Electron scattering from molecule CH4 at 10-5000eV

Electron scattering from molecules in the intermediate- and high-energy range is investigated employing the developed semi-empirical formula for electron scattering from diatomic molecules. Total cross sections of e-CH4 scattering are obtained over an incident energy range of 10--5000eV. The results agree well with other available experimental and theoretical data. According to our formula, some quantitative information of single Yukawa potential are also obtained.     

A new semi-empirical formula for total cross sections of electron scattering from triatomic molecules at 30-5000 eV

Total cross sections (TCSs) of electrons scattering from triatomic molecules over the energy range from 30 to 5000 eV are investigated employing a new semi-empirical formula. The TCSs of electrons scattering from triatomic molecules SO2, NO2, and CO2 are calculated. The quantitative TCSs are in good agreement with those obtained by experiments. It is shown that the results derived from the semi-empirical formula are much closer to the measurements than other calculations.     

A New Semi-Empirical Method for Total Cross Sections of Electron Scattering from Spherical Polyatomic Molecules at 30-5000 eV

Electron scattering from spherical polyatomic molecules in the intermediate and high energy range is studied by employing the developed semi-empirical formula for electron scattering from simple diatomic molecules. The total cross sections of electron scattering from CF4 and CC14 are obtained over the incident energy range 30-5000 eV. The quantitative total cross sections are compared with the measurements and with the other calculations wherever available including the results derived from the additivity rule model and the correlated optical potential [Chin. Phys. Left. 21 (2004) 474], and good agreement is obtained over the incident energy range 30-5000eV. It is shown that the calculations derived from the semi-empirical formula are much closer to the measurements than other calculations. Finally, some quantitative information of the single Yukawa potential is also obtained.     

Total cross sections for electron scattering from sulfur compounds

The original additivity rule method cannot give good results for electron scattering from SO,SO2,SO2Cl2,SO2ClF,and SO2F2 molecules at low energy,because the electron-molecule scattering is simply reduced to electron-atom scattering.Considering the difference between the bound atom in a molecule and the corresponding free atom,the original additivity rule is revised.With the revised additivity rule,the total cross sections for electron scattering from these molecules are calculated over a wide energy range below 3000 eV and compared with the available experimental and theoretical data.A better agreement between them is obtained.     

Absolute differential, elastic integrated and moment transfer cross sections for electron--OCS collisions at intermediate and high energies

A complex optical model potential modified by incorporating the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between atoms in a molecule, is firstly employed to calculate the absolute differential, elastic integrated and moment transfer cross sections for electron scattering by OCS over the incident energy range from 200 to 1000\,eV using the additivity rule model at Hartree--Fock level. The calculated results are compared with those obtained by experiment and other theories wherever available, and good agreement is obtained over a wide energy range. It is shown that the additivity rule model together with the modified potential is completely suitable for calculating the absolute differential, elastic integrated and moment transfer cross sections of electron scattering by molecules such as OCS.     

Additivity rule for electron--molecule total cross section calculations at 50--5000eV: a new geometrical approach

Taking into consideration the changes of the geometric shielding effect in a molecule as the energy of incident electrons varies, this paper presents an empirical fraction, which depends on the energy of incident electrons, the target＇s molecular dimension and the atomic and electronic numbers in the molecule. Using this empirical fraction, it proposes a new formulation of the additivity rule. Employing the new additivity rule, it calculates the total cross sections of electron scattering by C2H4, C6H6, C6H14 and C8H18 over the energy range from 50 to 5000eV. In order to exclude the calculation deviations caused by solving the radial Schrodinger equation of electron scattering by atoms, here the atomic cross sections are derived from the experimental total cross section results of simple molecules （H2, O2, CO） via the inversion algorithm. The quantitative total cross sections are compared with those obtained by experiments and other theories, and good agreement is obtained over a wide energy range, even at energy of several tens of eV.     

