Multidimensional dynamical-statistical model for describing the fission of excited nuclei

A multidimensional stochastic model for describing the decay of excited nuclei is presented. The model takes into account the dynamics of thermal fluctuations of collective variables, the dissipation of the kinetic energy of collective motion, and the emission of light particles from excited nuclei. The potential energy of a deformed nucleus is calculated within the liquid-drop model with a sharp surface and within the finiterange-interaction model. The friction parameters are calculated on the basis of the one-body-dissipation model. The inertia parameters are found in the Werner-Wheeler approximation. The drift components of forces are determined in terms of the entropy of an excited nucleus. The latter in turn is computed within the Fermi gas approximation with allowance for the deformation dependence of the density-level parameter. The fission probability, the mean multiplicity of neutrons emitted prior to scission (prescission neutrons), and the variances of the mass distributions of fission fragments at the most probable kinetic-energy value are calculated on the basis of the model developed here and are compared with experimental data. The dependences of these quantities on the model parameters are considered in detail.     

Spontaneous fission in actinides and heavy elements: A semiclassical view

The systematics of spontaneous fission in actinides and heavy elements are investigated within the framework of the semiclassical quantization. The interaction barrier is calculated by using the asymmetric two-centre shell model and its appropriate parameterization generates the analytical expression for the tunneling probability. The powerful semiclassical quantization technique lifts the degeneracy between the degenerate levels just after tunneling across the barrier. Our results clearly show that dissipation enhances the tunneling rate. It has also been seen that the sub-barrier fission from the excited state is a slow process. An appropriate condition for the fission isomeric state is also pointed out. The survival probability of heavy elements is a remarkable outcome of our model. We have tested our model for nuclei ₉₂ ²³⁶U , ₉₈ ²⁵²Cf , ₁₀₀ ²⁵⁴Fm and ₁₀₂ ²⁵²No .     

Search for heavy neutron clusters in nuclear fission

An experiment on search for heavy neutron clusters in fission of ²³⁵U nuclei has been carried out on a nuclear reactor. The method of searching for neutron clusters is based on irradiation of tellurium dioxide and lead oxide targets in reactor channels near the active zone and far from it. The method of γ-spectrometric analysis of irradiated targets was used to search for nuclei whose occurrence in the targets cannot be explained by other nuclear reactions, except for the reactions of original target nuclei with neutron clusters. The reactions of tellurium and lead nuclear fission by neutron clusters (nuclei) and direct capture of neutron clusters have been revealed.     

Results of search for heavy neutron clusters in nuclear fission

Experiments on search for heavy neutron clusters in the reaction of induced fission of ²³⁵U nuclei by neutrons have been carried out on the nuclear reactor, using the activation method. Two hypothetical reactions have been investigated: ⁹²Mo, ⁹⁴Mo, ⁹⁵Mo, ⁹⁶Mo, ⁹⁸Mo, ¹⁰⁰Mo(^xn, (x ? k)n)¹⁰⁵Mo → ¹⁰⁵Tc → ¹⁰⁵Ru → ¹⁰⁵Rh → ¹⁰⁵Pd, with a minimum transfer of 5 to 13 neutrons to activated Mo isotopes, and ¹²²Te(^xn, (x ? k)n)^{122 + k} Te → (β^?) → ^{122 + k} I, with a minimum transfer of 10 neutrons to activated ¹²²Te isotope. Radiochemical methods for selecting technetium isotopes from molybdenum and iodine from tellurium were used. For the first reaction, the upper limit on the probability of neutron cluster formation was found to be P _k ≤ 10^?8 per fission. For the second reaction, indications to the existence of heavy neutron clusters were obtained.     

Stochastic model of tilting mode in nuclear fission

A model of induced nuclear fission was developed with consideration of thermodynamically fluctuating orientation degree of freedom (tilting) of deformed nuclei. This model was applied to analysis of the experimental angular anisotropy of fission fragments in the ¹⁶O + ²³²Th, ²³⁸U, ²⁴⁸Cm, ²⁰⁸Pb, ²⁰⁹Bi; ¹²C + ²³⁶U; ¹⁹F + ²⁰⁸Pb; and ¹¹B + ²³⁷Np reactions. Information on the equilibrating time of the tilting mode was obtained. The text was submitted by the authors in English.     

A dumbbell model with five parameters describing nuclear fusion or fission

We propose a five-parameter dumbbell model to describe the fusion and fission processes of massive nuclei, where the collective variables are: the distance ρ between the center-of-mass of two fusing nuclei, the neck parameter ν, asymmetry D, two deformation variables β₁ and β₂ . The present model has macroscopic qualitative expression of polarization and nuclear collision of head to head, sphere to sphere, waist to waist and so on. The conception of the "projectile eating target" based on open mouth and swallow is proposed to describe the nuclear fusion process, and our understanding of the probability of fusion and quasi-fission is in agreement with some previous work. The calculated fission barriers of a lot of compound nuclei are compared with the experimental data.     

A multiparameter system for heavy nuclei fission study

A multiparameter system designed to measure as many as six parameters of a single fission event on line with an EC 1010 computer is described. The kinematics of emitted fragments and the calibration of light particle and fragment spectra are discussed. Fragment energy spectra from the thermal neutron induced fission of²³⁵U have been measured. Results of light particle emission from spontaneous fission of²⁵²Cf and from neutron induced fission of²³⁵U are presented.Dedicated to Professor Ivan Úlehla on the occasion of his sixtieth birthday.We would like to thank the following collaborators for their help and support during the course of these experiments: E. Kuli for the improvement of various measuring devices, J. Hoffmann, J. Badura and J. Novotny for the construction of the stabilization system, and J. ech and M. Keller for the construction of the real time interface unit. We are thankful to Z. Kosina for information accorded during the preparation of the data processing codes.     

