Comparison of eikonal-Born series and modified Gluaber approach for the study of elastic electron-hydrogen scattering

Elastic electron-hydrogen scattering at medium and high energies has been analysed in eikonal-Born series and modified Glauber approach forE _i ≥ 50 eV. We have used closed form expressions for evaluating the second Born term in the fixed scatterer approximation and for higher order terms of Glauber-eikonal series. The exchange effect has also been included via Glauber-Bonham-Ochkur type procedure. The fixed scatterer approximation calculations are compared with results obtained using other approximations for the second Born term available in the literature. The results compare fairly well with experimental data.     

Elastic scattering of electrons by helium atoms in high energy higher order Born approximation

The differential cross-sections forē-helium elastic scattering are calculated by using Yateshigh-energy higher order Born approximations, through 0 (K _i ^{Emphasis>−2} ) of the incident electron momentum, and comparisons have been made with the recent theoretical and experimental results.     

Vibrationally elastice − — H2O scattering at intermediate energies

Vibrationally elastic total cross-sections ofe ⁻—H₂O scattering are calculated at intermediate energiesE _i=10–300 eV. The interaction potentials are treated in spherical models. The dipole rotational excitation, which is significant but not dominant above 10 eV, is treated incoherently. Effects of electronic excitation-ionization, significant above 30 eV or so, are considered through a complex optical potential. A dynamically distorted charge-density is employed to calculate the imaginary part of the complex potential. Comparisons are made with recent theoretical and experimental data. The mutual agreement is better in total cross-sections than in differential cross-sections.     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.     

Temperature dependence of muonium spin exchange with O2 in the range 88 K to 478 K

Our group at TRIUMF reported earlier a study of the spin exchange reactions of Mu with O₂ and NO in the range 295 K to 478 K. We have extended the measurement with O₂ to a low temperature region down to 88 K. From 135 K to 296 K, the spin depolarization rate constantk _d(T) was found to vary according to the relative velocity of the colliding species,T ^1/2, which indicates that the spin exchange cross section of Mu-O₂ is temperature independent in this temperature range. The value ofk _d(T) at 296 K is in good agreement with our earlier study. However, it was found that below 105 K and above 400 K,k _d(T) tends to have stronger temperature dependences (T ⁿ , withn>1/2). This deviation fromT ^1/2-behavior can be attributed to the velocity (energy) dependence of the spin exchange cross section.     

Two Coulomb waves theory for direct excitation

A theoretical model of Dewangan, in which the total scattering wave function is approximated by a distorted wave containing two Coulomb wave functions, is discussed and its relation with the Brauner-Briggs-Klar model for ionization is examined. An important feature of the theory is that it includes a second Born amplitude naturally and in addition, contains, albeit approximately, both real and imaginary parts of all higher order Born terms. The theory is applied to study the 1s→2s excitation of hydrogen by electrons in the energy range 54.4 to 400eV. The differential and integral cross sections predicted by the theory are compared with the results of other theories and experimental data at 54.4eV and a good agreement is found.     

Exact calculation of three-body contact interaction to second order

For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle [`(E)](k<sub>f</sub>)\ensuremath \bar E(k_f) are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to [`(E)](k_f) ~ k_f¹⁰\ensuremath \bar E(k_f)\sim k_f^{10} with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction.     

Experimental and theoretical investigations of the first and second order optical susceptibilities of BiB3O6 single crystal

The first and second order optical susceptibilities of BiB₃O₆ are calculated using the full potential linear augmented plane wave method. We find that BiB₃O₆ is a semiconductor with an indirect energy gap of 3.97 eV, to be compared to the experimental value of 4.55 eV. The calculations of the first order optical susceptibilities are compared with our measurements. We present results for the birefringence, and real and imaginary parts of the frequency dependent linear and nonlinear optical response. The calculated birefringence at zero energy is negative, in agreement with our experiments. We calculated and measured the refractive indices, and good agreement is found. Calculations are reported for the frequency dependent complex second order nonlinear optical susceptibilities χ_abc ⁽²⁾(ω). BiB₃O₆ exhibits a larger second harmonic generation efficiency than other known materials, such as lithium borate, KTiOPO₄, and BaB₂O₄. Our X-ray photoelectron spectroscopic (XPS) technique measured the concomitant photoemitted electrons with discrete kinetic energies that characterize the emitting atoms and their bonding states. Our XPS measurements show that the BiB₃O₆ structure contains parallel layers of six-fold coordinated Bi atoms alternating with borate layers, which are constituted by BO₄ tetrahedra and BO₃ triangles. PACS 71.15.Ap; 78.40.Fy; 78.20.Ci; 61.50.Ks; 71.15.Mb     

