Probabilistic scission of a fissile nucleus into fragments

A probabilistic criterion is proposed for the scission of a fissile nucleus into fragments. The probability of the rupture of the neck between would-be fragments is estimated by considering scission as a fluctuation. The energy of the prescission configuration and the energy of the separated-fragment configuration are computed on the basis of a macroscopic model that takes into account a finite range of nuclear forces and the diffuseness of the nuclear surface. The effect of the probabilistic criterion of nuclear scission on fission-process observables, such as the moments of the mass-energy distribution of fission fragments, the mean multiplicity of prescission neutrons, and mean fission times, is demonstrated. It is shown that the Strutinsky criterion, according to which nuclear scission occurs at a finite neck radius of 0.3R₀, is a rather good approximation to the probabilistic scission criterion in Langevin dynamical calculations employing the one-body nuclear-viscosity mechanism modified in such a way that the wall-formula contribution is reduced, the reduction factor satisfying the condition k _s <05.     

Classification of <Emphasis Type="Italic">T</Emphasis>-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.     

The complex trajectory method and dissipation in fission

The sensitivity of the muon attachment probabilities to the light fragments of prompt fission W _l on the fission dynamics is discussed. It is shown that the final W _l value consists of two contributions: one from the point of scission and a second from avoided crossing of the levels. The relative contribution from the prescission phase turns out to be higher for more asymmetric fission.     

Sequential character of low-energy ternary and quaternary nuclear fission

An analysis of low-energy true ternary (quaternary) nuclear fission leads to the conclusion that these fission modes have a sequential two-step (three-step) character such that the emission of a third particle (third and fourth particles) and the separation of fission fragments occur at distinctly different instants, in contrast to the simultaneous emergence of all fission products in the case of onestep ternary (quaternary) fission. This conclusion relies on the following arguments. First, the emission of a third particle (third and fourth particles) from a fissile nucleus is due to a nonevaporative mechanism associated with a nonadiabatic character of the collective deformation motion of this nucleus at the stages preceding its scission. Second, the axial symmetry of the deformed fissile compound nucleus and the direction of its symmetry axis both remain unchanged at all stages of ternary (quaternary) fission. This circumstancemakes it possible to explain themechanism of the appearance of observed anisotropies and T — odd asymmeries in the angular distributions of products of ternary (quaternary) nuclear fission. Third, the T —odd asymmetry discovered experimentally in ternary nuclear fission induced by cold polarized neutrons obeys the T —invariance condition only in the case of a sequential two-step (three-step) character of true ternary (quaternary) nuclear fission. At the same time, this asymmetry is not a T —invariant quantity in the case of the simultaneous emission of products of true ternary (quaternary) nuclear fission from the fissile compound nucleus.     

A Rigidity Result for Extensions of Braided Tensor <Emphasis Type="Italic">C</Emphasis>*–Categories Derived from Compact Matrix Quantum Groups

Let G be a classical compact Lie group and G _μ the associated compact matrix quantum group deformed by a positive parameter μ (or \({\mu\in{\mathbb R}\setminus\{0\}}\) in the type A case). It is well known that the category of unitary representations of G _μ is a braided tensor C*–category. We show that any braided tensor *–functor \({\rho: \text{Rep}(G_\mu)\to\mathcal{M}}\) to another braided tensor C*–category with irreducible tensor unit is full if |μ| ≠ 1. In particular, the functor of restriction RepG _μ → Rep(K) to a proper compact quantum subgroup K cannot be made into a braided functor. Our result also shows that the Temperley–Lieb category \({\mathcal{T}_{\pm d}}\) for d > 2 can not be embedded properly into a larger category with the same objects as a braided tensor C*–subcategory.     

Nucleon-content effect on the fission lifetime of excited nuclei

It was shown previously that the fission lifetime of a nucleus excited to about 100 MeV depends strongly and nonmonotonically on the initial value of its angular momentum L ₀. This result was obtained on the basis of a refined version of the combined dynamical and statistical model. The present study is devoted to a theoretical analysis of the dependence of the fission time on the nucleonic composition of the nucleus involved. The respective calculations were performed within the same model. The dependence of the average fission time 〈t _f 〉 on the initial fissility parameter (Z ²/A)₀ appears to be of a resonance type and is similar to its dependence on L ₀. This dependence of the average fission time on (Z ²/A)₀ stems both from statistical calculations and from a dynamical simulation of the fission mode with allowance for friction. The conditions under which the average fission time reaches a maximum are specified. The dependence of the average fission time on (Z ²/A)₀ remains nonmonotonic in the fusion-fission reaction as well, in which case the distribution of compound nuclei with respect to the initial angular momentum is broad.     

