Time-dependent density-functional description of nuclear dynamics

Abstract

We present the basic concepts and recent developments in the time-dependent density functional theory (TDDFT) for describing nuclear dynamics at low energy. The symmetry breaking is inherent in nuclear energy density functionals (EDFs), which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, we treat the quantum fluctuations associated with slow collective motions assuming that time evolution of densities are determined by a few collective coordinates and momenta. The concept of collective submanifold is introduced in the phase space associated with the TDDFT and used to quantize the collective dynamics. Selected applications are presented to demonstrate the usefulness and quality of the new approaches. Finally, conceptual differences between nuclear and electronic TDDFT are discussed, with some recent applications to studies of electron dynamics in the linear response and under a strong laser field.

Transport properties of isospin asymmetric nuclear matter using the time-dependent Hartree-Fock method

“…Thus, TDHF simulations of these collisions with definite impact parameters are expected to yield quantitatively good agreement with the corresponding experimental data. While TDHF provides a good starting point for a fully microscopic theory of large amplitude collective motion [36][37][38], only in recent years has it become feasible to perform TDHF calculations on a three-dimensional Cartesian grid without any symmetry restrictions and with accurate numerical methods [63][64][65][66][67][68][69][70]. In addition, the quality of energy-density functionals has been substantially improved [71][72][73].…”

“…The mean-field approach such as the timedependent Hartree-Fock (TDHF) theory provides a microscopic basis for describing heavy-ion reaction mechanism at low bombarding energies [36][37][38]. TDHF collisions which result in well separated final fragments provide a means to study the deep-inelastic scattering of heavy-systems, allowing for the calculation of certain scattering observables, such as the final mass, charge, and scattering angles of the fragments.…”

Multinucleon transfer in central collisions of U238+U238

“…A number of models was developed for a description of the reaction mechanism in the multi-nucleon transfer process in quasi-fission reactions [1][2][3][4]. Within the last few years the time-dependent Hartree-Fock (TDHF) approach [5][6][7] has been utilized for studying the dynamics of quasifission [7][8][9][10][11][12][13][14][15][16][17] and scission dynamics [18][19][20][21][22][23]. Such calculations are now numerically feasible to perform on a 3D Cartesian grid without any symmetry restrictions and with much more accurate numerical methods [24][25][26].…”

Density Functional Approach to Superfluid Phonon in Inner Crust of Neutron Stars

“…we consider a single Wigner-Seitz cell of lattice with appropriate boundary conditions. We obtain selfconsistent configurations by solving the Kohn-Sham Bogoliubov-de Gennes equation (equivalent to the Hartree-Fock-Bogoliubov equation) [9] for given proton number Z in the cell and the neutron chemical potential λ n . To describe the neutron superfluidity we use the density-dependent contact interaction as an effective pairing force, the parameters of which is prepared to reproduce the neutron pairing gap obtained in the BCS approach with the bare nuclear force [13].…”

“…However, inhomogeneity of inner crust matter may affect the character of the SPH and the coupling to the lattice phonon, and therefore nuclear many-body approaches are required to provide microscopic information on SPH in the inner crust. Nuclear density functional theories and their extension to timedependent and linear response regime [9] may be useful to this problem. Martin and Urban [10] has described the SPH in uniform neutron matter.…”