@@@@@I@v
PHYSICS REPORTS OF KUMAMOTO UNIVERSITY Vol. 12, No. 2

## CONTENTS

Yuki Kamo, Satoshi Yajima, Yoji Higashida, Shin-Ichiro Kubota, Shoshi Tokuo and Makoto Fukuda @.....@181
@Studies of Resonance Conditions on Neutrino Oscillations in Matter
abstract

Makoto Fukuda}, Satoshi Yajima, Yoji Higashida, Shin-Ichiro Kubota, Shoshi Tokuo and Yuki Kamo @.....@197
@Calculation of Lorentz Anomaly in 4 Dimensions
abstract

Hideo Taira, Makoto Fukuda and Shoshi Tokuo @.....@201
@Scalar Field Represented by Vierbein on Two-Sheeted Riemann Space
abstract

Riou Nakamura, Masa-aki Hashimoto, Kiyotomo Ichiki and Kenzo Arai @.....@209
@Observational Constrains on a Decaying $\Lambda$ Cosmology
abstract

Nobutoshi Yasutake, Masa-aki Hashimoto, Kei Kotake, Shoichi Yamada and Kenzo Arai @.....@217
@Effects of QCD Phase Transition on the Collapse and Bounce of a Differentially Rotating Massive Star
abstract

Tsuneo Noda, Masa-aki Hashimoto, Masayuki Fujimoto and Kenzo Arai @.....@227
@Exotic Cooling on Isolated Neutron Stars with Different Surface Compositions
abstract

Reiko Kuromizu, Masa-aki Hashimoto, Tsuneo Noda, Masayuki Fujimoto and Kenzo Arai @.....@233
@Nuclear Flashes toward Superbursts in Accreting Neutron Stars Iron-Core
abstract

Nobuya Nishimura, Masa-aki Hashimoto, Shin-ichirou Fujimoto and Kenzo Arai @.....@243
@p-process Nucleosynthesis in a Core-Collapse Supernova
abstract

Masaomi Ono, Masa-aki Hashimoto, Nobuya Nishimura, Kei Kotake, Shoichi Yamada and Kenzo Arai @.....@251
@MHD Simulations of a Collapsar Model
abstract

Shinji Koide, Takahiro Kudoh and Kazunari Shibata @.....@259
@A General Relativistic MHD Simulation of Jet Formation around a Rapidly Rotating Black Hole
abstract

Ryuichi Matsuba, Shin-ichirou Fujimoto and Kenzo Arai @.....@263
@Global Structure of an Accretion Disk with Self-Gravity
abstract

Akihiro Tomita, Ryuichi Matsuba, Shin-ichirou Fujimoto and Kenzo Arai @.....@273
@Molecular Formation in an Accretion Disk around a Super Massive Black Hole
abstract

Takayuki Sugahara, Yasuhisa Miyata, Tetsuya Yoshikawa, Akihide Koura and Fuyuki Shimojo @.....@279
@ Numerical Procedures for Generating Ultrasoft Pseudopotentials
abstract

Masakazu Yarimitsu, Masaru Aniya and Fuyuki Shimojo @.....@295
@Pressure Dependence of Ag Diffusion in Ag3SI
@-- A Preliminary Molecular Dynamics Study --
abstract

Takaki Indoh and Masaru Aniya @.....@301
@ A Note on the Asymptotic Long Time Behavior of the Velocity Autocorrelation Function
abstract

Kikuo Itoh, Fusao Ichikawa, Yoshie Noguchi, Reiko Ishii, Masahiro Sudoh, Kunihiko Kariatumari, Ayumu Nakasone, Yutaka Mizobe, Kunito Okamoto, Tetsuji Uchiyama, Akihiko Nishida and Chihiro Takeuchi @.....@305
@Magnetic Analysis of Surface Structure of Al/Fe Multi-layers
abstract

Yuki Kamo, Satoshi Yajima, Yoji Higashida, Shin-Ichiro Kubota, Shoshi Tokuo and Makoto Fukuda
Studies of Resonance Conditions on Neutrino Oscillations in Matter

We analytically discuss the resonance conditions among several neutrinos in matter. The discriminant for the characteristic equation of the Hamiltonian is expressed by the coefficients of the equation. The result of the computation for the discriminants tells us that the neutrino energy and the matter density are in inverse proportion to each other at the resonance states in not only 2- but also 3- and 4-neutrino models.

Makoto Fukuda, Satoshi Yajima, Yoji Higashida, Shin-Ichiro Kubota, Shoshi Tokuo and Yuki Kamo
Calculation of Lorentz Anomaly in 4 Dimensions

We evaluate the Lorentz anomaly in the model for a massless Weyl fermion with spin 1/2 interacting with irreducible non-abelian boson fields in 4 dimensional Riemannian curved spacetime. The formal form of the anomaly is derived in the path integral method, and its tensorial form is given from the tensor component of the second asymptotic expansion coefficients $a_2$ of the heat kernel with respect to irreducible matrices which are the totally antisymmetric products of $\gamma$ matrices.

