The variances of the fission fragment mass distributions for symmetric fission over a wide range of the fissility of the compound nucleus have been investigated within the frame work of Random Neck Rupture Model (RNRM) proposed by Brosa et. al.,. The shape of the fissioning nucleus is generated using crel=1 in the RNRM model, which results in a smooth and continuous shape of fissioning nucleus. This modified shape of RNRM model has been used to analyse experimental data of mass variances for symmetric mass distributions of 27 systems leading to understanding of scission shape dynamics in a wide region of fissility 0.7-0.95. The neck radius is an important parameter of the RNRM model and this has been varied to fit the experimental mass variances data. The systematics of resulting neck radii are studied of as a function fissility and nuclear potential through γo, the surface energy coefficient. Further average total kinetic energies of fission fragments <TKE> are studied of as a function of fissility and γo parameter. It is observed that the neck radii that fit the experimentally observed variances of the mass distributions fall into two groups and these groups are related to two groups of experimentally observed <TKE>s. Empirical formulae have been obtained for the neck radii for these two groups of fissioning systems. Use of the empirical formulae for neck radii predict the mass variances reasonably well for these systems and it is shown that these empirical neck radii are better estimates than starting with the Rayleigh criterion.16pages,7 figures
The anatomy of neck configuration in the fission decay of Uranium and Thorium isotopes is investigated in a microscopic study using Relativistic mean field theory. The study includes $^{236}U$ and $^{232}Th$ in the valley of stability and exotic neutron rich isotopes $^{250}U$, $^{256}U$, $^{260}U$, $^{240}Th$, $^{250}Th$, $^{256}Th$ likely to play important role in the r-process nucleosynthesis in stellar evolution. Following the static fission path, the neck configurations are generated and their composition in terms of the number of neutrons and protons are obtained showing the progressive …
In the exothermic process of fission decay, an atomic nucleus splits into two or more independent fragments. Several aspects of nuclear fission are not properly understood, in particular the formation of the neck between the nascent fragments, and the subsequent mechanism of scission into two or more independent fragments. Using an implementation of time-dependent density functional theory, based on a relativistic energy density functional and including pairing correlations, we analyze the final phase of the process of induced fission of $^{240}$Pu, and show that the time-scale of neck formati…
The calculations of the potential energy surface are essential in the theoretical description of the fission process. In the constrained self-consistent approach, the smooth evolution of nuclear shape is described from the ground state until a very elongated one with a narrow neck. In all microscopic calculations, the rupture of the neck at scission is associated with a substantial change of nuclear matter density distribution and rapid energy decrease. In this paper, we show that there is no discontinuity of the potential energy surface at scission when multi-constrained calculations are appl…
Nuclear Science Division, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室核科学部）；NAPC, Nuclear Data Section, International Atomic Energy Agency（国际原子能机构核数据处）；Suncoast Data Evaluation（太阳海岸数据评估）；Physics Division, Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室物理分部）；Physics Department, University of California, Davis（加州大学戴维斯分校物理系）
A correlation is established between the neutron multiplicity and the neutrons number in the fission state of Curium and Californium isotopes within a microscopic study using relativistic mean field formalism. The study includes the isotopes of Cm and Cf nuclei near the valley of stability, and hence is likely to play an important role in the artificial synthesis of superheavy nuclei. The static fission path, the neutron$-$proton asymmetry, the evolution of the neck and their composition in terms of nucleon numbers are also estimated. We find a maximum ratio for average neutron to proton densi…
The fission-fragments mass-yield of 236U is obtained by an approximate solution of the eigenvalue problem of the collective Hamiltonian that describes the dynamics of the fission process whose degrees of freedom are: the fission (elongation), the neck and the mass-asymmetry mode. The macroscopic-microscopic method is used to evaluate the potential energy surface. The macroscopic energy part is calculated using the liquid drop model and the microscopic corrections are obtained using the Woods-Saxon single-particle levels. The four dimensional modified Cassini ovals shape parametrization is used…
An effective Fourier nuclear shape parametrization which describes well the most relevant degrees of freedom on the way to fission is used to construct a 3D collective model. The potential energy surface is evaluated within the macroscopic-microscopic approach based on the Lublin-Strasbourg Drop (LSD) macroscopic energy and Yukawa-folded single particle potential. A phenomenological inertia parameter is used to describe the kinetic properties of the fissioning system. The fission fragment mass yields are obtained by using an approximate solution of the underlying Hamiltonian. The predicted mas…
A recent analysis of experimental ternary fission fragment yields using a nucleation moderated statistical equilibrium model reproduced observed yields with fairly good accuracy. In the present work, the same approach is applied to neck emission in peripheral and mid-peripheral 124Sn+112,124Sn collisions at 26A MeV. The model can reasonably reproduce the yields of lithium to silicon isotopes with realistic time and temperature values. A comparison is made between equilibrium constants derived from the present data and those previously obtained for ternary fission of 242Pu.
