Absolute differential, elastic integrated and mqment 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.

Elastic Cross Sections for ³He + ⁵⁸Ni above the Coulomb Barrier

In this work, the elastic cross section is calculated at energies above the Coulomb barrier for 3He + 58Ni using a Woods-Saxon potential. The solutions of the radial Schrödinger equations are calculated numerically and they are introduced in the S matrix, after which the cross section is obtained. The parameters in the potential are adjusted to satisfy known experimental data.

Measurements of the Differential Elastic and Inelastic Scattering Cross Sections of ^(12)C

The differential elastic and inelastic scattering neutron cross sections of 12C atEn=14.7 MeV produced by the T（d,n）4He reaction were measured using an associatedparticle fast neutron TOF spectrometer at 15 angles ranging from 15° to 130°.Theflight path was 2.54 m.The neutron detector consisting of an ST-451 liquid scintillatorwas massively shielded.

Elastic scattering and total reaction cross sections of^(6)Li examined via a microscopic continuum discretized coupled-channels model

We present a systematic study of 6Li elastic scattering and total reaction cross sections at incident energies around the Coulomb barrier within the continuum discretized coupled-channels(CDCC)framework,where 6Li is treated in anα+d two-body model.Collisions with 27Al,64Zn,138Ba,and 208Pa are analyzed.The microscopic optical potentials(MOP)based on Skyrme nucleon-nucleon interaction forαand d are adopted in CDCC calculations and satisfactory agreement with the experimental data is obtained without any adjustment on MOPs.For comparison,αand d global phenomenological optical potentials(GOP)are also used in CDCC analysis and a reduction of no less than 50%on the surface imaginary part of deuteron GOP is required for describing the data.In all cases,the 6Li breakup effect is significant and provides repulsive correction to the folding model potential.The reduction on the surface imaginary part of GOP of deuteron reveals a strong suppression of the reaction probability of deuteron as a component of 6Li when compared with that of a free deuteron.Further investigation is performed by considering the d breakup process equivalently within the dynamic polarization potential approach,and the results show that d behaves in a manner similar to a tightly bound nucleus in 6Li induced reactions.

Design and Manufacture an Elastic Neutron Scattering Spectrometer at the Dalat Nuclear Reactor

The objective of this study is to design an elastic neutron scattering system according to the angle with a sample using thermal neutron beam at the Dalat Nuclear Reactor (DNR). The system is used for research and training in the field of material structure analysis by neutron scattering and diffraction techniques. It is designed on the basis of inheriting the neutron measurement spectrometer systems at the DNR and the scattered neutron measurement systems in the world. The measuring system, which was installed at the horizontal channel 4 of the DNR, consists of 5-helium-3 detectors and a fully electronic system to record the scatter counts and a mechanical system with the possibility of rotating at 15˚-75˚ angles. The constructed system is tested for evaluation of the accuracy, stability and reliability of the mechanical and electronic systems of moving detectors by angles.

Investigations on molecular constants of the CD(X^2Π) radical and elastic collisions between ground-state C and D atoms at low temperatures

The potential energy curve of the CD（X2∏） radical is obtained using the coupled-cluster singles-doublesapproximate-triples [CCSD（T）] theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions, aug-cc-pV5Z. The potential energy curve is fitted to the Murrell-Sorbie function, which is used to determine the spectroscopic parameters. The obtained Do, De, Re, ωe, ωeXe, αe and Be values are 3.4971 eV, 3.6261 eV, 0.11197 nm, 2097.661 cm^-1, 34.6963 cm^-1, 0.2083 cm^-1 and 7.7962 cm^-1, respectively, which conform almost perfectly to the available measurements. With the potential obtained at the UCCSD（T）/aug-cc-pV5Z level of theory, a total of 24 vibrational states have been predicted for the first time when J = 0 by solving the radial Schrodinger equation of nuclear motion. The complete vibrational levels, the classical turning points, the inertial rotation constants and centrifugal distortion constants are reproduced from the CD（X2∏） potential when J = 0, and are in excellent agreement with the available measurements. The total and the various partial-wave cross sections are calculated for the elastic collisions between the ground-state C and D atoms at energies from 1.0×10^-11 to 1.0 × 10^-4 a.u. when the two atoms approach each other along the CD（X2∏） potential energy curve. Only one shape resonance is found in the total elastic cross sections, and the resonant energy is 8.36×10^-6 a.u. The results show that the shape of the total elastic cross section is mainly dominated by the s partial wave at very low temperatures. Because of the weak shape resonances coming from higher partial waves, most of them are passed into oblivion by the strong total elastic cross sections.

