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Takashi Nakatsukasa ∗ , Makoto Ito †∗ ∗ , *Kazuhiro* *Yabana* ∗ and

, 2006

"... Fusion reaction of halo nuclei: A real-time wave-packet method for three-body tunneling dynamics ..."

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Fusion reaction of halo nuclei: A real-time wave-packet method for three-body tunneling dynamics

### ATOMIC SPECTRA IN A HELIUM BUBBLE

, 2002

"... Density functional theory (DFT) is applied to atomic spectra under perturbations of superfluid liquid helium. The atomic DFT of helium is used to obtain the distribution of helium atoms around the impurity atom, and the electronic DFT is applied to the excitations of the atom, averaging over the ens ..."

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Density functional theory (DFT) is applied to atomic spectra under perturbations of superfluid liquid helium. The atomic DFT of helium is used to obtain the distribution of helium atoms around the impurity atom, and the electronic DFT is applied to the excitations of the atom, averaging over the ensemble of helium configurations. The shift and broadening of the D1 and D2 absorption lines are quite well reproduced by theory, suggesting that the DFT may be useful for describing spectral perturbations in more complex environments. 1 Spectroscopy in liquid helium Spectroscopic measurements of impurity atoms and molecules in superfluid helium have been attracting considerable interest in recent years. 1,2 The repulsive force between an impurity and helium atoms induces a bubble around the impurity. This leads to a weak perturbation of helium atoms on the spectra of impurities. The line shifts and spectral shapes induced by the helium perturbation provide information on the properties of the bubble in the quantum liquid as well as the excited states of the impurity. Since the perturbation

### RESPONSE IN THE CONTINUUM FOR LIGHT DEFORMED NEUTRON-RICH NUCLEI ∗

, 2003

"... The time-dependent Hartree-Fock calculation with a full Skyrme energy functional has been carried out on the three-dimensional Cartesian lattice space to study E1 giant dipole resonances (GDR) in light nuclei. The outgoing boundary condition for the continuum states is treated by the absorbing compl ..."

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The time-dependent Hartree-Fock calculation with a full Skyrme energy functional has been carried out on the three-dimensional Cartesian lattice space to study E1 giant dipole resonances (GDR) in light nuclei. The outgoing boundary condition for the continuum states is treated by the absorbing complex potential. The calculation for GDR in 16 O suggests a significant influence of the residual interaction associated with time-odd densities in the Skyrme functional. We also predict a large damping for superdeformed 14 Be at the neutron drip line. 1. Time-dependent approach to nuclear response in the continuum The quantum-mechanical problems are usually solved in the energy (timeindependent) representation. Namely, we either solve an energy eigenvalue problem for bound states or, for scattering states, we calculate a wave function with a proper boundary condition at a given energy. However, if one wishes to calculate physical quantities in a wide energy region, the time-dependent approach is very useful because a single time propagation provides information for a certain range of energy. Another advantage may be an intuitive picture provided by the time evolution of the wave function. In Ref. 1, we have calculated molecular photoabsorption cross sections in the electronic continuum by using the time-dependent and timeindependent approaches. The results indicate the capability and efficiency

### Progress of Theoretical Physics Supplement 1 3D Real-Space Calculation of the Continuum Response

, 2002

"... We present that a linear response theory in the continuum can be easily formulated with Absorbing Boundary Condition (ABC). The theory is capable of describing continuum spectra and dynamical correlations. Application of the ABC does not require the spherical symmetry and the method is suitable for ..."

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We present that a linear response theory in the continuum can be easily formulated with Absorbing Boundary Condition (ABC). The theory is capable of describing continuum spectra and dynamical correlations. Application of the ABC does not require the spherical symmetry and the method is suitable for mesh representation in the real coordinate space. Isovector giant dipole resonances in beryllium isotopes are studied with the time-dependent Hartree-Fock with the Skyrme force in a three-dimensional mesh space with the ABC. The drip-line nuclei are finite fermion systems whose separation energy is nearly zero. For such weakly bound systems, the continuum should be properly taken into account in description of their structures and reactions. In the linear response regime, the inclusion of the single-particle continuum for particle-hole (p-h) excitations has

### Real-time Skyrme TDHF dynamics of giant resonances

, 2006

"... Nuclear dynamics of giant resonances are investigated with the real-time Skyrme TDHF method. The TDHF equation is explicitly linearized with respect to variation of singleparticle wave functions. The time evolution of transition densities are calculated for giant dipole resonances. The time-dependen ..."

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Nuclear dynamics of giant resonances are investigated with the real-time Skyrme TDHF method. The TDHF equation is explicitly linearized with respect to variation of singleparticle wave functions. The time evolution of transition densities are calculated for giant dipole resonances. The time-dependent densities of protons and neutrons suggest that the dynamics of giant dipole resonance in neutron-rich nuclei are significantly different from that in stable nuclei with N ≈ Z. 1.

### Nuclear dynamics in time-dependent picture

, 2006

"... Abstract. Using the time-dependent theory of quantum mechanics, we investigate nuclear electric dipole responses. The time evolution of a wave function is explicitly calculated in the coordinatespace representation. The particle continuum is treated with the absorbing boundary condition. Calculated ..."

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Abstract. Using the time-dependent theory of quantum mechanics, we investigate nuclear electric dipole responses. The time evolution of a wave function is explicitly calculated in the coordinatespace representation. The particle continuum is treated with the absorbing boundary condition. Calculated time-dependent quantities are transformed into those of familiar energy representation. We apply the method to a three-body model for 11 Li and to the mean-field model for 22 O, then discuss properties of E1 response. TIME-DEPENDENT METHOD FOR NUCLEAR RESPONSES Atomic nuclei exhibit a variety of responses to different experimental probes; Coulomb and nuclear excitations, spin- and isospin-dependent probes, high- and low-energy reactions. In order to investigate properties of these nuclear excitations, it is useful to study response function for a probe (external) operator of interest. Normally, these quantum many-body problems are theoretically studied using the energy representation, in which calculations are carried out by either diagonalizing the Hamiltonian matrices or solving differential equations with a fixed energy. These approaches are advantageous when we are interested in states within a limited energy range. However, when we calculate

### Resonance and Continuum States in Weakly Bound Systems

, 2008

"... Linear response theories in the continuum capable of describing continuum spectra and dynamical correlations are presented. Our formulation is essentially the same as the continuum random-phase approximation (RPA) but suitable for uniform grid representation in the three-dimensional (3D) Cartesian c ..."

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Linear response theories in the continuum capable of describing continuum spectra and dynamical correlations are presented. Our formulation is essentially the same as the continuum random-phase approximation (RPA) but suitable for uniform grid representation in the three-dimensional (3D) Cartesian coordinate assuming no spatial symmetry. Effects of the continuum are taken into account either by solving equations iteratively with a retarded Green’s function or by an absorbing boundary condition. The methods are applied to giant resonances in a deformed nucleus 12 C. 1