Masayuki Matsuo

Time-dependent density-functional description of nuclear dynamics

The basic concepts and recent developments in the time-dependent density-functional theory (TDDFT) for describing nuclear dynamics at low energy are presented. The symmetry breaking is inherent in nuclear energy density functionals, 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 the 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, the quantum fluctuations associated with slow collective motions are explicitly treated assuming that time evolution of densities is 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.

TETRAHEDRAL AND TRIANGULAR DEFORMATIONS OF Z= N NUCLEI IN MASS REGION A 60-80

Abstract We study static non-axial octupole deformations in proton-rich Z = N nuclei, 64 Ge, 68 Se, 72 Kr, 76 Sr, 80 Zr and 84 Mo, by using the Skyrme Hartree-Fock plus BCS calculation with no restrictions on the nuclear shape. The calculation predicts that the oblate ground state in 68 Se is extremely soft for the Y 33 triangular deformation, and that in 80 Zr the low-lying local minimum state coexisting with the prolate ground state has the Y 32 tetrahedral deformation.

Application of the adiabatic self-consistent collective coordinate method to a solvable model of prolate-oblate shape coexistence

The adiabatic self-consistent collective coordinate method is applied to an exactly solvable multi-O(4) model that is designed to describe nuclear shape coexistence phenomena. The collective mass and dynamics of large amplitude collective motion in this model system are analyzed, and it is shown that the method yields a faithful description of tunneling motion through a barrier between the prolate and oblate local minima in the collective potential. The emergence of the doublet pattern is clearly described.

Gauge-Invariant Formulation of the Adiabatic Self-Consistent Collective Coordinate Method

The adiabatic self-consistent collective coordinate (ASCC) method is a practical microscopic theory of large-amplitude collective motion in nuclei with superfluidity. We show that its basic equations are invariant under transformations involving the gauge angle in particlenumber space. By virtue of this invariance, a clean separation of the large-amplitude collective motion and the pairing rotational motion can be made, and this allows us to restore the particle-number symmetry broken by the Hartree-Fock-Bogoliubov (HFB) approximation. We formulate the ASCC method explicitly in a gauge-invariant form. In solving the ASCC equations, it is necessary to fix the gauge. Applying this new formulation to the multi-O(4) model, we compare different gauge-fixing procedures and demonstrate that calculations using different gauges indeed yield the same results for gauge-invariant quantities, such as the collective path and quantum spectra. We propose a gauge-fixing prescription that seems most convenient in realistic calculations.

RPA calculations with Gaussian expansion method

Abstract The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1 − , 2 + and 3 − collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in 60 Ca are investigated in some detail.

Continuum quasiparticle random-phase approximation for astrophysical direct neutron capture reactions on neutron-rich nuclei

I formulate a many-body theory to calculate the cross section of direct radiative neutron capture reaction by means of the Hartree--Fock--Bogoliubov mean-field model and the continuum quasiparticle random-phase approximation (QRPA). A focus is put on very-neutron-rich nuclei and low-energy neutron kinetic energy in the range from 1 keV to several MeV, which is relevant to the rapid neutron capture process of nucleosynthesis. I begin with the photoabsorption cross section and the

Surface-enhanced pair transfer amplitude in quadrupole states of neutron-rich Sn isotopes

E1

Continuum quasiparticle linear response theory using the Skyrme functional for multipole responses of exotic nuclei

strength function. Next, in order to apply the reciprocity theorem, I decompose the cross section into partial cross sections corresponding to different channels of one- and two-neutron emission decays of photo-excited states. A numerical example is shown for the photo-absorption of

Fluctuation properties of strength functions associated with giant resonances

^{142}\mathrm{Sn}

Microscopic derivation of the Bohr-Mottelson collective Hamiltonian and its application to quadrupole shape dynamics

and the neutron capture of