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 mass fragmentations for even-even Pt to Ra isotopes are compared with available experimental data. Their main characteristics are well reproduced when the neck rupture probability dependent on the neck radius is introduced.
With the improved scission-point model the mass distributions are calculated for induced fission of different Hg isotopes with the masses 180-196. The drastic change in the shape of the mass distribution from asymmetric to symmetric is revealed with increasing mass number of the fissioning Hg isotope, and the reactions are proposed to verify this prediction experimentally. The asymmetric mass distribution of fission fragments observed in the recent experiment on the fission of 180Hg is explained. The calculated mass distribution and mean total kinetic energy of fission fragments are in a good …
The cold binary fission of even-even 244-258Cf isotopes has been studied by taking the interacting barrier as the sum of Coulomb and proximity potential. The favorable fragment combinations are obtained from the cold valley plot (plot of driving potential vs. mass number of fragments) and by calculating the yield for charge minimized fragments. It is found that highest yield for 244,246,248Cf isotopes are for the fragments with isotope of Pb (Z=82) as one fragment, whereas for 250Cf and 252Cf isotopes the highest yield is for the fragments with isotope of Hg (Z=80) as one fragment. In the case…
Within the Unified ternary fission model (UTFM), the alpha accompanied ternary fission of even-even $^{244-260}$Cf isotopes has been studied by taking the interacting barrier as the sum of Coulomb and proximity potential. For the alpha accompanied ternary fission of 244^Cf isotope, the highest yield is obtained for the fragment combination 108^Ru+4^He+132^Te, which contain near doubly magic nuclei 132^Te (N=80, Z=52). In the case of 246^Cf and 248^Cf isotopes, the highest yield is obtained for the fragment combinations with near doubly magic nuclei 134^Te (N=82, Z=52) as the heavier fragment. …
We investigate the possibilities of producing neutron-rich nuclides in projectile fission of heavy beams in the energy range of 20 MeV/nucleon expected from low-energy facilities. We report our efforts to theoretically describe the reaction mechanism of projectile fission following a multinucleon transfer collision at this energy range. Our calculations are mainly based on a two-step approach: the dynamical stage of the collision is described with either the phenomenological Deep-Inelastic Transfer model (DIT), or with the microscopic Constrained Molecular Dynamics model (CoMD). The deexcitati…
Neutron- and proton-induced fission cross-sections of separated isotopes of tungsten (182W, 183W, 184W, and 186W) and natural tungsten relative to 209Bi have been measured in the incident nucleon energy region 50-200 MeV using fission chambers based on thin-film breakdown counters (TFBC) at quasi-monoenergetic neutrons from the 7Li(p,n) reaction and at the proton beams of The Svedberg Laboratory (TSL), Uppsala University (Uppsala, Sweden). The preliminary experimental data are presented in comparison with the recent data for nuclei in the lead-bismuth region, as well as with predictions by the…
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…
A new statistical method for systematizing the nuclei fission fragments, investigation of their mass and charge spectra and neutron fission parameters has been suggested. In proposed method, the mass and charge yields of nucleons are determined from the equilibrium conditions of the nuclear fragments post-fission ensemble. Here we consider protons and neutrons of different fragments as statistically non-equivalent. The abilities of the proposed statistical method for explanation of the U, Pa, Th, Ac and Ra post-fission fragments ordering and neutron emission function calculation have been demo…
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…
Fission-fragment mass and total-kinetic-energy distributions following fission of the fermium isotopes $^{256,258,260}\text{Fm}$ at low excitation energy have been calculated using the Brownian shape-motion model. A transition from asymmetric fission in $^{256}\text{Fm}$ to symmetric fission in $^{258}\text{Fm}$ is obtained. The total-kinetic-energy distributions for the three isotopes show radically different behaviour due to varying contributions from different fission modes, with a double-humped distribution for $^{258}\text{Fm}$.
Langevin equation is used to simulate the fission process of $^{112}$Sn + $^{112}$Sn and $^{116}$Sn + $^{116}$Sn. The mass distribution of the fission fragments are given by assuming the process of symmetric fission or asymmetric fission with the Gaussian probability sampling. Isoscaling behavior has been observed from the analysis of fission fragments of both reactions and the isoscaling parameter $α$ seems to be sensitive to the width of fission probability and the beam energy.
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 …
In the frame of proposed statistical method the calculation of fission-fragment yields mass and charge spectra for pre- actinide nuclei on example of natPb isotopes had been conducted.
Using the multidimensional dynamic--programming method (MDPM) in the four--dimensional deformation space $\{β_λ\}$ with $λ$=2, 4, 35 and 6 we were able to study evolution of the action integral for the fissioning nucleus $^{258}$Fm. We found the second minimum on the cross--section of the action integral for $β_2 \approx 1$ , what we interpret as the dynamical evidence of the bimodal fission in this heavy Fm isotope.
