Multiplicity distribution of prompt gamma rays in spontaneous ternary fission of252Cf

The first and the second moments of the multiplicity distribution of prompt gamma rays in spontaneous ternary fission of²⁵²Cf have been measured by the multiple coincidence technique. While both these moments were found to be nearly independent of the energy of the light charged particle accompanying the fission fragments, the width of the multiplicity distribution was larger than that in the case of normal binary fission by about 20%.     

Microscopic analysis of the fission barriers in <Superscript>256</Superscript>Fm and <Superscript>258</Superscript>Fm

The fission barriers of ²⁵⁶Fm and ²⁵⁸Fm have been analyzed in the HFB theory. The potential energy and the effective inertia parameter have been calculated in the two-dimensional deformation space of quadrupole and octupole moments. Fission paths for various octupole moments of the exit point from the fission barrier have been determined. The half-life along each path has been calculated. The shortest half-lives have been obtained for the paths with reflection symmetric shapes of nuclei in both the considered isotopes.     

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.     

Fission paths in Fm region calculated with the Gogny forces

The fission barriers of the nuclei ²⁵⁶Fm and ²⁵⁸Fm are investigated in a fully microscopic way up to the scission point. The analysis is based on the constrained Hartree-Fock-Bogolyubov theory and Gogny’s D1S force. The quadrupole, octupole, and hexadecapole moments, as well as the number of nucleons in the neck region, are used as constraints. Two fission paths, corresponding to bimodal fission, are found. The difference between fission of ²⁵⁶Fm and ²⁵⁸Fm is explained.     

CALCULATION OF THE NUCLEAR FISSION BY NUMERICAL SOLUTION OF F-P EQUATION

In this paper, the two-dimensional Fokker-Planck Equation is exactly solved by means of the numerical method. The velocity distribution at the saddle point, the second moments of the coordinate and velocity, and the time development of the nuclear fis-sion rate are studied. The maximum fission rate at a certain viscosity is exhibited by studying the dependence of the fission rate on the nuclear viscosity.     

An investigation of the properties of single-particle states in the second minimum of 237Pu

In connection with the recent measurement of the magnetic moments of the fission isomeric states in ²³⁷Pu, we investigate the following subjects: (i) The spin alignment of the lowest-lying states in a potential minimum which are populated by (α, 2nγ) reactions, and the fragment angular distributions in fission from isomeric states. (ii) The single-particle level scheme in a very deformed Woods-Saxon potential. (iii) The spin polarizability as a function of the quadrupole deformation.     

Dynamic treatment of ternary fission

The new dynamic model of light charged particle (LCP) formation in ternary fission is presented. The model is based on the assumption that light particles are formed as a result of two random neck ruptures during the time interval about one single-particle period. The connection of the final stage of ternary fission and of the saddle point descent stage was obtained in the framework of the density moments method. The analysis of LCP formation has shown that LCP mass and charge distributions are strongly governed by statistical nucleon exchange in the LCP-light fragment double system. New semiclassical expressions for the calculations of LCP yields and relative ternary fission probability are given. The results of calculations are in satisfactory agreement with the experimental data.     

Laser spectroscopy of cooled zirconium fission fragments

The first on-line laser spectroscopy of cooled fission fragments is reported. The r ions, produced in uranium fission, were extracted and separated using an ion guide isotope separator. The ions were cooled and bunched for collinear laser spectroscopy by a gas-filled linear Paul trap. New results for nuclear mean-square charge radii, dipole, and quadrupole moments are reported across the N=60 shape change. The mean-square charge radii are found to be almost identical to those of the Sr isotones and previously offered modeling of the radial changes is critically reviewed.     