The evaporation residue of Barium isotopes are investigated in a microscopic study using relativistic mean field theory. The investigation includes the isotopes of Barium from the valley of stability to exotic proton-rich region. The ground as well as neck configurations for these nuclei are generated from their total nucleonic density distributions of the corresponding state. We have estimated the constituents (number of nucleons) in the elongated neck region of the fission state. We found the $α$-particle as the constituent of neck of Ba-isotopes, referred to as the evaporated residue in hea…
Ternary fission probabilities for thermal neutron induced fission of plutonium are analyzed within the framework of an evaporation-based model where the complexity of time-varying potentials, associated with the neck collapse, are included in a simplistic fashion. If the nuclear temperature at scission and the fission-neck-collapse time are assumed to be ~1.2 MeV and ~10^-22 s, respectively, then calculated relative probabilities of ternary-fission light-charged-particle emission follow the trends seen in the experimental data. The ability of this model to reproduce ternary fission probabiliti…
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.
The fission-fragment mass and total kinetic energy (TKE) distributions are evaluated in a quantum mechanical framework using elongation, mass asymmetry, neck degree of freedom as the relevant collective parameters in the Fourier shape parametrization recently developed by us. The potential energy surfaces (PES) are calculated within the macroscopic-microscopic model based on the Lublin-Strasbourg Drop (LSD), the Yukawa-folded (YF) single-particle potential and a monopole pairing force. The PES are presented and analysed in detail for even-even Plutonium isotopes with $A=236 -246$. They reveal …
Influence of the Exit Channel in $^{235}$U(n,f) and $^{239}$Pu(n,f) Reactions in Time-Dependent Density Functional Theory
Facility for Rare Isotope Beams, Michigan State University（稀有同位素束设施，密歇根州立大学）；Department of Physics and Astronomy, Michigan State University（物理与天文学系，密歇根州立大学）；Theoretical Division, Los Alamos National Laboratory（理论部，洛斯阿拉莫斯国家实验室）；Cyclotron Institute, Texas A&M University（回旋加速器研究所，德克萨斯农工大学）
Static self-consistent methods usually allow to determine the most probable fission fragments mass asymmetry. We have applied random neck rupture mechanism to the nuclei in the configuration at the end of fission paths. Fission fragment mass distributions have been deduced from the pre-scission nuclear density distribution obtained from the self-consistent calculations. Potential energy surfaces as well as nuclear shapes have been calculated in the fully microscopic theory, namely the constrained Hartree-Fock-Bogolubov model with the effective Gogny D1S density-dependent interaction. The metho…
A formalism for semi-adiabatic cranking mass parameters is presented. For the fission process of 234U, the time-dependent pairing equations of motion were used to calculate the excitation energy and to extract values of the cranking inertia. A fission barrier is determined by minimizing the action trajectory in a five dimensional configuration space spanned by elongation, necking, deformations of fragments and mass-asymmetry. The deformation energy is computed in the the frame of the microscopic-macroscopic model. The two center shell model with Woods-Saxon potentials is used in this context. …
Making use of the semiclassical periodic orbit theory (POT), we propose, for the first time, a method to exclusively evaluate the shell effects associated with each of the nascent fragments (prefragments) generated by the neck formation in nuclear fission processes. In spite of the strong indication of such shell effects in asymmetric fragment mass distributions, they could not have been accessed by any previous theoretical approach since most of the single-particle wave functions are delocalized. In the POT, we have found that the prefragment shell effects can be naturally and unambiguously i…
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…
Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there exists no model with demonstrated predictive power for the fission fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good repr…
The potential energy of a deformed nucleus has been determined within a Generalized Liquid Drop Model taking into account the proximity energy, the microscopic corrections and compact and necked shapes. Multiple-humped potential barriers appear. A third minimum and third maximum exist in specific exit channels where one fragment is close to a magic spherical nucleus while the other one varies from oblate to prolate shapes. The heights of the fission barriers and half-lives of actinides are in agreement with the experimental results.
