Time-dependent mean-field investigations of the quasifission process

We demonstrate that the microscopic Time-dependent Hartree-Fock (TDHF) theory provides an important approach to shed light on the nuclear dynamics leading to the formation of superheavy elements. In particular, we discuss studying quasifission dynamics and calculating ingredients for compound nucleus formation probability calculations. We also discuss possible extensions to TDHF to address the distribution of observables.Comment: Proceedings of a talk given at FUSION17, Hobart, Tasmania, AU (20-24 February, 2017

Stochastic Semi-Classical Description of Fusion at Near-Barrier Energies

Fusion reactions of heavy ions are investigated by employing a simple stochastic semi-classical model which includes the coupling between relative motion and low frequency collective surface modes of colliding ions similarly to the quantal coupled-channels description. The quantal effect enters into the calculation through the initial zero-point fluctuations of the surface vibrations. Good agreement with the result of coupled-channels calculations as well as data is obtained for the fusion cross sections of nickel isotopes. The internal excitations in non-fusing events as well as the fusion time are investigated.Comment: 8 pages, 8 figures, Published in Phys. Rev.

Spinodal Instabilities in Nuclear Matter in a Stochastic Relativistic Mean-Field Approach

Spinodal instabilities and early growth of baryon density fluctuations in symmetric nuclear matter are investigated in the basis of stochastic extension of relativistic mean-field approach in the semi-classical approximation. Calculations are compared with the results of non-relativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher baryon densities around $\rho_{b}=0.4 ~\rho_{0}$ in the relativistic approach while most unstable behavior occurs at lower baryon densities around $\rho_{b}=0.2 ~\rho_{0}$ in the non-relativistic calculationsComment: 18 pages, 7 figure

On nucleon exchange mechanism in heavy-ion collisions at near-barrier energies

Nucleon drift and diffusion mechanisms in central collisions of asymmetric heavy-ions at near-barrier energies are investigated in the framework of a stochastic mean-field approach. Expressions for diffusion and drift coefficients for nucleon transfer deduced from the stochastic mean-field approach in the semiclassical approximation have similar forms familiar from the phenomenological nucleon exchange model. The variance of fragment mass distribution agrees with the empirical formula $\sigma^2_{AA}(t)= N_{\rm exc}(t)$. The comparison with the time-dependent Hartree-Fock calculations shows that, below barrier energies, the drift coefficient in the semiclassical approximation underestimates the mean number of nucleon transfer obtained in the quantal framework. Motion of the window in the dinuclear system has a significant effect on the nucleon transfer in asymmetric collisions.Comment: 10 pages, 10 figures, submitted for publicatio

Fluctuation and dissipation dynamics in fusion reactions from stochastic mean-field approach

By projecting the stochastic mean-field dynamics on a suitable collective path during the entrance channel of heavy-ion collisions, expressions for transport coefficients associated with relative distance are extracted. These transport coefficients, which have similar forms to those familiar from nucleon exchange model, are evaluated by carrying out TDHF simulations. The calculations provide an accurate description of the magnitude and form factor of transport coefficients associated with one-body dissipation and fluctuation mechanism.Comment: 9 pages, 5 figure

Sound modes in hot nuclear matter

The propagation of the isoscalar and isovector sound modes in a hot nuclear matter is considered. The approach is based on the collisional kinetic theory and takes into account the temperature and memory effects. It is shown that the sound velocity and the attenuation coefficient are significantly influenced by the Fermi surface distortion (FSD). The corresponding influence is much stronger for the isoscalar mode than for the isovector one. The memory effects cause a non-monotonous behavior of the attenuation coefficient as a function of the relaxation time leading to a zero-to-first sound transition with increasing temperature. The mixing of both the isoscalar and the isovector sound modes in an asymmetric nuclear matter is evaluated. The condition for the bulk instability and the instability growth rate in the presence of the memory effects is studied. It is shown that both the FSD and the relaxation processes lead to a shift of the maximum of the instability growth rate to the longer wave length region.Comment: 15 pages, 4 figures, submitted to Phys. Rev.

Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation

On the basis of the antisymmetrized molecular dynamics (AMD) of wave packets for the quantum system, a novel model (called AMD-V) is constructed by the stochastic incorporation of the diffusion and the deformation of wave packets which is calculated by Vlasov equation without any restriction on the one-body distribution. In other words, the stochastic branching process in molecular dynamics is formulated so that the instantaneous time evolution of the averaged one-body distribution is essentially equivalent to the solution of Vlasov equation. Furthermore, as usual molecular dynamics, AMD-V keeps the many-body correlation and can naturally describe the fluctuation among many channels of the reaction. It is demonstrated that the newly introduced process of AMD-V has drastic effects in heavy ion collisions of 40Ca + 40Ca at 35 MeV/nucleon, especially on the fragmentation mechanism, and AMD-V reproduces the fragmentation data very well. Discussions are given on the interrelation among the frameworks of AMD, AMD-V and other microscopic models developed for the nuclear dynamics.Comment: 26 pages, LaTeX with revtex and epsf, embedded postscript figure

Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei

Antisymmetrized molecular dynamics (AMD) with quantum branching processes is reformulated so that it can be applicable to the collisions of heavy nuclei such as Au + Au multifragmentation reactions. The quantum branching process due to the wave packet diffusion effect is treated as a random term in a Langevin-type equation of motion, whose numerical treatment is much easier than the method of the previous papers. Furthermore a new approximation formula, called the triple-loop approximation, is introduced in order to evaluate the Hamiltonian in the equation of motion with much less computation time than the exact calculation. A calculation is performed for the Au + Au central collisions at 150 MeV/nucleon. The result shows that AMD almost reproduces the copious fragment formation in this reaction.Comment: 24 pages, 5 figures embedde

Memory effects on descent from nuclear fission barrier

Non-Markovian transport equations for nuclear large amplitude motion are derived from the collisional kinetic equation. The memory effects are caused by the Fermi surface distortions and depend on the relaxation time. It is shown that the nuclear collective motion and the nuclear fission are influenced strongly by the memory effects at the relaxation time $\tau \geq 5\cdot 10^{-23}{\rm s}$. In particular, the descent of the nucleus from the fission barrier is accompanied by characteristic shape oscillations. The eigenfrequency and the damping of the shape oscillations depend on the contribution of the memory integral in the equations of motion. The shape oscillations disappear at the short relaxation time regime at $\tau \to 0$, which corresponds to the usual Markovian motion in the presence of friction forces. We show that the elastic forces produced by the memory integral lead to a significant delay for the descent of the nucleus from the barrier. Numerical calculations for the nucleus $^{236}$U shows that due to the memory effect the saddle-to-scission time grows by a factor of about 3 with respect to the corresponding saddle-to-scission time obtained in liquid drop model calculations with friction forces.Comment: 22 pages, 8 figures, submitted to Phys. Rev.

Quantum Statistical Effects on Fusion Dynamics of Heavy-Ions

In order to describe the fusion of two very heavy nuclei at near barrier energies, a generalized Langevin approach is proposed, which incorporates the quantum statistical fluctuations in accordance with the fluctuation and dissipation theorem. It is illustrated that the quantum statistical effects introduce an enhancement of the formation of compound nucleus, though the quantum enhancement is somewhat less pronounced as indicated in the previous calculations.Comment: 17 pages, 6 figure