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Register a new userSolitons in nuclear time-dependent density functional theory
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Authors
Yoritaka Iwata
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The soliton existence in sub-atomic many-nucleon systems is discussed. In many nucleon dynamics represented by the nuclear time-dependent density functional formalism, much attention is paid to energy and mass dependence of the soliton existence. In conclusion, the existence of nuclear soliton is clarified if the temperature of nuclear system is from 10 to 30 MeV. With respect to the mass dependence $^{4}$He and $^{16}$O are suggested to be the candidates for the self-bound states exhibiting the property of nuclear soliton.
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The time-dependent covariant density functional theory in 3D lattice space has been developed and applied to investigate the microscopic dynamics of the linear-chain cluster states for carbon isotopes in the reactions $^4$He$+^8$Be and $^4$He$+^{10}$Be without any symmetry assumptions. By examining the density distribution and its time evolutions, the structure and dynamics of the linear-chain states are analyzed, and the quasiperiodic oscillations of the clusters are revealed. For $^4$He$+^8$Be, the linear-chain states evolve to a triangular configuration and then to a more compact shape. In contrast, for $^4$He$+^{10}$Be, the lifetime of the linear-chain states is much more prolonged due to the dynamical isospin effects by the valence neutrons which slow down the longitudinal oscillations of the clusters and persist the linear-chain states. The dependence of the linear chain survival time and dynamical isospin effects on impact parameters have been illustrated as well.
The three-dimensional tilted axis cranking covariant density functional theory (3D-TAC CDFT) is used to study the chiral modes in $^{135}$Nd. By modeling the motion of the nucleus in rotating mean field as the interplay between the single-particle motions of several valence particle(s) and hole(s) and the collective motion of a core-like part, a classical Routhian is extracted. This classical Routhian gives qualitative agreement with the 3D-TAC CDFT result for the critical frequency corresponding to the transition from planar to aplanar rotation. Based on this investigation a possible understanding of tilted rotation appearing in a microscopic theory is provided.
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.
Time-dependent covariant density functional theory with the successful density functional PCPK1 is developed in a three-dimensional coordinate space without any symmetry restrictions, and benchmark calculations for the 16O + 16O reaction are performed systematically. The relativistic kinematics, the conservation laws of the momentum, total energy, and particle number, as well as the time-reversal invariance are examined and confirmed to be satisfied numerically. Two primary applications including the dissipation dynamics and above-barrier fusion cross sections are illustrated. The obtained results are in good agreement with the ones given by the nonrelativistic time-dependent density functional theory and the data available. This demonstrates that the newly developed time-dependent covariant density functional theory could serve as an effective approach for the future studies of nuclear dynamical processes.
Basic issues of the time-dependent density-functional theory are discussed, especially on the real-time calculation of the linear response functions. Some remarks on the derivation of the time-dependent Kohn-Sham equations and on the numerical methods are given.
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