Fission time-scale in experiments and in multiple initiation model

Rate of fission for highly-excited nuclei is affected by the viscose character of the systemmotion in deformation coordinates as was reported for very heavy nuclei with Z _C > 90. The long time-scale of fission can be described in a model of “fission by diffusion” that includes an assumption of the overdamped diabatic motion. The fission-to-spallation ratio at intermediate proton energy could be influenced by the viscosity, as well. Within a novel approach of the present work, the cross examination of the fission probability, time-scales, and pre-fission neutron multiplicities is resulted in the consistent interpretation of a whole set of the observables. Earlier, different aspects could be reproduced in partial simulations without careful coordination.     

Formation of heavy compound nuclei,their survival,and correlation with longtime-scale fission

Fusion of two massive nuclei with formation of a superheavy compound nucleus is driven by the potential energy gradient, as follows from the analysis of nuclear reaction cross sections. The conservative energy of the system is deduced in a simple approximation using regularized nuclear mass and interaction barrier values. Different reactions for the synthesis of Z = 110−118 nuclei are compared and favorable conditions are found for fusion of the stable W-Pt isotopes with radioactive fission fragment projectiles, like ⁹⁴Kr or ¹⁰⁰Sr. Thus, the cold-fusion method can be extended for a synthesis of elements with Z > 113. Survival of the evaporation residue is defined by the neutron-to-fission probability ratio and by the successful emission of gammas at the final step of the reaction. Numerical estimates are presented. Fixation of evaporation residue products must correlate with longtime-scale fission, and available experimental results are discussed. The text was submitted by the authors in English.     

Neutron-induced reaction rates for the <Emphasis Type="Italic">r</Emphasis>-process

Neutron-induced reaction rates for the formation of heavy and superheavy nuclei in the astrophysical r-process are presented. Neutron-induced reactions, including fission and neutron capture, at astrophysical temperatures are treated within the framework of the statistical model and calculated for targets with the atomic number 84 < Z < 118, using different mass and fission barrier predictions. The dependence of heavy element yields from nuclear explosions on the target nuclei, nuclear reactions, and nuclear models is discussed.     

Rate of excited-nucleus fission within a multidimensional stochastic approach

A stochastic approach to describing the dynamics of the nuclear-fission process is applied to study the effect of the number of dimensions on the fission rate within the dynamical model used. The time dependence of the fission rate is calculated on the basis of a multidimensional Langevin equation without taking into account particle evaporation. The one-, two-, and three-dimensional cases are considered for the example of the “c, h, α” parametrization of nuclear-surface shapes. The calculations are performed for a large number of compound nuclei whose parameter Z ²/A falls within the range 20 ≤ Z ²/A ≤ 40. The stationary level of the fission rate is found to increase considerably upon going over from the one- to the three-dimensional case. This increase is especially pronounced for light fissile nuclei in the vicinity of the Businaro-Gallone point. Also, the stationary fission-rate level obtained from our dynamical simulation is compared with its counterpart calculated by the Kramers formula generalized to the multidimensional case.     

Fusion-fission dynamics in the superheavy nucleus production

The fusion-fission reaction mechanism leading to the massive nucleus formation is studied. We investigate the superheavy nucleus formation in heavy-ion induced reactions by analysing the evaporation residue (ER) production in order to study the fusion dynamics and the decay properties of nuclei close to the stability island at Z=114. We consider the ⁶¹Ni+²⁰⁸Pb, ⁴⁸Ca+²³⁸U and ⁴⁸Ca+²⁴⁴Pu reactions that lead to the Z=110, 112 and 114 superheavy elements respectively. By using the dinuclear system (DNS) concept of the two interacting nuclei we calculate the quasifission-fusion competition in the entrance channel and the fission-evaporation competition along the de-excitation cascade of the compound nucleus. The dynamics of the entrance channel allows us to determine the beam energy window which is favorable to the fusion, while the dynamic evolution of the compound nucleus on the shell correction to the fission barrier and the dissipative effects influence the fission-evaporation competition in order to obtain the residue nuclei from the superheavy nucleus formation. We also calculate the τ _n /τ_tot ratio at each step of the de-excitation cascade of the compound nucleus and we present a systematics of τ _n /τ_tot (at first step of the cascade) for many reactions that lead to nuclei with Z=102–114.     

