improving the description of the measured data and i…
Sensitivity of Isotopic Fission Yields in Actinides to the Macroscopic Liquid-Drop Model: LSD vs ISOLDA
National Centre for Nuclear Research（国家核研究中心）；Maria Curie-Skłodowska University（玛丽亚·居里-斯克隆多斯卡大学）；China Institute of Atomic Energy（中国原子能科学研究院）；Tsinghua University（清华大学）
We have decomposed to symmetric and asymmetric modes the mass-TKE fission fragment distributions calculated by 4-dimensional Langevin approach and observed how the dominant fission mode and symmetric mode change as functions of $Z^2/\sqrt[3]{A}$ of the fissioning system in the actinides and trans-actinide region. As a result, we found that the symmetric mode makes a sudden transition from super-long to super short fission mode around $^{254}$Es. The dominant fission modes on the other hand, are persistently asymmetric except for $^{258}$Fm, $^{259}$Fm and $^{260}$Md when the dominant fission m…
Fission of atomic nuclei often produces mass asymmetric fragments. However, the origin of this asymmetry was believed to be different in actinides and in the sub-lead region [A. Andreyev {\it et al.}, Phys. Rev. Lett. {\bf 105}, 252502 (2010)]. It has recently been argued that quantum shell effects stabilising pear shapes of the fission fragments could explain the observed asymmetries in fission of actinides[G. Scamps and C. Simenel, Nature {\bf 564}, 382 (2018)]. This interpretation is tested in the sub-lead region using microscopic mean-field calculations of fission based on the Hartree-Fock…
A systematic analysis of the ground state and fission properties of actinides and superheavy nuclei important for the $r$ process modeling has been performed within the framework of covariant density functional theory for the first time in Ref. [1]. A brief review of the results related to the heights of primary fission barriers and systematic uncertainties in their prediction is presented. In addition, new results on the potential impact of the isospin dependence of pairing on fission barriers in fission cycling regions is provided for the first time.
Neutron star mergers (NSMs) are the first verified sites of rapid neutron capture (r-process) nucleosynthesis, and could emit gamma rays from the radioactive isotopes synthesized in the neutron-rich ejecta. These MeV gamma rays may provide a unique and direct probe of the NSM environment as well as insight into the nature of the r process, just as observed gammas from the 56Ni radioactive decay chain provide a window into supernova nucleosynthesis. In this work, we include the photons from fission processes for the first time in estimates of the MeV gamma-ray signal expected from an NSM event.…
Theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements have been investigated in a systematic way for a set of state-of-the-art covariant energy density functionals which represent major classes of the functionals used in covariant density functional theory. They differ in basic model assumptions and fitting protocols. Both systematic and statistical uncertainties have been quantified where the former turn out to be larger. Systematic uncertainties are substantial in superheavy elements and their behavior as a function of proton and neutron numbers…
Probability distribution of observables from a Bogoliubov vacuum projected onto good particle number: application to scission configurations of an actinide
A comparative study of fission of actinides specially $^{238}$U, by proton and bremsstrahlung photon is performed. Relative mass distribution of $^{238}$U fission fragments have been explored theoretically for both proton and photon induced fission. The integrated yield along with charge distribution of the products are calculated to find out the neutron richness in comparison to the nuclei produced by r-process in nucleosynthesis. Some r-process nuclei in intermediate mass range for symmetric fission mode are found to be produced almost two order of magnitude more for proton induced fission t…
A regular pattern, revealing the leading role of the light-fragment nuclear charge, is found to emerge from a consistent analysis of the experimental information collected recently on low-energy asymmetric fission of neutron-deficient nuclei around lead. The observation is corroborated by a theoretical investigation within a microscopic framework, suggesting the importance of proton configurations driven by quadrupole-octupole correlations. This is in contrast to the earlier theoretical interpretations in terms of dominant neutron shells. The survey of a wider area of the nuclear chart by a se…
It is well known that most actinides fission into fragments of unequal size. The first attempt to understand this difference suggested that division leading to one of the fragments being near doubly magic $^{132}$Sn is favored by gain in binding energy. After the Strutinsky shell-correction method was developed an alternative idea that gained popularity was that the fission saddle might be lower for mass-asymmetric shapes and that this asymmetry was preserved until scission. Recently it was observed [Phys. Rev. Lett. {\bf 105} (2010) 252502] that $^{180}$Hg preferentially fissions asymmetrical…
The concept of fission barrier - a parameter which enters in quantitative estimates of various observables related to nuclear fission - is presented from the point of view of theory based on the picture of nuclear deformation and energy dependent on it. We describe the macroscopic-microscopic method of calculating energy landscapes which is simpler than the selfconsistent mean field approach, and, due to its two-component nature, seems to be easier to adjust to experimental data. We present some models and methods used to find the fission saddles. For the purpose of illustration, we present re…
Potential Energy Surfaces of Actinide Nuclei from a Multi-dimensional Constraint Covariant Density Functional Theory: Barrier Heights and Saddle Point Shapes
