Langevin fission dynamics of hot rotating nuclei: Systematic application to Z 2/A=34–42 heavy nuclei

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations is used to calculate the mass-energy distributions of fragments originating from the fission of compound nuclei whose fissility parameter lies in the range Z ²/A=34–42. In these calculations, use was made of the liquid-drop model allowing for finite-range nuclear forces and the diffuseness of the nuclear surface in calculating the potential energy and a modified one-body mechanism of viscosity in describing dissipation. The emission of light prescission particles is taken into account on the basis of the statistical model. The calculations performed within three-dimensional Langevin dynamics reproduce well all parameters of the experimental mass-energy distributions of fission fragments and all parameters of the prefission-neutron multiplicity for various parameters of the compound nucleus. The inclusion of the third collective coordinate in the Langevin equations leads to a considerable increase (by up to 40–50%) in the variances of mass-energy distributions in relation to what was previously obtained from two-dimensional Langevin calculations. For the parameters of the mass-energy distributions of fission fragments and the parameters of the prefission-neutron multiplicity to be reproduced simultaneously, the reduction coefficient K _s must be diminished at least by a factor of 2(0.2≤K _s ≤0.5) in relation to that in the case of total one-body viscosity (K _s =1).     

Influence of nuclear dissipation on fission dynamics of the excited nucleus <Superscript>248</Superscript>Cf within a stochastic approach

A stochastic approach to fission dynamics based on two-dimensional Langevin equations was applied to calculate the anisotropy of the fission fragments angular distribution and average pre-scission neutron multiplicities for the compound nucleus ²⁴⁸Cf formed in the ¹⁶O+²³²Th reactions. Postsaddle nuclear dissipation strength of (12–14) × 10²¹ s^?1 was extracted for Cf nucleus by fitting the results of calculations with the experimental data. Furthermore, it was found that the results of calculations for the anisotropy of the fission fragments angular distribution and pre-scission neutron multiplicities are very sensitive to the magnitude of post-saddle nuclear dissipation.     

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.     

Do electron scattering and muonic x-ray data really require a central depression in the charge distribution of208Pb?

The charge distribution of²⁰⁸pb calculated in the Hartree-Fock (HF) approach using the density dependent nucleon-nucleon interaction of Ehlers and Moszkowski is tested by simultaneous comparison with experimental data from 502 MeV elastic electron scattering and muonic atoms. In both cases the agreement is very good and nearly as good as the best fits with a phenomenological charge distribution of Fermi type, if the effect of the polarization of the nucleus due to the presence of the muon is properly taken into account. In contradiction to the Fermi fits the HF distribution shows a hump at the center of the nucleus.     

Realistic Langevin Treatment of Fission-Fragment Energy Distribution

The average kinetic energy and its variance of fission fragments for the compound nucleus ²¹³At are calculated by four-dimensional Langevin equation. Two collective coordinates are taken into account: the distance p between the centers of the nascent fragments and the neck parameter h using the {c, h, a} parametrization. The model allows for a realistic coordinate dependence of all coeficien ts appearing in the Langevin equation as computed by the Werner-Wheeler method. The diffusion process for thc fissioning nuclear system from the ground state to the scission line on the realistic energy surface is investigated. The results are in good agreement with the experiments.     

Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, ??} parametrization. The evolution of the orientation degree of freedom (K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k _s = 0.25 and k _s = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k _s in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z ²/A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k _s with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, ??n _pre(M)??, and between, this multiplicity and the kinetic energy of fission fragments, ??n _pre(E _k )??, are also presented.     

Fission dynamics of the compound nucleus 213Fr formed in heavy-ion-induced reactions

A stochastic approach based on one-dimensional Langevin equations was used to calculate the average pre-fission multiplicities of neutrons, light charged particles and the fission probabilities for the compound nucleus ²¹³Fr and the results are compared with the experimental data. In these calculations, a modified wall and window dissipation with a reduction coefficient, k _s , has been used in the Langevin equations. It was shown that the results of the calculations are in good agreement with the experimental data by using values of k _s in the range 0.3?≤?k _s ?≤?0.5.     

Interaction barriers,nuclear shapes and the optimum choice of a compound nucleus reaction for producing super-heavy elements

Potential barriers and nuclear shapes are calculated for the first time in the fragmentation theory for the various target-projectile combinations. It is shown that the choice of the reaction partners of a cool compound nucleus reaction can be optimized on the basis of this information. Combinations with largest mass- and charge asymmetries, largest interaction radii and smallest interaction barriers are shown to be most favourable. The interaction radius, which is defined to be the radius of the compound nucleus at the top of the barrier, is shown to be related with both mass- and charge asymmetries of the reaction. The calculations are illustrated for the compound nuclei ²⁵⁸104 and ²⁶⁰106.     

Study of fission dynamics with the three-dimensional Langevin equations

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei ²¹⁰Po and ²²⁴Th formed in the fusion-fission reactions ⁴He + ²⁰⁶Pb , ¹⁶O + ²⁰⁸Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data.     

A study of the ground-state energy of He with nucleon–nucleon potentials

Ground-state properties are evaluated for the finite nucleus ⁴He starting from realistic nucleon–nucleon interactions within the framework of the Green’s function approach. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. For that purpose four high-quality modern nucleon–nucleon interactions represented in momentum space are employed: the Argonne V18, CD-Bonn, Bonn A and N³LO potentials. In these potentials, the effects of charge dependence are taken into account. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. It has been shown that the Green function results agree well with the results obtained by accurate methods for few-nucleon systems such as the Faddeev–Yakubovsky calculation. In this study, a comparison of the calculated ground-state energies, obtained by using the Green function approach and different nucleon–nucleon potentials, with experimental values is carried out. The results show good agreement between the calculated values and the experimental ones.     

The construction of wave functions in the <Superscript>7</Superscript>Li → d + <Superscript>5</Superscript>He channel by the projection method

Relative motion wave functions in the d + ⁵He channel were constructed by the projection method using the two-body αt model of ⁷Li nucleus. The asymptotic constants in this channel were calculated using various models of ⁵He{αn} wave function.     

Spectroscopic factors in the <Superscript>7</Superscript>Li → d + <Superscript>5</Superscript>He{α} fragmentation channel

The spectroscopic S _d factors of the separation of deuterons in the d + ⁵He channel were calculated using the two-body αt model of ⁷Li nucleus and various ⁵He{αn} wave function models.     

Negative parity states and ground state properties of theα—α—n system calculated by different forces

In recent years predictions on the off-shell behavior of composite particles interactions have been made by some theoretical models. The goal of this paper is to test them by using⁹Be nucleus. The bound state problem of⁹Be considered as aα—α—n three-cluster system is solved in configuration space. Several on-shell equivalent local and nonlocal forces for theα—α andn—α interactions are used for calculation of the low lying negative parity spectrum of⁹Be, and also of the charge density, quadrupole moment, and the correlation density of⁹Be ground state. The contributions to the calculated quantities of different partial waves of the two-body forces are examined and discussed.     

Theory of fusion for superheavy elements

A new model is proposed for fusion mechanisms of massive nuclear systems, where so-called fusion hindrance exists. The model describes the whole process in two steps: two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to ⁴⁸Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. A schematic case is solved in an analytic way, the results of which shed light on fusion mechanisms. Combined with statistical decay theory, residue cross sections for superheavy elements can be readily calculated. Examples are given.