Shunsuke Hara

The Scattering of Slow Electrons by Hydrogen Molecules

The differential and integrated cross sections are calculated for the elastic scattering of a slow electron by the hydrogen molecule. The short-range electrostatic interaction is expanded in terms of the spherical harmonics and only the first two terms are taken into account. The long-range polarization and quadrupole interactions are also included. Most of the calculations contained in this paper are carried out, however, for the spherical potential alone. To a certain approximation, the non-spherical potential has been found to be negligible. The exchange effect is taken into consideration through an approximate attractive potential function, similar to Slaters potential in the theory of atomic structure. Results of calculations agree fairly well with experimental data.

A Two-Center Approach in the Low Energy Electron-H2 Scattering

The differential and total cross sections for the elastic scattering of slow electrons by the hydrogen molecule are calculated by solving the scattering equation in two-center prolate spheroidal coordinates. The two nuclei are fixed in the calculation and the average over the molecular orientation is taken afterwards. The exchange effect is taken into account by properly antisymmetrizing the wave function with respect to three electrons in the system and the polarization effect is approximately represented by the adiabatic dipole polarization potential. The results of the calculation agree well with experimental data when the exchange and the polarization effects are taken into account. The change of the magnitude in the forward scattering as a function of the incident energy is explained by the polarization effect.

Rotational Excitation of H_2 by Slow Electrons

The differential and integrated cross sections for the rotational excitation (0→2 and 1→3) of the hydrogen molecule by show electrons are calculated in the adiabatic approximation. The effects of electron exchange and target polarization on the rotational excitation are investigated. Inclusion of these effects increases cross sections and results in good agreement with experimental data.

The Dipole-Polarization Potential in H2-Electron System

The adiabatic polarization potential in the system of hydrogen molecule and an electron is calculated by a variation perturbation method in two-center prolate spheroidal coordinates. In this calculation, a 16-term James-Coolidge type wave function is used for obtaining the dipole contribution to the potential. This is the first detailed calculation of the polarization potential of a diatomic molecule in two-center coordinates. The asymptotic forms of the dipole polarization potential in the direction parallel and perpendicular to the molecular axis are -5.975/5 r 4 and -4.359/2 r 4 in atomic units, respectively. The numerators of these asymptotic forms are to be compared with the exact values of the dipole polarizabilities 6.38049 and 4.55769 a. u. obtained by Kolos and Wolniewicz.

Rotational Excitation of the HD Molecule by Slow Electrons

Effective cross section for the rotational excitation of the HD molecule by low energy electron (incident energy of the electron ranges from 1.0 eV to 13.6 eV) is calculated for the transitions of the rotational state from J =0 to 1, 2 and from J =1 to 2. The adiabatic approximation is used to obtain these cross sections. It is found that the rotational excitation cross section with Δ J =2 is almost the same as the e –H 2 result and that the cross sections with Δ J =1 are about 10% of those with Δ J =2 in the above mentioned energy region.

MathBraille; a system to transform LATEX documents into Braille

LATEX[1] is a very well-known document preparation system which is particularly useful to produce documents containing mathematical formulae. Many scientific articles are presented in LATEX. But raw LATEX document is not suitable for the blind to read in Braille; that is, to read LATEX command as a sequence of symbols and alphabets is not a good way for understanding LATEX text. It is desirable to develop a system which transforms mathematical formula expressed by LATEX notation into corresponding Braille.In Japan, there exist several softwares which transform electronic documents into Braille[2]. However, they can cope only with literal documents. Therefore, almost all of the scientific Braille texts have been produced by human power who knows Braille rule for mathematics. There are many organizations and volunteer groups which are keen to prepare Braille texts. Nevertheless, Japanese Braille rule for mathematics is so complicated that very few can produce scientific texts. This causes lots of trouble to the blind who wants to study sciences. Shortage of Braille texts in science and technology is one of the most serious problems for blind students at high school and university. Therefore, it is also desirable to construct an automatic transformation system with which scientific Braille texts are produced easily.The aim of this research is to resolve these two problems. We have developed a system MathBraille[3] which transforms JLATEX (an extension of LATEX that contains Chinese characters and Japanese syllabaries fonts for typesetting) documents into Braille. Furthermore, by utilizing this system, one can produce Braille text for mathematics without knowing Braille rule. To prepare the input file for MathBraille, one must have a basic knowledge of LATEX commands. Nevertheless, to learn basic LATEX commands is not so difficult as to master complicated Japanese Braille rule for mathematics. One can confirm the correctness of written mathematical formulae by previewer in LATEX instead of reading the mathematical formulae in Braille.In this report, the system MathBraille is explained. The programme for the system is coded using the programming language C and compiled by Microsoft 32-bit C/C++ Standard Compiler Version 10.00. MathBraille works on the DOS/V computers.

Rotationally Resolved Photoelectron Asymmetry Parameter of H2 Using Ne-I 736Å Radiation

The photoelectron angular distribution of H 2 is measured using Ne-I 736A radiation. The asymmetry parameter β 0-2 for the (0-2) rotational transition in the (0-0) vibrational band is obtained using the regularity of the rotational transition and a deconvolution technique. The value of β 02 obtained is 0.66 (±0.17). This is in good agreement with the experimental data of Ruf et al . and with the theoretical calculation in which both the effect of electron exchange and the f-wave contribution of the ejected photoelectron are taken into account.

Variational Calculation for Muonic Molecules

Adopting the spheroidal variables to describe the muon coordinates, variational calculations are carried out for the ground and the excited states of the homo-nuclear muonic hydrogen molecular ion (ppµ) + and its isotopes with total angular momentum J =0 and 1. The best binding energies among those so far reported are obtained for several states.

The Radial and Rotational Coupling Terms between the Quasi-Molecular States of He2++

The radial and rotational coupling matrix elements between the 1 Σ g + (2sσ 2 ,2pσ 2 ,2pπ 2 ), \(^{1}\varPi_{\text{g}}(2\text{p}\sigma 2\text{p}\pi)\) and 1 Δ g (2pπ 2 ) quasi-molecular states of He 2 ++ have been calculated using an elaborate CI wave function in the range of internuclear separation from 0.0 to 0.5 atomic units. It is pointed out that, because of the configuration mixing, the rotational coupling matrix elements which are zero at the united atom limit or in the single configuration approximation have finite values at small R . The radial coupling matrix element between the 1 Σ g + (2sσ 2 ) and 1 Σ g + (2pσ 2 ) states is about 10 atomic units at the pseudo-crossing near R =0.2. The accuracy of the calculation of the radial coupling matrix elements is discussed.

Photoionization of Vibrationally Excited H2 by 584 Å Radiation

Rotationally-vibrationally resolved photoionization cross sections and asymmetry parameters for vibrationally excited H 2 are calculated for HeI-α 584 A radiation. Vibrationally resolved and vibrationally summed cross sections and asymmetry parameters for vibrationally excited H 2 are also determined based on these results.