Background: The role of angular momentum in fission has long been discussed but the observable effects are difficult to quantify. Purpose: We discuss a variety of effects associated with angular momentum in fission and present quantitative illustrations. Methods: We employ the fission simulation model $\mathtt{FREYA}$ which is well suited for this purpose because it obeys all conservation laws, including linear and angular momentum conservation at each step of the process. We first discuss the implementation of angular momentum in $\mathtt{FREYA}$ and then assess particular observables, including various correlated observables. We also study potential effects of neutron-induced fission of the low-lying isomeric state of $^{235}$U relative to the ground state. Results: The fluctuations inherent in the fission process ensure that the spin of the initial compound nucleus has only a small influence on the fragment spins which are therefore nearly uncorrelated. There is a marked correlation between the spin magnitude of the fission fragments and the photon multiplicity. We also consider the dynamical anisotropy caused by the rotation of an evaporating fragment and study especially the distribution of the projected neutron-neutron opening angles, showing that while it is dominated by the effect of the evaporation recoils, it is possible to extract the signal of the dynamical anisotropy by means of a Fourier decomposition. Finally, we note that the use of an isomeric target, $^{235 {\rm m}}$U($n_{\rm th}$,f), may enhance the symmetric yields and can thus result in higher neutron multiplicities for low total fragment kinetic energy.
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…
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.
T-odd angular correlations in ternary fission of 233-U and 235-U nuclei by slow polarized neutrons are not related to TRI (time reversal invariance) violation, but are caused by an effective spin-orbit interaction in the final state.
A comparative analysis of experiments on studying the (n, f), on one hand, and (n, n), on the other hand, angular correlations in fission is carried out, based on the model proposed by muonic conversion in fragments of prompt fission of 238U with negative muons. Their fundamental difference is shown in the sense of the information that can be inferred from them. Historically, the situation resembles the EPR paradox. An experimental check of the empirical relation between the alignment and polarization parameters, the former is twice as small as the latter one.
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）
During nuclear fission, a heavy nucleus splits into two rotating fragments. The associated angular momentum is large, yet the mechanism of its generation and its dependence on the mass of fragments remain poorly understood. In this Letter, we provide the first microscopic calculations of angular momentum distributions in fission fragments for a wide range of fragment masses. For the benchmark case of $^{239}$Pu($n_{\text{th}}$,f), we find that the angular momentum of the fragments is largely determined by the nuclear shell structure and deformation, and that the heavy fragments therefore typic…
The recent advent of experimental techniques in which the dynamical characteristics of fission fragments are determined more accurately, prompted us to investigate the angular momentum acquired by fragments in a model which describes the cold(neutronless) fission of $^{252}$Cf as the decay of a giant nuclear molecule. The molecular configuration is a consequence of the interplay between the attractive nuclear part and the repulsive Coulomb+nuclear forces. The basic ideea of the present approach is to separate the radial(fission) modes describing the decay of the molecule from the modes associa…
The mixing of the quasifission component to the fissionlike cross section causes ambiguity in the quantitative estimation of the complete fusion cross section from the observed angular and mass distributions of the binary products. We show that the partial cross section of quasifission component of binary fragments covers the whole range of the angular momentum values leading to capture. The calculated angular momentum distributions for the compound nucleus and dinuclear system going to quasifission may overlap: competition between complete fusion and quasifission takes place at all values of …
The strong quadrupolar component of the Coulomb field between newly formed fission fragments can affect the internal energy of the fragments and their angular momentum. Previous estimates of these effects gave contradictory conclusions about their magnitude. Here we calculate them by solving the time-dependent Hamiltonian equation for the daughter $^{100}$Zr produced in the fission reaction n + $^{235}$U $\rightarrow$ $^{136}$Te + $^{100}$Zr. The Hamiltonian was constructed from the projected angular momentum eigenstates of an aligned deformed mean-field configuration. For typical initial cond…
A recent analysis of experimental data [J. Wilson $et. al$, Nature $\mathbf 590$, 566 (2021)] found that the angular momenta of nuclear fission fragments are uncorrelated. Based on this finding, the authors concluded that the spins are therefore determined only $after$ scission has occurred. We show here that the nucleon-exchange mechanism, as implemented in the well-established event-by-event fission model $\mathtt{FREYA}$, while agitating collective rotational modes in which the two spins are highly correlated, nevertheless leads to fragment spins that are largely uncorrelated. This fact inv…
The anisotropy in the angular distribution of the fusion-fission and quasifission fragments for the $^{16}$O+$^{238}$U, $^{19}$F+$^{208}$Pb and $^{32}$S+$^{208}$Pb reactions is studied by analyzing the angular momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively. The orientation angles of axial symmetry axes of colliding nuclei to the beam direction are taken into account for the calculation of the variance of the projection of the total spin onto the fission axis. It is shown that the deviation of the experimental…
The strong deformation present immediately after scission has consequences for the angular momentum population of the fragments as well as the angular distribution of their decay radiation. We find that the usual spin-cutoff parameterization describes very well the angular momentum distribution associated with the deformation of the fragments at the scission point. Depending on the deformation, its contribution can comparable to the thermal contribution to the angular momentum of the newly formed fragments. The $M$-distribution of the angular momentum is highly polarized and gives rise to larg…
We extend a conventional description of the fusion-fission fragment angular distributions by introducing the correlation between compound nucleus states carrying different total angular momenta. This correlation results in the strong anisotropy and mass-angle correlation of fission fragments for compact saddle-point nuclear shapes for which the conventional description predicts almost isotropic angular distributions. The spin off-diagonal phase relaxation timescale, $\simeq 10^{-19}$ sec, obtained from analysis of anomalous fission fragment angular distributions in $^{12}$C+$^{236}$U, $^{16}$O…
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
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.)
