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PHYSICS REPORTS OF KUMAMOTO UNIVERSITY Vol. 13, No. 1

## CONTENTS

Satoshi Yajima, Makoto Fukuda, Yoji Higashida, Shin-Ichiro Kubota, Shoshi Tokuo, Yuki Kamo, Shinji Yamashita and Tomonori Oka @.....@1
@An Irreducible Form of Gamma Matrices for the Heat Kernel in 8 Dimensions
abstract

Junko Miyano, Takashi Kai, Ryuichi Matsuba, Shin-ichiro Fujimoto and Kenzo Arai @.....@19
@Molecular Cooling in an Accretion Disk around a Supermassive Black Hole
abstract

Yoshihiro Matsumoto, Ryuichi Matsuba, Shin-ichiro Fujimoto and Kenzo Arai @.....@27
@On a Self-Gravitaing Accretion Disk Model
abstract

Masaomi Ono, Masa-aki Hashimoto, Shin-ichiro Fujimoto and Kenzo Arai @.....@33
@Nucleosynthesis in a Helium Star of 32 Msun Related to MHD Jet of Supernova Explosions
abstract

Motoaki Saruwatari, Masa-aki Hashimoto and Kenzo Arai @.....@47
@Ejection of Neutron Rich Matter in Supernova Explosion for a Massive Star
abstract

Tsuneo Noda, Masa-aki Hashimoto, Masayuki Fujimoto and Kenzo Arai @.....@57
@Cooling Properties of Neutron Stars with Quark Matter
abstract

Masahiro Ikeda and Masaru Aniya @.....@63
@The Effect of Correlation in the Bond Strength - Coordination Number Fluctuation Model of Viscosity
abstract

Jean Leopold Ndeugueu and Masaru Aniya @.....@69
@Analysis of the AC Ionic Conductivity in (AgI)0.4(AgPO3)0.6 Glass by Using the Logarithmic Mixing Rule
abstract

Takaki Indoh and Masaru Aniya @.....@73
@The Effect of the Anharmonicity in the Atomic Diffusion in Liquids: A Simple Model
abstract

Satoshi Ohmura and Fuyuki Shimojo @.....@79
@Ab initio Molecular-Dynamics Study of Atomic Diffusion in Liquid B2O3 under Pressure
abstract

Kikuo Itoh, Fusao Ichikawa, Daisuke Teshima, Mitsuru Tazoe, Taketomo Furukawa, Keita Akasaki, Yoshiko Noguchi, Saori Kawahara and Kunito Okamoto @.....@87
@Magnetic Anisotropy in Pd/Co Films Evaporated at Oblique Incidence
abstract

Tomoki Okazawa, Masaru Takeshita, Takuya Matsuda, Satoru Yamabe, Yoshinori Nishino, Hiroki Sakurai, Shinya Kodama, Fusao Ichikawa and Kazumasa Makise @.....@99
@Preparation and Characterization of High Tc Superconductor Thin Films to Study Carrier-Concentration-Driven Superconductor-Insulator Transitions
abstract

Masahiro Hara, Takashi Kimura and Yoshichika Otani @.....@107
@Magnetic Interaction in a Submicron Ferromagnetic Disk/Superconductor Hybrid
abstract

Ichiro Akai, Tomoshige Shimamoto, Atsuhiro Fujii, Katsuichi Kanemoto, Tsutomu Karasawa, Hideki Hashimoto, Ikufumi Katayama, Jun Takeda and Mutsumi Kimura @.....@115
@Energy Transfer in Light-Harvesting Small Dendrimers Having $\pi$-Conjugated Aromatic Rings
abstract

Satoshi Yajima, Makoto Fukuda, Yoji Higashida, Shin-Ichiro Kubota, Shoshi Tokuo, Yuki Kamo, Shinji Yamashita and Tomonori Oka
An Irreducible Form of Gamma Matrices for the Heat Kernel in 8 Dimensions

In order to apply the HMDS coefficients of the heat kernel for the fermion interacting with bosonic background fields to calculation of some anomalies, it is useful to decompose the coefficients into tensorial components with irreducible matrices which are the totally antisymmetric products of $\gamma$ matrices. In 8 dimensional curved space, we present the formulae to give a tensorial form of the $\gamma$ matrix-valued quantities $X$, $\tilde{\Lambda}_{\mu\nu}$ and their product and covariant derivative in the heat kernel, with the irreducible matrices. The fourth HMDS coefficient obtained by repeating the application of the formulae simplifies the trace calculation on the $\gamma$ matrix and the derivation of the tensorial form of loop corrections.

