Symmetric and asymmetric scission properties

Existence of two kinds of scission configurations associated with the symmetric and asymmetric fission modes is pointed out in the fission of actinides: elongated and compact configurations. Each symmetric and asymmetric scission property is discussed in terms of shape elongation evaluated from fragment total kinetic energy (TKE). It is found that the shape elongation associated with the asymmetric fission mode is nearly constant for a wide range of fissioning nuclei, while that with the symmetric one is also constant except for low-energy induced fission and spontaneous fission (SF) of heavy nuclei. Prom the systematic study of the scission properties, the bimodal fission observed in SF of the heavy actinides is interpreted as the presence of the two fission paths of the ordinary asymmetric mode and a strongly shell-influenced symmetric one.     

Equilibrium configurations of rotating charged or gravitating liquid masses with surface tension. II

The equilibrium configurations of rotating charged or gravitating liquid masses with surface tension are investigated. The objective is to discuss in a unified manner configurations of idealized atomic nuclei, rotating liquid drops and rotating idealized astronomical masses. The present paper formulates the problem generally but the applications discussed are mostly to nuclei. These include the estimates of the geometrical characteristics, of the rigid moments of inertia, and of the energies and fission barriers of idealized nuclei throughout the periodic table and with any angular momentum. The existence of super-deformed nuclei, stretched out into cylinderlike configurations by the centrifugal force, is discussed.     

Nuclear dissipation with residual interactions studied by means of the Mori formalism

We apply correlation function techniques to the calculation of nuclear friction within the framework of a linear response theory. We make use of the fluctuation dissipation theorem to relate the response function to the correlation function which is evaluated by exploiting projection operator techniques. We go beyond the one-body dissipation approximation in the sense that we have taken into account the decay of particle-hole excitations into more complicated configurations. A rather simple formula for the frequency and temperature dependence of the friction coefficient is derived which we have applied to the high energy fission of²³⁸U. The friction coefficients for deformations around the first and second minima of the fission barrier have been calculated using this approach.     

Cold deformed fission in232U(n,f) and239Pu(n,f)

Masses, charges and kinetic energies of light fission fragments from the reactions²³²U(n, f) and²³⁹Pu(n, f) induced by thermal neutrons have been measured on the Cosi fan tutte spectrometer of the Institut Laue-Langevin in Grenoble. Both at very high and very low kinetic energies marked fine structures in the mass yields and odd-even staggerings in the charge yields are observed. In the framework of a scission point model the results are shown to point to compact and deformed scission configurations, respectively, where at scission the fragments carry no intrinsic excitation energy. The two limiting processes may, therefore, be called cold compact fission (usually known as cold fission) and cold deformed fission. The latter process as a general phenomenon of low energy fission has come into focus only recently.     

A TWO-PARAMETER ROTATING LIQUID DROP MODEL

Nuclear shapes in fission process have been described by using a generalized Cassinian ovals.The calculated fission barriers and effective moments of inertia of saddle-point configurations are in good agreement with the experimental data.The calculated fission barriers for a wide range of nuclei as a function of angular momentum are close to the prelicted values by the CPS Model based on describing nuclear shapes in terms of a spherical harmonic expansion with lowest nine even order terms.     

<Emphasis Type="Italic">P</Emphasis>-even correlations in binary and ternary nuclear fission induced by polarized neutrons

The evolution of a fissile nucleus from transition fission states specified at the saddle point of the deformation potential to fission states associated with prescission configurations of this nucleus and characterized by a pearlike shape of the nucleus is studied within the quantum-mechanical theory of fission processes that is based on the time-independent formalism. The coefficients of P-even asymmetries in the angular distributions of a light fragment and a third particle are calculated on the basis of the idea of the one-step mechanism of the production of a third particle and two fragments from the ternary fission of nuclei that is induced by polarized thermal neutrons. In order to confirm the developed concepts, it is proposed to repeat, at a higher level of statistical accuracy, experiments devoted to observing left-right asymmetries in the angular distributions of alpha particles from the ternary fission of nuclei.     

Angular Anisotropy of the Fission Fragments in the Dinuclear System Mo del

A theoretical evaluation of the collective excitation spectra of nucleus at large deformations is possible within the framework of the dinuclear system (DNS) model, which treats the wave function of the fissioning nucleus as a superposition of a mononucleus configuration and two-cluster configurations in a dynamical way, permitting exchange of nucleons between clusters. In this work the method of calculation of the potential energy and the collective spectrum of fissioning nucleus at scission point is presented. Combining the DNS model calculations and the statistical model of fission we calculate the angular distribution of fission fragments for the neutron–induced fission of 239Pu.     