In recent years, investigations of angular distributions of fragments in neutron-induced nuclear fission have been extended to intermediate energies, up to 200 MeV, as well as to a wide range of target isotopes. Using as an example the latest data obtained by our group for the reaction 237-Np(n,f), we discuss the specific features of fission fragment angular distribution and present a method for their simulation based on the code TALYS. It is shown that a simplified model reasonably describes energy dependence of the angular distribution in the whole range 1-200 MeV. The ways to improve the mo…
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…
Experimental data on angular distributions of gamma rays emitted from binary and ternary spontaneous fission of $^{252}{\rm Cf}$ are analyzed. Their difference indicates that the alignment of fragments is higher in ternary fission than in binary one. The consequences of possible relation between the mechanism of ternary fission and the excitation of collective modes during the saddle-to-scission stage are discussed.
Several sources of angular anisotropy for fission fragments and prompt neutrons have been studied in neutron-induced fission reactions. These include kinematic recoils of the target from the incident neutron beam and the fragments from the emission of the prompt neutrons, preferential directions of the emission of the fission fragments with respect to the beam axis due to the population of particular transition states at the fission barrier, and forward-peaked angular distributions of pre-equilibrium neutrons which are emitted before the formation of a compound nucleus. In addition, there are …
The angular distributions of fission fragments for the $^{32}$S+$^{184}$W reaction at center-of-mass energies of 118.8, 123.1, 127.3, 131.5, 135.8, 141.1 and 144.4 MeV were measured. The experimental fission excitation function is obtained. The fragment angular anisotropy ($\mathcal{A}_{\rm exp}$) is found by extrapolating the each fission angular distributions. The measured fission cross sections of the $^{32}$S+$^{182,184}$W reaction are decomposed into fusion-fission, quasifission and fast fission contributions by the dinuclear system model. The total evaporation residue excitation function…
The fusion excitation function is the important quantity in planning experiments for the synthesis of superheavy elements. Its values seem to be determined by the experimental study of the hindrance to complete fusion by the observation of mass, angular and energy distributions of the fissionlike fragments. There is ambiguity in establishment of the reaction mechanism leading to the observed binary fissionlike fragments. The fissionlike fragments can be produced in the quasifission, fast fission, and fusion-fission processes which have overlapping in the mass (angular, kinetic energy) distribu…
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 effect of the right-left asymmetry is considered in the angular distribution of gamma quanta from fission of U-235 by polarised thermal neutrons, which depends on the polarisation of the neutrons with respect to the gamma-fission plane. Electric dipole radiation from fission fragments arising due to the Strutinsky-Denisov induced polarisation mechanism may give rise to such an effect. Earlier, this mechanism was shown to fit the non-statistical part observed in the gamma spectrum from spontaneous fission of Cf-252. The calculated value of the magnitude of the asymmetry parameter is on the …
Microscopic Description of Rotational Nuclear Fission Elucidates Fragment Spin Generation and Scission Mechanism
Hangzhou International Innovation Institute of Beihang University（北京航空航天大学杭州国际创新学院）；School of Physics, and State Key Laboratory of Nuclear Physics and Technology, Peking University（北京大学物理学院及核物理与核技术国家重点实验室）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院现代物理研究所南方核科学理论中心）
An attempt to unfold the respective influence of the fusion and fission stages on typical fission observables, and namely the neutron pre-scission multiplicity, is proposed. A four-dimensional dynamical stochastic Langevin model is used to calculate the decay by fission of excited compound nuclei produced in a wide set of heavy-ion collisions. The comparison of the results from such a calculation and experimental data is discussed, guided by predictions of the dynamical deterministic HICOL code for the compound-nucleus formation time. While the dependence of the latter on the entrance-channel …
A model for ternary fission is discussed in which a third particle (alpha-particle) is emitted due to non-adiabatic change of the nuclear potential at neck rapture. An expression for energy and angular distribution of alpha-particles is proposed. It is shown that an interaction between spin of fissioning system and orbital momentum of alpha-particle (spin-orbit interaction in the final state) results in recently observed asymmetry of alpha-particle emission, which can be formally related to T-odd correlation. No strong dependence of the asymmetry on the angle of alpha-particle emission with re…
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Instituto Nazionale di Fisica Nucleare, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Institut Pluridisciplinaire Hubert Curien（于贝尔·居里多学科研究所）；Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）
The concept of collinear spontaneous true ternary fission of 252Cf is subject to critical analysis. The conclusion is that the collinear flight of the fragments turns out to be a natural and most probable mode. The collinearity arises in the model on the prescission stage as a result of the account of the principles of the collective Bohr's model. It is partly destroyed at the post-scission stage of spreading of the fragments due to their Coulomb interaction, with the allowance for the spin effects arising at the moment of scission. The final angular distribution of the fragments is calculated…
