Mass Distributions and Charge Dispersion for the Nuclear Fission

The theory of nuclear fission is reconsidered by introducing the charge asymmetry in the asymmetric two center shell model as a dynamical collective coordinate. The quantum mechanical fluctuations, which are accompanied with the collective motion as a function of the mass asymmetry, are responsible for the mass distributions in nuclear fission. Numerical calculations are carried out for the mass distributions and charge dispersions for the nuclear fission of the ²³⁶U and ²³⁸U nuclei. The present obtained theoretical calculations are in good agreement with the experimental measurements.     

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.     

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.     

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.     

Effect of the orientation degree of freedom on the rate and time of fission of highly excited nuclei

The effect of the dimensionality of the dynamical model used on the fission rate and mean time is studied within a multidimensional stochastic approach to fission dynamics. These features of fission of excited compound nuclei are calculated within four-dimensional Langevin dynamics, where the coordinate K, which is the projection of the total angular momentum onto the symmetry axis of the nucleus being considered, is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, a} parametrization. The evolution of this orientation degree of freedom (K mode) is described in terms of the Langevin equation in the overdamped regime. The effect of the orientation degree of freedom on the rate and mean time of fission of compound nuclei is studied. The introduction of the orientation degree of freedom is shown to lead to a substantial decrease in the fission rate and, accordingly, to an increase in the mean fission time upon going over from the three- to the four-dimensional model. The reactions induced by the interaction of ¹⁴N and ¹⁶O projectile ions with ¹⁹⁷Au, ²⁰⁸Pb, ²³²Th, and ²³⁸U nuclei at energies above the Coulomb fusion barrier are considered. The effect of the increase in the fission time because of the introduction of the K mode is so strong that it compensates almost completely for an opposite effect from introducing, in the one-dimensional model, the second and third collective coordinates that take into account, respectively, the evolution of the neck in the nuclear shape and the mass asymmetry. Ultimately, the difference between the results in the four- and one dimensional problems is not more than 5 to 25% for the reactions considered here.     

The dynamical description of the mass distribution of fission fragments

The variances of the mass distribution of fission fragments for nuclei in the fissility parameter range 30 < Z²/A < 40 have been calculated. The Fokker-Planck equation for the distribution function of collective variables is used as a dynamical equation to describe the descent of the fissioning nucleus from the saddle to scission. The calculations reproduce the experimentally observed increase of the mass variances with a growth of the parameter Z²/A. The increase of the calculated variances is due to a considerable decrease in the stiffness coefficients corresponding to the saddle points for heavy fissioning nuclei and to the non-equilibrium character of the descent.     

Description of the two-humped mass distribution of fission fragments of mercury isotopes on the basis of the multidimensional stochastic model

The dynamical model proposed earlier for describing fusion-fission reactions is applied to describing the two-humped mass distribution of fission fragments of mercury isotopes. In this model, the calculation of the time evolution of collective coordinates of the system is broken down into two stages. The first stage is that within which the projectile approaches the target nucleus, while the second is that of the evolution of the system formed after the touching of the projectile and target nuclei. The dynamical evolution of the system within both stages of the calculation is described on the basis of Langevin equations. The shell structure of colliding nuclei is taken into account at either stage of the calculation. Mass distributions are calculated for fragments originating from the fission of the mercury isotopes ^{190, 184}Hg formed in the fusion-fission reactions ⁴⁸Ca + ¹⁴²Nd → ¹⁹⁰Hg and ⁴⁰Ar + ¹⁴⁴Sm → ¹⁸⁴Hg. The process in which the isotope ¹⁸⁰Hg undergoes fission from the ground state is also calculated. The results obtained in this way are compared with the results of previous theoretical calculations and with available experimental data.     

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.     

Fine structure in 14C cluster emission from 225Ac

A fine structure in the ¹⁴C decay of ²²⁵Ac is predicted quantitatively by accounting dynamical aspects during the disintegration process. Transitions to the excited states of the daughter nucleus are considered to be mainly directed by the Landau–Zener promotion mechanism in the region of avoided crossing levels. The level scheme is evaluated with the superasymmetric two–center shell model. The half–lives are computed considering the cluster decay as a superasymmetric fission process. Received: 31 July 1998 / Revised version: 27 November 1998     

Variation of total kinetic energy and mass distributions in the fusion-fission reaction of 16O,19F + 209Bi at near barrier energies

