Polarization forces in water deduced from single molecule data

The intermolecular electrostatic and polarization interactions in water are determined using a minimal atomic multipole model constructed with distributed polarizabilities. Hydrogen bonding and other properties of water-water interactions are reproduced by only three multipoles mu(H), mu(O), and theta(O) and two polarizabilities alpha(O) and alpha(H), which characterize a single water molecule and are deduced from single-molecule data.     

Determining polarizability tensors for an arbitrary small electromagnetic scatterer

In this paper, we present a method to retrieve tensor polarizabilities of general bi-anisotropic particles from their far-field responses to plane-wave illuminations. The necessary number of probing excitations and the directions where the scattered fields need to be calculated or measured have been found. When implemented numerically, the method does not require any spherical harmonic expansion nor direct calculation of dipole moments, but only calculations of co- and cross-polarized scattering cross sections for a number of plane-wave excitations. With this simple approach, the polarizabilities can be found also from experimentally measured cross sections. The method is exemplified considering two bi-anisotropic particles, a reciprocal omega particle and a non-reciprocal particle containing a ferrite inclusion coupled to metal strips.     

Singular field decomposition based on path-independent integrals

A method is developed by which the field generated by a source (measured or numerically evaluated) is decomposed in a series of singular self-equilibrating linear elastic field components. These elementary sources form an elastic equivalent of the real source, the set of their magnitudes representing a ‘spectral decomposition’ of the investigated field. The decomposition is performed using path–independent interaction integrals computed through the field of interest, far from the source. The method may be used to investigate internal field sources, such as dislocations, as well as sources of field perturbation, such as crack tips or wedges. The method is applied to the analysis of the core structure of an edge dislocation in aluminium. The dislocation is represented in an atomistic simulation and a model core is sought in the form of a series of multipoles or elementary linear elastic field sources. The field of the dislocation is composed from the Volterra solution and higher–order components induced by the nonlinear behaviour of the material in the core region. The magnitude of the component elementary sources is determined from the numerically evaluated field far from the core. This expansion characterizes the core structure. Its variation associated with the core deformation as the dislocation is loaded against the Peierls barrier is investigated.     

Dipole polarizability of hydrogen atom at high pressures

Dipole polarizability of hydrogen atom at high pressures is investigated using the model of a trapped atom inside a spherical box with impenetrable surface. Both upper and lower bounds for the polarizability are obtained using accurate variational wavefunctions proposed recently. Buckingham polarizabilities calculated from the 1s state wavefunction are shown to be in good agreement with those calculated from the exact values of rⁿ for cage radii less than 2.5.     

Slow motion approximations in general relativity II. Gauge transformations

When the field equations of general relativity are expanded in powers of a small parameter, the general covariance of the exact theory implies a corresponding gauge invariance of the equations obtained in the expansion. In a slow motion expansion, the derivation of this gauge transformation is complicated by the fact that the time coordinate is singled out for special treatment. In a previous paper, a new (3 + 1)-dimensional decomposition of the field equations was obtained which is particularly suitable as a starting point for slow motion approximations. The present paper gives a systematic method, again using covariant techniques throughout, for obtaining the corresponding gauge transformations to arbitrarily high accuracy. The calculations are explicitly carried out as far as is required in the 2 1/2-post-Newtonian approximation.     

The quadrupole–quadrupole polarizability of a non-magnetic molecule

The quadrupole–quadrupole polarizability of a molecule introduced by Buckingham is not a unique molecular property, in the sense that it depends on an arbitrary choice of the origin of the molecular coordinates. To obtain a physically acceptable form of this property for a non-magnetic molecule, a linear combination is taken of molecular polarizabilities of the relevant multipole order (electric octopole-magnetic quadrupole). By requiring this combination to possess the desired space–time and symmetry properties, as well as origin independence, an acceptable quadrupole–quadrupole polarizability is obtained. Expressions are presented for the components of this polarizability for molecules of certain symmetries.     

Dielectric alignment of a non-polar molecule substituting a polar molecule in a lattice of molecular dipoles

The dielectric alignment of a dilute non-polar component in a polar solvent may be determined by NMR spectroscopy. In this paper a series expansion of the alignment up to second order terms in the dipolar interaction is presented for a non-polar molecule replacing a single polar molecule in a rigid lattice of molecular dipoles. Assuming isotropic polarizabilities for all molecules Van Vleck earlier applied the lattice model in a theory of the dielectric constant of a dilute solution.In the present calculation the polarizabilities of the non-polar molecule and the dipoles are assumed to be anisotropic and isotropic, respectively. The anisotropy of the non-polar molecule is relevant, since the value of the alignment is zero for the isotropic case. Different results are obtained for cubic lattices and for a lattice points are uniformly distributed.In absence of a rigid dipole moment of the solvent molecules the latter formula may be compared with that implicity deduced by Buckingham for the Kerr effect. In the limit of strong dipoles the orientation imposed by the rigid dipole moments appears to be the major contribution to the alignment of the non-polar molecule.     

Higher multipole polarizabilities of hadrons from compton scattering amplitudes

Starting with partial wave projections of the Compton scattering invariant amplitudes free of kinematical singularities or zeros, generalized electric and magnetic multipole polarizabilities of spin-0 and $\text{spin}\text{-}\text{1}\text{2}$ hadrons are introduced as threshold limits of the non-Born parts of the corresponding electric and magnetic Compton multipoles. These objects, which enter the higher low-energy theorems for elastic γ-hadron scattering, are shown to be acceptable quantum field theoretical generalizations of the usual static multipolar polarizabilities encountered in classical electrodynamics or non-relativistic quantum mechanics. Using the analyticity properties of the amplitudes, sum rules for the generalized electric and magnetic quadrupole polarizabilities of the proton and the pions are written down and evaluated numerically within the two-particle unitarity approximation.     

