Collective mass parameters in the nuclear fission process

The theory of nuclear fission process is considered. The effective mass parameters are calculated as a function of the following collective coordinates: the separation between the centres of harmonic oscillators, the mass asymmetry parameter and the necking parameter. Numerical calculations are carried out for the fission of²³⁶U and²³⁸U nuclei. Symmetric and asymmetric cases are considered. From the present calculation we see the importance of taking into account the necking parameter as a dynamical collective coordinate.     

Dynamical Behaviour of the Mass Asymmetry Mass Parameter in Nuclear Fission

The theory of nuclear fission is reconsidered. We study the behaviour of the mass parameter as a dynamical quantity of the mass asymmetry. The dependence of the mass asymmetry mass parameter is studied as a function of the five collective coordinates. These parameters are reconsidered by including the temperature to show the temperature dependence of the mass parameter. The cranking model is used in developing all the mathematical and theoretical expressions. Numerical calculations of the obtained analytical expressions are carried out for the two fissioning nuclei ²³⁶U and ²³⁸U. The mass asymmetry mass parameters are calculated including the temperature as a function of the different five collective coordinates. The present study shows that the values of this mass asymmetry mass parameters are stable against the change of the temperature for temperature values greater than 1 MeV for all the different five collective coordinates.     

Sequential fission angular distributions from mass-asymmetric heavy-ion reactions

The angular distributions of sequential fission fragments have been measured for the reactions of ⁴⁰Ar with ¹⁹⁷Au and ²³⁸U as a function of reaction Q-value and charge transfer. These angular, distributions are used to study the angular momentum and alignment of the deep-inelastic products which undergo fission. All of the fission fragment angular distributions are strongly focused into the plane defined by the beam and the projectile-like fragment velocity vectors. The in-plane angular distributions from reactions with uranium are isotropic for small energy losses and become anisotropic as the energy loss increases. For large negative Q-values, the in-plane anisotropy increases as the deep-inelastic products become more symmetric. The variation of the in-plane anisotropy with mass asymmetry for the two systems in this work was compared to a compilation of previous work and a consistent pattern was found. These alignment data are compared to equilibrium statistical calculations.     

Nuclear charge distribution of heavy fission fragments from thermal-neutron-induced fission of235U

Fragments from thermal-neutron induced fission of²³⁵U have been separated by a mass spectrometer with respect to their masses and kinetic energies within 1 μsec. The separation principles are briefly described. For masses 130 to 139 amu the charge distributions have been determined by counting the number of beta tracks emitted from the individual mass selected fission fragments in a nuclear photographic emulsion. In another method, the average number of beta particles for each fragment mass is determined by use of a 4π-proportional counter. The mean nuclear charge as a function of mass is compared with other experimental results and theoretical curves. Contradictory to the radiochemical results, this experiment yields a dip in the mean nuclear charge versus mass curve at mass 132 amu corresponding to the doubly magic nucleus (N=82,Z=50)¹³²Sn. Recent theoretical calculations of Nörenberg are in agreement with this finding.     

Correlation between fragment mass-distribution fine structure,charge distribution and nuclear structure for thermal-neutron-induced fission of 233U and 235U

Masses corresponding to observed fine-structure peaks in the fragment mass distributions for thermal-neutron-induced fission of ²³³U and ²³⁵U are shown to correspond to average measured masses for even-even nuclear charge splits. Evidence is presented that the yield enhancement for even-Z fragments is not restricted just to fission events with higher-than-average total kinetic energy. The anomalously high yield of fragments with mass 134 in ²³⁵U(n, f) as opposed to ²³³(n, f) is tentatively correlated with rapidly changing nuclear structure properties as a function of the mass of the complementary light (Z = 40) fragments.     

Electromagnetic fission of238U at 600 and 1000 MeV per nucleon

Electromagnetic fission of²³⁸U projectiles at E/A =600 and 1000 MeV was studied with the ALADIN spectrometer at the heavy-ion synchrotron SIS. Seven different targets (Be, C, Al, Cu, In, Au and U) were used. By considering only those fission events where the two charges added up to 92, most of the nuclear interactions were excluded. The nuclear contributions to the measured fission cross sections were determined by extrapolating from beryllium to the heavier targets with the concept of factorization. The obtained cross sections for electromagnetic fission are well reproduced by extended Weizsäcker-Williams calculations which include E1 and E2 excitations. The asymmetry of the fission fragments' charge distribution gives evidence for the excitation of the double giant-dipole resonance in uranium.Communicated by V. Metag     

Nuclide yields of light fission products from thermal-neutron induced fission of 233U at different kinetic energies

