Manifestation of anisotropic collisional generation of higher polarization moments in polarization of quadrupole emission

Direct observability of polarization moments of a higher order—octupole orientation of atomic angular momenta (κ=3) and their hexadecapole alignment (κ=4)—from polarization of quadrupole radiation is discussed. The case when atoms are excited through dipole absorption of light producing orientation or alignment of angular momenta with κ=1 or 2 and higher polarization moments are induced by collisions with a beam of particles is considered. It is shown that differences in the laws of transformation of polarization moments of various ranks κ in rotations of coordinate axes allow us to select the pure contribution of the higher polarization moment under study from the signal of polarization of quadrupole emission by excluding the contribution of orientation or alignment with κ=1 or 2. Optimum systems of coordinate axes for the observation of octupole orientation from circular polarization of light and for the observation of hexadecapole alignment from linear polarization of light, in which the pure contribution of the higher polarization moment under study to polarization of quadrupole emission reaches its maximum, are calculated.     

Angular momentum polarization in molecular collisions : Classical and quantum theory for measurements using resonance fluorescence

Inelastic or reactive collisions typically produce an anisotropic distribution of rotational angular momentum. An explicit and general treatment is given for the intensity and polarization of resonance fluorescence from molecules produced in such processes. Both classical and quantum results are expressed in terms of bipolar harmonics and state multipoles formed from linear combinations of density matrix elements. The treatment provides an inversion procedure for determining moments of the rotational angular momentum distribution ; twelve independent moments can be obtained. The combinations of angular momentum operators involved are even in eight of these moments and odd in four, with respect to reflection in a plane containing the initial and final relative velocity vectors. Measurements of the even moments require linearly polarized excitation and fluorescence, whereas measurements of the odd moments require circularly polarized excitation. The requisite experimental geometry and other practical aspects are discussed. In the three appendices are discussed the classical limits of transition intensities, a density matrix treatment of atom-rigid-rotor collisions, including analysis of state multipole symmetries ; and the coupling coefficients for parallel angular momenta.     

Manifestation of the second-order alignment in light scattering by polarized atoms

An expression for the cross section of light scattering by axisymmetrically aligned atomic systems is derived in a compact form. The cross section under consideration is proportional to the state multipole of the fourth rank. The effect of the second-order alignment determined by the fourth-rank state multipole on the polarization and the angular distribution of scattered light is investigated. The polarization of incident light can be arbitrary and, in the general case, is specified by the Stokes parameters. In particular, it is demonstrated that the second-order alignment cannot induce circular polarization of scattered light and does not influence the dissipation-induced effects of circular dichroism associated with the first-order alignment but leads to a change in the angular distribution and the degree of linear polarization of the scattered light.     

Interrelationship between the polarization moments of different parity upon optical pumping of atoms under magnetic resonance conditions: II. Theory

The mutual coupling between the polarization moments with ranks of different parity is theoretically considered. The manifestation of this mutual coupling has been revealed previously in experiments on magnetic resonance of optically oriented cesium atoms. The two well-known types of the coupling between the polarization moments are considered: the field coupling of these moments that occur due to the breaking of the hyperfine coupling between the electronic and nuclear moments of the alkali atom by the magnetic field and the light coupling of the moments due to the absorption of the pumping light by polarized atoms. The experimentally observed similarity in the shape of resonance signals of alignment and orientation upon circularly polarized pumping can be explained by the fact that, for alkali atoms, the generation of alignment by light at the wavelength of the D ₁ line is of low efficiency. Therefore, alignment arises mainly from orientation by means of either the field or the light coupling of polarization moments. For metastable 2³ S ₁ ⁴He atoms, no influence of the orientation on the alignment was observed because, in these atoms, the field coupling between the polarization moments is absent and the light coupling is not displayed because the generation of alignment by the circularly polarized pumping light is more efficient than the creation of alignment from orientation by means of light coupling of polarization moments.     

Interaction of a three-level atom with an elliptically polarized wave

The interaction of elliptically polarized radiation with a resonant medium consisting of atoms with an excited state split into a doublet was studied theoretically. Interference terms associated with the coherent interaction of the field with the excited sublevels of the doublet were found to appear in the refractive index. The dispersion dependence of the refractive index was studied. It was shown that the decay constants for the multipole moments of the current of a dipole-forbidden atomic transition can be determined by the choice of the wave polarization.     

