Frontiers in Nuclear and Particle Physics

We discuss some aspects of implementing the time-dependent Hartree-Fock method in the case of nuclear physics. Topics discussed include implementation of the time-stepping algorithm, considerations involving the effective interaction, and the use (or not) of particular optional terms in the energy density functional, and boundary conditions. Examples of application of the technique to giant resonances and reactions are given, concentrating on issues to do with numerical and conceptual interpretation.

In this manuscript we provide an outline of the numerical methods used in implementing the density constrained time-dependent Hartree-Fock (DC-TDHF) method and provide a few examples of its application to nuclear fusion. In this approach, dynamic microscopic calculations are carried out on a three-dimensional lattice and there are no adjustable parameters, the only input is the Skyrme effective NN interaction. After a review of the DC-TDHF theory and the numerical methods, we present results for heavy-ion potentials V (R), coordinate-dependent mass parameters M(R), and precompound excitation energies E*(R) for a variety of heavy-ion reactions. Using fusion barrier penetrabilities, we calculate total fusion cross sections σ(Ec:m:) for reactions between both stable and neutron-rich nuclei. We also determine capture cross sections for hot fusion reactions leading to the formation of superheavy elements.

Time-dependent Hartree-Fock (TDHF) theory has achieved a remarkable success in describing and understanding nuclear many-body dynamics from nucleons’ degrees of freedom. We here report our investigation of multinucleon transfer (MNT) processes employing the TDHF theory. To calculate transfer probabilities for channels specified by the number of protons and neutrons included in reaction products, a particle-number projection (PNP) method has been developed. The PNP method is also used to calculate excitation energies of reaction products. Combined use of the PNP method with a statistical model, we can evaluate MNT cross sections taking account of effects of particle evaporation. Using these methods, we evaluate MNT cross sections for 40,48Ca+124Sn, 40Ca+208Pb, and 58Ni+208Pb reactions. From systematic analyses, we find that cross sections for channels with a large reaction probability are in good agreement with experimental data. However, the agreement becomes less accurate as the number of transferred nucleons increases. Possible directions to improve the description are discussed.

The extension of Time Dependent Density Functional Theory (TDDFT) to superfluid systems is discussed in the context of nuclear reactions and large amplitude collective motion.

The determination of fragment particle number distributions in microscopic systems is a fundamental problem. It requires a proper quantum mechanical treatment accounting for indistinguishability of identical particles. The results also depend on the predictive power of the many-body dynamical theory used to describe the evolution of the system. The widely used timedependent Hartree-Fock (TDHF) mean-field approximation can describe quasielastic transfer probabilities, but it underpredicts the variance of the fragment particle number distributions in more violent reactions such as deep-inelastic collisions. The latter require beyond mean-field fluctuations which are described, e.g., within the time-dependent random-phase approximation (TDRPA). Applications of the TDHF formalism and its extension including pairing correlations at the BCS level, as well as TDRPA calculations are presented in the nuclear physics context. Examples include transfer reactions and fission. Numerical aspects are emphasised.

In the present note, a summary of selected aspects of timedependent mean-field theory is first recalled. This approach is optimized to describe one-body degrees of freedom. A special focus is made on how this microscopic theory can be reduced to a macroscopic dynamic for a selected set of collective variables. Important physical phenomena like adiabaticity/diabaticity, one-body dissipation or memory effect are discussed. Special aspects related to the use of a time-dependent density functional instead of a time-dependent Hartree-Fock theory based on a bare hamiltonian are underlined. The absence of proper description of complex internal correlations however strongly impacts the predictive power of mean-field. A brief overview of theories going beyond the independent particles/quasi-particles theory is given. Then, a special attention is paid for finite fermionic systems at low internal excitation. In that case, quantum fluctuations in collective space that are poorly treated at the meanfield level, are important. Several approaches going beyond mean-field, that are anticipated to improve the description of quantum fluctuations, are discussed: the Balian-V´en´eroni variational principle, the Time-Dependent Random Phase Approximation and the recently proposed Stochastic Mean-Field theory. Relations between these theories are underlined as well as their advantages and shortcomings.

The single-particle motions of nucleons and the cluster correlations are both essential in understanding dynamics of heavy-ion collisions in a wide range of incident energies from several ten to several hundred MeV/nucleon. The antisymmetrized molecular dynamics approach has been improved in two directions, by introducing wave packet splitting in the first way, and by taking into account cluster correlations explicitly in the second way. I will review the basic ideas for these extensions which are closely related to the important physics in heavy-ion collisions. Some representative results are also reviewed such as for multifragmentation reactions and for virtually equilibrated systems in a box.