Hideo Taira, Makoto Fukuda and Shoshi Tokuo
Scalar Field Represented by Vierbein on Two-Sheeted Riemann Space

We evaluate the Weyl anomaly in d = 4, N = 1 supergravity with contributions of four-gravitino interactions. As a preparation, we derive the Weyl anomaly in the model for a massless spinor with spin 1/2 in the presence of various non-Abelian fields in d = 4 Riemannian spacetime. Using the results and replacements, the Weyl anomaly in the supergravity is obtained explicitly.

Riou Nakamura, Masa-aki Hashimoto, Kiyotomo Ichiki and Kenzo Arai
Observational Constrains on a Decaying $\Lambda$ Cosmology

We investigate the evolution of the universe with a decaying cosmological term that is assumed to be a function of the scale factor. The cosmological term in this model is larger in the early universe, but the radiation energy density is lower compared to the model with the cosmological constant. We find that the effects of the decaying term on the expansion rate is negligible at the redshift z<2. On the other hand, the decrease in the radiation density leads to the photon decoupling at higher $z$. As a consequence, the decaying term affects on the cosmic microwave background anisotropy. Comparing the angular power spectrum with the Wilkinson Microwave Anisotropy Probe data, we derive the best fit values of the cosmological parameters.

Nobutoshi Yasutake, Masa-aki Hashimoto, Kei Kotake, Shoichi Yamada and Kenzo Arai
Effects of QCD Phase Transition on the Collapse and Bounce of a Differentially Rotating Massive Star

We perform two-dimensional, magnetohydrodynamical (MHD) core-collapse simulations of massive stars accompanying the QCD phase transition, and examine the the gravitational wave amplitudes during the core-bounce. It is found that the phase transition makes the maximum amplitudes larger up to about 10 % than the ones without the phase transition. On the other hand, the maximum amplitudes become smaller up to 10 % owing to the phase transition, when the iron core rotates differentially. These results are not affected by even extremely strong magnetic fields of 1017 G in the protoneutron star.

Tsuneo Noda, Masa-aki Hashimoto, Masayuki Fujimoto and Kenzo Arai 227
Exotic Cooling on Isolated Neutron Stars with Different Surface Compositions

We investigate the thermal evolution of isolated neutron stars, using both the standard and the exotic cooling processes, and two kinds of surface composition of He and Fe. Moreover, we employ nucleon superfluidity models, and adopt a critical temperature as a density-independent parameter. We find that there exist parameter regions for cooling curves which can be consistent with the observational data of the effective temperature.

Reiko Kuromizu, Masa-aki Hashimoto, Tsuneo Noda, Masayuki Fujimoto and Kenzo Arai
Nuclear Flashes toward Superbursts in Accreting Neutron Stars Iron-Core

We construct a model of superbursts by following thermal evolution of a realistic neutron star. It is found that the superburst is originated from thermonuclear burning ignited by accumulated fuels in the deep layers compared to normal X-ray bursts. The temperature reaches the deflagration temperature for a carbon flash accompanied with normal bursts. The flash could develop to dynamical phenomena of the deflagration, which may lead to a superburst.

Nobuya Nishimura, Masa-aki Hashimoto, Shin-ichirou Fujimoto and Kenzo Arai
p-process Nucleosynthesis in a Core-Collapse Supernova

We propose a new site of the p-process nucleosynthesis during the magnetohydrodynamic (MHD) explosion of supernova in a massive star of 13 Msun. We present nonspherical effects on the production of p-elements using adiabatic MHD explosion model. When the shock wave propagates into the oxygen-rich layer, the p-process occurs inside the MHD jets. It is found that the peak temperature along the jet is high enough to disintegrate heavy p-nuclei into light p-nuclei that survive during the passage of shock wave.

Masaomi Ono, Masa-aki Hashimoto, Nobuya Nishimura, Kei Kotake, Shoichi Yamada and Kenzo Arai
MHD Simulations of a Collapsar Model

We perform two-dimensional magnetohydrodynamic (MHD) simulations of collapsars for M = 13 - 130 Msun at the main sequence stage. Initial distributions of angular velocity and magnetic field are implemented to the presupernova models. It is found that a transient accretion disk forms around the black hole. Since the configuration is assumed to be symmetric about the rotational axis and the equatorial plane, strong shocks are produced along the rotational axis. The growth and propagation of the shock wave depends on the initial conditions just before the collapse.