The series of Uranium isotopes with $N=154 \sim 172$ around the magic number N=162/164 are identified to be thermally fissile. The thermal neutron fission of a typical representative $^{249}$U of this region amenable to synthesis in the radioactive ion beam facilities is considered here. Semiempirical study of fission barrier height and width shows this nucleus to be infinitely stable against spontaneous fission due to increase in barrier width arising out of excess neutrons. Calculation of probability of fragment mass yields and microscopic study in relativistic mean field theory, show this n…
The isotopic-yield distributions and kinematic properties of fragments produced in transfer-induced fission of 240Pu and fusion-induced fission of 250Cf, with 9 MeV and 45 MeV of excitation energy respectively, were measured in inverse kinematics with the spectrometer VAMOS. The kinematic properties of identified fission fragments allow to derive properties of the scission configuration such as the distance between fragments, the total kinetic energy, the neutron multiplicity, the total excitation energy, and, for the first time, the proton- and neutron-number sharing during the emergence of t…
Mean field calculations, based on the D1S, D1N and D1M parametrizations of the Gogny energy density functional, have been carried out to obtain the potential energy surfaces relevant to fission in several Ra isotopes with the neutron number 144 $\le$ N $\le$ 176. Inner and outer barrier heights as well as first and second isomer excitation energies are given. The existence of a well developed third minimum along the fission paths of Ra nuclei, is analyzed in terms of the energetics of the "fragments" defining such elongated configuration. The masses and charges of the fission fragments are stu…
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…
The simultaneous measurement of the isotopic fission-fragment yields and fission-fragment velocities of $^{239}$U has been performed for the first time. The $^{239}$U fissioning system was produced in one-neutron transfer reactions between a $^{238}$U beam at 5.88 MeV/nucleon and a $^{9}$Be target. The combination of inverse kinematics at low energy and the use of the VAMOS++ spectrometer at the GANIL facility allows the isotopic identification of the full fission-fragment distribution and their velocity in the reference frame of the fissioning system. The proton and neutron content of the fra…
Simple approach is used to a description of the experimental data for the widths of fission fragment mass yields in 197Au and 209Bi at low and intermediate energies. This approach based on both the expression for the temperature dependence of the width of fission fragment mass yield and the mass of the most probable fragment. The expression for the width of fission fragment mass yield depends on the mass of the most probable fragment, the surface terms of the energy level density parameter, the temperature and the stiffness parameter of the potential related to mass-asymmetric degree of freedo…
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 cold ternary fission of $^{238}$Pu, $^{240}$Pu, $^{242}$Pu and $^{244}$Pu isotopes, with $^{4}$He as light charged particle, in equatorial and collinear configuration has been studied within the Unified ternary fission model (UTFM). The fragment combination $^{100}$Zr+$^{4}$He+$^{134}$Te possessing the near doubly magic nuclei $^{134}$Te (N=82, Z=52) gives the highest yield in the alpha accompanied ternary fission of $^{238}$Pu. For the alpha accompanied ternary fission of $^{240}$Pu, $^{242}$Pu and $^{244}$Pu isotopes, the highest yield was found for the fragment combination with doubly m…
The fission fragment mass distributions have been measured in the reactions 16O + 184W and 19F+ 181Ta populating the same compound nucleus 200Pb? at similar excitation energies. It is found that the widths of the mass distribution increases monotonically with excitation energy, indicating the absence of quasi-fission for both reactions. This is contrary to two recent claims of the presence of quasi-fission in the above mentioned reactions.
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…
We propose a novel method to extract the prompt neutron multiplicity distribution, $P(ν)$, in fission reactions based on correlations between prompt neutrons, $γ$ rays, and fragment kinetic energy arising from energy conservation. In this approach, only event-by-event measurements of the total $γ$-ray energy released as a function of the total kinetic energy (TKE) of the fission fragments are performed, and no neutron detection is required. Using the $\texttt{CGMF}$ fission event generator, we illustrate the method and explore the accuracy of extracting the neutron multiplicity distribution wh…
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 …
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…
We study the role of different collective degrees of freedom in spontaneous fission process of even--even Fm isotopes. To find a proper collective space we examine a reach collection of nuclear shape parameters $\{β_λ\}$, with $λ$=2,3,4,5,6 and 8; as well as the paring degrees of freedom i.e. proton $Δ_{p}$ and neutron $Δ_{n}$ pairing gaps. On the basis of the multidimensional dynamic--programming method (MDPM) the optimal collective space $\{β_{2}, β_{4}, β_{6}, Δ_{p}, Δ_{n}\}$ for Fm isotopes was found.