Some of my recent works on the two-center shell model and its application to describing low-energy nuclear collisions within time-dependent approaches are reviewed and a perspective for their further use is given.

In this lecture note we address the dynamics of strongly interacting relativistic fields within the theory of Kadanoff and Baym and compare to the corresponding relativistic on-shell Boltzmann limit. As an example all expressions are given explicitly for the scalar Φ4-theory and numerical solutions are discussed in case of weak and strong coupling for Φ4-theory in 2+1 dimensions. Furthermore, the Kadanoff-Baym equations are expanded in first order gradients in phase space and off-shell transport equations are derived in the Botermans-Malfliet scheme for the Wightman function G<(x, p). Finally, a generalized testparticle Ansatz ist introduced for the real quantity iG<(x, p) which leads to transparent equations of motion for the testparticles and allows to solve the off-shell transport equations also for (moderately) inhomogeneous systems.

The linear chain structure of α clusters has been a long dream of nuclear structure physics. The stabilization is essentially difficult, and some extra mechanisms are needed to be introduced. One of the candidates is the increase of the isospin, which means adding valence neutrons. Even if the linear-chain configurations are difficult to be stabilized in the N = Z nuclei, it is considered that higher stability may be possible if we move on to the neutron rich side. It has been discussed mainly in the two α cluster cases that when the neutrons occupy the so-called σ orbit, which is parallel to the symmetry axis, an elongated shape is favored for the lowering of the energy of the valence neutron. This effect is further examined in the C isotopes, where three α clusters are located with a linear shape, and valence neutrons are added to these three α clusters. Another possible mechanism is the increase of the angular momentum by rotating the nucleus rapidly: the linear chain configuration with large moment of inertia is favored when the centrifugal force strongly acts. This effect is examined in 16O (four α linear chain) and 24Mg (six α linear chain). Finally, the appearance of rod shape in C isotopes is investigated in the framework of the cranking covariant density functional theory, and coherent effect of these two mechanisms, adding neutron (high isospin) and rotating the system (high spin) is discussed.

In this contribution, I will discuss two topics related to the clustering of atomic nuclei. The first is dual character of the ground state. Recently, it was pointed out that the ground states of atomic nuclei have dual character of shell and cluster implying that both of the single-particle excitation and cluster excitation occur as the fundamental excitation modes. The isoscalar monopole and dipole transitions are regarded as the triggers to induce the cluster excitation. By referring the Hartree-Fock and antisymmetrized molecular dynamics calculations, the dual character and those transitions are explained. The second is the linear-chain state of 16C in which the linearly aligned 3α particles are sustained by the valence neutrons. The rather convincing evidences for this exotic state are very recently reported by several experiments. Here, I introduce a couple of theoretical analysis and predictions.

Molecular dynamics simulations for nucleon many-body systems is briefly introduced. We employ quantum molecular dynamics (QMD) to investigate nuclear reactions with incident energy of a few to several hundred MeV/nucleon and also the ground state structures of nuclear matter. To use QMD model for such low-energy phenomena, improvement and refinement are necessary for several points such as inclusion of Pauli potential and taking care of the spurious zero-point energy of clusters. On the other hand, we have proposed a new application of MD to the quark system. Though there are many rooms of improvements, our MD for quark system shows some interesting results. In this review article, reported are the frameworks and the results already published by the author and his collaborators. However, it should be worth reviewing our works on MD, since it will be found that the similar frameworks can be applied to various subjects in the field of nuclear physics.

Attempts for synthesizing superheavy elements have to overcome the fusion hindrance as the large Coulomb repulsion of colliding system and the dissipation of the kinetic energy due to the strong nuclear friction. To describe the fusion-fission process and to estimate the possibility of synthesis of superheavy elements, the dynamical model based on fluctuation-dissipation theorem has been applied. The theory of Brownian motion is employed to describe the dynamical evolution of the whole fusion-fission process, with extremely small probability of residues of superheavy nuclei. First, as diffusion model, onedimensional Smoluchowski equation was applied, which taking account of the temperature dependence of the shell correction energy. A new mechanism for an optimum condition was found as a compromise of two conflicting requirements: higher incident energy for larger fusion probability and lower excitation energy of compound nuclei for larger survival probability. To describe fusion-fission process more realistically, the three-dimensional Langevin equation was applied. Using the model, we estimated the possibility of synthesis of superheavy elements and clarified the fusion-fission mechanism. We present these developments and main results.