Positron scattering from hydrocarbons

The total cross sections for positron impact on hydrocarbons have been calculated using the additivity rule in which the total cross section for a molecule is the sum of the total cross section for the constituent atoms. The energy range considered is from a few eV to several thousand eV. The total cross sections for positron impact on an atom are calculated by employing a complex spherical potential which comprises of a static, polarization and an absorption potential. We have good agreement with the experimental results for hydrocarbons for positron energy ⩾100 eV. Our results also agree with the available calculations for CH₄ and C₂H₂ which employed full molecular wavefunctions beyond 100 eV. Our absorption cross sections also agree with molecular wave-function calculations for C₂H₂ and CH₄ beyond 100 eV. We have shown the Bethe plots fore ⁺−C ande ⁺−H scattering systems and Bethe parameters have been extracted. We have fitted the cross section for positron impact on hydrocarbons in the formσ _t(C _n H _m )=naE ⁻ b+mcE ⁻ d in the energy range 300–5000 eV wherea=195.0543,b=0.7986,c=371.1757 andd=1.1379 withE in eV andσ _t in 10⁻¹⁶ cm².     

Configuration interaction calculations for the ground and excited states of ozone and its positive ion: Energy locations and transition probabilities

Large-scale configuration interaction calculations (including energy extrapolation) are reported for the various states of ozone and its positive ion. The first four dipole-forbidden electronic transitions in the O₃ spectrum are calculated to occur at 1.20, 1.44, 1.59, and 1.72 eV, respectively, while the corresponding low-energy-allowed species known as the Chappuis, Huggins, and Hartley bands are predicted to possess vertical excitation energies of 1.95, 3.60, and 4.97 eV, respectively. These results all appear to fit in quite well with the observed location of the pertinent spectral features, with respect to both energy and intensity. The 5- to 8-eV region of the ozone spectrum is found to be characterized by a series of double-excitation transitions out of the highest three occupied orbitals to the lowest unoccupied 2b₁(π^*) species. The strong features observed at 9.3 and 10.2 eV are thereupon calculated to result primarily from transitions into the 7a₁ (σ^*) MO (calculated 9.29 and 10.05 eV) and in the former case also from the 3s members of the various O₃ Rydberg series (calculated 9.21 and 9.38 eV). Finally the order of the first three ip's is found to be 6a₁, 4b₂, and 1a₂, while the feature in the neighborhood of 16 eV is attributed to a shake-up state of ²B₁ symmetry.     

Scattering of slow neutrons by arsenic and selenium isotopes

Coherent neutron scattering lengths and free cross sections were measured for arsenic, for ordinary selenium and its isolated isotopes. By means of the Cristiansen filter technique the following scattering lengths for the bound atoms were obtained (in fm):b(As) =6.58(1) [b ₊=6.04(5) andb _?=7.47(8)],b(Se)=7.970(9),b(⁷⁶Se)=12.2(1),b(⁷⁷Se) =08.25(8),b(⁷⁸Se)=8.24(9),b(⁸⁰Se)=7.48(3) andb(⁸²Se)=6.34(8). Transmission measurements with neutrons of 1.26 eV and 5.19 eV resulted in an energy independent free scattering cross section for arsenic ofσ _{s, t}=5.40(3)b (in the eV-region). For ordinary selenium energy dependent free cross sections ofσ _{s, t}(1.26 eV)=7.9(1)b andσ _{s, t} (5.19 eV)=7.55(3)b were found. The results were compared with the resonance parameters of the nuclei and with different sets of potential scattering radii. Thus it could be concluded that there is no evidence for a bound state of the neutron-nucleus compound⁷⁵As+n but a clear evidence for strong bound levels of⁷⁶Se+n and⁷⁷Se+n.     

Negative Ions,Ozone, and Metastable Components in dc Oxygen Glow Discharge

In a dc glow discharge in oxygen, the concentrations of minor components of O₂(a¹Δ_g), O₂(b¹ Σ_g), O₃, O(¹D), as well as nagative ions and electrons have been measured. Balance equations have been derived which describe satisfactorily the stationary concentrations of these components as functions of gas pressure and discharge current. For the first time, the rate constants of important aeronomical reactions (a) O^? + O₂(a¹Δ_g) → O₃ + e, (b) O₂^? + O₂(a¹Δ_g) → 2O₂ + e and (c) e + O₃ → O₂^? +O have been measured as functions of gas temperature T and mean energies of ions E_i and electron E₆: K_a = (2.5 ± 0.5) · 10^?9 · (T/300)^{4 ± 0.4}· (E_i/0.04)^{?2.6 ± 0.4} cm³/s for T = 385?605 K and E_i = 0.10 ? 0.66 eV; K_b = (1.0 ± 0.3) · 10^?10 · (T/300)^{?2 ± 0.5} · (E_i/0.04)^{0.23 ± 0.05} cm³/s for T = 330?605 K and E_i = 0.09 + 1.5 eV; K_c for E_e = 0.8÷5 eV.     

