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.     

Electric moments of carbon dichalcogenides

The dipole and quadrupole moments and parallel dipole polarizabilities of the carbon dichalcogenides XCY (X, Y = O, S, Se and Te) are evaluated at the level of the CCSD(T) approximation with HyPolX basis sets. The relativistic effects are taken into account by using the scalar version of the two-component Douglas–Kroll method. The reported calculations provide a systematic study of the electron correlation and relativistic effects in the investigated series of carbon dichalcogenides and their results agree well with best-known experimental data. Particular attention has been given to the OCS molecule and the present calculations combined with recent studies by other authors may help to resolve the ambiguities concerning its quadrupole moment. Changes of dipole and quadrupole moments in the studied series of molecules are interpreted in terms of the electronegativities of the chalcogene atoms and their changes due to relativistic effects. The latter have been found to lead to significant changes in the calculated quadrupole moments of the heavy members of the series of molecules. Study of the basis set dependence of the calculated data shows that both the earlier PolX and the recently developed HyPolX basis sets are suitable for calculations of reliable values of the low-multipole moments and dipole polarizabilities of molecules containing heavy elements.     

On the dipole moment of three identical spherical atoms

Martin's perturbation theory result [2] for the dipole moment of three identical spherical atoms at large separations is shown to simplify: There are two contributions to this three-atom dipole and the strength of each factors into a product of the dipole polarizability of one atom and a two-atom average of dipole and quadrupole matrix elements. The simplified results are used to obtain an improved evaluation of the three-atom dipole of three He atoms, employing extensive pseudo-spectral representations of the dipole and quadrupole excitations.     

Energy levels and radiative rates for Ne-like ions from Cu to Ga

Energy levels, lifetimes and wave function compositions are computed for 127 fine structural levels in Ne-like ions (\(Z=29{-}31\)). Configuration interaction has been included among 51 configurations (generating 1016 levels) and multiconfigurational Dirac–Fock method is used to generate the wave functions. Similar calculations have also been performed using the fully relativistic flexible atomic code (FAC). Transition wavelength, oscillator strength, transition probabilities and line strength are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground level. We compared our calculated results with the available data in the literature. The calculated results are found to be in close agreement with the previous results. Further, we predict some new atomic data which may be important for plasma diagnostics.     

Spectra of the quardupole-dipole superlattice

The possible enhancement of quadrupole and magnetic transitions coming into resonance with dipole transitions in superlattices has been studied. The frequency dependences of the effective permittivity tensor of the superlattice are determined. The dispersion functions of hybrid dipole-quadrupole polariton branches are obtained. The effective strength of the quadrupole transition is determined as a function of the parameters of the dipole transition, which makes it possible to control the intensity and frequency of the quadrupole radiation. Polaritons can have a negative group velocity if they propagate in a direction other than the optic axis of the superlattice.     

Isometric groups,selection rules and irreducible tensors of semi-rigid molecules

A systematic treatment of multipole selection rules of non-rigid molecules is presented, based on the isomorphism of the isometric group to the symmetry group of the rotation-internal motion hamiltonian. A classification of isometric groups and relations among the representations of the isometric group on various substrates are discussed. A set of general transformation formulae for irreducible tensor operators of semi-rigid molecular models is derived. These formulae are used for the derivation of dipole and quadrupole selection rules of a considerable number of semi-rigid models. The relations among the representations of the isometric group give rise to some theorems which allow a compact presentation of selection rules of non-rigid molecules.     

磁偶极和电四极在磁各向异性介质中的辐射功率

在经典电动力学的框架下,研究了磁各向异性介质中的电磁辐射问题,得到了磁偶极和电四极在磁各向异性介质中的辐射功率表达式.进一步地,通过把各向同性介质中的μrii代入所得辐射功率表达式,得到了与文献相符合的结果,验证了所得结果的正确性.研究结果表明磁偶极和电四极在磁各向异性介质中的辐射功率大小与磁各向异性介质的μrii大小有关,对判断磁偶极和电四极在磁各向异性介质中的辐射效果有较大的帮助.     

