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PHYSICS REPORTS OF KUMAMOTO UNIVERSITY Vol. 12, No. 1

## CONTENTS

Tsuyoshi Kiyan, Takayoshi Maekawa, Masamichi Masuda and Hideo Taira @.....@1
@On Disagreement between Unitary Gauge and $\xi \rightarrow 0$ Gauge in $R_\xi$ in General Cases
abstract

Satoshi Yajima, Yoji Higasida, Kiyotaka Kawano, Shin-Ichiro Kubota, Yuki Kamo and Shoshi Tokuo @.....@39
@Higher Coefficients in Asymptotic Expansion of the Heat Kernel
abstract

Yoji Higasida, Satoshi Yajima, Shin-Ichiro Kubota, Shoshi Tokuo and Yuki Kamo @.....@63
@Contributions of Four-gravitino Interactions to Weyl Anomaly in $d=4$, $N=1$ Supergravity
abstract

Ryuichi Matsuba, Kenzo Arai, Shin-ichirou Fujimoto and Masa-aki Hashimoto @.....@71
@Nitrogen Production inside an Accretion Disk around an Intermediate-Mass Black Hole
abstract

Masa-aki Hashimoto, Yoshinori Kuroda, Riou Nakamura, Sinya Gamow and Kenzo Arai @.....@81
@Big-Bang Nucleosynthesis in Brans-Dicke Cosmology with a $\Lambda$ Term
abstract

Nobutoshi Yasutake, Masa-aki Hashimoto, Yoshiharu Eriguchi and Kenzo Arai @.....@87
@Evolutionary Transition from Rapidly Rotating Neutron Stars to Strange Stars
abstract

Sunao Nishimura, Nobuya Nishimura, Masa-aki Hashimoto, Sin-ichirou Fujimoto and Kenzo Arai @.....@95
@R-Process Nucleosynthesis due to Inner Explosion of a Low Mass Iron-Core
abstract

Masaru Aniya @.....@101
@A Pseudopotential Study on Dielectric Theory of Electronegativity and Transverse Effective Charges in Zinc-Blende Structure Binary Compounds
abstract

Fuyuki Shimojo and Masaru Aniya @.....@109
@Ab initio Study on Structural and Electronic Properties of Nonsuperionic, Superionic and Molten Phases of Cuprous Iodide
abstract

Takaki Shinkawa and Masaru Aniya @.....@119
@A Possible Relationship between Ag Photodoping and Fragility in Amorphous Ge-S Systems
abstract

Kikuo Itoh, Fusao Ichikawa, Yoshie Noguchi, Reiko Ishii, Masahiro Sudoh and Kunito Okamoto @.....@125
@Surface Structure of Aluminum Columnar Grains in Al/Fe Multi-layers
abstract

Yoshie Noguchi, Fusao Ichikawa and Kikuo Itoh @.....@133
@Oxygen Effect of Co Thin Films Obliquely Deposited by Sputtering
-- Thickness Dependence at a Substrate Temperature of 492 K --
abstract

Atsuhiro Fujii, Masashi Tabuki, Koujiro Miyazaki, Hiroyuki Ueda and Tomosige Shimamoto @.....@139
@Time-Resolved Photo-Luminescence of Excitons Induced by Extrinsic Self-Trapping in TlBr(I)
abstract

Xun Xu, Shinji Kawano, Takanori Tsutaoka, Yoshikazu Ando, Makio Kurisu and Go Nakamoto @.....@147
@Neutron Diffraction Studies of Nd7Ni3
abstract

Xun Xu, Takao Mizusaki, Kunihide Okada, Sinji Kawano and Kazuo Yamakata @.....@157
@NMR Study of a Phase Transition of Antiferromagnet Mn(HCOO)2E2(NH2)2CO
abstract

Rui Goto, Keiichiro Nakamura, Muneaki Fujii and Kunihide Okada @.....@161
@NMR Study of Cu(HCOO)2E2H2O at Millikelvin Temperature
abstract

Taisi Matsumoto, Tomosige Shimamoto and Kunihide Okada @.....@167
@Hole-NMR
abstract

Toru Gobayashi, Tomoshige Shimamoto, Taisi Matsumoto and Kunihide Okada @.....@173
@An NMR Study of Triangular Lattice Antiferromagnet CsMnBr3 Made with a Zone Melting Furnace
abstract

