The moment of inertia at the saddle point of low energy fission of even-even nuclei

We use the molecular model of low energy fission, which describes the nucleus by two interacting fragments, to calculate the moment of inertia for U²³⁶ in the cranking approximation including BCS theory. We show that the moment of inertia at the saddle point:

1. depends almost linearly on the fragment distance.
2. is influenced only very weakly by the pairing constant and by the fragment deformations.
3. shows, as a function of the distribution of mass between the two fragments (A ₁ ,A ₂ ), a minimum near the magic configurationA ₁=132,Z ₁=50 and depends in this mass region strongly on the term structure near the Fermi energy.
4. is approximately that of a rigid body.

     

Isotopic invariance of fission fragment charge distributions for actinide nuclei at excitation energies above 10 MeV

The fragment mass and energy distributions from the proton-induced fission of compound nuclei ²³³Pa, ^{234,236,237,239}Np, ^{239,240,241,243}Am, and ²⁴⁵Bk at proton energy E _p =10.3 and 22.0 MeV have been experimentally studied. It was revealed that the shapes of the asymmetric fission mass distributions are mainly defined by the proton numbers of compound nuclei and demonstrate only a weak dependence on the neutron ones. The detailed study of the fission fragment mass yields for compound nuclei Np and Am isotopic chains has shown that the asymmetric fission fragment charge distributions calculated within the unchanged charge density hypothesis for nuclei with equal Z _C practically coincide.     

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.     

Charged particle induced ternary fission

Ternary fission has been investigated by irradiating a natural uranium target with 13.5 MeV deuterons. The energy and angular distributions of ternary alpha particles do not differ from those observed in spontaneous or thermal neutron induced fission. The angle between alpha particles and light fragments has a most probable value of \(\bar \vartheta _{\ell f - \alpha } = 82.1 \circ \pm 0.6 \circ \) with a dispersion (FWHM) of \(\Delta \vartheta = 18.4 \circ \pm 1.2 \circ \) . The corresponding values of the energy distribution are \(\bar E\alpha \) =(14.8 ±0.5)MeV and ΔE(FWHM)= (9.1±1.1)MeV. The peak-to-valley ratio of the ternary fission fragment mass distribution is found to increase with increasing alpha energy. For near-symmetric mass division a strong broadening of the angular distribution is observed.     

In-beam investigation of ternary fission

Nuclear fission accompanied by long-range alpha particles has been investigated. Fission was induced by irradiating a natural uranium target with 13.5 MeV deuterons. The alpha energy and angular distributions are similar to those observed in spontaneous or thermal neutron induced fission. The correlation angle between alpha particles and light fission fragments has a most probable value of \(\bar \vartheta _{l f - \alpha } = 82.1^\circ \pm 0.9^\circ \) and a dispersion (FWHM) of Δ?=18.4°±1.2°. The mean value and dispersion of the energy distribution are \(\bar {\rm E}_\alpha = 14.8 \pm 1.0 MeV\) and ΔE=9.1±1.2 MeV (FWHM), respectively. The peak-to-valley ratio of the ternary fission fragment mass distribution is found to increase with increasing alpha energy. For near-symmetric mass division, a strong broadening of the angular distribution is observed. The results are discussed in the frame of a multichannel-fission model.     

Independent yields of Kr and Xe isotopes in the photofission of heavy nuclei

The yields of Kr (A = 87–93) and Xe (A = 138–143) primary fission fragments produced in ²³²Th, ²³⁸U, and ²⁴⁴Pu photofission upon the scission of a target nucleus and neutron emission were measured in an experiment with bremsstrahlung from electrons accelerated to 25 MeV by a microtron, and the results of these measurements are presented. The experimental procedure used involved the transportation of fragments that escaped from the target by a gas flow through a capillary and the condensation of Kr and Xe inert gases in a cryostat at liquid-nitrogen temperature. The fragments of all other elements were retained with a filter at the capillary inlet. The isotopes of Kr and Xe were identified by the γ spectra of their daughter products. The mass-number distributions of the independent yields of Kr and Xe isotopes are obtained and compared with similar data on fission induced by thermal and fast neutrons; the shifts of the fragment charges with respect to the undistorted charge distribution are determined. Prospects for using photofission fragments in studying the structure of highly neutron-rich nuclei are discussed.     

