Scission Point Research Articles

Fully microscopic scission-point model to predict fission fragment observables

We present an upgraded version of the SPY model, called SPY2 for version 2 of the scission point yield, to estimate mainly the yields and the kinetic energy distributions of fission fragments: The theoretical framework is similar to our previous version, i.e., a statistical scission point model, but this version is based on fully microscopic nuclear ingredients describing the fragments properties at the scission point. These include the static properties of some 7000 nuclei at 120 axial quadrupole deformations, such as binding energies, proton densities, single-particle level schemes, and states densities, coherently calculated within the constrained Hartree-Fock-Bogoliubov model on the basis of the Skyrme BSk27 interaction. The use of microscopic ingredients has been extended to the proton density distribution and the nuclear states densities. Considering realistic proton densities of fragments allows us to improve the definition of the scission point as well as the prediction of the kinetic energy distribution and to link the kinetic energy to the diffuseness of the fragments' proton density. New microscopic nuclear states densities improve the general coherence of the model, in particular regarding the inclusion of the odd-even pairing effect. In this updated SPY2 version, the calculation of the fission yields and kinetic energy distributions is significantly improved and found to be in relatively good agreement with experiments, at least qualitatively. A detailed study is performed for three well known fissioning systems, namely, thermal neutron induced fission of $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$ and spontaneous fission of $^{252}\mathrm{Cf}$. A systematic analysis of the fission mode as well as mean fragments deformation and total kinetic energies has been performed for some 2000 fissioning nuclei with $78\ensuremath{\le}Z\ensuremath{\le}110$ lying between the proton and neutron drip lines.

Angular momentum of fission fragments

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 large anisotropies in the subsequent gamma cascade. We treat in detail a typical gamma cascade in a daughter nucleus, following usual model assumptions except for the anisotropy of the initial state. In principle, the observed anisotropy can provide information on the relative amounts of deformation and thermal energy present at the scission point.

Scission dynamics with K partitions

We propose a framework to calculate the dynamics at the scission point of nuclear fission, based as far as possible on a discrete representation of orthogonal many-body configurations. Assuming axially symmetric scission shapes, we use the $K$ orbital quantum number to build a basis of wave functions. Pre-scission configurations are stable under mean-field dynamics while post-scission configurations evolve to separated fragments. In this first exploratory study, we analyze a typical fission trajectory through to scission in terms of these configurations. We find that there is a major rearrangement of the $K$ occupancy factors at scission. Interestingly, very different fragment shapes occur in the post-scission configurations, even starting from the same pre-scission configuration.

Scission Point Calculations and Physical Treating of the 'Ni-bump' in 252Cf (sf)

In a series of the experiments at different time-of-flight spectrometers of heavy ions we have observed manifestations of a new at least ternary decay channel of low excited heavy nuclei. Due to specific features of the effect, it was called collinear cluster tri-partition (CCT). The experimental results obtained initiated a number of theoretical articles dedicated to different aspects of the CCT. In the report we compare the theoretical predictions with our experimental data, only partially published so far. The developed model of one of the most populated CCT modes that gives rise to the so called “Ni-bump” is discussed.

Study of photofission fragment mass distribution of 232Th, 238U, 237Np and 240Pu isotopes in various γ-ray energies

Photofission of [Formula: see text]Th, [Formula: see text]U, [Formula: see text]Np and [Formula: see text]Pu isotopes are investigated. Modified version of Gorodisskiy approach that is developed to study the neutron-induced fission are employed to simulate fission fragment mass distribution for these isotopes in different energies. The effect of emitted neutron prior to scission point is studied. Peak to valley ratio is also extracted. Obtained results using this approach are compared with original Gorodisskiy model as well as available experimental data. Satisfactory agreement is achieved between theoretical and experimental data especially in medium and low [Formula: see text]-ray energies than original formalism of Gorodisskiy.