An Empirical Formula Approach to Total Cross Sections for Electron Scattering on Polyatomic Molecules

Considering the real experimental process of e-molecule scattering a new empirical formula has been developed to calculate the total cross sections （TOSs） for electron scattering on polyatomic molecules （CH4, C2H2, CH3OH and CH3F）. The present results are compared with other available theoretical results and experimental data. The new formula incorporates an energy factor f（E） to represent the elastic and inelastic changing process during experiments. It depends on no adjustable parameters and has also extended the validity of the empirical approaches to lower energy range further.     

Vibrational Energy—Spectra and Infraned Absorption of α—Helical Protein Molecules

The quantum energy spectran,including high excited states,of vibrational amide-I or of intramolecular excitations in α-helical protein molecules,are calculated by the discrete nonlinear Schrodinger equation together with the parameters appropriate to the systems.The distribution of energy levels obtained is basically consistent with the experimental values obtained by infrared absorption and Raman scattering.Utilizing the energy spectra we explain the laser Raman spectrum from metabolically active escherichia coli and we present some further features of the infrared absorption of the protein molecules.     

Electron Scattering by C4H10 and C6H6 in the Energy Range 100--1000eV

We investigate the applicability of the independent atom model （IAM） to elastic electron scattering from complex polyatomic molecules, namely C4H10 and C6H6, in the energy range 100-1000eV. The cross sections of the elastic electron scattering are calculated by employing the IAM together with the relativistic partial waves. The incorporation of both the modified absorption potential and the extended structural factor in the IAM makes the elastic differential cross sections and momentum transfer cross sections have a good agreement with the available experimental data. The present simple model seems to be insensitive to the complexity of the target molecules so that the proposed procedure can be quite useful for calculation of electron scattering from bio-molecules.     

Applicability of ~9Be global optical potential to description of ~(8,10,11)B elastic scattering

We achieved a set of 9Be global phenomenological optical model potentials by fitting a large experimental dataset of the elastic scattering observable for target mass numbers from 24 to 209.The obtained 9Be global optical model potential was applied to predict elastic-scattering angular distributions and total reaction cross-sections of 8,10,11B projectiles.The predictions are made by performing a detailed analysis comparing with the available experimental data.Furthermore,these elastic scattering observables are also predicted for some lighter targets outside of the given mass number range,and reasonable results are obtained.Possible physical explanations for the observed differences are also discussed.     

Additivity Rule for Electron-Molecule Total Cross Section Calculations at 50-5000 eV： A Geometrical Approach

To quantify the changes of the geometric shielding effect in a molecule as the incident electron energy varies, we present an empirical fraction, which represents the total cross section （TCS） contributions of shielded atoms in a molecule at different energies. Using this empirical fraction, a new formulation of the additivity rule is proposed. Using this new additivity rule, the TCSs for electron scattering by CO2, C2H2, C6H12 （cyclo-hexane） and CsH16 （cyclo-octane） are calculated in the range 50-5000 e V. Here the atomic cross sections are derived from the experimental TCS results of simple molecules （H2, O2, CO）. The quantitative TCSs are compared with those obtained by experiments and other theories, and good agreement is attained over a wide energy range.     

Selection rules for electric multipole transition of diatomic molecule in scattering experiments

The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments.Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules(also known as optical selection rules). However, the selection rules for atoms and molecules in the scattering experiments are not identical to those in the optical experiments. In this paper, based on the theory of the molecular point group, the selection rules are derived and summarized for the electric monopole, electric dipole, electric quadrupole, and electric octupole transitions of diatomic molecules under the first Born approximation in scattering experiments. Then based on the derived selection rules, the electron scattering spectra and x-ray scattering spectra of H2, N2, and CO at different momentum transfers are explained, and the discrepancies between the previous experimental results measured by different groups are elucidated.     

Dissociation Energies of Diatomic Molecules

Molecular dissociation energies of 10 electronic states of alkali molecules of KH, ^7LiD, ^7 LiH, ^6LiH, NaK, NaLi and NaRb are studied using the highest three accurate vibrational energies of each electronic state, and an improved parameter-free analytical formula which is obtained starting from the LeRoy Bernstein vibrational energy expression near the dissociation limit. The results show that as long as the highest three vibrational energies are accurate, the current analytical formula will give accurate theoretical dissociation energies De^theory, which are in excellent agreement with the experimental dissociation energies De^expt.     