Shinji Koide, Takahiro Kudoh and Kazunari Shibata
A General Relativistic MHD Simulation of Jet Formation around a Rapidly Rotating Black Hole

We report numerical results of jet formation driven by magnetic field due to a current loop around a rapidly rotating black hole. Beside the current loop, there are magnetic flux tubes that bridge the region between the ergosphere and the rotating disk, which we call `magnetic bridges'. The numerical result shows that the magnetic bridges can not be stationary and expand explosively to form a jet when the black hole rotates rapidly.

Ryuichi Matsuba, Shin-ichirou Fujimoto and Kenzo Arai
Global Structure of an Accretion Disk with Self-Gravity

We have investigated structure of an accretion disk formed during the collapse of super-massive stars, in which self-gravity of the disk plays an important role. It is found that the self-gravity largely affects the strucute of the disk when the mass of the disk becomes comparable to the mass of the central object. In the self-gravity dominated region, rotation of gas deviates significantly from Keplerian and the infall velocity is faster than that without the self-gravity. The thickness of the disk reduces by a factor of about 2. It is expected that the self-gravitating disk may be thermally and gravitationally unstable, because the thermal time-scale is much shorter than that of the hydrostatic balance, and the Toomre parameter is negative.

Akihiro Tomita, Ryuichi Matsuba, Shin-ichirou Fujimoto and Kenzo Arai
Molecular Formation in an Accretion Disk around a Super Massive Black Hole

We investigate the formation of molecules in the accretion disk around the black hole of 108 Msun. A significant amount of H2O is formed in the region of 1017 - 1018 cm via CO and CO2, which is consistent with the observed regions of H2O maser emission in galaxies. It is found that almost all initial oxygen contained in the infall material is available to form H2O. If the mass of the black hole decreases, the formation region of molecules shifts inward in accordance with the shift of the temperature region of 10 - 1000 K.

Takayuki Sugahara, Yasuhisa Miyata, Tetsuya Yoshikawa, Akihide Koura and Fuyuki Shimojo
Numerical Procedures for Generating Ultrasoft Pseudopotentials

Numerical procedures for generating ultrasoft pseudopotentials are described in detail. Atomic radial pseudo-wave-functions are constructed so as to coincide with radial all-electron wave functions beyond a chosen cutoff radius with continuous derivatives up to the fourth order, which guarantees numerical stability in electronic-structure calculations for materials. %As well as the construction of pseudopotential data sets We present a method for solving the radial generalized eigenequation with the ultrasoft pseudopotentials, which is required to test their transferability.

Masakazu Yarimitsu, Masaru Aniya and Fuyuki Shimojo
Pressure Dependence of Ag Diffusion in Ag3SI
@-- A Preliminary Molecular Dynamics Study --

The pressure dependence of the diffusion coefficient in the superionic $\alpha$- and $\beta$-phases of Ag3SI has been studied by using the method of molecular dynamics. It is shown that the Ag diffusion coefficient decreases with pressure in the high temperature superionic $\alpha$-phase. On the other hand, it is found that in the intermediate temperature superionic $\beta$-phase, the Ag diffusion coefficient first increases with pressure, exhibits a maximum at around 2.8 GPa, and decreases by further application of pressure.

Takaki Indoh and Masaru Aniya
A Note on the Asymptotic Long Time Behavior of the Velocity Autocorrelation Function

The asymptotic long time behavior of the velocity autocorrelation function (VAF) in the hydrodynamic description is considered. It is shown that the model predicts a peaked behavior in the magnitude of the VAF at a certain value of the diffusion coefficient.

Kikuo Itoh, Fusao Ichikawa, Yoshie Noguchi, Reiko Ishii, Masahiro Sudoh, Kunihiko Kariatumari, Ayumu Nakasone, Yutaka Mizobe, Kunito Okamoto, Tetsuji Uchiyama, Akihiko Nishida and Chihiro Takeuchi
Magnetic Analysis of Surface Structure of Al/Fe Multi-layers

The direction of the habit plane at the top of Al columnar grains was investigated using the Al/Fe multi-layers. The stacks of multi-layer were [Al/Fe]3Al, [Al/Fe]6Al and [Al/Fe],sub>10Al. The deposition rate of Al layers R(Al) was varied from 16 to 2200 Hz/s and that of Fe layers R(Fe) was 5 Hz/s. The incidence angle of Al vapor beam was 60$^\circ$ , and those of Fe 30$^\circ$ and 77$^\circ$. In the incidence plane the easy direction of magnetization estimated using the torque curve was slightly different from the direction of (111) plane, which is regarded as the habit plane in Al films, suggesting the existence of another habit plane. In the Al/Fe multi-layers prepared in the incidence angle of Fe vapor beam of 77$^\circ$ the easy direction of magnetization was almost consistent with the [111] pole direction. These results indicate that there exist three kinds of habit planes, whose normals lie in the incidence plane, at the top of Al columns.

ȊwȂ̃z[y[W
Email: arai@sci.kumamoto-u.ac.jp

Last updated: January 23, 2007