Dynamical Aspects of Nuclear Fission

The following sections are included:

• DANF 2006 Conference Committee

• PREFACE

• CONTENTS

The dependence of the scission-neutron multiplicity on the mass ratio of the fragments in asymmetric fission of ²³⁶U was investigated in the frame of the sudden approximation. Only emission from neutron states characterized by the projection of the total angular momentum on the symmetry axis Ω = 1/2 was considered. This dependence was found to be different and less pronounced than for prompt neutrons.

Systems of intermediate fissility are characterized by an evaporation residues (ER) cross section comparable or larger than the fission cross section, and by a relatively higher probability for charged particle emission in the pre-scission channel. In a theoretical framework in which time scale estimates of the fission process rely on statistical model calculations, the analysis of particle emission in the ER channel is the source of additional constraints on the statistical and dynamical models. This contribution will offer an overall view of the systems studied so far and will provide new clues for interesting and contradictory physical cases. In particular, the analysis of the systems ³²S + ¹⁰⁰Mo at E_Lab = 200 MeV and ¹⁸O + ¹⁵⁰Sm at E_Lab = 122 MeV will be presented. Recent advancement will be briefly discussed on the interplay between the fission and the evaporation residues channels as implied by a dynamical (Langevin) approach to the description of the fission process.

An overview of the different experimental approaches to disentangle the quasi-fission and the fusion-fission processes in the heavy and superheavy mass region is presented. Indeed the separation of these two processes is essential in order to get a correct and complete insight of the mechanisms leading to the synthesis of superheavy elements. The importance of the neutron information through a new analysis protocol is detailed. Future perspectives are presented.

Results of the experiments aimed at the study of fission and quasi-fission processes in the reactions ⁴⁸Ca + ^144,154Sm, ¹⁶⁸Er, ²⁰⁸Pb, ²³⁸U, ²⁴⁴Pu, ²⁴⁸Cm; ⁵⁰Ti + ²⁰⁸Pb, ²⁴⁴Pu; ⁵⁸Fe + ²⁰⁸Pb, ²⁴⁴Pu, ²⁴⁸Cm, and ⁶⁴Ni + ¹⁸⁶W, ²⁴²Pu leading to the formation of heavy and super-heavy systems with Z = 82-122 are presented. Cross sections, mass-energy and angular distributions for fission and quasi-fission fragments have been studied at energies close and below the Coulomb barrier. The influence of the reaction entrance channel properties such as mass asymmetry, deformations, neutron excess, shell effects in the interacting nuclei and producing compound nucleus, the mechanism of the fusion-fission and the competitive process of quasi-fission are discussed.

The mass-energy and angular distributions of binary fission-like fragments produced in the reactions ⁴⁴Ca + ²⁰⁶Pb and ⁶⁴Ni + ¹⁸⁶W, leading to the same compound nucleus ²⁵⁰No have been measured at two CN excitation energies 30 and 40 MeV. The presence of quasifission component was observed for the both systems. But in the case of ⁶⁴Ni-ion the quasifission process dominates, while in the case of ⁴⁴Ca-ion the main process is fission of the compound nucleus ²⁵⁰No. From measured angular distributions the reaction times for quasifission and fission were found for both reactions.

The mass-energy distributions of the fission fragments, fusion-fission (σ_FF) and capture (σ_cap) cross-sections in the reactions ⁵⁸Pb+²⁰⁸Pb and ²⁶Mg + ²⁴⁸Cm were measured at the U400 accelerator of Flerov Laboratory of Nuclear Reactions (JINR, Russia) with use of double-arm time-of-flight spectrometer CORSET. The influence of reaction entrance channel on the competition between fusion-fission and quasi-fission processes was studied. Strong manifestation of the shell effects in mass distributions of fusion-fission and quasifission fragments was observed. The bimodal fission phenomena were found for both ²⁶⁶Hs and ²⁷⁴Hs nuclei at low excitation energies. For several beam energies of ²⁶Mg and ⁵⁸Fe studied in this work, the average neutron multiplicities 〈M_n〉 and γ–ray multiplicities 〈M_γ〉 in coincidence with fission fragments were also measured. Local minima are observed in 〈M_γ〉 as a function of mass suggesting the great influence of nuclear structure of fission fragments on 〈M_γ〉. The different dependence of 〈M_n〉 and 〈M_γ〉 as a function of fission fragment mass, total kinetic energy and excitation energy for fusion-fission and quasifission processes were observed.

After shortly reviewing some essential facts related to the sub-barrier fusion like the problem of the inner part of the Coulomb barrier, enhancement of fusion cross sections due to coupling to excited channels, the far-bellow the barrier data relevant for nuclear reactions in stars, we present calculations performed for the cases ⁵⁸Ni+⁵⁸Ni, ⁶⁴Ni+⁶⁴Ni, ⁶⁴Ni+⁷⁴Ge and ⁶⁴Ni+¹⁰⁰Mo where we were able to confirm the steep falloff of the cross sections. Along with the cross sections we present a diagnosis of the deep sub-barrier fusion using specific tools such as the S-factor and the logarithmic derivative L.