Measurement of the fission moment of inertia of medium mass nuclides

Measurements have been made, by means of mica nuclear track detectors, of the distributions in tracklength and the angular distributions with respect to the beam direction for the fission fragments from the systems Ag, Te and Au plus 80-MeV alpha particles. Analysis of the tracklength distributions indicated that, in each case, full momentum transfer from the incident projectile characterized those interactions that led to fission. Angular-momentum dependent statistical model calculations for the decay of the respective compound nuclei then provided information on fission-evaporation competition in the de-excitation processes, and in particular the distribution in nuclear temperature and angular momentum at which the fission events took place. This information was then employed in the analysis of the measured fission fragment angular distributions, and to extractK ₀ ² values. From these, the moments of inertia of the fission saddle point shapes were calculated, and the results are in good agreement with theoretical estimates.     

Stationary Fokker-Planck equation applied to fission dynamics

By use of both analytical and numerical techniques, we study the relaxation of time-dependent solutions of the Fokker-Planck equation for an inverted oscillator to Kramers' stationary solution. This is done by integrating over all time the time-dependent solutions for given initial conditions at the saddle point to obtain stationary solutions, whose densities and higher velocity moments are compared as functions of the coordinate with the corresponding quantities calculated from Kramers' stationary solution. For large values of the coordinate an a symptotic expansion of the density is obtained, but for general values of the coordinate and for higher velocity moments the time integration must be done numerically. With increasing dissipation the relaxation to Kramers' stationary solution occurs at successively smaller values of the coordinate. By use of Kramers' stationary solution, we derive analytical expressions as functions of nuclear temperature and dissipation strength for several quantities of interest in fission dynamics, including the mean time from the saddle point to scission, the mean fission-fragment kinetic energy at the scission point and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom. We apply these results to some examples that have been studied experimentally, including the mean saddle-to-scission time for the heavy-ion-induced fission of the compound nucleus ¹⁶⁸Yb and the mean fission-fragment kinetic energy at scission and the contribution to its variance for the α-particle-induced fission of the compound nucleus ²¹³At.     

Fragment angular momenta in low and medium energy fission of242Pu

Independent isomeric yield ratios of¹²⁸Sb were determined radiochemically in the thermal neutron induced fission of²⁴¹Pu and 34 MeV alpha particle induced fission of²³⁸U, both involving the same compound nucleus (²⁴²Pu). Fragment angular momenta estimated from the measured isomer ratios using the statistical model analysis showed significantly larger fragment angular momenta in the medium energy fissioning system compared to the low energy fissioning system. This has been attributed to the effect of higher excitation energy and angular momentum in the entrance channel leading to increased fragment temperature, moments of inertia and angular velocity. An attempt was made to calculate the fragment angular momentum in the medium energy fission using the Fermi gas model for the fissioning nucleus, taking into account the multichance fission, saddle shapes of the fissioning nuclei and the angular velocity components of the fissioning nuclei both along and orthogonal to the fission axis. The calculated angular momenta agree well with the experimental results.     

EFFECTIVE MOMENT OF INERTIA OF MEDIUM MASS NUCLEI AT THE SADDLE POINT

The angular distributions of fission fragments are measured for systems of 120MeV ¹⁴N+¹¹⁸Sn with mica track detectors and gold-surfacebarrier silicon detectors. The measured angular distributions can be fitted by the standard theory of fission angular distributions on the basis of statistical model. The effective moments of inertia of fissioning nuclei at saddle point are derived from angular distribution anisotropies. The shapes of saddle point of fissioning nuclei in the region of Z²/A<30 are discussed.     

Hyperdeformation and clustering in the actinide region

The excitation energy spectrum of fission resonances has been measured with high energy resolution using the ²³⁵U(d,pf) reaction in order to study hyperdeformed (HD) rotational bands and HD nuclear shapes. The moments of inertia of the rotational bands and the energy of the ground state in the third minimum were determined. Another signature of these highly deformed states, their enhanced α decay, was also observed. By studying cold or compact fission in the ²³²Th(n,f) reaction around HD resonances, we obtained data for heavy clustering.     