The yields of light fission products from thermal-neutron induced fission of ²³³U are measured as a function of their mass A, their nuclear charge Z, their kinetic energy E and their ionic charge state q at the recoil spectrometer Lohengrin of the Institut Laue-Langevin in Grenoble. The mass yields are determined by intercepting the fragments with an ionization chamber of high energy resolution positioned at the focal plane of the spectrometer. The nuclear charges and their yields are determined with the same ionization chamber by measuring the residual energy of fission products, selected monoenergetically by Lohengrin, behind a passive absorber made of parylene-C. The nuclear charge resolution enabled by this detector device is considerably improved to Z/dZ = 58. The nuclear charge and mass distributions summed over all ionic charge states are listed within the mass range 79 ⩽ A ⩽ 106 at 6 energies: E = 85.34, 90.41, 95.46, 100.50, 105.55 and 110.55 MeV. The energy-integrated nuclear charge and mass yields are also given. The isotonic and isotopic yields are shown. An odd-even effect in the yields is found for the protons as well as for the neutrons at all kinetic energies. The yield weighted total odd-even effect for the protons is found to be (22.1 ± 2.1)%, for the neutrons (5.4 ± 1.7)%. An odd-even effect for the protons in the mean kinetic energy is also observed. The displacement of the mean isobaric nuclear charges from the unchanged charge-density values and the variances of the isobaric nuclear-charge distributions reveal fine structures in their mass dependences.     

Threedimensional dynamics of nuclear decay modes

We study nondissipative fission dynamics in a wide range of mass asymmetry, covering three groups of nuclear decay modes: cluster radioactivities; alpha-decay and cold fission. The WKB action integral is calculated by using the Werner-Wheeler inertia tensor and the deformation energy within Yukawa-plus-exponential model extended to binary systems with different charge densities. The optimum dynamical trajectory in a threedimensional deformation space (elongation, necking-in and mass-asymmetry) is determined by solving a nonlinear system of differential equations. This new method is illustrated for three decay modes of²³⁴U:α-decay, Mg-radioactivity and cold fission with¹⁰⁰Zr as a light fragment.     

Medium energy proton induced fission in Tb,La and Ag

Coincidence studies with silicon surface barrier detectors have been used to determine fragment kinetic energies, angular correlations and fission cross sections in the fission of Ag,¹³⁹La,¹⁵⁹Tb and U nuclei induced by 600 MeV protons. Symmetric mass distributions are deduced for Ag and Tb, whereas La shows an indication of a stable asymmetric mass distribution. We find no indication of the Businaro-Gallone point. Fission-spallation competition calculations are used to deduce values of macroscopic fission barrier heights and nuclear level density parameter values at deformations corresponding to the saddle point shapes. We find macroscopic fission barriers lower than those predicted by macroscopic theories. The total kinetic energies at symmetric mass divisions follow closely the Viola prediction.     

The study of prompt and delayed muon induced fission

Mass yield and total kinetic energy release (TKE) distributions of fragments from prompt and delayed muon induced fission, separately, have been measured for the isotopes²³⁵U,²³⁸U,²³⁷Np and²⁴²Pu. The distributions from prompt muon induced fission are compared with the corresponding distributions from hadronic reactions and from spontaneous fission (s.f.). The distributions from the delayed muonic fission processes are compared to the distributions for neutron and proton-induced fission. No mass distributions measured in the prompt muonic fission process show any signature, which can be attributed to the presence of the muon. Differences observed between the TKE distributions of prompt muon induced and hadron induced fission can be explained by the screening effect of the negative charge of the muon bound in the orbit of one of the fission fragments. The observed yield of symmetric muon induced fission was found to be defined merely by the value of the excitation energy.     

Coulomb effects in low energy fission

The structures in the total kinetic energy (TKE) distributions in cold fission of²³⁴U and²³⁶U are interpreted in terms of the Coulomb interaction energy (C) between fragments at the scission point. The maximal value ofC, C _max, corresponding to the most compact scission configuration, is calculated for several mass fragmentations. It is shown that withQ being constant,C _max increases if one increases the charge asymmetry for a given primary fragmentation. This condition produces oscillations with a period of approximately 5 amu ofC _max as a function of the light fragment mass which are correlated with the observed oscillations of the maximal value of TKE. Moreover, the enhancement of the yields of the more asymmetric charge fragmentation for a given fragmentation is explained.     

Experimental studies of nuclear fission dynamics near the scission point

Conditions for formation of angular and energy distributions of light particles emitted in ternary fission of ^{233, 235}U, ²³⁹Pu, and ²⁴⁵Cm nuclei induced by cold polarized neutrons have been studied in the course of investigating T-odd asymmetry in emission of these particles with respect to the plane formed by the fission axis and the polarization axis of the fissioning nucleus. The results obtained lead to the conclusion that in ternary fission charged particles are emitted by the fissioning nuclear system rotating around the polarization direction.     

Symmetric and asymmetric fission modes in proton-induced fission at 660 MeV of <Superscript>238</Superscript>U

Fission product cross sections of intermediate-energy fission of ²³⁸U were used in order to construct the charge and mass yield distributions. Enriched target of ²³⁸U was irradiated by proton beam with energy 660 MeV for several hours at the LNP Phasotron, Joint Institute for Nuclear Research (JINR), Dubna, Russia. The charge distribution of the fission fragments was analyzed for calculation of isobaric cross sections. The mass yield curves were expanded into symmetric and asymmetric components according multimodal fission approach. The fissility values of actinides were calculated at given proton energy. The obtained results have been compared to the same data for targets ²³⁷Np and ²⁴¹Am.     