The paper is focused on reaction dynamics of superheavy nucleus formation and decay at beam energies near the Coulomb barrier. The aim is to review the things we have learned from recent experiments on fusion-fission reactions leading to the formation of compound nuclei with Z ≥ 102 and from their extensive theoretical analysis. The choice of collective degrees of freedom playing a principal role and finding the adiabatic multi-dimensional driving potential regulating the whole process are discussed. Dynamics of heavy-ion low energy collisions is studied within the realistic model based on multi-dimensional Langevin equations. Theoretical predictions are made for synthesis of SH nuclei in symmetric and asymmetric fusion reactions as well as in damped collisions of transactinides.

The problem of description of low-energy nuclear dynamics and derivation of multi-dimensional potential energy surface depending on several collective degrees of freedom is discussed. Multi-dimensional adiabatic potential is constructed basing on extended version of the two-center shell model. It has correct asymptotic value and height of the Coulomb barrier in the entrance channel (fusion) and appropriate behavior in the exit one, giving required mass and energy distributions of reaction products and fission fragments. Explicit time-dependence of the driving potential was introduced in order to take into account difference of diabatic and adiabatic regimes of motion of nuclear system at above-barrier energies and also difference of nuclear shapes in fusion and fission channels (neck formation). Derived driving potential is proposed to be used for unified analysis of the processes of deep-inelastic scattering, fusion and fission at low-energy collisions of heavy ions.

The talk is aimed to discussion of the problems around production and study of superheavy elements. Different nuclear reactions leading to formation of superheavy nuclei are analyzed. Dynamics of heavy-ion low energy collisions is studied within the realistic model based on multi-dimensional Langevin equations. Interplay of strongly coupled deep inelastic scattering, quasi-fission and fusion-fission processes is discussed. Collisions of very heavy nuclei (²³⁸U+²³⁸U, ²³²Th+²⁵⁰Cf and ²³⁸U+²⁴⁸Cm) are investigated as an alternative way for production of superheavy elements with increasing neutron number. Large charge and mass transfer was found in these reactions due to the inverse (anti-symmetrizing) quasi-fission process leading to formation of surviving superheavy long-lived neutron-rich nuclei. Lifetime of the composite system consisting of two touching nuclei is studied with the objective to find time delays suitable for the observation of spontaneous positron emission from super-strong electric field.

Recent macroscopic-microscopic studies on the static fission-barrier height of heaviest nuclei, done in our Warsaw group, are shortly reviewed. The studies have been motivated by the importance of this quantity in calculations of cross sections for synthesis of these nuclei. Large deformation spaces, including as high multipolarities of deformation as λ = 8, are used in the analysis of . Effects of various kinds of deformations, included into these spaces, on the potential energy of a nucleus are illustrated. In particular, the importance of non-axial shapes for this energy is demonstrated. They may reduce by up to more than 2 MeV.

Fusion-fission process in superheavy mass region is investigated on the basis of the fluctuation-dissipation dynamics. We analyze the trajectory in three-dimensional coordinate space with the Langevin equation. To investigate the fusion-fission process more precisely, we propose to take into account the pre-scission neutron multiplicity in connection with fission fragments. For the survival process, we apply the dynamical model instead of the statistical model. The possibility of synthesizing a doubly magic superheavy nucleus, ²⁹⁸114₁₈₄, is investigated taking into account the temperature dependence of the potential energy owing to neutron emission.

Thirty-four new nuclides with Z = 104-116, 118 and N = 161-177 have been synthesized in the complete-fusion reactions of ²³⁸U, ²³⁷Np, ^242,244Pu, ²⁴³Am, ^245,248Cm, and ²⁴⁹Cf targets with ⁴⁸Ca beams. The masses of evaporation residues were identified through measurements of the excitation functions of the xn-evaporation channels and from cross bombardments. The decay properties of the new nuclei agree with those of previously known heavy nuclei and with predictions from different theoretical models. A discussion of self-consistent interpretations of all observed decay chains originating from the parent isotopes ^282,283112, ²⁸²113, ^286-289114, ^287,288115, ^290-293116, and ²⁹⁴118 is presented. Decay energies and lifetimes of the neutron-rich superheavy nuclei as well as their production cross sections indicate a considerable increase in the stability of nuclei with an increasing number of neutrons, which agrees with the predictions of theoretical models concerning the decisive dependence of the structure and radioactive properties of superheavy elements on their proximity to the nuclear shells with N = 184 and Z = 114.