The transformation of an atomic nucleus into two excited fission fragments is modeled as a strongly damped evolution of the nuclear shape, until scission occurs at a small critical neck radius, at which point the mass, charge, and shape of each fragment are extracted. The available excitation energy then is divided statistically on the basis of the microscopic level densities. This approach takes account of the important (and energy-dependent) finite-size effects. After the fragments have been fully accelerated and their shapes have relaxed to their equilibrium form, they undergo sequential ne…
At a certain finite neck radius during the descent of a fissioning nucleus from the saddle to the scission point, the attractive nuclear forces can no more withstand the repulsive Coulomb forces producing the neck rupture and the sudden absorption of the neck stubs by the fragments. At that moment, the neutrons, although still characterized by their pre-scission wave functions, find themselves in the newly created potential of their interaction with the separated fragments. Their wave functions become wave packets with components in the continuum. The probability to populate such states gives …
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）
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）
We discuss the origin of the narrowness of the single peak at mass-symmetric division in the fragment mass-yield curve for spontaneous fission of $^{258}$Fm. For this purpose, we employ the macroscopic-microscopic model, and calculate a potential-energy curve at the mass-symmetric compact scission configuration, as a function of the fragment mass number, which is obtained from the single-particle wave-function densities. In the calculations, we minimize total energies by varying the deformations of the two fragments, with constraints on the mass quadrupole moment and keeping the neck radius ze…
Background: Recent experiments on beta-delayed fission in the mercury-lead region and the discovery of asym- metric fission in 180 Hg [1] have stimulated theoretical interest in the mechanism of fission in heavy nuclei. Purpose: We study fission modes and fusion valleys in 180 Hg and 198 Hg to reveal the role of shell effects in pre-scission region and explain the experimentally observed fragment mass asymmetry and its variation with A. Methods: We use the self-consistent nuclear density functional theory employing Skyrme and Gogny energy density functionals. Results: The potential energy surf…
We report here the signature of bi-modal fission, one asymmetric and the other symmetric, in Uranium nuclei in the mass range A = 230 to 236. The finding is unexpected and striking and is based on a model independent analysis of experimental mass distributions (cumulative yields) at various excitations from about 23 to 66 MeV in the alpha induced fission of 232Th. It has been found that the observed asymmetry in the mass distributions and the unusually narrow peak in the symmetry region, can both be explained in a consistent manner if one assumes: a) multi-chance fission, b) bi-modal fission a…
The mass and total kinetic energy distributions of the fission fragments in the fission of even-even isotopes of superheavy elements from Hs (Z=108) to Og (Z=118) are estimated using a pre-scission point model. We restrict to nuclei for which spontaneous fission has been experimentally observed. The potential energy surfaces are calculated with Strutinsky's shell correction procedure. The parametrization of the nuclear shapes is based on Cassini ovals. For the just before scission configuration we fix $α$=0.98, what corresponds to $r_{neck}\approx 2$ fm, and take into account another four defo…
We propose a method to calculate the two-dimensional (2D) fission-fragment yield $Y(Z,N)$ versus both proton and neutron number, with inclusion of odd-even staggering effects in both variables. The approach is to use Brownian shape-motion on a macroscopic-microscopic potential-energy surface which, for a particular compound system is calculated versus four shape variables: elongation (quadrupole moment $Q_2$), neck $d$, left nascent fragment spheroidal deformation $ε_{\rm f1}$, right nascent fragment deformation $ε_{\rm f2}$ and two asymmetry variables, namely proton and neutron numbers in eac…
