The generation of angular momentum in fissioning nuclei is not well understood. The predictions of different models disagree, particularly concerning the correlation between the fragments' angular momenta. In this article, a time-dependent collective Hamiltonian model is proposed to treat the generation of the angular momentum in the fission fragments due to the quantum uncertainty principle as well as the dynamics of the collective wave function during and after scission. The model is constructed in the framework of the frozen Hartree-Fock approximation using a Skyrme energy functional to extract deformations of the fission fragments as well as the interactions in a derived collective Hamiltonian. The fission reactions studied are $^{240}$Pu $\rightarrow$ $^{132}$Sn+$^{108}$Ru and $^{240}$Pu $\rightarrow$ $^{144}$Ba+$^{96}$Sr. The model can account for a large part of the angular momentum found in experimental data. The orientation of the angular momentum of each fragment is found to be mainly in the plane perpendicular to the fission axis, in agreement with the experiment. The magnitudes of the angular momenta in the two fragments are nearly uncorrelated, in agreement with the recent experimental data of Wilson et al., Nature (London) 590, 566 (2021). Some of the conclusions of the traditional collective vibration model are supported by the present model but some are not. Surprisingly, it is found that the angular momenta of the fragments are slightly correlated positively as in a wriggling mode. It is also found that the presence of an octupole deformation in a fragment can significantly increase the generated angular momentum.
We elucidated the reason why the average total kinetic energy (TKE) of fission fragments decreases when the excitation energy of the fissioning systems increases as indicated by experimental data for the neutron-induced fission events. To explore this problem, we used a method based on the four-dimensional Langevin equations we have developed. We have calculated the TKE of fission fragments for fissioning systems $^{236}$U$^{*}$ and $^{240}$Pu$^{*}$ excited above respective fission barriers, and compared the results with experimental data for n + $^{235}$U and n + $^{239}$Pu reactions, respect…
The Hauser-Feshbach fission fragment decay model, $\mathtt{HF^3D}$, which calculates the statistical decay of fission fragments, has been expanded to include multi-chance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input pre-scission quantities - fission probabilities and the average energy causing fission - and post-scission quantities - yields in mass, charge, total kinetic energy, spin, and parity. From these fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions, allowing for the calculatio…
Isoscaling of the Fission Fragments with Langevin Equation
用Langevin方程模拟了$^{112}$ Sn + $^{112}$ Sn和$^{116}$ Sn + $^{116}$ Sn的裂变过程。假设裂变过程为对称裂变或非对称裂变，采用高斯概率抽样，给出了裂变碎片的质量分布。对两个反应的裂变碎片分析都观察到了等标度行为，等标度参数$α$似乎对裂变几率宽度和束流能量敏感。
Measurement of the $^{236}$U fission cross section and angular distributions of fragments from fission of $^{235}$U and $^{236}$U in the neutron energy range of 0.3-500 MeV
When two fragments are created in a fission decay, any torque due to nuclear and Coulomb interaction can change the fragment's angular momentum. This article explores the character and magnitude of the angular momentum as a function of the initial conditions around the scission point using the time-dependent Hartree-Fock theory. To understand the torque acting on the fragments, the Frozen Hartree-Fock method is also used to determine the collective potential at scission. Two $^{240}$Pu fission channel ( $^{132}$Sn+$^{108}$Ru and $^{144}$Ba+$^{96}$Sr ) are studied. These two channels cover diff…
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.
Quantum shell effects are known to affect the formation of fragments in nuclear fission. Shell effects also affect quasi-fission reactions occurring in heavy-ion collisions. Systematic time-dependent Hartree-Fock simulations of 50Ca+176Yb collisions show that the mass equilibration between the fragments in quasi-fission is stopped when they reach similar properties to those in the asymmetric fission mode of the 226Th compound nucleus. Similar shell effects are then expected to determine the final repartition of nucleons between the nascent fragments in both mechanisms. Future experimental stud…
The intrinsic spins and their correlations are the least understood characteristics of fission fragments from both theoretical and experimental points of view. In many nuclear reactions the emerging fragments are typically excited and acquire an intrinsic excitation energy and an intrinsic spin depending on the type of the reactions and interaction mechanism. Both the intrinsic excitation energies and the fragments intrinsic spins and parities are controlled by the interaction mechanism and conservations laws, which lead to their correlations and determines the character of their de-excitation…
Fission of relativistic nuclei with fragment excitation and reorientation
相对论性核碰撞中诱发裂变的实验研究表明，在裂变和其他次级碎片衰变之前，初级碎片的激发能系统地增强了约2倍。虽然人们普遍认为，将单粒子态的能量加倍可能会产生与裂变数据更好的一致性，但它并没有证明完全成功，因为它不能解释轻和中等质量碎片的产量。最先进的计算成功地描述了碎片质量分布的总体形状，但对于大量的单个产率，在2-10的系数内失败。在这里，我们提出了一种新的方法，提供了一个帐户的额外的激发的初级片段，由于最终状态与目标的相互作用。我们的方法被应用到238 U +208 Pb反应在1 GeV/核子（适用于其他能量），裂变研究的原型情况下，相对论重离子，在那里我们发现，通过最终状态激发的巨大共振的碎片中的能量吸收的大概率可以大大修改最终碎片的同位素分布，更好地与数据一致。最后，我们表明，大的角动量转移到弹丸和初级碎片通过相同的机制意味着需要更精细的理论方法比目前现有的。
Microscopic Spin-Parity Distributions of Fission Fragments
Université de Toulouse, CNRS/IN2P3, L2IT（图卢兹大学）；University of Zagreb, Faculty of Science, Department of Physics（萨格勒布大学理学院）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
A simplified, though realistic, model describing two receding and accelerating fission fragments, due to their mutual Coulomb repulsion, shows that fission fragments share excitation energy well after they ceased to exchange nucleons. This mechanism leads to a lower total kinetic energy of the fission fragments, particularly if the pygmy resonances in the fission fragments are excited. Even though the emphasis here is on fission, similar arguments apply to fragments in heavy-ion reactions.