An overview of the recent progress in production of neutron-rich nuclei in the nucleus-nucleus collisions around the Fermi energy is presented and the possibilities to produce the very neutron-rich nuclei in the region of mid-heavy to heavy nuclei is examined. Possible scenarios for the new generation of rare nuclear beam facilities such as Eurisol are discussed. Isoscaling is investigated as a possible tool to predict the production rates of exotic species in reactions induced by both stable and radioactive beams.

The longitudinal momentum distribution (P_//) of fragments after one-proton removal from ²³Al and reaction cross sections (σ_R) for ^23,24Al on carbon target at 74AMeV have been measured using 135AMeV ²⁸Si primary beam on RIPS in RIKEN. P_// is measured by a direct time-of-flight (TOF) technique, while σ_R is determined using a transmission method. An enhancement in σ_R is observed for ²³Al compared with ²⁴Al. The P_// for ²²Mg fragments from ²³Al breakup has been obtained for the first time. FWHM of the distributions has been determined to be 233±14 MeV/c. The experimental data are discussed by use of the Few-Body Glauber Model (FBGM). Analysis of P_// indicates a dominant d-wave configuration for the valence proton in the ground state of ²³Al. The possibility of an enlarged ²²Mg core for proton-rich nucleus ²³Al is demonstrated.

The results from a series of experiments performed with a novel inverse-kinematics approach using the experimental installations of GSI, Darmstadt, gave a new global insight into the nuclide production in fission reactions. Combined with previous results, this large body of data has been used to develop a new semi-empirical macroscopic-microscopic fission model.

Triple coincidence data from the fission of ²⁵²Cf were used to deduce the intensity of the proposed "hot" mode in barium channels. γ – γ – γ and α – γ – γ fission data were analyzed to find the neutron multiplicity distribution for several binary and ternary charge splits. The binary channels Xe-Ru and Ba-Mo were analyzed, as well as the Ba-α-Zr, Mo-α-Xe, and Te-α-Ru ternary channels. An improved method of analysis was used in order to avoid many of the complexities associated with fission spectra. With this method, we were able to place an upper limit of 1.25% for the relative intensity of the second mode in the Ba-Mo case. For the Ba-α-Zr case, we found a relative intensity of 17% for the second mode.

We present a brief review of the results obtained by our collaboration in the frame of the program aimed at searching for new type of multibody decay of actinides, which was arbitrarily called as "collinear cluster tripartition" (CCT). First indications of new decay mode obtained for ²⁴⁸Cm (sf) and ²⁵²Cf (sf) let one to suppose that at least ternary almost collinear decay of the initial nucleus into the fragments of comparable masses appear to occur with the probability of about 10^-5 per binary fission. The process is strongly influenced by shell effects in the decay partners. The results under discussion were obtained by the "missing mass" method i.e. only two of the decay products were detected in coincidence while the conservation laws indicate a presence of at least third partner.

We have dedicated a new experiment to remeasuring the ternary α-particle energy spectrum in ²⁵²Cf spontaneous fission using an array of unshielded silicon detectors and unambiguously discriminating α-particles from neighboring isotopes by time-of-flight techniques using fission fragments as the start. Compared to many previous experiments, which entailed detection thresholds of 6 to 9 MeV α-particle energy due to the ∆E-E method applied and use of protection foils on detectors, the energy distribution of ternary α-particles could, for the first time, be measured down to 1 MeV. Furthermore, the energy spectrum of ⁶He could be analysed, albeit with weak statistics, and the yield ratio ⁶He/⁴He was deduced. For ⁴He, an excess in the yield as compared to a Gaussian shape is observed at energies below 9 MeV whose magnitude is in close agreement with data presented by Tishchenko et al. in 2002. On the other hand, the data formerly published by Loveland in 1974 exceed the low-energy yield of ternary α particles by up to a factor of two. We present our results on the ternary α-particle spectrum, and also the data on ⁶He, and discuss prospects for future measurements.

First results of experiment aimed at searching for collinear cluster tripartition channel in the reaction ²³⁸U+⁴He (40 MeV) are presented. Such unusual decay mode was observed earlier in ²⁵²Cf (sf). A two-arm TOF-E (time-of-flight vs. energy) spectrometer with micro- channel plate detectors and mosaics of PIN diodes was used. Among ternary events detected there are some presumably due to the decay of Pu shape-isomers built on the pairs of magic clusters. Fission of these states results in forming of long lived dinuclear molecule like systems which can disintegrate via inelastic scattering on the materials on the flight path.