Comparison between the symmetric fission and fusion paths

The symmetric fission path leading to smooth extended shapes and the fusion or new fission path going through the two tangent sphere configuration are investigated within the liquid-drop model including the nuclear proximity energy. Analytical formulae are given for the various shape-dependent functions which govern the dynamics. The quadrupole moment, the perpendicular moment of inertia and the Coulomb energy are similar in the two paths. In contrast, the neck radius, the rupture point between the fragments, the parallel and effective moments of inertia, the surface energy and the critical angular momentum against fission are quite different in the two valleys. The introduction of the proximity energy strongly lowers the deformation energy in the fusion valley and for the light, medium and very heavy nuclei the barrier heights are nearly equal in the two paths. This flattening of the potential surface by the proximity forces allows to better understand the sudden transition between the one- and two-body configurations.     

Static electric quadrupole and hexadecapole moments of nuclei

Ground-state static electric quadrupole and hexadecapole moments of even nuclei are calculated microscopically. Rare-earth, actinide and neutron-deficient nuclei with 50 <Z, N < 82 and neutron-rich nuclei with 28 < Z < 50, 50 < N < 82 are studied. Fairly good agreement with experiment is found. In the actinide region, the electric moments of fission isomers are also examined.     

Angular and spin distributions of primary fission fragments

It is demonstrated that the formation of the fissile nucleus prescission configuration with two fission prefragments connected by a neck is possible only with the simultaneous appearance of high values of relative orbital moments [(L)\vec]\vec L of the abovementioned prefragments, independently of their form. It is found that conservation of the fissile nucleus spin when its values are low leads to the formation of high values of prefragment spins [(J)\vec]₁\vec J_1, [(J)\vec]₂\vec J_2 that are oriented antiparallel to the moment [(L)\vec]\vec L and perpendicular to the fissile nucleus symmetry axis. It is shown that for two deformed fission prefragments, the pumping mechanism of high values of their relative moments [(L)\vec]\vec L and spins [(J)\vec]₁\vec J_1, [(J)\vec]₂\vec J_2 is due to the combined influence of bending- and wriggling- vibrations, the latter predominating. It is found that the high values of spherical fission prefragments are not related to thermal excitations but is determined by the excitation of the initial high-spin double quasiparticle states, due to the nonadiabatic collective deformation motion of the fissile nucleus in the vicinity of its rupture point.     

Statistical emission of large fragments: A general theoretical approach

A theory for the statistical emission of large fragments is developed. In analogy with the fission saddle point, a ridge line in the potential energy surface is defined which controls the decay width of the system into any two given fragments. The normal modes at the ridge are separated into three classes: decay modes, amplifying modes, and non-amplifying modes. Amplifying modes are those whose thermal fluctuations are amplified and lead to a broadening of the kinetic energy distribution. Analytical expressions for the kinetic energy distributions are developed for various combinations of amplifying and non-amplifying modes. The limit for large amplifications is a Gaussian kinetic energy distribution. The limit for no amplification is a Maxwellian-like distribution. Thus the formalism comprehends the fission decay on one hand and the neutron evaporation on the other. The angular distributions are evaluated in terms of the ridge line principal moments of inertia. A general analytical expression has been derived which predicts, correctly in both limits, the angular distributions of the evaporated neutrons and of the fission fragments.     

Fission of highly excited fragments from collisions of 750 A.MeV 238U-ions on 208Pb

Fragments of relativistic 750 A.MeV U-projectiles were investigated by using the fragment separator FRS for magnetic selection of reaction products including ray-tracing and ΔE-ToF techniques. For elements between Ge and Sb, measurements of isotopic yield distributions and velocities revealed three processes: fragmentation, low-energy fission, and high-energy fission. The last of these regimes is presently reported. First and second moments of distributions of mass numbers, atomic numbers and velocities of the corresponding fragments allowed us to identify ¹⁰¹ ₄₃Tc₅₆ as the most probable fragment of a high energy symmetric fission reaction. Moreover, we could deduce a hypothetical mean fissioning fragmentation product ²⁰⁸Rn and its highly excited pre-fragmentation parent ²²⁷Ra produced in a primary abrasion reaction at an excitation energy of about 290 MeV. Received: 26 January 1998 / Revised version: 16 March 1998     

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.