Accurate calculation of the elastic scattering properties of ^7Li atoms at ultralow temperatures

The elastic scattering properties for collisions between two ^7Li atoms are investigated in the cold and ultracold regimes separately. Based on recent theoretical and experimental results, we present the improved hybrid potentials for the singlet X^1 ∑g^＋ and triplet a^3 ∑u^＋ ground states of the Li2, Our calculated values for the scattering lengths α and the effective ranges re are compared with previous ones, and found them to be in good agreement. The scattering lengths are 34.6α0 for the singlet state and -27.6α0 for the triplet state. Shape resonances occur in the collisions at low energies. We also calculate the total cross sections and the energy positions of shape resonances for both X^1 ∑g^＋ and a^3 ∑u^＋ states.

Elastic scattering of two H(~2S_g) and N(~4S_u) atoms at low temperatures and accurate spectroscopic parameters of NH (X^3Σ^-) radical

This paper reports that the interaction potential for the X3Z- state of NH radical is constructed at the CCSD（T）/ cc-PV6Z level of theory. Using this potential, this paper calculates the spectroscopic parameters （De, Re, ωe, ωeχe, αe and Be） and their values are of 3.578eV, 0.10368nm, 3286.833cm^-1, 78.433cm^-1, 0.6469cm^-1 and 16.6735cm^-1 respectively, which are in excellent agreement with the experiments. Then the total of 14 vibrational states has been found when J=0 by solving the radial Schrodinger equation of nuclear motion. For each vibrational state, the vibrational manifolds are reported for the first time. And last, the total cross sections, s-wave, p-wave and d-wave cross sections are computed for the elastic collisions between two ground-state atoms （hydrogen and nitrogen） at low temperatures. It finds that the total elastic cross sections are dominated by s-wave scattering when the collision energy is below 10^-6a.u. The pronounced shape resonance is found at energy of 6.1 × 10^-6a.u. Calculations have shown that the shape resonance comes from the p-wave contributions.

Elastic collisions of sulfur and hydrogen in their ground states at low temperatures and spectroscopic parameters of SH(X^2Π ) radical

This paper constructs the interaction potential of the SH（X^2∏） radical by using the coupled-cluster singlesdoubles-approximate-triples theory combining the correlation-consistent quintuple basis set augmented with the diffuse functions, aug-cc-pV5Z, in the valence range. Employing the potential, it accurately determines the spectroscopic parameters. The present De, Re, ωe, ωeχe, ae and Be values are of 3.7767eV, 0.13424nm, 2699.846 cm^-1, 47.7055 cm^-1, 0.2639cm^-1 and 9.4414 cm^-1, respectively, which are in excellent agreement with those obtained from the measure- ments. A total of 19 vibrational states has been found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the experimental results. The total and various partial-wave cross sections are computed for the elastic collisions of sulfur and hydrogen in their ground states at low temperatures when two atoms approach each other along the SH（X^2∏） potential energy curve. Over the impact energy range from 1.0×10^-11 to 1.0×10^-4 a.u., eight shape resonances have been found in the total elastic cross sections. For each shape resonance, the resonant energy is accurately calculated. Careful investigations have pointed out that these resonances result from the 1 = 0, 1, 2, 3, 4, 6, 7, 8 partial-wave contributions.