Unique definitions for the band strength and the electronic-vibrational dipole moment of diatomic molecular radiative transitions

Unique definitions of the band strength and the electronic-vibrational dipole moment are inferred from a recently published fundamental discussion on the line strength of rotational transitions in diatomic molecules. In addition, consistent relations between these quantities and the transition probability or oscillator strength are presented.     

Paramagnetic magnetochiral effect in the H h and V h components of Rayleigh light scattering by molecular systems

A static magnetic field, acting on an isotropic medium composed of paramagnetic chiral molecules perpendicular to the propagation direction of the optical beam, is shown to induce an axial differential effect—magnetochiral Rayleigh light scattering. Diamagnetic and paramagnetic contributions to the effect are given in terms of the linear and nonlinear electric dipole, magnetic dipole and electric quadrupole polarizabilities responsible also for natural optical activity, the Faraday effect as well as magnetochiral birefringence. Specific cases are discussed.     

Liquid–vapour equilibrium of multipolar square-well fluids.Gibbs ensemble simulations and equation of state

Simulation results for a system comprising a square well plus either a point dipole or a point quadrupole are presented. The properties obtained are the vapour–liquid equilibrium densities and the critical properties. Critical densities are not very sensitive to the values of dipole or quadrupole, while critical temperatures increase significantly when the multipole strength rises. A comparison with a perturbation theory for multipolar square-well systems is presented. Overall agreement between simulated and theoretical values is good when comparison is restricted to quadrupoles or dipoles corresponding to the most relevant real polar substances but is only moderate for the largest multipolar strengths considered.     

Application of the nuclear liquid drop model to atomic and molecular physics problems

The liquid drop model is applied to describe some basic properties of atoms, homoatomic molecules, metallic clusters of atoms and fullerene molecules. Equilibrium atomic size, energy and polarizability of the atom are calculated. Collective modes of oscillations (dipole, quadrupole and monopole, or breathing, ones) are regarded. Electromagnetic radiation by an atom, passing through a barrier is studied. Equilibrium volume of a homoatomic molecule of two atoms, axes ratio, dissociation energy and the frequencies of the dipole oscillations are calculated. Models to describe some properties of clusters and fullerene molecules are proposed. The size of the metallic cluster, its energy and the frequency of dipole oscillations are calculated. The frequencies of the dipole and breathing mode oscillations of the fullerene molecules are obtained. The calculated frequency of the dipole oscillations was found to be in a rather good accord with the experimental one.     

The interaction of transverse domain walls

The interaction between transverse domain walls is calculated analytically using a multipole expansion up to third order. Starting from an analytical expression for the magnetization in the wall, the monopole, dipole, and quadrupole moments are derived and their impact on the interaction is investigated using the surface and volume charges. The surface charges are important for the dipole moment while the volume charges constitute the monopole and quadrupole moments. For domain walls that are situated in different wires it is found that there is a strong deviation from the interaction of two monopoles. This deviation is caused by the interaction of the monopole of the wall in the first wire with the dipole of the wall in the second wire and vice versa. The dipole-dipole and the quadrupole-monopole interactions are found to be also of considerable size and non-negligible. A comparison with micromagnetic simulations shows a good agreement.     

Shifts of one-electron ions lines from n = 0 interactions with electrons in hot and dense plasma

This paper is concerned with lineshifts of hydrogen-like ions due to electron collisions in dense and hot plasmas. These collisions are treated by including all effects due to monopole, dipole, and quadrupole interactions between radiator and electron perturbers. The latter follow exact hyperbolic trajectories with a possible penetrating part inside atomic orbits. A simple closed form for the line shift has been derived. Comparison between our semi-classical results and the quantum mechanical ones shows good agreement for a large range of high electron densities and temperatures. Received: 30 June 1997 / Revised: 28 April 1998 / Accepted: 29 April 1998     

基于HIRFL-CSR中剥离器的支束线物理设计

介绍了通过剥离器后不同电荷态的束流在弯曲磁铁中的传输情况,由此引出一种切割束流的方法,在此基础上设计了一条支束线,以实现两个实验终端同时供束,增加供束时间.在束运线设计过程中,根据HIRFL CSR的实际条件,对束流的中心轨迹和束流包络做了详细的计算,给出了束流输运线的几何布局和各个元件的基本物理参数. A new branch beam line downstream of the stripper located between SFC and SSC is designed to collect the beams with the charge states other than the most intensive one. The layout of the branch beam line and the physical parameters for each dipole and quadrupole are given based on careful calculations.     