Impact of nuclear structure on production and identification of new superheavy nuclei

Using the microscopic-macroscopic approach based on the modified two-center shell model, the low-lying quasiparticle spectra, ground-state shell corrections, mass excesses and Q _α -values for even Z superheavy nuclei with 108 ≤ Z ≤ 126 are calculated and compared with available experimental data. The predicted properties of superheavy nuclei show that the next doubly magic nucleus beyond ²⁰⁸Pb is at Z ≥ 120. The perspective of using the actinide-based complete fusion reactions for production of nuclei with Z = 120 is studied for supporting future experiments.     

Mechanisms for the appearance of prescission γ-rays and their related T-odd asymmetries

Conditions for the appearance and observation of prescission γ-rays emitted by a fissioning nucleus before its separation into fission fragments were investigated within the quantum theory of fission. It was demonstrated that these conditions can be fulfilled in the γ-decay of giant electric isovector dipole resonances in a fissioning nucleus that become excited due to the nonadiabaticity of the collective deformation motion of the nucleus at the final stages of its prefission evolution. Angular and energy distributions of prescission γ-rays emitted by unpolarized fissioning nuclei were analyzed. Characteristics of T-odd asymmetries in angular distributions of prescission γ-rays were investigated for fission of unpolarized target nuclei induced by polarized cold neutrons, and these correlations were shown to be similar in nature to the T-odd ROT correlations earlier found for α-particles emitted in ternary nuclear fission.     

Synthesis of superheavy nuclei in the reactions of 244Pu and 248Cm with 48Ca

This paper presents results of the experiments aimed at producing long-lived superheavy elements located near the spherical-shell closures with Z ⩾ 114 and N ⩾ 172 in the ²⁴⁴Pu + ⁴⁸Ca and ²⁴⁸Cm + ⁴⁸Ca reactions. The large measured α-particle energies of the newly observed nuclei, together with the long decay times and spontaneous fission terminating the chains, offer evidence of the decay of nuclei with high atomic numbers. The decay properties of the synthesized nuclei are consistent with the consecutive α-decays originating from the parent nuclides ^{288, 289}114 and ²⁹²116, produced in the 3n and 4n evaporation channels with cross-sections of about a picobarn. The present observations can be considered as experimental evidence of the existence of the “island of stability” of superheavy elements. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: utyonkov@sungns.jinr.ru     

Problem of the conservation of the fissile-nucleus-spin projection onto the fissile-nucleus symmetry axis and quantum dynamics of the low-energy fission process

Within quantum-mechanical fission theory, it is shown that, in the low-energy fission of actinide nuclei, the projection K of the spin of a fissile nucleus onto its symmetry axis is conserved as this nucleus traverses the second well of the deformation potential and the region of descent from the external fission barrier to the scission point, this spin projection being an integral of motion despite the effect of Coriolis interaction. This leads to the conclusion that the fission probability is determined by the concerted effect of the internal- and external-fission-barrier penetration factors. A global analysis of information that can be extracted from experimental investigations of (n, f) and (γ, f) reactions and which can be employed in theoretically describing fission mechanisms is performed.     

Light particle accompanied quasifission in superheavy composite systems

The dynamics of the excited superheavy system with Z = 118 in the reaction ⁸⁶Kr + ²⁰⁸Pb at E _Kr = 460, 500, and 600 MeV has been investigated. The mass and kinetic energy of binary fragments were measured by the time-of-flight method. Double-differential distributions of protons and α particles were measured in coincidence with fragments. The proton spectra can be described considering only evaporation from fragments. Evidence of the neck fragmentation was obtained from analysis of double-differential α spectra. Properties of the α-particle neck fragmentation component are close to those known from the ternary fission of actinide nuclei, but the multiplicity is much larger than can be expected from extrapolation of the ternary fission data. The text was submitted by the authors in English.     

