Collective Properties of Low-lying Octupole Excitations in 82208Pb126^{208}_{82}Pb_{126}, 2060Ca40^{60}_{20}Ca_{40} and 828O20^{28}_{8}O_{20}

The octupole strengths of $\beta$-stable nucleus $^{208}_{82}Pb_{126}$, a neutron skin nucleus $^{60}_{20}Ca_{40}$ and a neutron drip line nucleus $^{28}_{8}O_{20}$ are studied by using the self-consistent Hartree-Fock calculation plus the random phase approximation (RPA) with Skyrme interaction. The collective properties of low-lying excitations are analyzed by using particle-vibration coupling. The results show that the lowest isoscalar states above threshold in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$ are the superpositions of collective excitations and unperturbed transitions from bound state to nonresonance states. For these three nuclei, both the low-lying isoscalar states and giant isoscalar resonance carry isovector strength. The ratio B(IV)/B(IS) is checked. It is found that, for $^{208}_{82}Pb_{126}$, the ratios are equal to $(\frac{N-Z}{A})^2$ in good accuracy, while for $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$, the ratios are much larger than $(\frac{N-Z}{A})^2$. This results from the excess neutrons with small binding energies in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$.Comment: 14 pages, 10 figure

Kinetic energy and spin-orbit splitting in nuclei near neutron drip line

Two important ingredients of nuclear shell-structure, kinetic energy and spin-orbit splitting, are studied as a function of orbital angular momenta \ell and binding energies, when binding energies of neutrons decrease towards zero. If we use the standard parameters of the Woods-Saxon potential in \beta stable nuclei and approach the limit of zero binding energy from 10 MeV, the spin-orbit splitting for n=1 orbitals decreases considerably for \ell=1, while for \ell > 2 little decreasing is observed in the limit. In contrast, the kinetic energy decreases considerably for \ell \simleq 3. The smaller the \ell values of orbitals, the larger the decreasing rate of both kinetic energy and spin-orbit splitting. The dependence of the above bservation on the diffuseness of potentials is studied.Comment: 12 pages, 3 figures, submitted to Nucl. Phy

Chiral Symmetry and Electron-Electron Interaction in Many-Body Gap Formation in Graphene

We study a many-body ground state of graphene in perpendicular magnetic fields. Chiral symmetry in graphene enables us to determine the many-body ground state, which turns out to be a doubly degenerate chiral condensate for the half-filled (undoped) case. In the ground state a prominent charge accumulation emerges along zigzag edges. We also show that gapless excitations are absent despite the presence of the robust edge modes, which is consistent with the Chern number C = 0.Comment: 4 pages, 3 figures, proceeding of 26th International Conference on Low Temperature Physics (LT26

Interplay between one-particle and collective degrees of freedom in nuclei

Some developments of nuclear-structure physics uniquely related to Copenhagen School are sketched based on theoretical considerations versus experimental findings and one-particle versus collective aspects. Based on my personal overview I pick up the following topics; (1) Study of vibration in terms of particle-vibration coupling; (2) One-particle motion in deformed and rotating potentials, and yrast spectroscopy in high-spin physics; (3) Triaxial shape in nuclei: wobbling motion and chiral bands; (4) Nuclear structure of drip line nuclei: in particular, shell-structure (or magic numbers) change and spherical or deformed halo phenomena; (5) shell structure in oblate deformation.Comment: 19 pages, 9 figure

Gauge Theory of Massive Tensor Field

In order to construct a massive tensor theory with a smooth massless limit, we apply the Batalin-Fradkin algorithm to the ordinary massive tensor theory. By introducing an auxiliary vector field all second-class constraints are converted into first-class ones. We find a gauge-fixing condition which produces a massive tensor theory of desirable property.Comment: 13 pages, LaTe

Massless Limits of Massive Tensor Fields

In order to construct a massive tensor theory with a smooth massless limit, we apply two kinds of gauge-fixing procedures, Nakanishi's one and the BRS one, to two models of massive tensor field. The first is of the Fierz-Pauli (FP) type, which describes a pure massive tensor field; the other is of the additional-scalar-ghost (ASG) type, which includes a scalar ghost in addition to an ordinary tensor field. It is shown that Nakanishi's procedure can eliminate massless singularities in both two models, while the BRS procedure regularizes the ASG model only. The BRS-regularized ASG model is most promising in constructing a complete nonlinear theory.Comment: LaTeX, 15 pages, uses ptptex.sty and ptp-prep.st

Possible Presence and Properties of Multi Chiral Pair-Bands in Odd-Odd Nuclei with the Same Intrinsic Configuration

Applying a relatively simple particle-rotor model to odd-odd nuclei, possible presence of multi chiral pair-bands is looked for, where chiral pair-bands are defined not only by near-degeneracy of the levels of two bands but also by almost the same expectation values of squared components of three angular-momenta that define chirality. In the angular-momentum region where two pairs of chiral pair-bands are obtained the possible interband M1/E2 decay from the second-lowest chiral pair-bands to the lowest chiral pair-bands is studied, with the intention of finding how to experimentally identify the multi chiral pair-bands. It is found that up till almost band-head the intraband M1/E2 decay within the second chiral pair-bands is preferred rather than the interband M1/E2 decay to the lowest chiral pair-bands, though the decay possibility depends on the ratio of actual decay energies. It is also found that chiral pair-bands in our model and definition are hardly obtained for $\gamma$ values outside the range $25^{\circ} < \gamma < 35^{\circ}$, although either a near-degeneracy or a constant energy-difference of several hundreds keV between the two levels for a given angular-momentum $I$ in "a pair bands" is sometimes obtained in some limited region of $I$. In the present model calculations the energy difference between chiral pair-bands is always one or two orders of magnitude smaller than a few hundreds keV, and no chiral pair-bands are obtained, which have an almost constant energy difference of the order of a few hundreds keV in a reasonable range of $I$.Comment: 15 pages, 14 figure

Gauge Theory of Massive Tensor Field II --- Covariant Expressions ---

Covariant forms are given to a gauge theory of massive tensor field. This is accomplished by introducing another auxiliary field of scalar type to the system composed of a symmetric tensor field and an auxiliary field of vector type. The situation is compared to the case of the theory in which a tensor field describes a scalar ghost as well as an ordinary massive tensor. In this case only an auxiliary vector field is needed to give covariant expressions for the gauge theory.Comment: 14 pages, uses ptptex.sty for LaTe