Investigation of the heavy nuclei fission with anomalously high values of the fission fragments total kinetic energy

Binary fission of 232Th and 238U induced by fast neutrons were under intent investigation in the IPPE during recent years. These measurements were performed with a twin ionization chamber with Frisch grids. Signals from the detector were digitized for further processing with a specially developed software. It results in information of kinetic energies, masses, directions and Bragg curves of registered fission fragments. Total statistics of a few million fission events were collected during each experiment. It was discovered that for several combinations of fission fragment masses their total kinetic energy was very close to total free energy of the fissioning system. The probability of such fission events for the fast neutron induced fission was found to be much higher than for spontaneous fission of 252Cf and thermal neutron induced fission of 235U. For experiments with 238U target the energy of incident neutrons were 5 MeV and 6.5 MeV. Close analysis of dependence of fission fragment distribution on compound nucleus excitation energy gave us some explanation of the phenomenon. It could be a process in highly excited compound nucleus which leads the fissioning system from the scission point into the fusion valley with high probability.

Formation and distribution of fragments in the spontaneous fission of 240Pu

The goal of this paper is to better understand the structure of fission fragment distributions by investigating the competition between the static structure of the collective manifold and stochastic dynamics. In particular, we study the characteristics of the tails of yield distributions, which correspond to very asymmetric fission. We use the stochastic Langevin framework to simulate the nuclear evolution after the system tunnels through the multi-dimensional potential barrier. For a representative sample of different initial configurations along the outer turning-point line, we define effective fission paths by computing a large number of Langevin trajectories. We extract the relative contribution of each such path to the fragment distribution. We then use nucleon localization functions along effective fission pathways to analyze the characteristics of prefragments at pre-scission configurations. We find that non-Newtonian Langevin trajectories, strongly impacted by the random force, produce the tails of the fission fragment distribution. The prefragments deduced from nucleon localizations are formed early and change little as the nucleus evolves towards scission. On the other hand, the system contains many nucleons that are not localized in the prefragments, even near the scission point. Such nucleons are rapidly distributed at scission to form the final fragments. Our study shows that only theoretical models of fission that account for some form of dissipative/stochastic dynamics can give an accurate description of the structure of fragment distributions. In particular, it should be nearly impossible to predict the tails of these distributions within the standard formulation of time-dependent density functional theory. At the same time, the large number of non-localized nucleons during fission suggests that adiabatic approaches are ill-suited to describe fission fragment properties.

Transitions between symmetric and asymmetric modes in the region of heavy actinides

Using the improved scission-point model, the mass and charge distributions of fragments resulting from the fission of californium, fermium, and nobelium isotopes are calculated and compared with the available experimental data. For the fissioning Fm and No nuclei, the transitions from a two-peaked to a single-peaked mass distributions are predicted. The transition between asymmetric and symmetric fission modes with the variation of neutron number is shown to be related to the change of the potential energy surface at scission point.

Decisive role of wriggling vibrations in the formation of angular and spin distributions of products originating from binary and ternary fission of oriented nuclei

It is shown that the multiplicities and angular and energy distributions of neutrons and photons evaporated from thermalized fragments originating from the spontaneous and low-energy induced fission of nuclei, the relative yields of ground and isomeric states of final fragments, and the features of delayed neutrons emitted upon the beta decay of the above fragments can successfully be described by employing nonequilibrium distributions of spins and relative orbital angular momenta of fission fragments formed in the vicinity of the scission point for the fissile nucleus being studied. It is also shown that these distributions, which are characterized by large mean values of the spins and orbital angular momenta directed orthogonally to the symmetry axis of the fissioning nucleus are successfully constructed upon simultaneously taking into account zero-mode transverse wriggling and bending vibrations of a fissile compound nucleus in the vicinity of its scission point, the wriggling vibrations being dominant. It is confirmed that the zero-mode wriggling vibrations considered immediately above are directly involved in the formation of the angular distributions of fragments originating from the spontaneous and low-energy fission of nuclei. This makes it possible to describe successfully such distributions for photofission fragments.