Perturbation allowed transitions in the infrared spectrum of 14ND3: determination of the K-dependent parameters in the ground state

ABSTRACT

Accurate values of the K-dependent constants ^{( i )} C, ^{( i )} D_K and ^{( i )} H_K in the ground state of ¹⁴ND₃, with i = s, a, have been determined for the first time thanks to the detections of ‘perturbation allowed’ transitions in the ν₁, ν₂, ν₃, ν₄ and 2ν₄ infrared bands. The rotation–inversion and inversion transitions from the literature, together with 7289 ground state combination differences from the infrared vibration–rotation–inversion transitions have been simultaneously analysed. The adopted rotation–inversion Hamiltonian includes distortion constants up to the eighth power and the Δk = ±3 and Δk = ±6 interaction terms. Precise values of the diagonal constants and of the Δk = ±3 interaction coefficients have been obtained. Accurate values of the ground state term values have been calculated for both s and a levels up to J = 21.     

O3+与H2碰撞中非解离电荷转移过程的全量子计算

应用全量子的分子轨道强耦合方法,研究了基态的O³⁺(2s²2p ²P)与氢分子碰撞的非解离电荷转移过程,计算了不同方位角(25°,45°,89°),能量分别为100,500,1000和5000eV/u时的单电子俘获的振动分辨的态选择截面及相应的微分截面.分子轨道强耦合计算中采用了自旋耦合价带理论计算的三原子分子势能面和径向耦合矩阵元.对氢分子的自身转动,采用无限阶的冲量近似方法;对体系的电子运动同H₂或H^{+< 关键词： 非解离电荷转移过程 全量子的分子轨道强耦合方法 无限阶冲量近似 振动冲量近似国家自然科学基金(批准号：10604011 10574020)和国家高技术研究发展计划(863)惯性约束聚变领域资助的课题.}     

Elastic scattering of electrons from oxygen and ozone molecules at high energies

Elastic differential cross-sections for thee-O₂ ande-O₃ systems are obtained in the independent atom model at high energies (E _i ⩾ 300 eV). The basic atomic scattering amplitudes are obtained in the partial wave method through a sum of static exchange and polarization potentials. Oure-O₂ results agree with experiments except for small angles. No data are available for O₃, for comparison.     

Biquadratic exchange interaction between Ru5+ ions in (Ru2O9) clusters

The energy levels of a Ru₂O₉ cluster have been calculated, including a higher order spin interaction. The Ru⁵⁺-Ru⁵⁺ coupling is described by the Hamiltonian ?= -2JS₁· S₂ ?j(S₁·S₂)². The temperature dependence of the magnetic susceptibility is used to determine the values of the bilinear J and biquadratic j exchange integrals: J/k = -161K and j/k = 6.6K. The second term in the Hamiltonian corresponds to a fourth order perturbation involving low spin states.     

Total electron scattering cross-sections for O atoms: O2 and O3 molecules

Total (elastic+inelastic) cross sections fore ⁻-O,e ⁻-O₂ ande ⁻-O₃ scattering have been calculated at sample energies between 100 and 1000eV. The basice ⁻-O atom scattering amplitudes are obtained from the partial wave analysis with a complex optical potential. Thee ⁻-O₂ ande ⁻-O₃ cross-sections are obtained through the independent atom model. Oure ⁻-O₂ cross-sections reproduce the experimental data quite well. Adequate comparisons are made in all the three cases.     

Static structure function of turbulent flow from the Navier-Stokes equations

The velocity field of a fully developed isotropic turbulent flow is decomposed into a smoothed fieldu _i ^(r) and a strongly fluctuating part _i ^(r) depending on a lengthr which is varied through all scales. The eddies described byu _i ^(r) loose their energy either by direct dissipation or by energy transfer to the _i ^(r) -eddies. Both contributions can be traced back to the second order static structure functionD(r) and the Lagrangian time correlation function. The latter can also be evaluated in terms ofD(r). The energy balance then gives an integro-differential equation forD(r) which determinesD(r) uniquely. The solution is not only in agreement with the scaling behaviour in the viscous and inertial subranges as predicted by dimensional arguments, but it also gives the correct transition between the two regimes. A comparison with experimental data is offered.     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}