Coriolis interaction in the second well of deformation potential and low-energy fission

It is shown that, because of sufficiently large energy spacing between neutron resonance states (NRS-II) in the second well of the deformation potential for actinide nuclei, the Coriolis interaction, mixing the states of an axially symmetric deformed nuclei with different values of the projection K of the nuclear spin J onto the symmetry axis, is week, and the K value in the wave functions of NRS-II is a good quantum number. It is concluded that the K distribution for the states of fissile actinide nuclei in the vicinity of their scission point into fission fragments is determined by simultaneous influence of the internal and external fission barriers, which allows to coordinate the experimental data on subbarrier photofission with the P-odd and P-even correlations in the angular distributions of fission fragments.     

Analysis of fragment mass distribution in asymmetric area at fission of <Superscript>235</Superscript>U induced by thermal neutrons

The fragment mass yields in fission of ²³⁵U induced by thermal neutrons for A = 145–160 and E_K = 50–75 MeV were measured using a mass spectrometer. The fine structure is observed at A = 153, 154 and E_K = 50–60 MeV. The obtained results were described in the framework of a model based on the dinuclear system concept. The analyzed correlation between the total kinetic energy and mass distribution of fission fragments is connected with the shell structure of the formed fragments of fission. From this correlation and the time dependence of the calculated mass distribution of the binary reaction products, one can conclude that the descent time from a saddle point to a scission point for the more deformed fragments is longer than that for fragments of more compact shape.     

Stochastic model of angular distributions of fragments originating from the fission of excited compound nuclei

The anisotropy of angular distributions of fission fragments and the average multiplicity of prescission neutrons were calculated within a stochastic approach to fission dynamics on the basis of three-dimensional Langevin equations. This approach was combined with a Monte Carlo algorithm for the degree of freedom K (projection of the total angular momentum I onto the fission axis). The relaxation time τ _K in the coordinate K was considered as a free parameter of the model; it was estimated on the basis of a fit to experimental data on the anisotropy of angular distributions. Specifically, the relaxation time τ _K was estimated at 2 × 10^?21 s for the compound nuclei ²²⁴Th and ²²⁵Pa and at 4 × 10^?21 s for the heavier nuclei ²⁴⁸Cf, ²⁵⁴Fm, and ²⁶⁴Rf. The potential energy was calculated on the basis of the liquid-drop model with allowance for finiteness of the range of nuclear forces and for the diffuseness of the nuclear surface. A modified one-body viscosity mechanism featuring a coefficient k _s that takes into account the reduction of the contribution from the wall formula was used to describe collective-energy dissipation. The coefficient k _s was also treated as a free parameter and was estimated at 0.5 on the basis of a fit to experimental data on the average prescission multiplicity of neutrons.     

Vaidya spacetime in the diagonal coordinates

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric and cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g ₀₀ = 0 or g ₀₀ = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.     

Neutron-neutron angular correlations in spontaneous fission of <Superscript>252</Superscript>Cf

An experiment has been carried out to study neutron-neutron angular correlations in spontaneous fission of ²⁵²Cf. Angular dependences of the number of neutron-neutron coincidences obtained in the experiment were compared with the results of the Monte Carlo calculations for various neutron detection thresholds in the range 425–1600 keV. It was inferred that 10–11% of the total number of prompt neutrons from ²⁵²Cf (s.f.) in the laboratory system were emitted isotropically and may probably be interpreted as neutrons directly associated with the instant of scission of the nucleus. The analysis allowed their energy distribution to be determined as well. A similar method was also used to describe the angular correlation of prompt neutrons that accompanied the reaction ²³⁵U(n _th ,f).     

Asymmetries of various <Emphasis Type="Italic">P</Emphasis>- and <Emphasis Type="Italic">T</Emphasis>-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and <Emphasis Type="Italic">T</Emphasis>-invariance

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.     

Unified Mechanism behind the Appearance of <Emphasis Type="Italic">T</Emphasis>-Odd TRI and ROT Asymmetries in Actinide Fission Induced by Cold Polarized Neutrons

Some shortcomings of the approaches that are used to describe T-odd ROT and TRI asymmetries in true ternary fission via reactions involving the emission of prescission alpha particles and which are based on employing the classical method of trajectory calculations are analyzed. These shortcomings are caused by the disregard of the interference between the fission widths of different sJ_s neutron resonance states formed in the first well of the deformation potential of fissile compound nuclei. It is shown that the method used in some studies to determine T-odd TRI-asymmetries for prescission alpha particles is at odds with basic concepts of the generalizedmodel of the nucleus and approaches to constructing collective (for example, bending) vibrations of a fissile compound nucleus. Quantum-mechanical fission theory is generalized via employing a unified mechanism of formation of T-odd TRI and ROT asymmetries for prescission alpha particles and evaporated photons (neutrons). The proposed mechanism takes correctly into account the effect of quantum rotation of a fissile compound nucleus on the angular distributions of fission fragments and alpha particles for true ternary fission, as well as on the angular distribution of prompt photons (neutrons) emitted by fragments originating from the delayed fission of the aforementioned nuclei.     