Prompt gamma radiation from fission fragments due to the Strutinsky-Denisov polarisation

The hard electric dipole radiation from fission fragments of ²³⁵U by thermal neutrons is predicted. The radiation arises due to the Strutinsky-Denisov-induced polarisation mechanism. The probability of the radiation is at the level of 0.0025 per fission, which is in agreement with experiment. The angular distribution exhibits left-right asymmetry with respect to the plane perpendicular to the neutron polarisation axis. That means that the emission of gamma quanta at the given angle depends on the neutron polarisation. The asymmetry is at the level of 10^-3. This effect is similar to that observed earlier for gamma quanta in binary and alphas in ternary fission. The study of this effect will give information about dissipation of the collective energy of the surface vibration in fragments with large amplitude, and gives a picture of the process of snapping back the nuclear surface.     

Nuclear charge distribution of mass-separated isobars from thermal-neutron-induced fission of 235U

The nuclear charge distribution of fission products with mass numbers A = 90, 91, 94, 99, 100, 101 and 104 provided by the mass separator “Lohengrin” was measured. Adjacent elements in the group of the light fission products could be separated by their different energy loss in a carbon absorber. The Z-yields were found to be strongly dependent on the kinetic energy of the fission products. The widths of the nuclear charge distributions are very small, in general, and strongly dependent on A as well as on the kinetic energy. The influence of the neutron evaporation and odd-even effects are clearly detected. An asymmetric nuclear charge distribution was found for A = 104 indicating the suppression of fission fragments with Z = 43. The average nuclear charges of the fission products at their average kinetic energy are in good agreement with the results from measurements of the number of β-decays and K X-ray measurements. The average nuclear charge of the isobar A = 132 was measured at its average kinetic energy with a calibrated secondary electron detector to be Z = 51.14 ± 0.15 which is in very good agreement with the radiochemical results. Thus previous physical measurements indicating a large independent yield for the doubly magic nucleus ¹³²Sn could not be confirmed.     

Shell effects in the evolution of the mass asymmetry in heavy-ion collisions leading to composite systems withZ=108

Fragment mass distributions are presented obtained in the heavy-ion reactions²²Ne+²⁴⁹Cf,³²S+²³⁸U,⁴⁰Ar+²³²Th and⁵⁶Fe+²⁰⁸Pb leading to composite systems with equal nuclear charge numberZ=108. The experiments were performed at the heavy-ion cyclotron U 300 of the Laboratory of Nuclear Reactions in Dubna. The spectrometer DEMAS was used to measure the time-of-flight values and the laboratory angles of the correlated fragments. The shape of the mass distributions strongly depends on the initial mass asymmetry. When decreasing the bombarding energy down to values near the Coulomb barrier, the mass distributions obtained in the reactions³²S+²³⁸U and⁴⁰Ar+²³²Th exhibit relative maxima ofM≈205 interpreted to be due to stabilizing effects of nuclear shells during the fragmentation process.     

Mass and charge distributions in the very asymmetric thermal neutron induced fission of the odd-Z nucleus 242mAm

Yields of light fission products (A = 68, 70–84, 87, 88, 94, 96, 98, 102 and 106–108), their kinetic energies and nuclear charge distributions (A = 71–84, 87 and 88) in the thermal neutron induced fission of the odd-Z nucleus ^242mAm(Z = 95) were measured using the mass-separator Lohengrin at the Institute Laue-Langevin in Grenoble (France). The mass yield curve shows a fine structure at A = 70, probably due to shell and/or odd-even effects affecting also the nuclear charge distribution. The analysis of isotopic chain yields gives evidence for a very low excitation energy of the lightest fission fragments observed. A preferential formation of fragments with even Z is found for this odd-Z compound nucleus. Calculated values for the local odd-even effect are comparable with those for the neighbouring even-Z fissile nuclides and increase from 13% to 30% with increasing asymmetry of the mass split (A_L = 84 to 68 and Z_L = 35 to 28). The neutron odd-even effect shows a similar but less pronounced behaviour.     

Investigation of parity violation and interference effects in the angular distributions of fragments originating from 233U fission induced by resonance neutrons

Three interference asymmetry effects in the angular distributions of fragments originating from ²³³U fission induced by resonance neutrons were measured. The energy dependences of the asymmetry factors being studied show sizable irregularities that are associated, according to modern theory, with the interference of s and p resonances at the stage of a compound nucleus. The basic features of weak p-wave resonances in the low-energy region were obtained from a global theoretical analysis of the asymmetry factors as functions of energy. The first estimates of nuclear matrix elements of weak interaction were derived for a few p-wave resonances.     

Theory of mass-yield distributions in “quasi-fission” reactions

A two-step process of “fission after a few nucleon transfer” is studied for the mass-yield distributions in the reaction of 605 MeV⁸⁴Kr ions with²³⁸U. The general agreement between the theory and experiment is qualitatively good. Based on the phenomenological considerations, sequential fission is also included partially. The transfer process is also shown to be given by the charge dispersion calculations.