Mass Equilibration Research Articles

Time-dependent Hartree-Fock study of quasifission trajectories in reactions forming Og294

Background: Fission modes in superheavy nuclei are expected to be impacted by quantum shell effects. Similar shell effects may be present in quasifission reactions, acting to hinder the mass equilibration process in heavy-ion collisions.Purpose: To investigate quasifission mechanisms in five different reactions forming $^{294}\mathrm{Og}$ as a compound nucleus and compare quasifission trajectories with predicted fission modes.Methods: The potential energy surface (PES) of $^{294}\mathrm{Og}$ is calculated using the static Hartree-Fock approach with BCS pairing correlations. Quasifission trajectories for central collisions at various energies are studied with the time-dependent Hartree-Fock theory.Results: The exit channel strongly depends on initial mass asymmetry and orientation, but it only exhibits small dependencies in the reaction energy. The $^{48}\mathrm{Ca}+^{246}\mathrm{Cf}$ reaction is affected by the PES topography, leading to either fusion or asymmetric fission. $^{126}\mathrm{Sn}+^{168}\mathrm{Er}$ reactions exhibit large total kinetic energies and compact scission configurations, which could be interpreted as an effect of the $Z=50$ spherical magic gap.Conclusions: Quasifission trajectories can be interpreted in terms of the underlying PES for low excitation energies. Future investigations of quasifission with temperature- and angular-momentum-dependent PES could be considered.

Mass Equilibration and Fluctuations in the Angular Momentum Dependent Dynamics of Heavy Element Synthesis Reactions.

Mass and angle distributions for the ^{52}Cr+^{198}Pt and ^{54}Cr+^{196}Pt reactions (both forming ^{250}No) were measured and subtracted, giving new information on fast quasifission mass evolution, and the first direct determination of the dependence of sticking times on angular momentum. TDHF calculations showed good agreement with average experimental values, but experimental mass distributions unexpectedly extended to symmetric splits while the peak yield remained close to the initial masses. This implies a strong role of fluctuations in mass division early in the collision, giving insights into the transition from fast energy dissipative deep-inelastic collisions to quasifission.

Comparison of fission and quasi-fission modes

Quantum shell effects are known to affect the formation of fragments in nuclear fission. Shell effects also affect quasi-fission reactions occurring in heavy-ion collisions. Systematic time-dependent Hartree-Fock simulations of 50Ca+176Yb collisions show that the mass equilibration between the fragments in quasi-fission is stopped when they reach similar properties to those in the asymmetric fission mode of the 226Th compound nucleus. Similar shell effects are then expected to determine the final repartition of nucleons between the nascent fragments in both mechanisms. Future experimental studies that could test these observations are discussed.

Timescales of Quantum Equilibration, Dissipation and Fluctuation in Nuclear Collisions.

Understanding the dynamics of equilibration processes in quantum systems as well as their interplay with dissipation and fluctuation is a major challenge in quantum many-body theory. The timescales of such processes are investigated in collisions of atomic nuclei using fully microscopic approaches. Results from time-dependent Hartree-Fock and time-dependent random-phase approximation calculations are compared for 13 systems over a broad range of energies. The timescale for full mass equilibration (∼2×10^{-20} s) is found to be much larger than timescales for neutron-to-proton equilibration, kinetic energy, and angular momentum dissipations which are on the order of 10^{-21} s. Fluctuations of mass numbers in the fragments and correlations between their neutron and proton numbers build up within only a few 10^{-21} s. This indicates that dissipation is basically not impacted by mass equilibration, but is mostly driven by the exchange of nucleons between the fragments.

