We present simple equations for a canonical-basis (Cb) formulation of the time-dependent Hartree-FockBogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the Cb. The Cb formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasiparticle random-phase approximation with Skyrme functionals. We show systematic studies of E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, which include the neutron excess, the separation energy, the neutron-shell effects, the deformation, and the pairing.

Large-amplitude collective dynamics of shape phase transition in the low-lying states of 30−36 Mg is investigated by solving the five-dimensional (5D) quadrupole collective Schrödinger equation. The collective masses and potentials of the 5D collective Hamiltonian are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random phase approximation method. Good agreement with the recent experimental data is obtained for the excited 0 + states as well as the ground bands. For 30 Mg, the shape coexistence picture that the deformed excited 0 + state coexists with the spherical ground state approximately holds. On the other hand, large-amplitude quadrupole-shaped fluctuations dominate in both the ground and the excited 0 + states in 32 Mg, providing a picture that is different from the interpretation of the "coexisting spherical excited 0 + state" based on the naive inversion picture of the spherical and deformed configurations.Nuclei exhibit a variety of shapes in their ground and excited states. A feature of the quantum phase transition of a finite system is that the order parameters (shape deformation parameters) always fluctuate and vary with the particle number. Especially, the large-amplitude shape fluctuations play a crucial role in transitional (critical) regions. Spectroscopic studies of low-lying excited states in transitional nuclei are of great interest to observe such unique features of the finite quantum systems.Low-lying states of neutron-rich nuclei at approximately N = 20 attract great interest, as the spherical configurations associated with the magic number disappear in the ground states. In neutron-rich Mg isotopes, the increase of the excitation energy ratio E(4 1 + )/E(2 1 + ) [1-3] and the enhancement of B(E2; 2 1 + → 0 1 + ) from 30 Mg to 34 Mg [4-6] indicate a kind of quantum phase transition from spherical to deformed shapes taking place around 32 Mg. These experiments stimulate microscopic investigations on quadrupole collective dynamics unique to this region of the nuclear chart with various theoretical approaches: the shell model [7-10], the Hartree-Fock-Bogoliubov (HFB) method [11,12], the parityprojected Hartree-Fock (HF) [13], the quasiparticle random phase approximation (QRPA) [14,15], the angular-momentum projected generator coordinate method (GCM) with [16] and without [17,18] restriction to the axial symmetry, and the antisymmetrized molecular dynamics [19]. Quite recently, excited 0 + states were found in 30 Mg and 32 Mg at 1.789 MeV and 1.058 MeV, respectively, and their characters are presently under hot discussion [20-23]. For 30 Mg, the excited 0 2 + state is interpreted as a prolately deformed state which coexists with the spherical ground state. For 32 Mg, from the observed population of the excited 0 2 + state in the (t,p) reaction on 30 Mg, it is suggested [22] that the 0 2 + state is a spherical state coexisting with the deformed ground state and that their relative energies are inverted at N = 20. However, available shell-mod...

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Microscopic structure of the low-lying isovector dipole excitation mode in neutron-rich $^{26,28,30}$Ne is investigated by performing deformed quasiparticle-random-phase-approximation (QRPA) calculations. The particle-hole residual interaction is derived from a Skyrme force through a Landau-Migdal approximation. We have obtained the low-lying resonance in $^{26}$Ne at around 8.5 MeV. It is found that the isovector dipole strength at $E_{x}<10$ MeV exhausts about 6.0% of the classical Thomas-Reiche-Kuhn dipole sum rule. This excitation mode is composed of several QRPA eigenmodes, one is generated by a $\nu(2s^{-1}_{1/2} 2p_{3/2})$ transition dominantly, and the other mostly by a $\nu(2s^{-1}_{1/2} 2p_{1/2})$ transition. The neutron excitations take place outside of the nuclear surface reflecting the spatially extended structure of the $2s_{1/2}$ wave function. In $^{30}$Ne, the deformation splitting of the giant resonance is large, and the low-lying resonance is overlapping with the giant resonance.Comment: 8 pages, 9 figures and 5 table