Photonuclear reactions of actinides in the giant dipole resonance region

Photonuclear reactions at energies covering the giant dipole resonance (GDR) region are analyzed with an approach based on nuclear photoabsorption followed by the process of competition between light-particle evaporation and fission for the excited nucleus. The photoabsorption cross-section at energies covering the GDR region is contributed by both the Lorentz-type GDR cross-section and the quasi-deuteron cross-section. The evaporation-fission process of the compound nucleus is simulated in a Monte Carlo framework. Photofission reaction cross-sections are analyzed in a systematic manner in the energy range of ∼ 10-20 MeV for the actinides ²³²Th , ²³⁸U and ²³⁷Np . Photonuclear cross-sections for the medium-mass nuclei ⁶³Cu and ⁶⁴Zn , for which there are no fission events, are also presented. The study reproduces satisfactorily the available experimental data of photofission cross-sections at GDR energy region and the increasing trend of nuclear fissility with the fissility parameter Z ²/A for the actinides.     

Fission barriers of super-heavy nuclei produced in cold-fusion reactions

Excitation functions of super-heavy evaporation residues formed in cold-fusion reactions were analyzed with the aim of getting information on the fission barrier height of these nuclei. The method uses the location of the maximum of 1n and 2n excitation functions. The results obtained on nuclei from Z = 104 to 112 are compared to three theoretical predictions.PACS: 25.70.Jj Fusion and fusion-fission reactions - 24.75. + i General properties of fission     

Registration of hydrogen-like leptonic bound states ( e-μ+) and ( e+μ-) in reactions of high-energy scattering of polarized electrons and positrons by nuclei with Z ～ 100 and analysis of CPT invariance

The cross-sections for the reactions of muonium (anti-muonium) production in the high-energy electron (positron) scattering by nuclei e ^-(e ⁺) + Z↦Z + M ⁰(ˉM) + μ^-(μ⁺) are calculated in dependence on energy and polarization of the initial electron (positron) and polarization of the final μ^-(μ⁺)-meson. Since this is a coherent phenomenon the cross-sections are proportional to Z². For Z ∼ 100, due to the factor Z², the cross-sections are large enough to be measured at the energies available for the HERA Collider at DESY. The results are discussed in connection with a test of CPT invariance. Received: 24 September 2002 / Accepted: 12 March 2003 / Published online: 27 May 2003     

Systematics of asymmetry in fission based on order-disorder model

According to Order-Disorder Model (ODM), in the early stages of fission, the charges in a fissioning nucleus gets polarised into two impending parts along with corresponding most stable neutrons which are calculated from the minimum in isobaric mass parabola. This polarisation into two most stable configuration leaves a small number of neutrons as balance neutrons i.e.N _bal. The distribution of theseN _bal for various polarisation modes, shows a very profound correlation with the yield distribution. Judging from this striking correlation between these two distributions, it can be predicted that the asymmetry in fission decreases gradually and ultimately disappear for nuclei havingZ ⋍ 102 but reappears again for the nuclei in super heavy region.     

Exotic decay: Transition from cluster mode to fission mode

Exotic decay of some heavy nuclei with Z≥100 formed in heavy ion ‘cold fusion’ reaction were studied taking interacting barrier consisting of Coulomb and proximity potential. Calculated half-life time shows that some modes of decay are well within the present upper limit for measurements (T _1/2<10³⁰ s). Cluster formation probabilities are calculated for different clusters within fission model. It is found that transition from cluster mode to fission mode take place at mass of the cluster, A ₂=20 in exotic decay which is comparable with the value A ₂=16 of Shanmugam et al based on cubic plus Yukawa plus exponential model (CYEM).     