Exploring quasifission characteristics forS34+Th232formingSg266

Background: Fission fragments from heavy ion collisions with actinide nuclei show mass-asymmetric and mass-symmetric components. The relative probabilities of these two components vary rapidly with beam energy with respect to the capture barrier, indicating a strong dependence on the alignment of the deformed nucleus with the partner in the collisions.Purpose: To study the characteristics of the mass-asymmetric quasifission component by reproducing the experimental mass-angle distributions to investigate mass evolution and sticking times.Methods: Fission fragment mass-angle distributions were measured for the $^{34}\text{S}+^{232}\text{Th}$ reaction. Simulations to match the measurements were made by using a classical phenomenological approach. Mass ratio distributions and angular distributions of the mass-asymmetric quasifission component were simultaneously fit to constrain the free parameters used in the simulation.Results: The mass-asymmetric quasifission component---predominantly originating from tip (axial) collisions with the prolate deformed $^{232}\text{Th}$---is found to be peaked near $A=200$ at all energies and center-of-mass angles. A Monte Carlo model using the standard mass equilibration time constant of $5.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ s predicts more symmetric mass splits. Three different hypotheses assuming (i) a mass halt at $A=200$, (ii) a slower mass equilibration time, or (iii) a Fermi-type mass drift function reproduced the main experimental features.Conclusions: In tip collisions for the $^{34}\text{S}+^{232}\text{Th}$ reaction, mass-asymmetric fission with $A\ensuremath{\sim}200$ is the dominant outcome. The average sticking time is found to be $\ensuremath{\sim}7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ s, independent of the scenario used for mass evolution.

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

Background: At energies near the Coulomb barrier, capture reactions in heavy-ion collisions result either in fusion or in quasifission. The former produces a compound nucleus in statistical equilibrium, while the second leads to a reseparation of the fragments after partial mass equilibration without formation of a compound nucleus. Extracting the compound nucleus formation probability is crucial to predict superheavy-element formation cross-sections. It requires a good knowledge of the fragment angular distribution which itself depends on quantities such as moments of inertia and excitation energies which have so far been somewhat arbitrary for the quasifission contribution. Methods: We investigate the evolution of the nuclear density in time-dependent Hartree-Fock (TDHF) calculations leading to quasifission. Our main goal is to extract ingredients of the formula used in the analysis of experimental angular distributions. These include the moment-of-inertia and temperature. We study the dependence of these quantities on various initial conditions of the reaction process. Results: The evolution of the moment of inertia is clearly non-trivial and depends strongly on the characteristics of the collision. The temperature rises quickly when the kinetic energy is transformed into internal excitation. Then, it rises slowly during mass transfer. Conclusions: Fully microscopic theories are useful to predict the complex evolution of quantities required in macroscopic models of quasifission.

Interplay between quantum shells and orientation in quasifission.

The quasifission mechanism hinders fusion in heavy systems through breakup within zeptoseconds into two fragments with partial mass equilibration. Its dependence on the structure of both the collision partners and the final fragments is a key question. Our original approach is to combine an experimental measurement of the fragments' mass-angle correlations in (40)Ca+(238)U with microscopic quantum calculations. We demonstrate an unexpected interplay between the orientation of the prolate deformed (238)U with quantum shell effects in the fragments. In particular, calculations show that only collisions with the tip of (238)U produce quasifission fragments in the magic Z=82 region, while collisions with the side are the only ones that may result in fusion.

Evidence of quasifission in asymmetric reactions forming the250Cf compound system

Mass-angle correlations and mass ratio distributions of fission fragments have been measured in ${}^{12}\mathrm{C}+{}^{238}\mathrm{U}$ and ${}^{18}\mathrm{O}+{}^{232}\mathrm{Th}$ reactions, both leading to the same compound nucleus ${}^{250}$Cf (fissility = 0.86), with matching excitation energies at near and sub-barrier energies. In both systems, there is no mass-angle correlation in the entire energy region studied. However, it is found that the variance of the mass ratio distribution in the ${}^{18}\mathrm{O}+{}^{232}\mathrm{Th}$ system is consistently higher than in the ${}^{12}\mathrm{C}+{}^{238}\mathrm{U}$ system at all excitation energies. This points to the fact that mass equilibration has not been fully achieved in the ${}^{18}\mathrm{O}+{}^{232}\mathrm{Th}$ reaction in comparison to the ${}^{12}\mathrm{C}+{}^{238}\mathrm{U}$ reaction, indicating the presence of quasifission in the ${}^{18}\mathrm{O}+{}^{232}\mathrm{Th}$ system.