Tsuyoshi Kiyan, Takayoshi Maekawa, Masamichi Masuda and Hideo Taira
On Disagreement between Unitary Gauge and $\xi \rightarrow 0$ Gauge in $R_\xi$ in General Cases

It is shown that in the case of breaking the symmetry by some steps such as SU(n)\otimes U(1)_{N^{n}} $\rightarrow$ SU(n-1)\otimes U(1)_{N^{n-1}} $\rightarrow\cdots\rightarrow$ SU(2)\otimes U(1)_{N_Y} \rightarrow U(1)_{em} by introducing the scalar fields considered as the irreducible components of a scalar field. The unitary gauge condition, which is satisfied for the scalar fields given by the Higgs mechanism, is not satisfied for those given by the limiting gauge of $\xi \rightarrow 0$ in the $R_\xi$ gauge. Thus it is concluded that the limiting gauge of $\xi \rightarrow 0$ disagrees in general with the U gauge in contrast to the case realized by a step of the breaking such as in the standard model and to treat the theory with the U gauge will not generally lead to a renormalizable result.

Satoshi Yajima, Yoji Higasida, Kiyotaka Kawano, Shin-Ichiro Kubota, Yuki Kamo and Shoshi Tokuo
Higher Coefficients in Asymptotic Expansion of the Heat Kernel

By applying the covariant Taylor expansion method, the lowest five coefficients in the asymptotic expansion of the heat kernel associated with a fermion of spin 1/2 in curved space are manifestly given. These coefficients in Riemann-Cartan space is derived by simple replacements from those obtained in Riemannian space.

Yoji Higasida, Satoshi Yajima, Shin-Ichiro Kubota, Shoshi Tokuo and Yuki Kamo
Contributions of Four-gravitino Interactions to Weyl Anomaly in d = 4, N = 1 Supergravity

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.

Ryuichi Matsuba, Kenzo Arai, Shin-ichirou Fujimoto and Masa-aki Hashimoto
Nitrogen Production inside an Accretion Disk around an Intermediate-Mass Black Hole

We have investigated nucleosynthesis inside accretion disks around intermediate-mass ($50 - 500 \, M_\odot$) black holes located in the circumnuclear region of starburst galaxies. Nuclear reactions in the disks proceed through the hot CNO cycle to produce large amounts of 14O and 15O, which eventually decay to 14N and 15N, respectively. The calculated relation of N/O -- O/H is found to be consistent with the observed values in the most metal-poor galaxies. We propose that the accretion disk may be one of the promising sites of nitrogen production and nucleosynthesis inside the disk is responsible for the nitrogen excess observed in starburst galaxies.

Masa-aki Hashimoto, Yoshinori Kuroda, Riou Nakamura, Sinya Gamow and Kenzo Arai
Big-Bang Nucleosynthesis in Brans-Dicke Cosmology with a $\Lambda$ Term