Elastic scattering of two ground-state N atoms

An interaction potential for an N2（X^1∑g^＋） molecule is constructed by using the highly accurate valence internally contracted multireference configuration interaction method and the largest basis set, aug-cc-pV6Z, in the valence range. The potential is used to investigate the elastic scattering of two N atoms at energies from 1.0×10^-11 to 1.0 × 10^-4 a.u. The derived total elastic cross sections are very large and almost constant at ultralow temperatures, and the shape of total elastic cross section curve is mainly dominated by the s-partial wave at very low collision energies. Three shape resonances are found in the total elastic cross sections. Concretely, the first one is very sharp and strong. It results from the g-partial-wave contribution and the resonant energy is 3.645 × 10^-6 a.u. The second one is contributed by the h-partial wave and the resonant energy is 1.752 × 10^-5 a.u. This resonance is broadened by those from the d- and f-partial waves. The third one comes from the l = 6 partial wave contribution and the resonant energy is 3.522 × 10^-5 a.u. This resonance is broadened by those from the g- and h-partial waves. The N2（X1∑g＋） molecular parameters, which are determined at the current theoretical level, achieve very high accuracy due to the employment of the largest correlation-consistent basis set in the valence range.

Elastic collisions between Si and D atoms at low temperatures and accurate analytic potential energy function and molecular constants of the SiD(X^2Π) radical

Interaction potential of the SiD（χ^2П） radical is constructed by using the CCSD（T） theory in combination with the largest correlation-consistent quintuple basis set augmented with the diffuse functions in the wlence range. Using the interaction potential, the spectroscopic parameters are accurately determined. The present Do, De, Re, ωe, αe and Be values are of 3.0956 eV, 3.1863 eV, 0.15223 nm, 1472.894 cm^-1, 0.07799 cm^-1 and 3.8717 cm^-1, respectively, which are in excellent agreement with the measurements. A total of 26 vibrational states is predicted when J = 0 by solving the radial Schroedinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the available experiments. The total and various partial-wave cross sections are calculated for the elastic collisions between Si and D atoms in their ground states at 1.0× 10^-11-1.0×10^-3 a.u. when the two atoms approach each other along the SiD（χ^2П） potential energy curve. Four shape resonances are found in the total elastic cross sections, and their resonant energies are of 1.73×10^-5, 4.0×10^-5, 6.45×10^-5 and 5.5×10^-4 a.u., respectively. Each shape resonance in the total elastic cross sections is carefully investigated. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave at very low temperatures. Because of the weakness of the shape resonances coming from the higher partial waves, most of them are passed into oblivion by the strong s partial-wave elastic cross sections.

Calculation of the elastic scattering properties for cold and ultracold 39K atoms in a triplet state

The elastic scattering properties for collisions between cold and ultracold 39K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet α3∑u^＋ ground state of K2. Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578α0 and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the α3∑u^＋ state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the α3∑u^＋ state are calculated.

Polarization and exchange effects in elastic scattering of electron with atoms and ions

Laser-induced electron diffraction（LIED）, in which elastic scattering of the returning electron with the parent ion takes place, has been used to extract atomic potential and image molecular structures with sub-？A precision and exposure time of a few femtoseconds. So far, the polarization and exchange effects have not been taken into account in the theoretical calculation of differential cross section（DCS） for the laser-induced rescattering processes. However, the validity of this theoretical treatment has never been verified. In this work, we investigate the polarization and exchange effects on electron impact elastic scattering with rare gas atoms and ions. It is found that, while the exchange effect generally plays a more important role than the polarization effect in the elastic scattering process, the exchange effect is less important on electron–ion collisions than on electron–atom collisions, especially for scattering in backward direction. In addition, our calculations show that, for electron–atom collisions at incident energies above 50 e V, both the polarization and exchange effects can be safely neglected, while for electron–ion collisions, both the polarization and exchange potentials do not make substantial contributions to the DCS at incident energies above 20 e V and scattering angles larger than 90？. Our investigation confirms the validity of the current LIED method.

High Energy Proton-Proton Elastic Scattering in the Pomeron Exchange Model

We study high energy proton-proton elastic scattering in the framework of Pomeron exchange model. The cross section of the process are calculated without any free parameters. Our finding is that Pomeron exchange theory gives perfect fits to total cross section at the energy of√s higher than 10 GeV and to differential cross section at the momentum transfer [t] less than 1.5 GeV2. For total cross section at lower energy √s ＜ 10 GeV and differential cross section at larger momentum transfer region of |t| ＞ 1.5 GeV2, the Pomeron exchange theory needs to be improved.