Effect of the nuclear charge of a fast structural ion on its internal effective stopping in collisions with atoms

The energy losses of fast structural ions in collisions with atoms have been considered in the eikonal approximation. The structural ions are ions consisting of a nucleus and a certain number of electrons bound to it. The effect of nuclear charge Z of the ion on its effective deceleration κ^(p) (energy losses associated with excitation of only intrinsic ion shells) has been analyzed. It is shown that the allowance for the interaction of an atom with the ion nucleus for Z _a Z/v > 1, where Z _a is the charge of the atomic nucleus and v is the velocity of collisions in atomic units, considerably affects the value of κ^(p), which generally necessitates taking into account nonperturbatively the effect of both charges Z _a and Z on κ^(p).     

Prompt-fission-neutrons spectra of <Superscript>238</Superscript>U

The spectra of prompt fission neutrons from the reaction ²³⁸U(n, F) for neutrons of energy in the range E _n ≤ 20 MeV are interpreted within the statistical model. It is shown that exclusive spectra of prefission neutrons emitted in (n, xnf) reactions play a decisive role in describing the observed promptfission-neutron spectra and determine the average energies of prompt-fission neutrons. The dependence of the effect of prefission neutrons on the fissility of a target nucleus is demonstrated for the reactions ²³²Th(n, F), ²³⁵U(n, F), and ²³⁹Pu(n, F).     

Neutrino-astrophysics,nuclear physics,and particle physics at intense,pulsed, stopped-pion sources

Intense pulsed proton beams of ～ 1 GeV impinging on high-Z targets are intense sources of ν_μ from the (τ=26 ns) decay of π⁺, and \(\bar \nu _\mu \) and ν_e from the stopped μ⁺ decays. A pulse structure, narrow in time, allows the separation of reactions due to ν_μ from those from reactions involving \(\bar \nu _\mu\) and ν_e. The energy spectra are in the energy range of interest to nuclear astrophysics. A number of possible experiments relevant to solar neutrinos, supernovae collapse, weak interactions in nuclei, and intrinsic properties of neutrinos are discussed.     

Coherent Planar Symmetric Spacetimes Generated by Progressive Waves of Nambu–Goldstone Bosons

Within a SO(3,1) ?gauge invariant pseudo-orthonormal (Cartan) formalism, in the present paper, we are going to deal with the Einstein–Nambu–Goldstone system of equations, for a manifold with at least G₄ up to G₆ group of motion and a massless source-field excited along the z ?direction. This is also equivalent with the pure radiation energy–momentum tensor coming from circularly polarized waves generated by a rotating magnetic field. The corresponding essential equation which establishes the connection between the spacetime geometry and the matter-field is solved in some physically interesting cases.     

On the asymptotical normality of statistical solutions for wave equations coupled to a particle

We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein–Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function which has some mixing properties. We study the distribution μ _t of the random solution at time moments t ∈ R. The main result is the convergence of μ _t to a Gaussian probability measure as t→∞. The application to the case of Gibbs initial measures is given.     

Corona effect in <Emphasis Type="Italic">AA</Emphasis> collisions at the LHC

Following our earlier finding based on RHIC data on the dominant jet production from nucleus corona region, we reconsider this effect in nucleus–nucleus collisions at the LHC energies. Our hypothesis was based on experimental data, which raised the idea of a finite formation time for the produced medium. At the RHIC energy and in low-density corona region, this time reaches about 2 fm/c. Following this hypothesis, the nuclear modification factor R _AA at high p _t should be independent on particle momentum, and the azimuthal anisotropy of high p _t particles, v ₂, should be finite. A separate prediction held that, at the LHC energy, the formation time in the corona region should be about 1 fm/c. New LHC data show that R _AA is not flat and is rising with p _t . We add to our original hypothesis an assumption that a fast parton traversing the produced medium loses the fixed portion of its energy. A shift of about 7 GeV from the original power law p ^?6 production cross section in pp explains well all the observed R _AA dependencies. The shift of about 7 GeV is also valid at the RHIC energy. We also show that the observed at the LHC dependence of v ₂ at high p _t and our previous predictions agree.