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Register a new userTime-dependent density-functional calculation of nuclear response functions
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Authors
Takashi Nakatsukasa
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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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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.
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.
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.
Nonequilibrium Greens functions represent underutilized means of studying the time evolution of quantum many-body systems. In view of a rising computer power, an effort is underway to apply the Greens functions formalism to the dynamics of central nuclear reactions. As the first step, mean-field evolution for the density matrix for colliding slabs is studied in one dimension. The strategy to extend the dynamics to correlations is described.
Following a previous paper [Y. Shi, Phys. Rev. C 98, 014329(2018)], we present an extension of the density-functional theory to allow for dynamic calculations based on the obtained static Hartree-Fock results. We perform extensive benchmark calculations, by comparing the calculated results with that of an existing code Sky3D. To perform linear-response calculations using the TDDFT method, comparisons have been made with the finite-amplitude quasiparticle random-phase approximation (FAM-QRPA) method. We plan to apply the TDDFT method to a systematic description of the IVD resonances in the Zr, Mo, and Ru isotopes. The strengths of IVD resonances are calculated using two complementary methods: TDDFT and FAM-QRPA methods. For the TDDFT results, additional benchmark calculations have been performed using the well-tested code Sky3D. In these three models, the important ingredients which have major influence on the results, such as time-odd potentials, boundary conditions, smoothing procedures, spurious peaks etc., have been carefully examined. The current TDDFT and the Sky3D codes yield almost identical response functions once both codes use the same time-odd mean fields and absorbing boundary conditions. The strengths of the IVD resonances calculated using the TDDFT and FAM-QRPA methods agree reasonably well with the same position of the giant dipole resonance. Upon seeing a reasonable accuracy offered by the implemented code, we perform systematic TDDFT calculations for spherical Zr and Mo isotopes near $N=50$, where experimental data exist. For neutron-rich Zr, Mo, and Ru isotopes where shape evolution exist we predict the photoabsorption cross sections based on oblate and triaxial minima.
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