SHEAR STRESS ANALYSIS OF TIMOSHENKO'S BEAM WITH MULTIPLY CONNECTED CROSS SECTION

In this paper, a finite element method is developed to numericallyevaluate the shear coefficient of Timoshenko's beam with multiplyconnected cross section. With focus on analyzing shear stressesdistributed at the neutral axis of the beam, an improved definitionof the shear coeffi- cient is presented. Based on this definition, aGalerkin-type finite element formulation is proposed to analyze theshear stresses and shear deflections. Numerical solutions of theexamples for some typical cross-sections are compared with thetheoretical results. The shear coefficient of tower sections of theTsing Ma Bridge is calculated by use of the proposed approach, sothat the finite element modeling of The bridge can be developed withthe accurate values of the sectional properties.

Calculation of scattering parameters for ultracold ~6 Li-~7 Li elastic collisions

This paper theoretically studies the elastic scattering properties in a mixture of 6Li and 7Li atoms at cold and ultracold temperatures. Based on the constructed accurate interatomic potential of the triplet state for 6Li7Li mixture by the mass scaling method, it calculates the interspecies s-wave scattering lengths and the p-wave scattering lengths by the variable phase method and the semiclassical method, respectively. The scattering length is in good agreement with the experiment. The partial-wave and total cross sections are also calculated and a rich resonance structure is found.

Calculation of the elastic collision properties of Na and Li atoms at ultracold temperature

This paper firstly reports a theoretical study of elastic scattering properties in a mixture of 23Na and 7Li atoms at cold and ultracold temperatures in detail. Based on the new constructed accurate singlet X1∑g＋ and the triplet a3∑u＋ states interatomic potentials for 23Na7Li mixture, it calculates the scattering lengths and the effective ranges by three computational methods, and obtains good agreements. Using the mass scaling method, it also calculates 23Na6Li scattering lengths and s-wave and total elastic cross sections, whose rich resonance structures were found and interpreted in terms of quasibound diatomic levels trapped behind a centrifugal barrier.

Elastic scattering of sodium and cesium atoms at ultracold temperatures

The elastic scattering properties in a mixture of sodium and cesium atoms are investigated at cold and ultracold temperatures. Based on the accurate interatomic potential for the NaCs mixture, the interspecies s-wave scattering lengths, the effective ranges and the p-wave scattering lengths are calculated by the quantal method and the semiclassical method, respectively. The s-wave scattering lengths are 512.7a0 for the singlet state and 33.4a0 for the triplet state. In addition, the spin-change and elastic cross sections are also calculated, and the g-wave shape resonance is found in the total elastic cross sections.

Elastic electron scattering with formamide-(H_(2)O)_(n) complexes(n=1,2):Influence of microsolvation on the π^(*) and σ^(*) resonances

We report elastic cross sections for low-energy electron scattering with formamide-(H_(2)O)n complexes(n=1,2)in the energy region of 0.01-8 eV.The scattering calculations are performed using the R-matrix method in the static-exchange(SE)approximation.We consider three structures of formamide-H_(2)O and six structures of formamide-(H_(2)O)_(2)in the present work.Our purpose is to investigate effects of water molecules hydrogen-bonding to formamide.We focus on the influence of microsolvation on theπ*andσ*resonances of formamide.The scattering result for complexes shows that the position ofπ*resonance appears at lower or higher energies in the cluster than in the isolated formamide depending on the complex structure and the water role in the hydrogen bonding.We explain this behavior according to the net charge of the solute.It is found that the microsolvation environment has a substantial effect on the width ofπ*resonance.Our results indicate that surrounding water molecules may affect the lifetime of the resonances,and hence the process is driven by the anion state,such as the dissociative electron attachment.

Elastic electron scattering with CH_(2)Br_(2)and CCl_(2)Br_(2):The role of the polarization effects

We present elastic electron scattering cross sections with holmethane molecules CH_(2)Br_(2)and CCl_(2)Br_(2)in the lowenergy region ranging from 0.01 e V to 20 e V.The calculations are performed with the R-matrix method in static-exchange plus polarization(SEP)and close-coupling(CC)approximations.The integral,differential,and momentum transfer cross sections are calculated.The convergence of the obtained cross sections is checked at four different levels of SEP approximation.The predicted positions of the resonances agree well with available results.The precise resonance parameters are found to be sensitive to the treatment of polarization effects employed.We find that the polarization has a substantial effect on the cross sections,and this effect becomes even more important for lower impact energies.