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PHYSICS REPORTS OF KUMAMOTO UNIVERSITY Vol. 10, No. 2

## CONTENTS

Toshinori Takemiya @.....@75
@On the Proton-Deuteron Scattering
abstract

Tetsuya Yoneda @.....@99
@Behaviour of Quantum Mechanical System in Macroscopic Matter --Toward Construction of Model of Detector--
abstract

Tetsuya Ogura, Sohnosuke Yodogawa and Tetsuya Yoneda @.....@109
@Quantum Communication by Three Photons Corresponding to the Reverse Bennett Scheme
abstract

Kenzo Arai, Kenji Nishimura and Masa-aki Hashimoto @.....@113
@Primordial Nucleosynthesis with Degenerate Neutrinos
abstract

Ryuichi Matsuba, Shoji Ikeda, Yasushi Ohta, Shin Fujimoto and Kenzo Arai @.....@125
@Equilibrium Structure of Advection Dominated Accretion Disks around Black Holes
abstract

Shin Fujimoto, Ryuichi Matsuba, Yasushi Ohta and Kenzo Arai @.....@135
@Stability of an Advection-Dominated Accretion Flow around a Black Hole
abstract

Osamu Koike, Masa-aki Hashimoto, Kenzo Arai and Shinya Wanajo @.....@145
@Thermonuclear Shell Flash Model on Accreting Neutron Stars
abstract

Masaru Aniya @.....@161
@Analysis of the Bond Ionicity in Solids: Searching a Guideline for the Design of New Superionic Conducting Materials
abstract

Masaru Aniya @.....@173
@Speculations About Bonding and Electronic Properties of Liquid Silver Chalcogenides
abstract

Satoshi Yajima, Yoji Higashida, Kiyotaka Kawano and Shin-Ichiro Kubota @.....@185
@Heat Kernel of Second Order Elliptic Differential Operator in Riemann-Cartan Space
abstract

Atsuhiro Fujii, Shin Akamatsu and Hideo Shida @.....@201
@Exciton Absorption Spectra of TlCl Micro-cystals in Evaporated Thin Films}
abstract

Wei Yu and Atsuhiro Fujii @.....@209
@Diffusion of Thallous Ions into Potassium Chloride and Sodium Chloride Single Crystals
abstract

Kunihide Okada, Tomosige Shimamoto, Xun Xu and Muneaki Fujii @.....@215
@Cross-spin Correlation Function and Spin-lattice Relaxation of Br-NMR in Triangular Lattice Antiferromagnet CsMnBr$_3$
abstract

Toshinori Takemiya
On the Proton-Deuteron Scattering

A new method that is no use of partial wave expansion is proposed for a scattering problem. Assuming the different kinds of particles for the proton and the neutron and using the present method, we can exactly incorporate the Coulomb potential into the Faddeev equation of the proton-deuteron scattering. The different masses for the proton and the neutron can be assumed. Only the antisymmetrization between the two protons in the wave function of the proton-deuteron system is taken into account.
It is clarified that, unlike the $p$-$p$ scattering, the interferences between the Coulomb and the nuclear amplitudes appear at the forward angles but never appear at the backward angles in the $p$-$d$ scattering. The present theory can be used for the charge symmetry breaking and the charge independence breaking potential. The theory can be also applied to the neutron-deuteron scattering, if the Coulomb wave function is replaced by a plane wave. The three-body force is not taken into account.

Tetsuya Yoneda
Behaviour of Quantum Mechanical System in Macroscopic Matter --Toward Construction of Model of Detector--

Although many models of detector have been proposed, effort for their improvement is still continued by many authors. In this paper, preliminary results for the construction of a new possible model of detector are reported. The index of refraction plays an important role in this research.

Tetsuya Ogura, Sohnosuke Yodogawa and Tetsuya Yoneda
Quantum Communication by Three Photons Corresponding to the Reverse Bennett Scheme

A model for quantum communication by three photons corresponding to the reverse Bennett scheme is investigated.

Kenzo Arai, Kenji Nishimura and Masa-aki Hashimoto
Primordial Nucleosynthesis with Degenerate Neutrinos

Primordial nucleosynthesis is investigated with including degenerate neutrinos. An excess density of neutrinos causes speedup in the expansion rate of the universe, leading to enhanced production of $^4$He and $^7$Li. Electron-neutrino degeneracy shifts $\beta$-equilibrium to less neutrons and compensates the overproduction of $^4$He. Comparing the calculated abundances with the observed abundances, we find new constraints for the baryon density $\rho_{_{\rm B0}}$ and the lepton asymmetries $\xi_{\rm e}$ and $|\xi_\mu|$.

Ryuichi Matsuba, Shoji Ikeda, Yasushi Ohta, Shin Fujimoto and Kenzo Arai
Equilibrium Structure of Advection Dominated Accretion Disks around Black Holes

Steady flows of optically thin advection dominated accretion are obtained around a Schwarzschild black hole for wide ranges of such parameters as a mass accretion rate and $\alpha$-viscosity. Our calculated flows are consistent with the self similar solution except for the very inner region of the disk where the infall velocity increases significantly. The accreting gas is heated up to the virial temperature, but the density is extremely low. For a model with $\alpha>0.01$, the flow has $\alpha$ times free fall velocity and sub-Keplerian angular velocity. It is just like a spherical Bondi flow rather than a disk flow. When $\alpha<0.01$ there exists a point where pressure becomes maximum and angular velocity exceeds its Keplerian value. It is one of the characteristics of geometrically thick disks, so that the flow is regarded as an alternative model of ion tori.