Analogy between linear sound scattering processes in a viscous liquid and in an isotropic elastic medium

Expressions for velocities and forces responsible for the monopole, dipole, quadrupole, and rotational oscillations of a spherical particle in an arbitrary sound field, as well as in fields of plane waves and waves scattered by other particles, are derived. The expressions are valid for both liquid and isotropic elastic media.     

Stark broadening of isolated lines: calculation of the diagonal multiplet factor for complex configurations (n1l1 n n2l2 m n3l3 p)

Owing to the increasing sensitivity of detectors, accurate line profiles are needed for accurate stellar atmospheres modelling and for laboratory and technological plasmas as well. So, Stark broadening parameters of isolated lines of complex atoms and ions within the impact and quasistatic approximation are needed, even if the atomic abundance of the considered element is low. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are needed. The aim of this paper is to extend the previous calculations of this diagonal multiplet factor which were obtained for configurations of the type lⁿ and l₁ ⁿl₂ ^m to more complex configurations in LS coupling. To study the Stark broadening of isolated lines in the impact and quasistatic approximation, we use the semi-classical-perturbation treatment, including both dipole and quadrupole contribution in the expansion of the electrostatic interaction between the optical electron and the perturber. We also use the Fano-Racah algebra. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are calculated. New diagonal multiplet factor formulae for more complicated configurations such as (n₁l₁ ⁿ(L_nS_n)n₂l₂ ^m(L_mS_m)n₃l₃ ^p(L_pS_p)) are provided. These formulae can enter the computer Stark semi-classical perturbation codes.     

Lithium quadrupole properties and Van der Waals constants using pseudo-state techniques

Pseudo-spectral techniques are used to evaluate the moments of the quadrupole oscillator strength distribution for the ground-state Li atom and the dipole-quadrupole Van der Waals constants for the ground-state Li-Li, Li-He and Li-H interactions. The analysis of the pseudo-state data allows an error to be assigned to each calculated Li quadrupole property and Van der Waals constant. The pseudo-state approach also allows a quantitative estimate of the contributions of the Li atom quadrupole resonance, principal series and inner shell transitions to each Li atom quadrupole properly. The convergence of the sum over states expressions for the quadrupole properties of Li is quite different than for the corresponding dipole properties.     

Thermodynamics of mixtures of non-spherical molecules

Thermodynamic properties of liquid mixtures in which strong anisotropic intermolecular forces exist are studied using the Padé approximant method used by Stell et al. for pure fluids. Equations for the third-order perturbation term are derived for a general intermolecular potential of multipolar type. Using a mixture of Lennard-Jones molecules as the reference system, the effects of adding point dipole, quadrupole and anisotropic overlap potentials are calculated. Numerical results are presented (at low pressures) for the effect of these forces on the excess functions, and on the vapor-liquid equilibrium curves. These anisotropic forces lead to positive deviations from Raoult's law. Strong polar and quadrupolar forces may cause liquid-liquid immiscibility to occur. Numerical calculations are presented to illustrate such behaviour; these systems have upper critical solution points.     

Scaling theory for homogenization of the Maxwell equations

A scaling theory for homogenization of the Maxwell equations is developed upon the representation of any field as a sum of its dipole, quadrupole, and magnetic dipole moments. This representation is exact and is connected neither with multipole expansion nor with the Helmholtz theorem. A chain of hierarchical equations is derived to calculate the moments. It is shown that the resulting macroscopic fields are governed by the homogenized Maxwell equations. Generally, these fields differ from the mean values of microscopic fields.     

A self-consistent microscopic description of the giant resonances including the particle continuum

The distribution of strength for the isovector dipole and isoscalar quadrupole modes in ¹⁶O and ²⁰⁸Pb is calculated in the framework of the RPA. Effects due to the self-consistency as well as the single-particle continuum are included. The various collective models and the coupled-channel reaction theory are related through the RPA sum rules.