In this work, we predict a new physical phenomenon, induced fission-like process and chain reaction of hadronic molecular states. As a molecular state, if induced by a $D$ meson, the $X(3872)$ can split into $D\bar{D}$ final state which is forbidden due to the spin-parity conservation. The breeding of the $D$ meson of the reaction, such as $D^0X(3872)\to D^0\bar{D}^0D^0$, makes the chain reaction of $X(3872)$ matter possible. We estimate the cross section of the $D$ meson induced fission-like process of $X(3872)$ into two $D$ mesons. With very small $D^0$ beam momentum of 1 eV, the total cross…
Several computer codes based on phenomenological models are being developed with the aim of obtaining fission observables, such as neutron and gamma multiplicities and product yields. Key points in these calculations, which are handled differently by the various codes, are the sharing of the total excitation energy between the fragments and the generation of angular momenta. After the initial states of the fragments is set, the de-excitation through the emission of neutrons and photons can be model. However, many models also include tunable parameters that are used to make the calculations con…
Detailed information on the fission process can be inferred from the observation, modeling and theoretical understanding of prompt fission neutron and $γ$-ray~observables. Beyond simple average quantities, the study of distributions and correlations in prompt data, e.g., multiplicity-dependent neutron and \gray~spectra, angular distributions of the emitted particles, $n$-$n$, $n$-$γ$, and $γ$-$γ$~correlations, can place stringent constraints on fission models and parameters that would otherwise be free to be tuned separately to represent individual fission observables. The FREYA~and CGMF~codes…
The effect of the coupling between the neutron multiplicity and the fission competition on the evaporation residue cross sections of the $^{48}$Ca$+^{244}$Pu reaction
New Uzbekistan University（新乌兹别克斯坦大学）；Institute of Nuclear Physics（核物理研究所）
A study of medium-mass heavy-ion reactions leading to two fragments in the exit channel from barrier to 18A MeV is proposed. A special focus is made on fission and quasi-fission for events with two fragments ($Z\geq10$) in the exit channel selected. Reactions induced by $^{129}Xe$ projectiles on $^{nat}Sn$ and on $^{197}Au$ at energies ranging from $8A$ MeV to $18A$ MeV were analyzed. Using the fragment ($Z\geq10$) multiplicity equal to 2, fission and quasi-fission events were studied for the lowest beam energies using the fission fragment charge distributions, the total kinetic energy distrib…
Mass distributions of the fragments in the fission of $^{206}$Po and the N=126 neutron shell closed nucleus $^{210}$Po have been measured. No significant deviation of mass distributions has been found between $^{206}$Po and $^{210}$Po, indicating the absence of shell correction at the saddle point in both the nuclei, contrary to the reported angular anisotropy and pre-scission neutron multiplicity results. This new result provides benchmark data to test the new fission dynamical models to study the effect of shell correction on the potential energy surface at saddle point.
Starting from a quantum theory of dissipation for nuclear collective motion, the time-dependent generator coordinate method (TDGCM) is extended to allow for dissipation effects in the description of induced fission dynamics. The extension is based on a generalization of the GCM generating functions that includes excited states, and the resulting equation of motion in the collective coordinates and excitation energy. With the assumption of a narrow hamiltonian kernel, an expansion in a power series in collective momenta leads to a Schrödinger-like equation that explicitly includes a dissipation…
The atomic numbers and the masses of fragments formed in quasi-fission reactions have been simultaneously measured at scission in 48 Ti + 238 U reactions at a laboratory energy of 286 MeV. The atomic numbers were determined from measured characteristic fluorescence X-rays whereas the masses were obtained from the emission angles and times of flight of the two emerging fragments. For the first time, thanks to this full identification of the quasi-fission fragments on a broad angular range, the important role of the proton shell closure at Z = 82 is evidenced by the associated maximum production…
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）
The emission of neutrons and gamma rays by fission fragments reveal important information about the properties of fragments immediately following scission. The initial fragment properties, correlations between fragments, and emission competition give rise to correlations in neutron-gamma emission. Neutron-gamma correlations are important in nonproliferation applications because the characterization of fissionable samples relies on the identification of signatures in the measured radiation. Furthermore, recent theoretical and experimental advances have proposed to explain the mechanism of angul…
Experimental studies of fission induced in relativistic nuclear collisions show a systematic enhancement of the excitation energy of the primary fragments by a factor of ~ 2, before their decay by fission and other secondary fragments. Although it is widely accepted that by doubling the energies of the single-particle states may yield a better agreement with fission data, it does not prove fully successful, since it is not able to explain yields for light and intermediate mass fragments. State-of-the-art calculations are successful to describe the overall shape of the mass distribution of frag…