Shin Fujimoto, Ryuichi Matsuba, Yasushi Ohta and Kenzo Arai
Stability of an Advection-Dominated Accretion Flow around a Black Hole

We investigate stability of an advection-dominated accretion flow around a black hole. By performing a local linear stability analysis, we conclude that (a) the outward (inward) going acoustic modes are unstable(stable), (b) the viscous modes are stable, (c) the thermal modes are unstable, (d) the growth rates of the acoustic modes are proportional to $\alpha^0$ while those of the thermal and the viscous modes are $\alpha^1$ where $\alpha$ is the viscous parameter, and that (e) the stability of ADAFs weakly dependent on parameters of the flows, such as the viscous parameter and the ratio of specific heats. Then we discuss global stability of the advection-dominated flows for the locally unstable thermal and outward-going acoustic modes. We find that the thermal modes are globally stable and that the outward-going acoustic modes can grow into large disturbances only around the sonic point.

Osamu Koike, Masa-aki Hashimoto, Kenzo Arai and Shinya Wanajo
Thermonuclear Shell Flash Model on Accreting Neutron Stars

The rapid proton capture process on accreting neutron stars is investigated with the use of the current nuclear data and extended nuclear reaction networks. A simple but crucial model is adopted to investigate the detailed nucleosynthesis during the burst: the plane parallel (one zone) model. The peak temperature becomes higher due to the rapid break out from the hot CNO cycle. The amount of the fuel left after the burst depends on the still uncertain $Q$-values of $\rm (p,\gamma)$ reactions for nuclei like $\rm ^{64}Ge$ and $\rm ^{68}Se$. It is also demonstrated that the uncertainties in the nuclear data should influence significantly the profile of the light curve in the burst models.

Masaru Aniya
Analysis of the Bond Ionicity in Solids: Searching a Guideline for the Design of New Superionic Conducting Materials

The bond ionicity of a binary compound is analyzed by using the dielectric theory of electronegativity and the bond orbital model. The effect of varying the number of valence electrons, the bond length, and the interatomic interaction parameter is studied. By connecting the result of the analysis with the bond fluctuation model of superionic conductors suggested by the author, possible guidelines for the development of new superionic conducting materials is discussed.

Masaru Aniya
Speculations About Bonding and Electronic Properties of Liquid Silver Chalcogenides

Recently, unusual electronic properties of liquids Ag-S and Ag-Se have been discovered. The electronic conductivity of these systems exhibits a maximum and a negative temperature derivative at the stoichiometric composition ${\rm Ag}_2$S and ${\rm Ag}_2$Se. In a similar alloy Ag-Te and Cu-chalcogenides such anomalies have not been observed. In the present paper, the origin of the anomalies is investigated from a chemical bond point of view. It is suggested that the anomalous behavior is controlled by the connection of the interaction between the second nearest neighbor orbitals. Such connection depends on the electronegativity difference between the constituent elements of the system and is intimately related with a model of superionic conductors suggested by the author

Satoshi Yajima, Yoji Higashida, Kiyotaka Kawano and Shin-Ichiro Kubota
Heat Kernel of Second Order Elliptic Differential Operator in Riemann-Cartan Space

The algorithm for the calculation of the asymptotic expansion coefficients of the heat kernel associated with a non-negative second order elliptic differential operator $H = D_{\mu} D^{\mu} + 2 Q^{\mu} D_{\mu} + Z$ for the fermion of spin 1/2 in an arbitrary dimensional Riemann-Cartan space-time is formulated by using the covariant Taylor expansion method. The coincidence limit of the lowest four coefficients in the approach is presented.

Atsuhiro Fujii, Shin Akamatsu and Hideo Shida
Exciton Absorption Spectra of TlCl Micro-cystals in Evaporated Thin Films

Optical absorption spectra of the direct exciton of TlCl micro-crystals are measured in evaporated thin films at 5.0 K. The energy of the absorption bands shift to higher energy with decreasing micro-crystal size. A new absorption band, which was not observed in a bulk crystal, is found in a micro-crystal. The experimental results are discussed with the quantum size effect on exciton states.

Wei Yu and Atsuhiro Fujii
Diffusion of Thallous Ions into Potassium Chloride and Sodium
Chloride Single Crystals

The diffusion processes of thallous ions into single crystals of potassium chloride and sodium chloride are studied at various temperatures from 360 $^\circ$C to 500 $^\circ$C. The diffusion coefficient of thallous ion is evaluated by the optical density of the characteristic absorption band of the thallous ions in the single crystals of potassium chloride and sodium chloride. The activation energies of the diffusion in potassium chloride and sodium chloride are 1.67 eV and 1.86 eV respectively.

Kunihide Okada, Tomosige Shimamoto, Xun Xu and Muneaki Fujii
Cross-spin Correlation Function and Spin-lattice Relaxation of Br-NMR in Triangular Lattice Antiferromagnet CsMnBr3

We have studied the spin-lattice relaxation time ($T_1$) of Br-NMR in triangular lattice antiferromagnet CsMnBr$_3$ at helium temperatures. The usual theory of $T_1$ with the self-correlation function of Mn$^{2+}$ electronic spins can not explain the experimental data on the temperature dependence of $T_1$. Since the Br nuclear spin is closely connected to two neighboring atoms in the c-axis, the cross-spin correlation functions between two spins along the c-axis are important in addition to the self-spin correlation function. Our calculation taking it into account is in good agreement with experimental data.

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

Last updated: November 22, 1998