Nuclear molecular structure in heavy mass systems

A study is made of nuclear molecular configurations involving one heavy mass partner. The stability of these configurations to mass flow and to fission is investigated as well as their population in fusion reactions. It is concluded that shell effects in combination with the effects of angular momentum may be important in stabilizing certain configurations. The spectrum of rotational and vibrational transitions within molecular configurations is investigated. For sufficiently mass-asymmetric systems the energies of vibrational transitions are comparable to the neutron separation energy. Gamma radiation from such transitions may then be observable above the background of statistical transitions. The gamma spectrum and the directional distribution of the radiation following fusion reactions with¹²C and¹⁶O are calculated.     

The determination of the Coulomb energy of a nuclear system at the scission point upon fission

The dependence of the Coulomb energy of deformed nuclei on the shape and the nuclear matter density distribution is considered. For an ellipsoidal shape of the nucleus and a homogeneous distribution of nuclear matter, the result was obtained in a simple analytical form convenient for further use. Separate attention was paid to the consideration of a Fermi-like distribution of nuclear matter using different shapes of the nucleus that reflect several different kinds of collective motions. After these considerations, the dependence of the Coulomb energy of the fission products at the scission point of binary fission reactions on configurations, shapes and nuclear matter distributions was investigated. Calculation of the dependence of the shape of the nuclei deformation parameters at the scission point from their total kinetic energies was made in detail. Finally, the influence of shell effects on the mass yield of fission products is discussed. The text was submitted by the authors in English.     

Semi-microscopical description of the scission configuration in the neutronless fission of 252Cf

The neutronless fission of ²⁵²Cf is studied in the frame of a molecular model in which the scission configuration is described by two aligned fragments interacting by means of Coulomb (+ nuclear) forces. The study is carried out for different distances between the fragments tips and excitation energies. For a given deformation, the fragment's total energy is computed via the constrained Hartree-Fock + BCS formalism. The total excitation energy present in the fragments is supposed to contribute only to the fragments deformation and the asymptotic value of the kinetic energy is equated to the inter-fragment potential at scission. These two constraints are yielding a few fission channels for a fixed tip distance and excitation energy. Discarding those fission channels corresponding to a disequilibrium in the sharing of the excitation energy between the two fragments, we establish the most likely scission configurations for a specified excitation energy. Received: 24 September 1999     

Axial Distributions of Fission Reaction Rates in the Annular Core of the ASTRA Critical Facility with Poison Profiling Elements in the Internal Reflector

Physics of Atomic Nuclei - Computational modeling of experiments on measurement of axial distributions of fission reaction rates in configurations of the ASTRA critical facility simulating a HTGR...     

A calculation of nuclear fissilities for medium-heavy nuclei

The results of a fission-spallation competition calculation for medium heavy nuclei are presented. The fission probabilities were calculated with different sets of fission barrier heights. A comparison with experimental fissility values for both photons and alpha-particles shows that a modified liquid drop model due to Krappe and Nix yields fission barrier heights in better agreement with experimental trends than are given by earlier versions of the liquid drop model. Quantitative determination of the fission barrier heights is prevented by uncertainties inherent in existing experimental data as well as in the fission-spallation competition calculations.     

On the kinetic energy of fission fragments with even and odd numbers of protons

In order to compare the distributions of the prompt energy release in the fission of a doubly even nucleus into even-Z and odd-Z fragments, the spectra of fragment kinetic energy and the coincident K X-rays were measured in a two-parameter mode with high statistical accuracy for the case of ²⁵²Cf spontaneous fission. By means of computer spectrum decomposition techniques data were obtained for average kinetic energies of fragments with even and odd atomic number. The comparison did not show any noticeable correlation of the mean fragment kinetic energy with oddness or evenness of the fragments.     