Microscopic calculations of fission barriers and critical angular momenta for excited heavy nuclear systems

An extended version of Strutinsky's macro-microscopic method is used to calculate effective potential energies for rotating, excited heavy compound nuclei undergoing fission. Nuclear deformation is parameterized in terms of Lawrence's family of shapes. A two-center single-particle potential corresponding to these shapes is employed, with BCS pairing added. Statistical excitation is introduced by temperature-dependent occupation of (quasi-) particle energy levels. We calculate shell corrections to the energy, the free energy and the entropy as functions of deformation and temperature. The associated average quantities are derived from a temperature-dependent liquid drop model. The resulting static deformation energy is augmented by the rotational energy to yield the isothermal effective potential energy as a function of deformation, temperature and angular momentum. Moments of inertia are obtained from the adiabatic cranking model with temperature-dependent pairing included.We have also calculated the effective potential for constant entropy rather than constant temperature. Although this isentropic process physically is more appropriate than the isothermal process, it has not been treated before. For the same amount of excitation energy in the spherical state of the compound nucleus, the isentropic barriers turn out higher than the isothermal ones. For both processes we have extracted the critical angular momentum (defined as the one for which the barrier approximately vanishes) as a function of excitation. Our model is applied to the super-heavy nuclei ²⁷⁰110, ²⁷⁸110, ²⁹⁸114, ²⁹²118 and ³²²128, which have been tried to form in krypton and argon induced heavy ion reactions.     

A quark signature in the nuclear fireball model of heavy ion collisions

It seems possible that a definite quark matter signature may be observed in the near future in nuclear heavy ion collisions. For example, in experiments yielding a fireball temperature of at least 180 MeV, a lab energy of ～ 11 GeV/nucleon must be reached for a ²⁰Ne + U collision. These energies should be sufficient to produce quark matter in the fireball. The signature of this transition is observed by comparing particle spectra at higher energies. It is expected that once quark matter is reached the spectrum will remain constant at temperature greater than ～ 180 MeV, rather than continue to change with energy.     

Cluster aspects of nuclear fission

Experimental fission data for nuclei in the mass regionA = 210 toA =258 are discussed from a unified point of view using cluster representations of nuclei. It is shown that these data can be described as resulting from a superposition of two different modes, one determined by energetically favoured cluster correlations, the other due to liquid-drop effects only. For all nuclei lighter than Fermium the above distinction coincides with that of symmetric and asymmetric fission. Contrary to that in Fermium-isotopes, both symmetric and asymmetric fission are associated with energetically favoured cluster correlations at the Fermi surface.     

A double core model for fission

A fission model formed of two cores of stable nuclei is proposed. Fission is viewed as a neutron excess problem. Suggested yield formula takes account of the core stabilities, the neutron excess and neutron acceptibility of the cores.     

A semi-classical model for asymmetric fission

An asymptotic expansion for the smooth and fluctuating parts of the level density for deformed nuclei is used for the calculation of fission maps.     

Separation of Coulomb fission from nuclear fission at medium energies

The cross sections for fission induced by one neutron transfer and by the electromagnetic field in the reaction 24.3 MeV/u ²³⁸U + ¹⁹⁷Au are calculated and compared to the experimental data. It turns up that the two calculated cross sections differ by five orders of magnitude at a distance of closest approach of 25 fm. It is shown that in the experiment in which one is able to select the events corresponding to a large distance of closest approach, a separation of Coulomb fission from nuclear fission events can be efficiently obtained.     

Angular correlations in nuclear fission

Interference effects in the angular distributions of products originating from binary and ternary nuclear fission induced by slow neutrons are reviewed.     

Energy partition in nuclear fission

A scission point model (two spheroid model TSM) including semi-empirical, temperature-dependent shell correction energies for deformed fragments at scission is presented. It has been used to describe the mass-asymmetry-dependent partition of the total energy release on both fragments from spontaneous and induced fission. Characteristic trends of experimental fragment energy and neutron multiplicity data as function of incidence energy in the Th — Cf region of fissioning nuclei are well reproduced. Based on model applications, information on the energy dissipated during the descent from second saddle of fission barrier to scission point have been deduced.     

Interference effects in nuclear fission

Various interference effects governing the character of angular distributions of binary and ternary nuclear fission products and P-odd, P-even, and T-odd asymmetries in these angular distributions have been studied within the quantum theory of spontaneous and low-energy induced nuclear fission.     

Viscosity coefficients for nuclear fission

An expression for the energy dissipation during nuclear fission (or heavy-ion) processes has been derived in the first-order viscosity approximation. Irrotational flow and incompressibility have been assumed in order to calculate a quadratic form for the heat production, microscopically interpreted as particle-hole excitations. A modified algebraic parameterization of the nuclear shape has been found, which is more suitable than the usual ones to describe shapes close to spheroids (or spheres). Furthermore, it allows for analytical solutions of the fluid equations for one degree of freedom (and in special eases of the nuclear shapes, for all degrees).