Photofission of nuclei with allowance for wriggling vibrations of fissioning nuclei

It is confirmed that one source of the large relative orbital momenta L of fragments in spontaneous and stimulated low-energy nuclear fission is quantum transverse zero-point wriggling vibrations of the fissioning system near its scission point. The angular distributions of fragments of low-energy photofission of actinide nuclei, calculated using the quantum theory of fission, are compared. Vibrations are allowed for by using parameter C w determined by Nix and Swiatecki. Agreement between the experimental and theoretical angular distributions for 234U, 236U, 238U, 238Pu, 240Pu, 242Pu nuclei is observed. The strong sensitivity of the theoretical angular distributions for 238Pu, 240Pu, 242Pu nuclei toward the choice of parameters of transient fissioning states at the external and internal fission barriers is demonstrated.

Fourier expansion of deformed nuclear shapes expressed as the deviation from a spheroid

A Fourier decomposition of nuclear shapes is proposed and shown to be able to cover a very wide range of nuclear deformations up to the scission point. This Fourier shape parametrization is applied to the deviations of a nuclear liquid-drop profile from a spheroidal shape. It is shown that such a shape profile expansion is not only very rapidly converging, but also gives an excellent description of nuclear shapes all along the path to fission. Some examples of the liquid-drop and the macroscopic–microscopic potential energy surfaces in this new shape parametrization are presented and the connection with Bohr deformation parameters is given.

Investigation of the 16O+194Pt reaction: One- and two-dimensional dynamical interpretation

In this paper, we applied the Langevin dynamical model to investigate the different aspects of the [Formula: see text]O+[Formula: see text]Pt reaction. Elongation and orientation degree of freedom ([Formula: see text] coordinate) which are the first and second dimensions of dynamical calculations, are presented here. Fission time, fission cross-section, pre-scission neutron multiplicity, and fission probability were calculated using one- and two-dimensional Langevin equations. Also, anisotropy of fission-fragments angular distribution has been investigated based on the transition state model, one- and two-dimensional Langevin dynamical models. It was found that by adding the orientation degree of freedom to calculations, the fission time and pre-scission neutrons multiplicity increases whereas fission cross-section, and fission probability decreases. The two-dimensional dynamical calculations are a better match to the experimental data than the one-dimensional dynamical calculations, when using nominal values for the reduced dissipation coefficient and shape-dependent level density parameter. However, if model parameters are adjusted to reproduce the fission cross-section data, then both the one- and two-dimensional models give a satisfactory match to the fission fragment anisotropy data. Nonequilibrium [Formula: see text] distributions in the dynamical model can better explain the experimental anisotropy of the angular distribution of fission-fragments with respect to the equilibrium [Formula: see text] distribution in saddle and scission point transition state models.

Investigation of fission fragments average spin based on four dimensional Langevin dynamical model

We applied the four dimensional Langevin dynamical model to investigate the average spin of fission fragments. Elongation, neck thickness, asymmetry parameter, and the orientation degree of freedom (K coordinate) are the four dimensions of the dynamical model. We assume that the collective modes depend on the emission angle of the fragments, then different parameters related to the average spin of fission fragments are calculated dynamically. The angle dependence of average spin of fission fragments is investigated by calculating the spin at angles 90° and 165°. Also, the obtained results based on the transition state model at scission point are presented. One can obtain better agreement between the results of the dynamical model and experimental data in comparison with the results of the transition state model.