Junko Miyano, Takashi Kai, Ryuichi Matsuba, Shin-ichiro Fujimoto and Kenzo Arai
Molecular Cooling in an Accretion Disk around a Supermassive Black Hole

We investigate formation and destruction of molecules and their IR emission inside the accretion disk around a supermassive black hole. The mass of the hole is taken to be $3.9 \times 10^7 M_\odot$ observed in NGC 4258. Taking into account energy balance between viscous heating and line cooling of molecules, distribution of molecular abundance is calculated in accordance with the strucure of the disk. A significant fraction of H$_2$O is formed in the region of $10^{17} - 10^{18}$ cm from the black hole. Being compared with the emission regions of water maser observed in NGC 4258, the mass accretion rate is found to be $10^{-2} - 10^{-3} M_\odot$ yr$^{-1}$, which is in agreement with the value derived from spectral fitting in an advection-dominated accretion flow.

Yoshihiro Matsumoto, Ryuichi Matsuba, Shin-ichiro Fujimoto and Kenzo Arai
On a Self-Gravitaing Accretion Disk Model

We investigate structure of an accretion disk around a supermassive black hole. Taking into account gravitational potential of a thin disk, we examine radial configurations of the disk model with self-gravity. It is found that density increases outwards, angular velocity deviates from the Keplerian distribution, and temperature is higher than that of a standard disk model due to larger viscous heating.

Masaomi Ono, Masa-aki Hashimoto, Shin-ichiro Fujimoto and Kenzo Arai
Nucleosynthesis in a Helium Star of 32 Msun Related to MHD Jet of Supernova Explosions

We investigate nucleosynthesis of a massive star whose mass in the main sequence stage is $M_{\rm{ms}}=70 M_{\odot}$ that corresponds to the helium core and/or helium star of $M_\alpha =32 M_{\odot}$. Numerical calculations of nucleosynthesis {are} performed during the stage of hydrostatic stellar evolution until the core composed of iron-group nuclei begins to collapse. A collapsar model is constructed whose jets are driven by two-dimensional magneto-hydrodynamical effects of differentially rotating core. The explosive nucleosynthesis inside the jets is followed along the trajectories of stream lines. We combine both results of hydrostatic and explosive nucleosyntheses to compare the solar system abundances. We find that the agreement is almost similar to the case of spherical explosion. The overproduction problem is also avoidable for of neutron rich elements such as $^{58}$Ni.

Motoaki Saruwatari, Masa-aki Hashimoto and Kenzo Arai
Ejection of Neutron Rich Matter in Supernova Explosion for a Massive Star

We investigate the possibility of the $r$-process during the magnetohydrodynamical (MHD) explosion of supernova in a massive star of 13 $M_{\odot}$ with the effects of neutrinos induced. Contrary to the case of the spherical explosion, jet-like explosion due to the combined effects of rotation and magnetic field lowers the electron fraction significantly inside the layers. We find that the ejected material of low electron fraction responsible for the $r$-process comes out from the inner deep region of the core that is made up of iron-group nuclei. This leads to the production of the second to third peak in the solar $r$-process elements. We suggest that there are many variations in the $r$-process nucleosynthesis according to the initial conditions of rotational and magnetic fields.

Tsuneo Noda, Masa-aki Hashimoto, Masayuki Fujimoto and Kenzo Arai
Cooling Properties of Neutron Stars with Quark Matter

We investigate the thermal evolution of isolated neutron stars that include quark matter in the central region. We present cooling curves by changing the transition periods of nuclear matter into quark matter in a parametric manner. It is found that the surface temperature becomes too low due to the strong cooling through neutrino emission via quark $\beta$-decay. Taking into account effects of a mixed phase of quark-hadron phases that has particular structure of quark matter, we find that the {\it over-cooling} is suppressed because of the reduced rate of quark $\beta$-decay.

Masahiro Ikeda and Masaru Aniya
The Effect of Correlation in the Bond Strength - Coordination Number Fluctuation Model of Viscosity

A model is derived for the temperature dependence of the viscosity of the melt by introducing a correlation factor between the bond strength and the coordination number in the total bond strength distribution. It is shown that the shape of the distribution function changes considerably depending on the magnitude and sign of the correlation factor.

Jean Leopold Ndeugueu and Masaru Aniya
Analysis of the AC Ionic Conductivity in (AgI)0.4(AgPO3)0.6 Glass by Using the Logarithmic Mixing Rule

The ac ionic conductivity of the glassy system (AgI)$_{0.4}$(AgPO$_{3}$)$_{0.6}$ has been analyzed by the logarithmic mixing rule. The analysis reveals that the rule is also applicable to AgI-based oxide superionic glasses.

Takaki Indoh and Masaru Aniya
The Effect of the Anharmonicity in the Atomic Diffusion in Liquids: A Simple Model

A simple analytical expression has been derived for the velocity autocorrelation function and diffusion coefficient that incorporates the effect of the anharmonicity. It is shown that the diffusion coefficient increases with the increase in the anharmonicity.

Satoshi Ohmura and Fuyuki Shimojo
Ab initio Molecular-Dynamics Study of Atomic Diffusion in Liquid B2O3 under Pressure

The microscopic mechanism of atomic diffusion in liquid B$_2$O$_3$ under pressure is investigated by {\em ab initio} molecular-dynamics simulations. It is found that the covalent bonds. a non-bridging oxygen double bonded to a two-fold coordinated boron is always involved with atomic diffusion accompanied by the rearrangement of the covalent bonds at ambient pressure. It is seen that the concerted reactions with two BO$_4$ groups take place when the pressure is over 10 GPa. For pressures over 100 GPa, almost all boron atoms are coordinated to four oxygen atoms with $sp^3$ bonding, and atomic diffusion occurs through the threefold-coordinated state with $sp^2$ bonding.