Improved convergence of the ‘atoms in molecules’ multipole expansion of electrostatic interaction

We study the anisotropic electrostatic interaction with high rank multipoles (? = 5) for a set of 10 van der Waals complexes and 27 DNA base pairs. Multipoles are generated by the distributed multipole analysis (DMA) and by the topological quantum theory of ‘atoms in molecules’ (AIM). The convergence of the multipolar expansion of the interaction between topological atoms is improved by distributing the moments over extra off-nuclear sites via a shifting procedure. A clear theoretical distinction is made between partitioning and distributing. A substantial improvement in the convergence of the AIM multipole expansion is observed for the smaller van der Waals molecules. An AIM representation with extra sites on the bond midpoints performs as well as DMA with just nuclear sites. However, for the larger DNA base pairs no improvement follows from the introduction of extra sites with AIM. For these larger systems AIM and DMA expansions perform equivalently, provided that now DMA allows for extra sites. This work further encourages the development of a topological intermolecular force field.     

Manifestation of higher polarization moments of the electronic shell of an atom in the collisional population transfer between the hyperfine-structure levels

The contributions of the relaxation of electronic polarization moments of various orders κ to the probabilities for the population transfer between the hyperfine-structure levels of an atom under the action of collisions are studied. It is shown that the contributions of higher electronic polarization moments with κ > 2 are comparable with the contributions of the orientation (κ=1) and the alignment (κ=2) or even exceed them in magnitude. This opens up the possibility of studying the collisional relaxation of higher polarization moments which are usually not observed and not involved in the emission and absorption of light under dipole transitions. The bounds for the allowable values of the rate constants for the collisional relaxation of higher polarization moments are obtained from the condition for nonnegativity of the total probabilities of population transfer between different hyperfine-structure levels under the action of collisions.     

Approaches to the Monopole-Dynamic Dipole Vacuum Solution Concerning the Structure of Its Ernst Potential on the Symmetry Axis

The FHP (Fodor, Hoenselaers, Perjés) algorithm [1] allows to obtain the relativistic multipole moments of a vacuum stationary axisymmetric solution in terms of coefficients which appear in the expansion of its Ernst potential on the symmetry axis. First of all, we will use this result in order to determine, at a certain approximation degree, the Ernst potential on the symmetry axis of the metric whose only multipole moments are mass and angular momentum. By using Sibgatullin's method [2] we then analyse a series of exact solutions with the afore mentioned multipole characteristic; besides, we present an approximate solution whose Ernst potential is introduced as a power series of a dimensionless parameter. The calculation of its multipole moments allows us to understand the existing differences between both approximations to the proposed pure multipole solution.     

Higher Electric Multipole Moments for Some Polyatomic Molecules from Accurate SCF Calculations

Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical andexperimental ones.     

Higher Electric Multipole Moments for Some Polyatomic Molecules from Accurate SCF Calculations

Higher electric multipole moments for the ground-state electronic configuration of some polyatomic molecules, i.e. CH₄, NH₃, H₂O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets. The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical and experimental ones.     

The Interaction Energy of Well-Separated Skyrme Solitons

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space. We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.     

Coherence and saturation properties of second-harmonic generation with a nonlinear crystal inside the laser cavity

The basic equations for second-harmonic generation including noise are derived for the case that the nonlinear crystal is put inside the laser cavity. A realistic model of a (detuned) laser with two-level atoms in single-mode operation is taken using the nonlinear theory of laser noise which describes the laser saturation effects, the phase diffusion and the intensity fluctuations. The reaction of the second-harmonic field on the fundamental field is taken into account as well as the reaction of the fundamental field on the laser. The nonlinear crystal is described by microscopic anharmonic oscillator equations (without introducing nonlinear susceptibilities by perturbation theory). The saturation of the polarization of the nonlinear medium is taken into account exactly with the only assumption that the influence of third and higher harmonics should be small. The electromagnetic field is described semiclassically by stochastic equations. In all equations, the damping is introduced simultaneously with Markoffian fluctuating forces by coupling to heatbaths. The equations are solved exactly in the stationary state without noise (the time dependent solution including noise will be presented in a subsequent paper). The most important saturation effect is a frequency shift which depends on the laser intensity.     

Special features of the dynamics of multipole moments of atoms at rest in weak light fields

The dynamics of radiative relaxation of multipole moments of atoms at rest in the ground state is considered for a low degree of dipole transition saturation. Using the field representation in the bipolar harmonic basis, the special features of the characteristic relaxation times are studied as functions of the j_g j_e transition type, ellipticity, and field frequency offset from resonance.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 57–64, December, 2004.     

Adaptation and performance of the Cartesian coordinates fast multipole method for nanomagnetic simulations

An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the program appropriate for nanomagnetic simulations, including magnetic nanoparticles and ferrofluids. The performance is optimized in terms of cell size and parameter set (expansion order and opening angle) and the trade off between computing time and accuracy is quantitatively studied. A rule of thumb is proposed to decide the appropriate average number of dipoles in the smallest cells, and an optimal choice of parameter set is suggested. Finally, the superiority of Cartesian coordinate FMM is demonstrated by comparison to spherical harmonics FMM and FFT.     

