Monopole Excitation to Cluster States

We discuss strength of monopole excitation of the ground state to cluster states in light nuclei. We clarify that the monopole excitation to cluster states is in general strong as to be comparable with the single particle strength and shares an appreciable portion of the sum rule value in spite of large difference of the structure between the cluster state and the shell-model-like ground state. We argue that the essential reasons of the large strength are twofold. One is the fact that the clustering degree of freedom is possessed even by simple shell model wave functions. The detailed feature of this fact is described by the so-called Bayman-Bohr theorem which tells us that SU(3) shell model wave function is equivalent to cluster model wave function. The other is the ground state correlation induced by the activation of the cluster degrees of freedom described by the Bayman-Bohr theorem. We demonstrate, by deriving analytical expressions of monopole matrix elements, that the order of magnitude of the monopole strength is governed by the first reason, while the second reason plays a sufficient role in reproducing the data up to the factor of magnitude of the monopole strength. Our explanation is made by analysing three examples which are the monopole excitations to the $0^+_2$ and $0^+_3$ states in $^{16}$O and the one to the $0^+_2$ state in $^{12}$C. The present results imply that the measurement of strong monopole transitions or excitations is in general very useful for the study of cluster states.Comment: 11 pages, 1 figure: revised versio

Hydrodynamics of Internal Shocks in Relativistic Outflows

We study the hydrodynamical effects of two colliding shells, adopted to model internal shocks in various relativistic outflows such as gamma-ray bursts and blazars. We find that the density profiles are significantly affected by the propagation of rarefaction waves. A split-feature appears at the contact discontinuity of the two shells. The shell spreading with a few ten percent of the speed of light is also shown to be a notable aspect. The conversion efficiency of the bulk kinetic energy to internal one shows deviations from the widely-used inelastic two-point-mass-collision model. Observational implications are also shortly discussed.Comment: 6 pages, 4 figures, Proceeding of International Symposium on High Energy Gamma-ray Astronomy (July 26-30, 2004, Heidelberg, Germany

Chiral dynamics of Σ\Sigma-hyperons in the nuclear medium

Using SU(3) chiral perturbation theory we calculate the density-dependent complex mean field $U_\Sigma(k_f)+ i W_\Sigma(k_f)$ of a $\Sigma$-hyperon in isospin-symmetric nuclear matter. The leading long-range $\Sigma N$-interaction arises from one-kaon exchange and from two-pion exchange with a $\Sigma$- or a $\Lambda$-hyperon in the intermediate state. We find from the $\Sigma N\to \Lambda N$ conversion process at nuclear matter saturation density $\rho_0 = 0.16$fm$^{-3}$ an imaginary single-particle potential of $W_\Sigma(k_{f0}) =-21.5$ MeV, in fair agreement with existing empirical determinations. The genuine long-range contributions from iterated (second order) one-pion exchange with an intermediate $\Sigma$- or $\Lambda$-hyperon sum up to a moderately repulsive real single-particle potential of $U_\Sigma(k_{f0})= 59$ MeV. Recently measured $(\pi^-,K^+$) inclusive spectra related to $\Sigma^-$-formation in heavy nuclei give evidence for a $\Sigma$-nucleus repulsion of similar size. Our results suggest that the net effect of the short-range $\Sigma N$-interaction on the $\Sigma$-nuclear mean field could be small.Comment: 7 pages, 2 figures, published in: Phys. Rev. C 71, 068201 (2005

On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture

We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4\pi}$ is the area radius of $S$. A consequence of this inequality is that for connected black holes the following lower bound on the area holds: $r\geq m-\sqrt{m^2-q^2}$. In conjunction with the upper bound $r\leq m + \sqrt{m^2-q^2}$ which is expected to hold always, this implies the natural generalization of the Riemannian Penrose inequality: $m\geq 1/2(r+q^2/r)$.Comment: 4 pages; 1st revision, added a generalization, added a reference; 2nd revision, minor correction

Modified Laplace transformation method and its application to the anharmonic oscillator

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral representation. The modification of the Laplace transformation is such that the upper limit of integration is cut off and an extra term is added for the compensation. For the non-Gaussian integral, we find that the perturbation series can give accurate result and the obtained approximation converges to the exact result in the $N \to \infty$ limit ($N$ denotes the order of perturbation expansion). In the case of anharmonic oscillator, we show that several order result yields good approximation of the ground state energy over the entire parameter space. The large order aspect is also investigated for the anharmonic oscillator.Comment: 26 pages including tables, Late

Mott transition and ferrimagnetism in the Hubbard model on the anisotropic kagom\'e lattice

Mott transition and ferrimagnetism are studied in the Hubbard model on the anisotropic kagom\'e lattice using the variational cluster approximation and the phase diagram at zero temperature and half-filling is analyzed. The ferrimagnetic phase rapidly grows as the geometric frustration is relaxed, and the Mott insulator phase disappears in moderately frustrated region, showing that the ferrimagnetic fluctuations stemming from the relaxation of the geometric frustration is enhanced by the electron correlations. In metallic phase, heavy fermion behavior is observed and mass enhancement factor is computed. Enhancement of effective spatial anisotropy by the electron correlations is also confirmed in moderately frustrated region, and its effect on heavy fermion behavior is examined.Comment: 5 pages, 6 figure

A Parametric Study of the Acoustic Mechanism for Core-Collapse Supernovae

We investigate the criterion for the acoustic mechanism to work successfully in core-collapse supernovae. The acoustic mechanism is an alternative to the neutrino-heating mechanism. It was proposed by Burrows et al., who claimed that acoustic waves emitted by $g$-mode oscillations in proto-neutron stars (PNS) energize a stalled shock wave and eventually induce an explosion. Previous works mainly studied to which extent the $g$-modes are excited in the PNS. In this paper, on the other hand, we investigate how strong the acoustic wave needs to be if it were to revive a stalled shock wave. By adding the acoustic power as a new axis, we draw a critical surface, an extension of the critical curve commonly employed in the context of neutrino heating. We perform both 1D and 2D parametrized simulations, in which we inject acoustic waves from the inner boundary. In order to quantify the power of acoustic waves, we use the extended Myers theory to take neutrino reactions into proper account. We find for the 1D simulations that rather large acoustic powers are required to relaunch the shock wave, since the additional heating provided by the secondary shocks developed from acoustic waves is partially canceled by the neutrino cooling that is also enhanced. In 2D, the required acoustic powers are consistent with those of Burrows et al. Our results seem to imply, however, that it is the sum of neutrino heating and acoustic powers that matters for shock revival.Comment: 20 pages, 19 figures, accepted by Ap

Metastability of R-Charged Black Holes

The global stability of R-charged AdS black holes in a grand canonical ensemble is examined by eliminating the constraints from the action, but without solving the equations of motion, thereby constructing the reduced action of the system. The metastability of the system is found to set in at a critical value of the chemical potential which is conjugate to the R-charge. The relation among the small black hole, large black hole and the instability is discussed. The result is consistent with the metastability found in the AdS/CFT-conjectured dual field theory. The "renormalized" temperature of AdS black holes, which has been rather ad hoc, is suggested to be the boundary temperature in the sense of AdS/CFT correspondence. As a byproduct of the analysis, we find a more general solution of the theory and its properties are briefly discussed.Comment: 36 pages, 7 figures, v2 is the published version. the exposition is made slightly shorter and hopefully cleare