Kikuo Itoh, Fusao Ichikawa, Daisuke Teshima, Mitsuru Tazoe, Taketomo Furukawa, Keita Akasaki, Yoshiko Noguchi, Saori Kawahara and Kunito Okamoto
Magnetic Anisotropy in Pd/Co Films Evaporated at Oblique Incidence

The effect of Pd seed layer on the magnetic anisotropy in Cobalt films evaporated at oblique incidence was investigated. The deposition rate of Pd layers $R$(Pd) was varied from 0.1 to 1.7 \AA/s and that of Co layers $R$(Co) was from 0.1 to 4.5 \AA/s. The incidence angle of Pd vapor beam was 30$^\circ$ and that of Co 60$^\circ$. Negatively large magnetic anisotropy and large coercive force parallel to the incidence plane appeared in Pd/Co films evaporated at low deposition rates of Pd (0.1 \AA/s) and Co (0.2 \AA/s) and small thicknesses of Pd(100 \AA) and Co (about 140 \AA) layers. In these films the anisotropy of the reflection coefficient was positive though the magnetic anisotropy was negative. Therefore, it is considered that the negative magnetic anisotropy does not originate from the shape anisotropy of the columnar grains but the magnetocrystalline anisotropy through the textural structure.

Tomoki Okazawa, Masaru Takeshita, Takuya Matsuda, Satoru Yamabe, Yoshinori Nishino, Hiroki Sakurai, Shinya Kodama, Fusao Ichikawa and Kazumasa Makise
Preparation and Characterization of High Tc Superconductor Thin Films to Study Carrier-Concentration-Driven Superconductor-Insulator Transitions

It is necessary to make many samples changed the composition for the research of carrier-concentration-driven superconductor-insulator transitions in high $T_c$ superconductors. We have deposited YBa$_2$Cu$_3$O$_{7-\delta}$ thin films by DC sputtering using a small target that has the advantage of making the target easily. There are several technological difficulties. One of the problems is a way to heat a substrate with oxygen gas. Another is a temperature-measuring method of the substrate. After several developments in this study, we could make thin films with critical temperature $T_{\mathrm c} \sim 85$ K.

Masahiro Hara, Takashi Kimura and Yoshichika Otani
Magnetic Interaction in a Submicron Ferromagnetic Disk/Superconductor Hybrid

We have investigated magnetization behavior in a single submicron ferromagnetic (FM) disk/superconductor (SC) cross hybrid by using a two-dimensional electron gas (2DEG) as a high-sensitive magnetic field detector. We find that the stray field profile in the hybrid structure is different between FC (field cooling) and ZFC (zero field cooling). The annihilation field of the vortex core in the magnetization of the FM disk shifts higher when the SC cross becomes the superconducting state. The field shift is comparable to the amplitude of the field generated by the superconducting current induced in the SC cross. Normal component of an external magnetic field induces quantum vortex penetrations in the SC. The nucleation sites of the vortices depends on the magnetization in the FM disk since the inhomogeneous stray field from the FM disk is comparable to the flux quantum.

Ichiro Akai, Tomoshige Shimamoto, Atsuhiro Fujii, Katsuichi Kanemoto, Tsutomu Karasawa, Hideki Hashimoto, Ikufumi Katayama, Jun Takeda and Mutsumi Kimura
Energy Transfer in Light-Harvesting Small Dendrimers Having $\pi$-Conjugated Aromatic Rings

We investigate rapid energy transfer and its temperature dependence in a star-shaped stilbenoid phthalocyanine (SSS1Pc) dendrimer having $\pi$-conjugated light-harvesting (LH) antennas, and develop an appropriate model. In SSS1Pc, an intense core photoluminescence (PL) band appears under the selective excitation of the absorption bands of the LH antenna due to highly efficient energy transfer at room temperature. The transient response of core-absorption bleaching and the temporal behaviours of the PL intensities of the core and antenna reveal that energy transfer from the LH antenna occurs rapidly prior to achieving quasi-equilibrium in the photoexcited state of the LH antenna. In addition, it is also clarified that the energy transfer quantum efficiency in SSS1Pc degrades at temperatures lower than $\sim$100~K. To understand these results, we develop an energy transfer model based on a $\pi$-conjugating network between the LH antenna and the core that accounts for steric hindrance between the LH antenna and the torsional vibration of the LH-antenna subunit. This model reveals that highly efficient energy transfer occurs at room temperature through the $\pi$-conjugated network mediated by the thermally activated torsional vibration of the LH-antenna subunit.

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Email: arai@sci.kumamoto-u.ac.jp

Last updated: January 18, 2009