Macroscopic potential-energy surfaces for symmetric fission and heavy-ion reactions

We calculate the macroscopic potential energy of deformation for symmetric configurations of interest in fission and heavy-ion reactions. The shape of the system is characterized in terms of two moments of the matter distribution. These moments correspond to the distance between the centers of mass of the two halves of the system and to the elongation of each half about its center of mass. The configurations studied include a continuous sequence of shapes from the sphere to two-, three-, and four-fragment scission lines. Beyond the scission lines and prior to the line of first contact in heavy-ion reactions we represent the system in terms of separated oblate and prolate spheroids. The macroscopic energy is calculated as the sum of a Coulomb energy and a nuclear macroscopic energy that takes into account the finite range of the nuclear force. For systems throughout the periodic table we display the calculated energy as a function of the two moments in the form of contour maps. Some important features of the contour maps are the binary, ternary, and quaternary saddle points, the fission and fusion (or two-fragment) valleys, and the three- and four-fragment valleys. The maps illustrate how the topography of the potential energy changes as a function of the nuclear system considered. For example, as we move from lighter to heavier nuclear systems the binary saddle point moves from outside the point of first contact in heavy-ion reactions to inside the contact point. Because of this, the formation of a heavy compound nucleus requires additional energy relative to the maximum in a one-dimensional interaction barrier. The maps also illustrate for moderately heavy systems the presence of separate valleys for binary fission and fusion. For still heavier systems the ternary and quaternary saddle points are no longer present. This means that the ternary and quaternary valleys are accessible by paths that decrease monotonically in energy beyond the binary saddle point. Finally, for nuclear systems heavier than about ³⁰⁰120, the binary saddle point itself disappears, which in the absence of single-particle effects precludes altogether the formation of a compound system.     

Delayed fission of atomic nuclei (To the 50th anniversary of the discovery)

The history of the discovery of delayed nuclear fission is presented, and the retrospective of investigations into this phenomenon that were performed at various research centers worldwide is outlined. The results obtained by measuring basic delayed-fission features, including the fission probability, the total kinetic energy of fission fragments, and their mass distributions, are analyzed. Recommendations concerning further studies in various regions of nuclear map with the aim of searches for and investigation of atomic nuclei undergoing delayed fission are given. Lines of further research into features of delayed fission with the aim of solving current problems of fission physics are discussed.     

Transition fission states for heated nuclei

Induced fission reactions of fissioning compound nuclei that result from the capture of various incident particles (nucleons, γ rays, multiply charged ions) by target nuclei are investigated using the generalized nucleus model and the Wigner random matrix method. The effect produced on the fission widths of the compound nucleus by the competition between the excitation energies of its collective vibrational degrees of freedom that lead to its scission into fission fragments and its rotational and multi-quasiparticle states is analyzed. Bohr’s concept of transition fission states developed for near-barrier nuclear fission is generalized to the induced fission of nuclei with the excitation energies noticeably higher than the fission barriers. The temperature of the fissioning nucleus in the vicinity of the point of its scission into fission fragments is estimated.     

Determination of fragment isotopic yields in the fission of 252Cf accompanied by light charged particles

High resolution measurements of prompt γ-rays emitted from fission fragments accompanied by light charged particles (LCP) and those emitted from normal binary fission fragments in ²⁵²Cf fission were simultaneously carried out using a 30 cm³ Ge(Li) detector. A “sandwich” type of arrangement in the source-detector assembly was used to eliminate Doppler broadening of the γ-ray lines in both cases. About thirty γ-ray lines were assigned to specific fission fragments by comparison with the published results for binary fission, and the ratios of intensities of these γ-ray lines in LCP fission and binary fission were determined. Assuming that 2⁺ → 0⁺ transition intensities of doubly even isotopes are a measure of their yields, the yields of several such isotopes in LCP accompanied fission relative to that in binary fission were obtained.     

Description of true and delayed ternary nuclear fission accompanied by the emission of various third particles

The mechanisms and the features of the main types of nuclear ternary fission (that is, true ternary fission, in which a third particle is emitted before the rupture of the fissioning nucleus into fragments, and delayed ternary fission, in which a third particle is emitted from fission fragments going apart) are investigated within quantum-mechanical fission theory. The features of T-odd asymmetry in true ternary nuclear fission induced by cold polarized neutrons are investigated for the cases where alpha particles, prescission neutrons, and photons appear as third particles emitted by fissioning nuclei, the Coriolis interaction of the spin of the polarized fissioning nucleus with the spin of the third particle and the interference between the fission amplitudes for neutron resonances excited in the fissioning nucleus in the case of projectile-neutron capture being taken into account. For the cases where third particles emitted by fission fragments are evaporated neutrons or photons, T-odd asymmetries in delayed ternary nuclear fission induced by cold polarized neutrons are analyzed with allowance for the mechanism of pumping of large fission-fragment spins oriented orthogonally to the fragment-emission direction and with allowance for the interference between the fission amplitudes for neutron resonances.