In this paper we report on the energy distribution and the emission probability of ³H, ⁴He and ⁶He particles emitted in the spontaneous ternary fission of ²⁴⁴Cm (E_exc = 0 MeV) and in the neutron induced ternary fission of ²⁴³Cm (E_exc = 6.8 MeV). Both measurements were performed using suited ΔE-E telescope detectors, at the IRMM (Geel, Belgium) for the spontaneous fission and at the ILL (Grenoble, France) for the neutron induced fission measurements. By combining these results with similar data obtained for the fissioning systems ²⁴⁶Cm and ²⁴⁸Cm, a different impact of the excitation energy on the emission probability of ternary alphas and tritons could be demonstrated, which is ascribed to the influence of the α-cluster preformation probability on the ternary alpha emission.

Average preequilibrium , average statistical prescission and postscission neutron multiplicities as well as average γ-ray multiplicity 〈M_γ〉, average energy 〈E_γ〉 emitted by γ-rays and average energy per one gamma quantum 〈ε_γ〉 as a function of mass and total kinetic energy 〈TKE〉 of fission fragments were measured in the proton induced reactions p+²³²Th→²³³Pa, p+²³⁸U→²³⁹Np and p+²⁴²Pu→²⁴³Am (at proton energy E_p=13, 20, 40 and 55 MeV) and spontaneous fission of ²⁵²Cf. The fragment mass and energy distributions (MEDs) have been analyzed in terms of the multimodal fission. The decomposition of the experimental MEDs onto the MEDs of the distinct modes has been fulfilled in the framework of a method that is free from any parameterization of the distinct fission mode mass distribution shapes [1]. The main characteristics of symmetric and asymmetric modes have been studied in their dependence on the compound nucleus composition and proton energy. The manifestation of multimodal fission in average γ-ray multiplicity 〈M_γ〉 of fission fragments was studied in this work.

Measurements of fission fragment yields, neutron and gamma-ray multiplicities and average energies emitted by gamma rays have been carried out for the six fragment pairs (Z_L/Z_H = 44/46, 42/48, 40/50, 38/52, 36/54 and 34/56) in ²⁰⁸Pb(¹⁸O,f) at beam energy E=85 MeV, using the γ–ray spectroscopy technique to analyze γ–γ–γ coincidence data.

Recent experiments designed for the multi-parameter analysis of ²⁵²Cf spontaneous fission are described. The technique of multiple γ-ray spectroscopy was supplemented with the measurements of kinematical characteristics of fission fragments and light charged particles emitted in ternary fission.

A large variety of shapes may be observed in Sr and Zr nuclei of the A = 100 region when the number of neutrons increases from N = 58 to N = 64. The lighter isotopes are rather spherical. It is also well established that three shapes co-exist in the transitional odd-A, N = 59, Sr and Zr nuclei. For N > 59, strongly deformed axially symmetric bands are observed. Recently, a new isomer of half-life 1.4(2) µs was observed in ⁹⁵Kr, the odd-odd ⁹⁶Rb has been reinvestigated and a new high spin isomer observed in the even-even ⁹⁸Zr. Beyond N = 60 nuclei, the neutron-rich Mo isotopes represent well deformed nuclei, but at the same time, the triaxial degree of freedom plays an important role. We have re-investigated the odd ¹⁰⁵Mo and ¹⁰⁷Mo and found that odd and even Mo in the neutron range N = 62-66 have comparable quadrupole and triaxial deformation. These nuclei were studied by means of prompt γ-ray spectroscopy of the spontaneous fission of ²⁴⁸Cm using the EUROGAM 2 Ge array and/or measurements of µs isomers produced by fission of ^239,241Pu with thermal neutrons at the ILL (Grenoble).

The Relativistic Hartree-Bogoliubov (RHB) density functional with density dependent coupling constants is applied in the description of exotic nuclei. This approach provides an improved description of the isovector properties of finite nuclei at and away from stability line.

We have calculated binding energies of light even-even atomic nuclei. The calculations have been performed in the framework of the relativistic mean-field theory. The comparision with experimental data is not satisfactory because two systematical deviations have been discovered. The possibility to improve model predictions incorporating phenomenological Wigner term has been studied and new parameters of Wigner term have been obtained.

New exciton model of preequilibrium decay (Monte Carlo Preequilibrium) to compute spectra of multiparticle emission during an establishment of statistical equilibrium in the composite system is proposed. MCP stage of calculation was included into the standard scheme of the nucleon spectra calculation between the intranuclear cascade stage and statistical model stage. Systematic comparison of calculation results with the experimental spectra of nucleons from (p,xn), (p,xp), (n,xn) and (n,xp) reactions in a wide projectile energy region from 10 up to 160 MeV for targets from ²⁷Al up to ²⁰⁹Bi has been carried out. The short description of the MCP model and results obtained are presented in the given work.

The multidimensional data acquisition, processing and visualization system for analysis of experimental data in nuclear physics is briefly described in the paper. The system includes a large number of sophisticated algorithms of the multidimensional nuclear spectra processing, including background elimination, deconvolution, peak searching and fitting.

The following sections are included:

• LIST OF PARTICIPANTS

• AUTHOR INDEX