Investigation on electromagnetic scattering from rough soil surface of layered medium using the small perturbation method

Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.     

Determination of bulk viscosity of liquid water via pulse duration measurements in stimulated Brillouin scattering

We present a method by which to determine the bulk viscosity of water from pulse duration measurements of stimulated Brillouin scattering （SBS）. Beginning from a common model of Brillouin scattering, the bulk viscosity is shown to play an important role in Brillouin linewidth determination. Pulse durations of SBS back-reflected optical pulses are measured over the temperature range of 5-40℃. SBS linewidths are de- termined via Fourier transformation of the time-domain results, and the bulk viscosity of water is measured and derived from the obtained values. Our results show that the proposed method for measurement of pulse durations is an effective approach for determining bulk viscosity. The method can be easily extended to determine bulk viscosities of other Newtonian liquids.     

Total cross sections for electrons scattering from C2F4 and SO2 at 30- 5000 eV: considering the geometric shielding effect

Considering the changes of the geometric shielding effect in a molecule as the incident electron energy varing, an empirical fraction, which is dependent on the incident electron energy, is presented. Using this empirical fraction, the total cross sections (TCSs) for electrons scattering from complex polyatomic molecules C2F4 and SO2 are calculated over a wide energy range from 30 to 5000 eV together with the additivity rule model at Hartree-Fock level. In the TCS calculations, the atoms are presented by the spherical complex optical potential, which is composed of static, exchange, polarization and absorption contributions. The quantitative TCSs above 100 eV are in good agreement with those obtained by experiments and other theories. It is proved that the empirical fraction, which exhibits the TCS contributions of shielded atoms in a molecule at different energies, is reasonable.     

Total cross sections for electrons scattering from C_2F_4 and SO_2 at 30-5000 eV: considering the geometric shielding effect

Considering the changes of the geometric shielding effect in a molecule as the incident electron energy varing, an empirical fraction, which is dependent on the incident electron energy, is presented. Using this empirical fraction, the total cross sections (TCSs) for electrons scattering from complex polyatomic molecules C2F4 and SO2 are calculated over a wide energy range from 30 to 5000 eV together with the additivity rule model at Hartree-Fock level. In the TCS calculations, the atoms are presented by the spherical complex optical potential, which is composed of static, exchange, polarization and absorption contributions. The quantitative TCSs above 100 eV are in good agreement with those obtained by experiments and other theories. It is proved that the empirical fraction, which exhibits the TCS contributions of shielded atoms in a molecule at different energies, is reasonable.     

Anchoring properties of substrate with a grating surface

The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal (NLC) in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters (amplitude and pitch) of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.     

Simple formula for the ionization rate of diatomic molecules in an intense laser field using the velocity gauge

We derive a general ionization rate formula for the system of diatomic molecules in the velocity gauge. A more concise expression of the photoionization rate in the tunnel region is obtained for the first time. Comparisons are made among the different versions of strong-field approximation. The numerical study shows that the ionization rate in the velocity gauge is underestimated by a few orders compared with that in the length gauge. Our simple formula of ionization rate may provide an insight into the ionization mechanism for the system of diatomic molecules.     

Scattering properties of the ultracold 133Cs2 triplet state

The elastic scattering properties of ultracold 133Cs2 triplet state are investigated in detail.We construct a potential curve of the 133Cs2 triplet state,based on the latest ab initio molecular potential data and show how the scattering parameters are obtained by using three methods:the Numerov method,the semiclassical method and the variable phase method,where the scattering lengths of the 133Cs2 triplet state,i.e.301.79a0,300.67a0 and 310.81a0 are obtained respectively,with a0 being the Bohr radius.We also calculate the effective range and the number of bound states for the 133Cs2 triplet state.Our results are in agreement with the recent experimental data and the theoretical calculations.This confirms that the results of the scattering properties of the ultracold 133Cs2 triplet state,calculated by using these three methods,are reliable.