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.     

Messung der Kettenlänge für den β-Zerfall der Spaltprodukte bei der thermischen Spaltung von U235

The various masses of fission products of U²³⁵-thermal fission were spacially separated by a helium filled magnetic mass separator. The number and energy of theβ-decays to the stable nuclides were counted and measured by a scintillation spectrometer. The time dependance of theβ-activity andβ-energy of the total of the U²³⁵ fission products was measured. The number ofβ-decays/fission was found to be (6,9±0,4)β-particles fission, the energy liberated byβ-decays (8,1±0,4) MeV/fission. A calculation of the totalβ-decay energy is given and compared with experimental data. The chainlengths ofβ-decay chains as a function of mass of the fission products were measured. Data on prompt neutron emission from fission products combined with the chainlength measurement give the mass dependance of the most probable charge of the primarily formed fission products. A recent model of asymmetric fission is shown to agree with the experimental data. The data give strong evidence that the filled nucleon shells ofZ=50 andN=50 are responsible for the asymmetric fission mechanism.     

Photofission accompanied by pion emission

For the nuclear-fission process induced by photons of energy in the range 150 < E_γ < 600 MeV and accompanied by pion emission, the total cross section; the angular and differential distributions of pions; the excitation-energy, mass, and charge distributions of compound nuclei; and the mass distribution of the fission fragments are predicted on the basis of the cascade-evaporation-fission model. These features are compared for the cases of nuclear fission induced by photons and protons of initial energy in the same range.     

Determination of the fission fragment excitation energy with allowance for neutron multiplicity

The study of the excitation energy distribution of fission fragments as a function of their mass and charge is important for revealing the nuclear fission mechanism and useful for many applications. To measure directly the excitation energy of primary fission fragments (before emission of neutrons) is a great problem. A method of obtaining these excitation energies from calculated neutron multiplicities and experimental values for differential yields of fragment pairs after emission of neutrons is considered. The Empire-II code was used to calculate neutron multiplicities as a function of various characteristics of the nuclear structure, fission process, and fission fragment deexcitation.     

A simplified two-dimensional diffusion model for calculating the fission-fragment kinetic-energy distribution

The variance \(\sigma _{E_k }^2\) of the fission-fragment kinetic-energy distribution is calculated in describing the dynamics of fission of an excited nucleus by a Fokker-Planck equation for the quantum distribution function of two collective coordinates (the distance between the centers of mass of the nascent fragments and the neck parameter) and their conjugate momenta. In the calculations fluctuations in collective coordinates near scission and prescission kinetic energy have been taken into account simultaneously. The results of statistical model calculations for the case of high friction in fission mode and those of the calculations in the framework of a dynamical model for zero nuclear viscosity are the limiting cases of the proposed model. The dependence of \(\sigma _{E_k }^2\) upon the fissility parameter is studied.     

Thorium fission by 4.8 and 14 MeV neutrons

The fission of natural Thorium byE _n =4.8 and 14.0 MeV neutrons has been investigated by measuring the kinetic energies of both fragments in surface barrier detectors. The fragments were detected forE _n =14.0 MeV neutron energy at 90 ° to the neutron beam, forE _n =4.8 MeV at 0 ° and 90 °. The results given are the distributions of mass and of energy correlative to the fragment mass, and the correlation between anisotropy and fragment mass atE _n =4.8 MeV. The average total kinetic energy before prompt neutron emission atE _n =4.8 and 14.0 MeV neutron energy has been found to be \(\overline {E_K^* } \) =170.47±0.03 and 168.1 ± 0.05 MeV respectively. Within the limits of statistical error the anisotropy atE _n =4.8 MeV is independent of the fragment mass. The results are analysed in the framework of the Two-Mode-Fission-Hypothesis. It appears, that the behaviour of the kinetic energy is too complicated as to be well described by the Two-Mode-Fission-Hypothesis. Both the Cluster Model of fission and the Fragment Shell Theory are suited to reproduce qualitatively the observed energetics of fission.     