Scission-point model predictions of fission-fragment mass and total kinetic energy distributions for 236U and 252Cf

The total deformation energy at the moment of the neck rupture for 236 U and 252 Cf is calculated using the Strutinsky's prescription and nuclear shapes described in terms of Cassinian ovals generalized by the inclusion of four additional shape parameters: α1 , α2 , α3 , and α4 . The corresponding fragment-mass distributions are estimated supposing that each point in the deformation space is occupied according to a canonical distribution. The energy distributions of fission fragments are calculated assuming the point-charge approximation for the Coulomb interaction of fission fragments. Finally, an alternative definition of the nuclear scission point configuration relying on the minimization of liquid drop energy (optimal shape method) is used. Both definitions lead, for these two nuclei, to a reasonably good agreement with the experimental data.

Study of five-dimensional potential-energy surfaces for actinide isotopes by the macroscopic-microscopic method

In this work, the nuclear potential-energy of the deformed nuclei as a function of shape coordinates is calculated in a five-dimensional (5D) parameter space of the axially symmetric generalized Lawrence shapes, on the basis of the macroscopic-microscopic method. The liquid-drop part of the nuclear energy is calculated according to the Myers-Swiatecki model and the Lublin-Strasbourg-drop (LSD) formula. The Woods-Saxon and the folded-Yukawa potentials for deformed nuclei are used for the shell and pairing corrections of the Strutinsky-type. The pairing corrections are calculated at zero temperature, T, related to the excitation energy. The eigenvalues of Hamiltonians for protons and neutrons are found by expanding the eigen-functions in terms of harmonic-oscillator wave functions of a spheroid. Then the BCS pair is applied on the smeared-out single-particle spectrum. By comparing the results obtained by different models, the most favorable combination of the macroscopic-microscopic model is known as the LSD formula with the folded-Yukawa potential. Potential-energy landscapes for actinide isotopes are investigated based on a grid of more than 4,000,000 deformation points and the heights of static fission barriers are obtained in terms of a double-humped structure on the full 5D parameter space. In order to locate the ground state shapes, saddle points, scission points and optimal fission path on the calculated 5D potential-energy surface, the falling rain algorithm and immersion method are designed and implemented. The comparison of our results with available experimental data and others' theoretical results confirms the reliability of our calculations.

The nucleon localization function in static and time-dependent DFT

Static and time-dependent density functional theory (DFT) calculations are often used to predict fission fragment distributions or fusion cross sections with great success. However, nuclear shell structure and clusterization effects are usually studied using the density distribution of the nucleons which is a poor indicator of these phenomena. In this work, we employ a measure called the localization function, which was first introduced in chemistry to visualize electronic bonds and recently applied to nuclear physics for light nuclei to reveal α-clustering. We show, that the localization function reveals the shell structure of the fragments in fission long before the scission point and also illustrates the shell structure of intermediate states in time-dependent DFT calculations.

Fission in Inverse Kinematics: A path to new experimental observables

Historically, experimental fission studies were based on reactions in direct kinematics with fixed target-like fissioning systems. Besides its advantages, this technique suffers from some drawbacks such as the difficulty of producing exotic fissioning systems and the seldom measurement of the fragment atomic number. Inverse kinematic provides an alternative to ease these issues and offers a new set of experimental observables that improves our level of information about the fission process, including an unprecedented access to the scission point. In this document, we review some of the observables obtained from the experimental campaign based on inverse kinematics, performed at VAMOS/GANIL.

Late-time emission of prompt fission γ rays

The emission of prompt fission $\ensuremath{\gamma}$ rays within a few nanoseconds to a few microseconds following the scission point is studied in the Hauser-Feshbach formalism applied to the deexcitation of primary excited fission fragments. Neutron and $\ensuremath{\gamma}$-ray evaporations from fully accelerated fission fragments are calculated in competition at each stage of the decay, and the role of isomers in the fission products, before $\ensuremath{\beta}$ decay, is analyzed. The time evolution of the average total $\ensuremath{\gamma}$-ray energy, the average total $\ensuremath{\gamma}$-ray multiplicity, and the fragment-specific $\ensuremath{\gamma}$-ray spectra is presented in the case of neutron-induced fission reactions of $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$, as well as spontaneous fission of $^{252}\mathrm{Cf}$. The production of specific isomeric states is calculated and compared to available experimental data. About 7% of all prompt fission $\ensuremath{\gamma}$ rays are predicted to be emitted between 10 ns and 5 $\ensuremath{\mu}\mathrm{s}$ following fission, in the case of $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}\phantom{\rule{4pt}{0ex}}({n}_{\mathrm{th}},f)$ reactions, and up to 3% in the case of $^{252}\mathrm{Cf}$ spontaneous fission. The cumulative average total $\ensuremath{\gamma}$-ray energy increases by 2% to 5% in the same time interval. Finally, those results are shown to be robust against significant changes in the model input parameters.