Combined dynamical and statistical approach to describing induced fission of heavy nuclei

A combined dynamical and statistical approach to describing induced fission of heavy nuclei is proposed. This approach takes into account the nuclear-dissipation phenomenon and the double-humped structure of the fission barrier. A method that is intended for calculating the angular distribution of fission fragments and which is applicable over a broad range of excitation energies is discussed. The potential of the approach is demonstrated by addressing the problems of self-consistently describing experimental data on fission probabilities for plutonium and americium isotopes, the yields of shape isomers in the α+²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV and the d+^242,240Pu reactions at deuteron energies in the range E _d = 20–30 MeV, fission times in the α + ²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV, and angular distributions of fission fragments in the α + ²³⁸U, ²³⁷Np reactions at alpha-particle energies in the range E _α = 20–100 MeV.     

e + e − pair production in ultrarelativistic heavy-ion collisions at intermediate impact parameters

Using the semiclassical Green’s function in the Coulomb field, we analyze the probabilities of single and multiple e ⁺ e ⁻ pair production at a fixed impact parameter b between colliding ultrarelativistic heavy nuclei. We perform calculations in the Born approximation with respect to the parameter Z _Bα and exactly in Z _Aα, where Z _A and Z _B are the charge numbers of the corresponding nuclei. We also obtain the approximate formulas for the probabilities valid for Z _Aα, Z _Bα ≲ 1. The text was submitted by the authors in English.     

Shifting the closed proton shell to Z = 122 —A possible scenario to understand the production of superheavy elements Z = 112−118

The recent experiments at FLNR, Dubna, demonstrated that cross-sections to produce SHEs by ⁴⁸Ca-induced reactions on actinide targets increase beyond Z = 111, reach a maximum of 5 pb at Z = 114 and fall below the 1 pb level at Z = 118. A scenario is proposed to understand the findings within the frame of former experimental results of heavy-element production and theoretical predictions about the stability of the nuclides concerned. New ingredients introduced are: 1) to shift the next proton shell beyond Pb from Z = 114 to Z = 122; 2) the isotopes of the elements Z = 112 to Z = 118 are deformed and their nuclei have oblate shapes; 3) the fission barriers around the next nucleus with doubly closed shells ₃₀₆¹⁸⁴122 are larger than the neutron separation energies and reach values in the range of 10MeV. The ascent of the flat top at ₃₀₆¹⁸⁴122 is described by the proposed scenario, which likewise excludes reaching the doubly closed shell region at the top by today’s experimental methods. Communicated by T.S. Bíró     

Correlation between fractional independent yields and neutron-to-proton ratio of fission products in low energy fission

Fractional independent yields of fission products in the thermal neutron-induced fission of²³³U,²³⁵U,²³⁹Pu,²⁴¹Pu and in the spontaneous fission of²⁵²Cf have been correlated with the neutron-to-proton ratio of the fission products. The yields of the products from a fissioning system, when plotted as a function of neutron-to-proton (N/Z) ratio of fission preducts, fall on two Gaussian distribution corresponding to light and heavy fission products. The centroids of the distribution or the most probable value of neutron-to-proton ratio is found to be very close to theN/Z of the fissioning nucleus. From the most probable value ofN/Z the various parameters of charge distribution e.g. most probable massA _p, most probable chargeZ _p, the mass dispersionσ _Aand the charge dispersionσ _Zhave been obtained and are in good agreement with the experimental values ofA _pandZ _p.     

A systematic study of the fission and evaporation residue excitation functions in complete fusion reactions with weakly bound stable nuclei

We carry out a systematic study on the fusion-fission and evaporation residue excitation functions for the reactions of ^6,7Li, ⁹Be, ^10,11B + ²⁰⁹Bi and ^6,9Li, ⁹Be + ²⁰⁸Pb, in which the projectiles are loosely bound and have low threshold energies against breakup. The fusion cross sections are calculated by the coupled-channel model. The compound nuclei decay are analyzed with the standard statistical model. The fission and evaporation residue excitation functions are well reproduced by our calculations, proving the validity of the standard statistical model in describing the compound nuclei decay in these characteristic reactions. For the compound nuclei with A=215-220 and Z=86-88, the liquid drop fission barriers need to be scaled by 0.80-1.02 to reproduce the experimental data. And a decreasing trend of the scaling factor with increasing fissionability parameter Z²/(50A) is found.