Ab initio calculations of the second dynamic hyperpolarizability of LiH by means of Floquet theory approach

Floquet theory is used to describe the response of a molecule to applied radiation electric field. The method of ab initio calculation of frequency dependent (hyper)polarizabilities based on combination of perturbation theory with the finite field method has been developed. Electron correlation is taken into account by means of the CIPSI algorithm. The total wave function expansion involves spectral, pseudo-spectral states and polynomial terms. The developed approach is applied to the calculation of the second hyperpolarizability of the lithium hydride molecule subjected to the superposition of harmonic and static electric fields. The method can be used to calculate the higher order nonlinear properties of molecules. Received 23 November 2000 and Received in final form 25 March 2001     

Analysis of general multipolar images on dielectric layers for the calculation of DEP force

An axisymmetric field problem of a sphere and a multi-layered planer dielectric body is investigated based on the multipolar expansion method. First, the multipolar potential, produced by the sphere and expressed in the spherical coordinate system, is re-written in the cylindrical coordinate system as an integral of Bessel function. Then the field problem is solved with the boundary conditions at the planer interface of the dielectrics, and the obtained potential is written back to spherical harmonics, which can be regarded as “image multipoles” inside the dielectric body. The “images” influences back the “multipoles” on the sphere, and the field can be determined by solving these relations in self-consistent manner. DEP force exerted on the particle is calculated as the multipolar interaction, as well as the capacitance for the case involving a conducting sphere and a conducting plane.     

半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。      

Determination of static dipole polarizabilities of Yb atom

We determine the static values of the scalar and tensor dipole polarizabilities of the ground, 6s6p~3P_0~o, and 6s6p~3P_1~o states of the Yb atom. These results can be useful in many experiments undertaken using this atom. We employed a combined configuration interaction(CI) method and a second-order many-body perturbation theory(MBPT) to evaluate energies and electric dipole(E1) matrix elements of many low-lying excited states of the above atom. These values are compared with the other available theoretical calculations and experimental values. By combining these E1 matrix elements with the experimental excitation energies, we estimate the dominant valence correlation contributions to the dipole polarizabilities of the above states. The core contribution is obtained from the finite field approach. We also compare these values with the other theoretical results as there are no precise experimental values that are available for these properties.     

Exchange effects in photon scattering off the deuteron

Detailed calculations of elastic photon-deuteron scattering cross sections for photon energies up to about the π-production threshold are presented. The scattering amplitude is decomposed into scalar, vector and tensor polarizabilities for the various electric and magnetic multipole combinations. This includes a general multipole expansion of the two-photon operator. The imaginary part of the polarizabilities is determined from the contribution to the total cross section using the optical theorem. The real part is then obtained from dispersion relations. Special emphasis is laid on the discussion of exchange effects for both the resonance and the two-photon amplitude. These affect strongly the resonance amplitude whereas for the two-photon amplitude we find only a small effect beyond the important low-energy limit. Another important result is the large vector polarizability at higher energies related to the optical activity of the deuteron.     

Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium

We present a systematic derivation of the dynamical polarizability and the ac Stark shift of the ground and excited states of atoms interacting with a far-off-resonance light field of arbitrary polarization. We calculate the scalar, vector, and tensor polarizabilities of atomic cesium using resonance wavelengths and reduced matrix elements for a large number of transitions. We analyze the properties of the fictitious magnetic field produced by the vector polarizability in conjunction with the ellipticity of the polarization of the light field.     

Fits to new calculations of photoionization cross sections for low-Z elements

Analytical approximations to results of new calculations of partial (i.e. by subshell) photoionization cross sections of elements (2 < Z < 30, Z = 36) are presented which cover the photon energy range from near threshold to 300 keV. The computer program developed by Brysk and Zerby, which is based on the single-electron model and uses screened self-consistent field and Dirac-Slater wave function data furnished by Cromer, Waber and Liberman, was used. Sufficient multipoles were included to calculate the partial cross sections within a few per cent, on the assumed model. Results for several elements are compared with other calculations and measurements of total photoionization cross sections. The results are presented in a form most convenient for calculations of opacities of hot gases.     

Coulomb interactions and optically-active vibrations of Ionic crystals—I: Theory and application to NaNO3

A method is given for polarizable-ion model calculations of optically-active vibration frequencies of ionic crystals together with an illustrative application. Frequency splittings originating from Coulomb interactions between induced dipoles are explained satisfactorily by the calculations. Important discrepancies remaining in rigid-ion treatments are considerably reduced by taking into account the electronic polarizabilities. Some effects of anisotropy of the ionic polarizabilities on crystal vibrations are discussed briefly.     

A maximum entropy mean field method for driven diffusive systems

We introduce a method of generating systematic mean field (MF) approximations for the nonequilibrium steady state of ferromagnetic Ising driven diffusive systems (DDS), based on the maximum entropy principle due to Jaynes. In the phase coexistence region, MF approximations to the master equation do not provide a closed system of equations in the MF variables. This can be traced to the conservation of the order parameter by the stochastic dynamics. Our maximum entropy mean field (MEMF) approximation method is applicable to high temperatures as well to the low-temperature phase coexistence region. It is based on a derivation of a generalized variational free energy from the maximum entropy principle, with the MF evolution equations playing the role of constraints. In the phase coexistence region this free energy is nonconvex and is interpreted by means of a Maxwell construction. We use a pair-level variant of the MEMF approximation to calculate quantities of interest for the ferro-magnetic Ising DDS on a square lattice. Results of calculations with several different choices of transition rates satisfying local detailed balance are discussed and compared with those obtained by other methods.