Classification of T-odd asymmetries for prescission and evaporated light particles in ternary and quaternary nuclear fission induced by cold polarized neutrons

A unified mechanism of the emergence of T-odd ROT- and TRI-asymmetries is proposed for describing experimental T-odd asymmetry coefficients D(θ) in the angular distributions of prescission alphaparticles that are emitted in true ternary and quaternary nuclear fission reactions induced by cold polarized neutrons. The mechanism is related to the different ways in which the Coriolis interaction of the total spin of a polarized compound fissile nucleus with the orbital moment of alpha-particles affects even (for ROT-asymmetries) and odd (for TRI-asymmetries) components of the amplitude of an undisturbed angular distribution of emitted alpha-particles. Coefficients D ROT(θ) and D TRI(θ) derived with this mechanism for T-odd ROT- and TRI-asymmetries successfully describe the dependences of corresponding experimental coefficients for 235U and 239Pu nuclei over the range of angles θ, and for the 233U nucleus in the angular range of 60° < θ < 110°. It is explained why only ROT-type T-odd asymmetries emerge for evaporated neutrons and γ-quanta emitted by fission fragments in similar reactions if we allows for the Coriolis interaction of the total spin of the compound fissile nucleus with the orbital moments of the fission fragments and the wriggling vibrations of the above nucleus near its scission point.

Collision-Induced Dissociation of Electrosprayed Protein Complexes: An All-Atom Molecular Dynamics Model with Mobile Protons.

Electrospray ionization mass spectrometry (ESI-MS) has become an indispensable technique for examining noncovalent protein complexes. Collision-induced dissociation (CID) of these multiply protonated gaseous ions usually culminates in ejection of a single subunit with a disproportionately large amount of charge. Experiments suggest that this process involves subunit unfolding prior to separation from the residual complex, as well as H(+) migration onto the unravelling chain. Molecular dynamics (MD) simulations are a promising avenue for gaining detailed insights into these CID events. Unfortunately, typical MD algorithms do not allow for mobile protons. Here we address this limitation by implementing a strategy that combines atomistic force fields (such as OPLS/AA and CHARMM36) with a proton hopping algorithm, focusing on the tetrameric complexes transthyretin and streptavidin. Protons are redistributed over all acidic and basic sites in 20 ps intervals, subject to an energy function that reflects electrostatic interactions and proton affinities. Our simulations predict that nativelike conformers at the onset of collisional heating contain multiple salt bridges. Collisional heating initially causes subtle structural changes that lead to a gradual decline of these zwitterionic patterns. Many of the MD runs show gradual unfolding of a single subunit in conjunction with H(+) migration, culminating in subunit separation from the complex. However, there are also instances where two or more chains start to unfold simultaneously, giving rise to charge competition. The scission point where the "winning" subunit separates from the complex can be attained for different degrees of unfolding, giving rise to product ions in various charge states. The simulated product ion distributions are in close agreement with experimental CID data. Proton enrichment in the departing subunit is driven by charge-charge repulsion, but the combination of salt bridge depletion, charge migration, and proton affinity causes surprising compensation effects among the various energy terms. It appears that this work provides the most detailed account to date of the mechanism whereby noncovalent protein complexes disassemble during CID.