We investigate evolution of the universe and primordial nucleosynthesis in a Brans-Dicke model with a decaying $\Lambda$ term using the Monte-Carlo method and likelihood analysis. Cosmic expansion rate in our model changes appreciably compared to that of standard model. The produced abundances of 4He and D are consistent with the observational abundances when the baryon to photon ratio $\eta = (5.47 - 6.64)\times 10-10, which is in agreement with the value deduced from Wilkinson Microwave Anisotropy Probe (WMAP). Nobutoshi Yasutake, Masa-aki Hashimoto, Yoshiharu Eriguchi and Kenzo Arai Evolutionary Transition from Rapidly Rotating Neutron Stars to Strange Stars We present a formation scenario of strange stars due to the spin-down of rapidly rotating neutron stars left after supernova explosions. Assuming that the total baryon mass is conserved but the angular momentum is lost due to emission of gravitational waves and/or the magnetic braking, we find that the transition is possible from rapidly rotating neutron stars to slowly rotating strange stars; enough amount of energy$\sim$1053 ergs is released. The liberated energy becomes a new energy source for delayed explosion of supernova. Furthermore, our scenario suggests that the supernova associated with gamma-ray bursts becomes a target in the future observations of gravitational waves. Sunao Nishimura, Nobuya Nishimura, Masa-aki Hashimoto, Sin-ichirou Fujimoto and Kenzo Arai R-Process Nucleosynthesis due to Inner Explosion of a Low Mass Iron-Core We investigate r-process due to the explosion from an inner region of the iron-core. It is shown that the solar r-process abundances are rather well reproduced in terms of an explosion model for a He-core of 3.3$M_\odot$which corresponds to 13$M_\odot$in the main sequence stage. We examine whether the fission affects the r-process path by using the full nuclear reaction network with both spontaneous and$\beta$-delayed fissions. Particular attention is paid for the mass formula which affects the r-process peaks. It is found that the extended Thomas-Fermi model is better than the liquid drop model in reproducing the abundance pattern. Masaru Aniya A Pseudopotential Study on Dielectric Theory of Electronegativity and Transverse Effective Charges in Zinc-Blende Structure Binary Compounds The parameters of the dielectric theory of electronegativity such as heteropolar gap and ionicity, have been calculated by using pseudopotentials. By analyzing the results obtained, the confidences of the pseudopotentials used are checked. The transverse effective charges have been also calculated. The result suggests the importance of effective valence and effective number of valence electrons in the evaluation of this quantity. Among the binary compounds considered, special emphases have been given to superionic materials. Discussions on how the considered physical quantities are related with the properties of these materials are given. Fuyuki Shimojo and Masaru Aniya Ab initio Study on Structural and Electronic Properties of Nonsuperionic, Superionic and Molten Phases of Cuprous Iodide The structural and the electronic properties of nonsuperionic, superionic, and molten phases of CuI are studied by means of {\em ab initio} molecular-dynamics simulations. From the first-peak positions of partial pair distribution functions, we confirm that, in the superionic and the molten phases, the nearest-neighbor distance for Cu-Cu pair is almost the same as that for Cu-I pair in spite of the correlation between the same type of ions. Takaki Shinkawa and Masaru Aniya A Possible Relationship between Ag Photodoping and Fragility in Amorphous Ge-S Systems By analyzing the composition dependence of the total amount of Ag photodissolved into amorphous GexS1-x and the fragility of GexS1-x, it has been found that there exists an inverse correlation between these two quantities. The possible origin of the correlation found has been discussed by using the constraint theory and the model of fragility and ion transport proposed by one of the authors. Kikuo Itoh, Fusao Ichikawa, Yoshie Noguchi, Reiko Ishii, Masahiro Sudoh and Kunito Okamoto Surface Structure of Aluminum Columnar Grains in Al/Fe Multi-layers The surface structure of Al columnar grains was investigated using the Al/Fe multi-layers. The deposition rate of Al layers$R$(Al) was varied from 16 to 2200 Hz/s and that of Fe layers$R$(Fe) was 5 Hz/s. The incidence angles of Al and Fe vapor beams were 60 and 30$^{\circ}$, respectively. The$R$(Al) dependence of magnetic anisotropy originating from Fe layers is consistent with that of optical anisotropy of Al top surface indicating that the anisotropy of Fe layers reproduces exactly that of Al layers. The angle$\beta$was negative which indicates that the easy direction of magnetization of Fe layers in the incidence plane reflects the direction of the habit plane at the top of Al columns. Furthermore the shape of the torque curve in the incidence plane suggests the existence of two kinds of habit planes: One is parallel to the film plane and another deviates from the film plane to the inverse side of