Potential energy surfaces and fission barriers of superheavy nuclei are analyzed in the macroscopic-microscopic model. The Lublin-Strasbourg Drop (LSD) is used to obtain the macroscopic part of the energy, whereas the shell and pairing energy corrections are evaluated using the Yukawa-folded potential. A standard flooding technique has been used to determine the barrier heights. It was shown the Fourier shape parametrization containing only three deformation parameters reproduces well the nuclear shapes of nuclei on their way to fission. In addition, the non-axial degree of freedom is taken in…
Isotopic yield in cold binary fission of even-even $^{244-258}$Cf isotopes
采用库仑势与邻近势之和作为相互作用势垒，研究了244- 258 Cf同位素偶偶冷裂变。从冷谷图（驱动电位与碎片质量数的关系图）和通过计算电荷最小化碎片的产率获得有利的碎片组合。发现244、246、248 Cf同位素的最高产率是以Pb（Z=82）为一个碎片的碎片，而250 Cf和252 Cf同位素的最高产率是以Hg（Z=80）为一个碎片的碎片。在254、256、258 Cf同位素的情况下，最高产率是以Sn（Z=50）作为一个片段的片段。因此，具有最大产额的碎片组合揭示了双幻核和近双幻核在二裂变中的作用。发现质量数为A252的Cf同位素有利于不对称分裂< 250 and symmetric splitting is favoured for Cf isotopes with A >.在A=252的Cf同位素的情况下，不对称分裂和对称分裂的概率相等。将252 Cf冷裂变的单个产额与γ- γ- γ符合技术的实验数据进行了比较。
The generation of fission fragments (FF) spins and of their relative orbital angular momentum has been debated for more than six decades and no consensus has been yet achieved so far. (The published abstract, being too long, can be found in the manuscript.)
We present the first fully unrestricted microscopic calculations of the primary fission fragment intrinsic spins and of the fission fragments' relative orbital angular momentum for $^{236}$U$^*$, $^{240}$Pu$^*$, and $^{252}$Cf using the time-dependent density functional theory framework. Within this microscopic approach, free of restrictions and unchecked assumptions and which incorporates the relevant physical observables for describing fission, we evaluate the triple distribution of the fission fragment intrinsic spins and of their fission fragments' relative orbital angular momentum and sho…
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…
Fissioning nuclei and fission fragments, nuclear fragments emerging from energetic collisions, or nuclei probed with various external fields can emit one or more pre-equilibrium neutrons, protons, and potentially other heavier nuclear fragments. I describe a formalism which can be used to evaluate the pre-equilibrium neutron emission probabilities and the excitation energies of the remnant fragments.
Nuclear fission produces fragments whose spins are coupled to the relative angular motion via angular momentum conservation. It is shown how ensembles of such spins can readily be obtained by either direct microcanonical sampling or by sampling of the associated normal modes of rotation. The resulting distribution of the spin-spin opening angle is illustrated in various three- and two- dimensional scenarios and it is demonstrated how recent mutually conflicting model calculations can be well reproduced with different assumptions about the scission geometry.
The ternary cluster decay of heavy nuclei has been observed in several experiments with binary coincidences between two fragments using detector telescopes (the FOBOS-detectors, JINR, Dubna) placed on the opposite sides from the source of fissioning nuclei. The binary coincidences at a relative angle of 180$^0$ deg. correspond to binary fission or to the decay into three cluster fragments by registration of two nuclei with different masses (e.g.$^{132}$Sn,$^{52-48}$Ca,$^{68-72}$Ni). This marks a new step in the physics of fission-phenomena of heavy nuclei. These experimental results for the co…
Intrinsic generation of angular momenta and entanglement in fission
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与技术国家重点实验室）；Institute of Theoretical Physics, Chinese Academy of Science（中国科学院理论物理研究所）；Physics Department, Faculty of Science, University of Zagreb（萨格勒布大学理学院物理系）
We investigate the angular momentum removal from fission fragments (FFs) through neutron and $γ$-ray emission, where we find that about half the neutrons are emitted with angular momenta $\ge 1.5\hbar$ and that the change in angular momentum after the emission of neutrons and statistical $γ$ rays is significant, contradicting usual assumptions. Per fission event, in our simulations, the neutron and statistical $γ$-ray emissions change the spin of the fragment by 3.5 -- 5~$\hbar$, with a large standard deviation comparable to the average value. Such wide angular momentum removal distributions c…
The CGMF code implements the Hauser-Feshbach statistical nuclear reaction model to follow the de-excitation of fission fragments by successive emissions of prompt neutrons and $γ$ rays. The Monte Carlo technique is used to facilitate the analysis of complex distributions and correlations among the prompt fission observables. Starting from initial configurations for the fission fragments in mass, charge, kinetic energy, excitation energy, spin, and parity, $Y(A,Z,KE,U,J,π)$, CGMF samples neutron and $γ$-ray probability distributions at each stage of the decay process, conserving energy, spin an…