We consider the collinear ternary fission which is a sequential ternary decay with a very short time between the ruptures of two necks connecting the middle cluster of the ternary nuclear system and outer fragments. In particular, we consider the case where the Coulomb field of the first massive fragment separated during the first step of the fission produces a lower pre-scission barrier in the second step of the residual part of the ternary system. In this case, we obtain a probability of about $10^{-3}$ for the yield of massive clusters such as \nuclide[70]{Ni}, \nuclide[80-82]{Ge}, \nuclide…
We show that the sharp maximum corresponding to 107Mo in the fragment distribution of the 252Cf cold fission is actually a Sn-like radioactivity, similar to other decay processes in which magic nuclei are involved, namely alpha-decay and heavy cluster emission, also called Pb-like radioactivity. It turns out that the mass asymmetry degree of freedom has a key role in connecting initial Sn with the final Mo isotopes along the fission path. We suppose the cold rearrangement of nucleons within the framework of the two center shell model, in order to compute the cold valleys in the charge equilibr…
$\textbf{Background}$ More than half of all the elements heavier than iron are made by the rapid neutron capture process (or r process). For very neutron-rich astrophysical conditions, such at those found in the tidal ejecta of neutron stars, nuclear fission determines the r-process endpoint, and the fission fragment yields shape the final abundances of $110\le A \le 170$ nuclei. The knowledge of fission fragment yields of hundreds of nuclei inhabiting very neutron-rich regions of the nuclear landscape is thus crucial for the modeling of heavy-element nucleosynthesis. $\textbf{Purpose}$ In thi…
Cluster radioactivity is the emission of a fragment heavier than $α$ particle and lighter than mass 50. The range of clusters observed in experiments goes from $^{14}$C to $^{32}$Si while the heavy mass residue is always a nucleus in the neighborhood of the doubly-magic $^{208}$Pb nucleus. Cluster radioactivity is described in this paper as a very asymmetric nuclear fission. A new fission valley leading to a decay with large fragment mass asymmetry matching the cluster radioactivity products is found. The mass octupole moment is found to be more convenient than the standard quadrupole moment a…
Microscopic description of the fission process including intrinsic excitations. Part I: 240Pu adiabatic and asymmetric fission path within the Schrodinger Collective Intrinsic Model
CEA, DAM, DIF（法国原子能委员会）；Université Paris-Saclay（巴黎萨克雷大学）；CEA, DES, IRESNE, DER, SPRC, LEPh（法国原子能委员会）；Center for Computational Simulation, Universidad Politécnica de Madrid（马德里理工大学计算模拟中心）；Departamento de Física Teórica and CIAFF, Universidad Autónoma de Madrid（马德里自治大学理论物理系及CIAFF）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学）；Nuclear Science Division, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室核科学部）
The scission of a nucleus into two fragments is at present the least understood part of the fission process, though the most important for the formation of the observables. To investigate the potential energy landscape at the largest possible deformations, i.e. at the scission point (line, hypersurface), the Strutinsky's optimal shape approach is applied. For the accurate description of the mass-asymmetric nuclear shape at the scission point, it turned out necessary to construct an interpolation between the two sets of constraints for the elongation and mass asymmetry which are applied success…
A three-center phenomenological model able to explain, at least from a qualitative point of view, the difference in the observed yield of a particle-accompanied fission and that of binary fission was developed. It is derived from the liquid drop model under the assumption that the aligned configuration, with the emitted particle between the light and heavy fragment is obtained by increasing continuously the separation distance, while the radii of the light fragment and of the light particle are kept constant. During the first stage of the deformation one has a two-center evolution until the ne…