Thermoacoustic and buoyancy-driven transport in a square side-heated cavity filled with a near-critical fluid

The mechanisms of heat and mass transport in a side-heated square cavity filled with a near-critical fluid are explored, with special emphasis on the interplay between buoyancy-driven convection and the Piston Effect. The Navier–Stokes equations for a near-critical van der Waals gas are solved numerically by means of an acoustically filtered, finite-volume method. The results have revealed some striking behaviour compared with that obtained for normally compressible gases: (i) heat equilibration is still achieved rapidly, as under zero-g conditions, by the Piston Effect before convection has time to enhance heat transport; (ii) mass equilibration is achieved on a much longer time scale by quasi-isothermal buoyant convection; (iii) due to the very high compressibility, a stagnation-point effect similar to that encountered in high-speed flows provokes an overheating of the upper wall; and (iv) a significant difference to the convective single-roll pattern generated under the same conditions in normal CO2 is found, in the form of a double-roll convective structure.

Equilibrators for Planar Linkages

This manuscript provides a mathematical basis for comparing the complexity of equilibrator methodologies, extends the applications of those methodologies, and develops new methodologies. Two methodologies exist for spring equilibration of two degree of freedom revolute joint planar linkages. Extensions of both methodologies are now demonstrated for equilibration of all rigid body planar linkages having lower and/or higher order kinematic pairs. Reduction in complexity of these general methodologies is demonstrated when kinematic chains include only revolute joints. A mathematical description of the complexity of each of three equilibration methodologies is introduced to provide a means of comparing the effectiveness of each approach. Examples demonstrate the appropriate equilibrator design choice for particular applications, based on the mathematical description of system complexity. A new approach for equilibration of linkages having higher order planar kinematic pairs (1R1T) is introduced. A solution to the problem of spring mass in equilibrator design is presented. Examples are included to demonstrate the effectiveness of both the 1R1T equilibrator design scheme, and the spring mass equilibration scheme. The 1R1T design represents a first equilibration of pantograph type mechanisms.

Evolution towards equilibration in orbiting interactions.

We have studied the evolution towards mass equilibration in $^{24}\mathrm{Mg}$${+}^{16}$O orbiting interactions. $^{24}\mathrm{Mg}$ beams of energies between 75 and 115 MeV were used to bombard targets of $^{16}\mathrm{O}$. Targetlike particles were detected at forward angles to determine the yields from orbiting interactions. The ratio of the orbiting yields of $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ exit channels rises continuously with energy from values below unity to above. The data are interpreted as demonstrating a strong entrance channel dependence at low energies, and an evolution towards mass equilibration with increasing energy.

Dynamics of the fusion process

The binary reaction products from the interaction of a 208Pb beam with targets of 26Mg, 27Al, 48Ca, 50Ti, 52Cr, 58Fe and 64Ni have been studied with the aid of a large position-sensitive ring counter, operated in a two-particle coincidence mode. The intensity of γ-rays and X-rays per event was also recorded. Within a broad range around mass symmetry, the center of mass angular distributions, γ-ray multiplicities, total kinetic energy distributions, and absolute mass yields have been determined as a function of the bombarding energy, ranging from 1.0 to 1.8 times the interaction barrier. When analysed on the basis of fusion models, the cross section for the mass equilibration reaction demonstrates that deformations induced at contact influence the fusion of these heavy systems significantly and characteristically. The γ-ray multiplicities appear to be strongly influenced by statistical angular momentum components that remain with the fragments after separation. Their magnitudes indicate that during the reaction, the collision complex becomes at least as compact as the liquid-drop saddle shape appropriate to a non-rotating nucleus with the same total mass and charge. Finally, some angular distributions show that the entire process of coalescence and reseparation can occur before the system has made one-half revolution; i.e. within a time of 5–10 × 10 −21 s. No X-ray emission from the combined system 208Pb + 48Ca is observed.

The influence of the potential energy surface on neutron excess and mass equilibration in the 136Xe + 56Fe system

Using magnetic spectrometer first and second moments of the nuclide distributions of Xe-like reaction products from 5.9 MeVu 136Xe on 56Fe were measured as a function of excitation energy. The drift path in the N versus Z plane follows the gradient of the two-dimensional potential energy surface (PES). Qualitatively the reaction process can be understood as a stochastical PES-governed exchange of nucleons.

The evolution of dissipative phenomena in collisions between heavy nuclei

Experimental information gained in recent years on dissipative collisions is reviewed. Besides a description of the general characteristics and of the domain of occurrence, particular attention is devoted to the derivation of an average interaction time, to the initial stage of the collision and to the mass equilibration after capture.