Fission fragment mass and energy distributions and their correlations have been measured for the ¹⁶O and ¹⁹F + ²⁰⁹Bi reactions over a wide range of excitation energies ( E ^* = 30-50 MeV). It is observed that in the case of ¹⁶O + ²⁰⁹Bi reaction, the average total fragment kinetic energy, <TKE> is nearly independent of the bombarding energy. However, in the case of ¹⁹F + ²⁰⁹Bi reaction, the average total kinetic energy of the fission fragments shows a peaking behaviour near the barrier. The variation in <TKE> at near barrier energies in the ¹⁹F + ²⁰⁹Bi system seems to be correlated with corresponding strong variation in the variance of the fragment mass distribution. The present results may imply certain dynamical effects leading to compact scission configurations in the fission of ¹⁹F + ²⁰⁹Bi system at near barrier bombarding energies. Received: 9 April 2001 / Accepted: 26 May 2001     

Design and commissioning of a timestamp-based data acquisition system for the DRAGON recoil mass separator

The fission fragment mass distribution followed by neutron emission is studied for the ²³⁸U(¹⁸O,f) reaction using the asymmetric two-center shell model. Within the thermodynamic approach, excitation energy carried by the compound nucleus is dissipated in the emission of a pair of neutrons in several consecutive steps. Therefore, we have considered 2–12 (in step of 2) neutron emission channels in our formalism. The mass distribution corresponding to 8-neutron emission channel compares reasonably well with the experimental data. The observed fine structure dips corresponding to shell closure (Z = 50 and N = 82 of individual fission fragment arise mainly due to shell structure in the mass parameters. However, an exact location and magnitude of the dip at A = 124 in the mass distribution depends on how the temperature modifies masses and, also, on the precise information of pre- and post-neutron emission data. This suggests a possible importance of extending these calculations to get new insight into an understanding of the dynamical behaviour of fragment formation in the fission process.     

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.     

Some dynamical aspects of the fission process

The properties of the nuclear mass parameter and its influence on the fission process are discussed. In particular, correlations between dynamical and statical paths to fission are considered. The least action trajectories idea is used for finding the dynamical path to fission. Ritz method for the action integral minimalization is applied. An example of the nucleus ²⁵²Fm is considered.     

Fragments' mass and energy characteristics in the spontaneous fission of 236Pu, 238Pu, 240Pu, 242Pu,and 244Pu

The results of a systematic study of the mass and energy of fission fragments emitted in the spontaneous fission of ^{236,238,240,242,244}Pu are reported. A comparison of the fragments' mass and energy distributions demonstrates the occurrence of different fission modes with varying relative probability. These results are discussed in terms of the random neck rupture model as well as in terms of the scission point model, showing the influence of the neutron number of the fissioning system. Finally an improved method of analysis allows the investigation of the cold fission region.     

Indication for hyperdeformed cluster states in <Superscript>233</Superscript>Th

An activation technique was used to investigate relative yields of fission products from the reaction ²³²Th(n, f ) for neutron energies between 1.3 and 1.8MeV covering the region around the first hyperdeformed resonances. Intensities of characteristic γ-ray transitions were analyzed to search for changes in the mass distribution for neutron energies corresponding to the resonances and below the resonances. Relative increases in yield between 7 and 23% are observed for A ≈ 100 and 132 in the resonance region around 1.6MeV. It is proposed that the yield enhancement of daughter nuclei of the preformed fragments ¹³²Sn and ¹⁰¹Zr arises from cold fission of a di-cluster configuration. The experimental results support theoretical predictions for the existence of hyperdeformed octupole shapes based on the di-nuclear configuration ¹³²Sn + ¹⁰¹Zr.     

Fissionlike exit channel in the 5.8 MeV/u84Kr on24Mg reaction

Fissionlike (FL) phenomena for systems around mass 100 have been shown previously interpretable in terms of dynamical fission. This appears to be dependent on the entrance channel mass asymmetry. We have studied the fissionlike exit channel in the⁸⁴Kr+²⁴Mg reaction atE(Kr)=5.8 MeV/u. This energy is just above the threshold of fission, so that a clear separation between the Deep Inelastic Component (DIG) and the FL one can be achieved. The bombarding energy corresponds to the same excitation energy in the composite system¹⁰⁸Cd (E ^*=101 MeV) as in the³²S (158 MeV) on⁷⁶Ge reaction we studied earlier and for which fusion-evaporation along with fission-like contributions were measured. The width of the FL distribution confirms the previously observed dependence with the mass asymmetry in the entrance channel which is consistent with the extra push model.     

Cold and “hot” fragmentation in thermal neutron induced fission of 245Cm

In thermal neutron induced fission of ²⁴⁵Cm a fine structure in mass distribution is observed in cold and “hot” fragmentation regions for light as well as for heavy fragments. The complementarity of the light and heavy fragment masses in the fine structures is discussed.