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.     

Semi-empirical interpretation of nuclear fission based on deformed-shell effects

The main features of the fragment mass and charge distribution in the fission of nuclides from Po to Fm are accounted for using a correlation of minimum potential energy with fragment yield. The potential energy is calculated from a liquid drop surface with deformed-fragment shell and pairing corrections at a particular deformation for the nascent fission fragments.     

Investigation of the reaction <Superscript>208</Superscript>Pb(<Superscript>18</Superscript>O, <Emphasis Type="Italic">f</Emphasis>): Folding angular distributions of fission fragments and gamma-ray multiplicity

Correlations between folding angular distributions of fission fragments and the gamma-ray multiplicity are studied for ¹⁸O + ²⁰⁸Pb interactions at energies of the beam of ¹⁸O ions in the range E _lab = 78–198.5 MeV. The probabilities are determined for complete-and incomplete-fusion processes inevitably followed by the fission of nuclei formed in these processes. It is found that the probability of incomplete fusion followed by fission increases with increasing energy of bombarding ions. It is shown that, for the incomplete-fusion process, folding angular distributions of fission fragments have a two-component structure. The width of folding angular distributions (FWHM) for complete fusion grows linearly with increasing energy of ¹⁸O ions. The multiplicity of gamma rays from fission fragments as a function of the linear-momentum transfer behaves differently for different energies of projectile ions. This circumstance is explained here by the distinction between the average angular momenta of participant nuclei in the fusion and fission channels, which is due to the difference in the probabilities of fission in the cases where different numbers of nucleons are captured by the target nucleus.     

Parity nonconservation and Brosa modes in nuclear fission

The parity nonconserving (PNC) asymmetry coefficient for the angular distribution of fragment emission from binary fission of²³³U irradiated by polarized thermal neutrons has been measured. Complementary fragments were detected by a double ionization chamber with high resolving power. The experiment was carried out at the high flux reactor of the ILL, Grenoble. Integrated over all masses and energies of light fragments from asymmetric fission of²³⁴U^h, the PNC asymmetry coefficient is found to be =(3.29±0.31) × 10^–4.The positive sign of indicates a preferential emission of light fragments parallel to the spin of neutrons inducing fission. Theory claims that PNC effects are sensitive to the properties of the fission barrier. On the other hand, one may wonder whether characteristics of eventual fragments are already specified at the barrier. The measurement of PNC asymmetries for distinct mass-energy ranges of fragments has been utilized to answer this question. Mass-energy distributions of fragments were analyzed along the lines of the Brosa model of fission as a superposition of individual modes. Within experimental uncertainty no mode dependence of asymmetric fission could be disclosed. The result is in keeping with the Brosa model where asymmetric modes bifurcate only once the standard fission barrier has been passed.     

Perturbation Theory for Proton-Neutron Scattering: Perturbing the Energy

Using the time-independent Schrödinger equation with a velocity-dependent potential the energy dependence of the corresponding scattering phase shifts, when the energy is changed by a small amount ΔE from an arbitrary unperturbed value E ₀, is studied. We expand kcot?δ as a power series in ΔE and obtain analytic formulas for the effective range expansion parameters to all orders in the perturbing energy. Formulas for the corresponding wave function changes are also developed. At low energies the Bethe formula for the effective range is reproduced and an expression for the shape-dependent term is obtained. The derived formalism is relevant to fields like nuclear and atomic physics. Examples that demonstrate the effectiveness of the derived formalism are presented.     

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.