Astrophysically significant solutions of the Einstein and Einstein-Maxwell equations from the Laplace’s seed

The stationary solutions given by Amenedo and Manko generated from known solutions of Laplace’s equation as seed have been generalised to include the electromagnetic field. Further, the exterior solution of an axially symmetric rotating body with higher multipole moments and a solution corresponding to a Kerr object embedded in a gravitational field are given. We also give a method for constructing stationary vacuum solutions from static magnetovac solutions and vice versa and discuss a specific application of this method.     

The theory of particle diffusion in a strong random magnetic field with an allowance for higher multipole moments of the distribution function

The kinetic equation including a small-scale collisional integral for the particles propagating in a strong random and regular magnetic field [29] is solved by expanding the distribution function into series in spherical harmonics of the particle momentum angles. Using methods of the quantum theory of the angular moment [41], the equations for higher multipole moments of the distribution function in the space of momentum angles are derived and solved in the stationary case for the galactic cosmic rays in interplanetary space. The observed amplitudes and phases of the diurnal variation harmonics can be explained using the results of measurements of the interplanetary magnetic field performed on board the Ulysses spacecraft [12–14] and other satellites [45, 46] with an allowance for redistribution of the interplanetary and interstellar magnetic field lines. The spatial structure of the convection and diffusion fluxes of the galactic cosmic rays is refined. Formulas taking into account a change in the Earth’s axis tilt relative to the direction toward the Sun are derived, which allow the annual changes in contributions to the diurnal variation harmonics to be determined. The equation of diffusion taking into account the 2nd harmonic is obtained, and the contribution of this effect to the relative particle density in the cosmic rays in a spherically symmetric case is analyzed.     

Angular spectrum representation of the electromagnetic multipole fields, and their reflection at a perfect conductor

Angular spectrum representations are derived for electric and magnetic multipole fields of arbitrary order. The result involves generalized spherical harmonics and generalized vector spherical harmonics, and the representations are in the form of integrals over the k_∥-plane. The representations are especially useful for the study of reflection and transmission of multipole radiation by a plane interface. As an example, we have considered the reflection at a perfect conductor. The reflected field of a multipole field could be expressed in the form of an angular spectrum with a very simple relation to the angular spectrum of the source field. The radiation pattern of a multipole near the perfect conductor is obtained with the method of stationary phase. We also introduce a method for determining the mirror image of the source of an arbitrary multipole.     

Theory of multiphoton and tunnel ionization in a bichromatic field

The imaginary-time method [6, 7] is used to calculate the multiphoton and tunnel ionization probabilities for atoms in a laser radiation field part of which is converted into the second harmonic. We assume that the first harmonic has a linear or elliptical polarization and the second harmonic is polarized linearly, with its polarization vector making an arbitrary angle with that of the first harmonic. The mean momentum of the photoelectrons knocked out from atoms is shown to depend on the phase shift between the first and second harmonics and their mutual polarization and to be identically equal to zero for a monochromatic field. An important difference between the case of elliptical polarization and the case of linear polarization of both harmonics is the absence of conditions under which the conditions for dominance of one of the two generation mechanisms considered here can be identified during the generation of terahertz radiation from the region of optical breakdown in a gas.     

Calculations of molecular multipole electric moments of a series of exo-insaturated four-membered heterocycles,Y = CCH2CH2X

The influence of ring puckering angle on the multipole moments of sixteen four-membered heterocycles (1-16) was theoretically estimated using MP2 and different DFTs in combination with the 6-31+G(d,p) basis set. To obtain an accurate evaluation, CCSD/cc-pVDZ level and, the MP2 and PBE1PBE methods in combination with the aug-cc-pVDZ and aug-cc-pVTZ basis sets were performed on the planar geometries of 1-16. In general, the DFT and MP2 approaches provided an identical dependence of the electrical properties with the puckering angle for 1-16. Quantitatively, the quality of the level of theory and basis sets affects significant the predictions of the multipole moments, in particular for the heterocycles containing C=O and C=S bonds. Convergence basis sets within the MP2 and PBE1PBE approximations are reached in the dipole moment calculations when the aug-cc-pVTZ basis set is used, while the quadrupole and octupole moment computations require a larger basis set than aug-cc-pVTZ. On the other hand, the multipole moments showed a strong dependence with the molecular geometry and the nature of the carbon-heteroatom bonds. Specifically, the C-X bond determines the behavior of the μ(?), θ(?) and ?(?) functions, while the C=Y bond plays an important role in the magnitude of the studied properties.