the vapor beams in the incidence plane. Yoshie Noguchi, Fusao Ichikawa Oxygen Effect of Co Thin Films Obliquely Deposited by Sputtering -- Thickness Dependence at a Substrate Temperature of 492 K -- Magnetic anisotropy field increases monotonically with oxidizing in sputtered cobalt films prepared by introducing oxygen at a substrate temperature of 492 K. In order to study this behavior, the magnetic properties and surface structure have been investigated as a function of thickness. It is found that the direction of easy axis in films without oxygen changes with increasing thickness. However the anisotropy becomes small in films deposited by introducing oxygen. At this substrate temperature both the oxygen flow and the thickness play an important role for the film growth process. Atsuhiro Fujii, Masashi Tabuki and Koujiro Miyazaki, Hiroyuki Ueda and Tomosige Shimamoto Time-Resolved Photo-Luminescence of Excitons induced by Extrinsic Self-Trapping in TlBr(I) Luminescence spectra have been measured in TlBr doped with I- ions under pulsed-light excitation. Two broad emission bands were observed at 2.2 eV and 2.45 eV. The emission band at 2.2 eV decayed non-exponentially with a t-1 dependence at long delay, and was attributed to radiative annihilation of a self-trapped exciton at the nearest neighbor of an I- ion. The exciton was formed by tunneling recombination of a hole trapped at the nearest neighbor of an I- ion and an electron trapped at a distant lattice position. The emission band at 2.45 eV, which decayed with two time constants of 0.5$\mu$s and less than 20 ns, was attributed to annihilation of another type of a self-trapped exciton in Br--rich region of the crystal. These emission bands are discussed with a theory on extrinsic self-trapping in a mixed crystal, and ascribed to the two types of extrinsic self-trapping of the excitons. Xun Xu, Shinji Kawano, Takanori Tsutaoka, Yoshikazu Ando, Makio Kurisu and Go Nakamoto Neutron Diffraction Studies of Nd7Ni3 Neutron diffraction on the hexagonal compound Nd7Ni3 has been performed in the temperature range from 1.7 to 35 K in zero external field and in an external field from 0 to 3 T. In zero external field, the magnetic structure is conical at 1.7 K with a basal plane helix with a propagation vector Q = (0,0,1/3), whereas the c-axis component is ferromagnetic. Above 8 K, the c-axis ferromagnetic component disappears, while the basal plane helical component remains up to the Neel temperature (= 25 K). The propagation vector changes from Q = (0,0,1/3) at 1.7 K to Q = (0,0,0.257) at 20 K. In an external field, at 4.2 K and below 1.3 T, the magnetic structure is conical with a basal plane helical component having a propagation vector Q = (0,0,1/3) and the c-axis ferromagnetic component. Above 1.3 T the c-axis component disappears, while the basal plane component remains up to 2.7 T. Below 0.3 T, the magnetic structure changes from conical at about 8 K. A rough (H, T) phase diagram is given and is generally consistent with the results of magnetization measurements. Xun Xu, Takao Mizusaki, Kunihide Okada, Sinji Kawano and Kazuo Yamakata NMR Study of a Phase Transition of Antiferromagnet Mn(HCOO)2E2(NH}2)2CO The NMR study of tetragonal-lattice antiferromagnet Mn(HCOO)2E2(NH}2)2CO has been carried out. Below T_N(= 3.78 K), anomalies are observed in spin-echo intensity and in spin-lattice relaxation time (T_1). The spin-lattice relaxation time decreases rapidly from 1.95 K, reaches a minimum about 1.68 K and, then, increases with decreasing temperature. This suggests an existence of a phase transition around 1.68 K. Rui Goto, Keiichiro Nakamura, Muneaki Fujii and Kunihide Okada NMR Study of Cu(HCOO)2E2H2O at Millikelvin Temperature We have studied magnetic properties of Cu(HCOO)2E2H2O using SQUID-NMR and pulsed NMR. A large peak of Cu-NMR signal in Cu(HCOO)2E2H2O is observed around 250 MHz at 230 mK. The temperature dependence of NMR frequency has been studied. Taisi Matsumoto, Tomosige Shimamoto and Kunihide Okada Hole-NMR Eu-NMR in EuxSr1-xTe for x = 0.85 has been studied using a coherent pulsed NMR apparatus at 4.2 K under an external field of 5000 Gauss. After a 90$^\circ$rf-pulse, a free induction signal has not been observed. However, when a week and long rf-pulse is applied before the 90$^\circ$rf-pulse, a free induction signal is observed. It is because that the pre-pulse makes a hole in NMR spectrum. As an interval of the pre-pulse and 90$^\circ\$ rf-pulse increases, the intensity and the decay constant of free induction signal decrease. The results are in good agreement with a spectral diffusion theory.

Toru Gobayashi, Tomoshige Shimamoto, Taisi Matsumoto and Kunihide Okada
An NMR Study of Triangular Lattice Antiferromagnet CsMnBr3 Made with a Zone Melting Furnace

We have made single crystals of CsMnBr3 which are purified specially with a zone melting technique. Using the crystals, we have measured NMR at liquid helium temperatures. The NMR frequencies around 40 MHz steeply depends upon the external magnetic field.

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

Last updated: December 9, 2004