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…
Bremsstrahlung emission accompanying ternary fission of \isotope[252]{Cf}
Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；Wigner Research Centre for Physics（维格纳物理研究中心）；Institute for Nuclear Research, National Academy of Sciences of Ukraine（乌克兰国家科学院核物理研究所）；Heavy Ion Science and Technology Key Laboratory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子科学与技术重点实验室）；School of Nuclear Sciences and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
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）
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…
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…
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.
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…
The two stages dynamical stochastic model developed earlier for description of fusion-fission reactions is applied to the calculation of mass- and energy-distributions of fission fragments of platinum isotopes in reaction ${\rm ^{36}Ar + ^{142}Nd \to ^{178-x}Pt + xn}$. The first stage of this model is the calculation of the approaching of projectile nucleus to the target nucleus. On the second stage of the model, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by three-dimensional L…
The alpha accompanied cold ternary fission of even-even 244Cm, 246Cm, 248Cm, 250Cm and 252Cm isotopes have been studied by taking the interacting barrier as the sum of Coulomb and proximity potential with the fragments in equatorial configuration. The favorable fragment combinations are obtained from the cold reaction valley plot and by calculating the relative yield for the charge minimized fragments. In the alpha accompanied ternary fission of 244Cm isotope, the highest yield is found for the fragment combination 110Ru+4He+130Sn, which possess near doubly magic nuclei 130Sn. For the ternary …
Fission-fragment mass distributions are asymmetric in fission of typical actinide nuclei for nucleon number $A$ in the range $228 \lnsim A \lnsim 258$ and proton number $Z$ in the range $90\lnsim Z \lnsim 100$. For somewhat lighter systems it has been observed that fission mass distributions are usually symmetric. However, a recent experiment showed that fission of $^{180}$Hg following electron capture on $^{180}$Tl is asymmetric. We calculate potential-energy surfaces for a typical actinide nucleus and for 12 even isotopes in the range $^{178}$Hg--$^{200}$Hg, to investigate the similarities a…
Ternary fission yields in the reaction 241Pu(nth,f) are calculated using a new model which assumes a nucleation-time moderated chemical equilibrium in the low density matter which constitutes the neck region of the scissioning system. The temperature, density, proton fraction and fission time required to fit the experimental data are derived and discussed. A reasonably good fit to the experimental data is obtained. This model provides a natural explanation for the observed yields of heavier isotopes relative to those of the lighter isotopes, the observation of low proton yields relative to 2H …
Spontaneous fission and alpha decay are the main decay modes for superheavy nuclei. The superheavy nuclei which have small alpha decay half-life compared to spontaneous fission half-life will survive fission and can be detected in the laboratory through alpha decay. We have studied the alpha decay half-life and spontaneous half-life of some superheavy elements in the atomic range Z = 100-130. Spontaneous fission half-lives of superheavy nuclei have been calculated using the phenomenological formula and the alpha decay half-lives using Viola-Seaborg-Sobiczewski formula (Sobiczewski et al. 1989)…
Superheavy isotopes are highly neutron rich nuclei in the vicinity of neutron drip-line, stabilized by shell effect against the instability due to repulsive component of nuclear force, analogous to superheavy elements similarly stabilized against Coulomb instability. Here we discuss the stability and fission decay properties of such nuclei in the $^{254}$Th region and show that they are stable against $α$ and fission decay and have $β$-decay life time of several tens of seconds. In particular, the $^{254}$Th nucleus has a low fission barrier and unusally large barrier width. This makes it an i…
The predictions on the mode of decay of the odd-even and odd-odd isotopes of heavy and superheavy nuclei with Z = 99-129, in the range 228 \leg A \leg 336, have been done within the Coulomb and proximity potential model for deformed nuclei (CPPMDN). A comparison of our calculated alpha half lives with the values computed using other theoretical models shows good agreement with each other. An extensive study on the spontaneous fission half lives of all the isotopes under study has been performed to identify the long-lived isotopes in the mass region. The study reveals that the alpha decay half …
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…
Constrained mean-field calculations, based on the Gogny-D1M energy density functional, have been carried out to describe fission in the isotopes $^{250-260}$No. The even-even isotopes have been considered within the standard Hartree-Fock-Bogoliobov (HFB) framework while for the odd-mass ones the Equal Filling Approximation (HFB-EFA) has been employed. Ground state quantum numbers and deformations, pairing energies, one-neutron separation energies, inner and outer barrier heights as well as fission isomer excitation energies are given. Fission paths, collective masses and zero-point quantum vib…
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.
