Manifestation of higher polarization moments in the dipole emission under conditions of stepwise excitation and anisotropic collisions

The induction of higher polarization moments-the octupole orientation and the hexadecapole alignment—in the case of two-step excitation of atoms through dipole transitions and their manifestation in the polarization of dipole emission under conditions of anisotropic collisions are studied. For all channels of the two-step excitation process J ₀→J ₁ J, the efficiencies of production of higher polarization moments with integer and half-integer angular momenta from J=2 to J=7 through the absorption of linearly or circularly polarized light are calculated. The rates of collisional relaxation and interconversion of higher polarization moments, for both orientation and alignment, as functions of frequency detuning of the laser line from the center of the Doppler profile are calculated. The theory is illustrated by an example of two channels of excitation of the atomic state J=2 by circularly polarized light: J ₀=0→J ₁=1J=2 and J ₀=3→J 1=2 (or 3)→J=2. In the first case, the octupole orientation enhances or attenuates the signal of circular polarization depending on the laser frequency detuning. In the second case, it represents the only source producing orientation and circular polarization of the emitted light.     

Contribution of hexadecapole alignment to the polarization of quadrupole emission under laser excitation conditions

The linear polarization of quadrupole emission by the J=2-J ₀=0 transition under conditions of laser excitation in a gas medium is studied. Cases of excitation through dipole and quadrupole absorption of monochromatic laser radiation are considered. Taking into account the anisotropy of collisional relaxation, the contributions of polarization moments of the second and fourth ranks, i.e., those with usual and hexadecapole alignments, to the signal of linear polarization of quadrupole emission are calculated. The dependence of this signal on the laser frequency, the density of the gas medium, and the angles determining the orientation of the system of axes of observation of light polarization relative to a laser ray is studied. The numerical calculations of contributions of usual and hexadecapole alignment to the signal of linear polarization are made for the magnetic quadrupole transition J=2-J ₀=0 between the states 2p ⁵(² P ₁ ^2/0 )3p′[3/2]₂ and 2p ⁵(² P ₁ ^2/0 )3s 3s′[1/2]⁰ of neon atoms in the xenon atmosphere.     

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.     

Signal of collisional beatings of polarization of light as a function of the angular momentum of an excited atomic state

A comparative study of the beats of circular polarization generated by anisotropic atomic collisions is carried out on the basis of theoretical calculations for the states J=1, 3/2, and 2 of neon atoms and ions excited by monochromatic laser radiation in xenon atmosphere. Contributions made by ordinary alignment and higher polarization moments (octupole orientation and dodecapole alignment) in the collisional generation of orientation and the signal of beatings of circular polarization are compared.     

Angular momentum polarization of the molecules in the Li + HF reaction

A theoretical analysis of the orientation and alignment of the rotational angular momenta of the reactants and products of the Li + HF(v _r = 0, j _r = 3) → LiF(v, j) + H reaction at a collision energy of E _coll = 0.317 eV is performed. The polarization of the angular momentum of the molecules involved in the reaction is based on the technique of spherical tensor operators (state multipoles). Quantum-mechanical calculations of the S-matrix of the reaction are carried out using the wave packet method. In particular, the influence of the orientation of the angular momentum of the HF reactant on the differential cross section is examined. It is shown that the contribution to the differential cross section comes only from be reactants with an angular momentum perpendicular to the reaction plane. In addition, the angular dependence of the orientation and alignment of the angular momenta of the reaction products are examined. It is shown that, for an isotropic distribution of reactant molecules, the orientation of the angular momenta of the products differs from zero only in the direction perpendicular to the reaction plane. Different experimental geometries, based on radiation enhanced multiphoton ionization, are proposed to detect the predicted effects.     

Calculation of the fine structure of the level in Rydberg state of lithium

The level shift and level formula of lithium atom in Rydberg states are achieved by means of the calculation of polarization of the atomic core (including the contribution of dipole moment, quadrupole moment and octupole moment);meanwhile, the effect of relativity theory, the orbital angular momentum L and the spin angular momentum S coupling (LS coupling), and high order correction of the effective potential are considered. The some fine structures (N=5～12,L=4～9,J=L±1/2) and the corresponding level intervals in Rydberg states can be calculated by the above-mentioned level formula and compared with correlated experimental data.     

Angular momentum partitioning and hexacontatetrapole moments in impulsively excited argon ions

We have studied polarized electron collisions with Ar in which the target is simultaneously ionized and excited to form Ar+(3p(4)(1D)4p) states. We measured the integrated Stokes parameters of the subsequent fluorescence emitted by the (2)F(7/2), (2)F(5/2), (2)D(5/2), and (2)P(3/2) states along the direction of electron polarization. The Rubin-Bederson hypothesis is shown to hold for the L and S multipoles of these states. The electric quadrupole and hexadecapole of the 1D core are derived. By recoupling these moments with the electric quadrupole moment of the 4p electron, we calculate higher moments of the total ionic orbital angular momentum, including its hexacontatetrapole (64-pole) moment.     

Dipolar Order in Molecular Fluids: II. Molecular Influence

The influence on the short-range packing in dipolar fluids by molecular shape and by additional higher order electrostatic moments has been investigated by molecular dynamic simulations. The dipole polarization was found to decrease as the particles were elongated parallel to the dipole and to increase for elongation perpendicular to the dipole, eventually forming a nematic order. The addition of a quadrupole lead to a reduction of the polarization, and the influence of an axial octupole was weaker and more complex. Both a decrease and an increase of the polarization is possible depending on the relative dipole–dipole and octupole–octupole interaction strengths and the relative direction of the symmetry axes of the moments. These observations were attributed to the different parity of a dipole and a quadrupole and the same parity of a dipole and an axial octupole under reflection. In addition, further insights into the formation of dipole polarization were obtained. Short polar and long equatorial radii and strong dipole–dipole interaction are particle properties that promote a fluid with a high dipole polarization.     

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.     

Probing the largest scale structure in the universe with polarization map of galaxy clusters

We introduce a new formalism to describe the polarization signal of galaxy clusters on the whole sky. We show that a sparsely sampled, half-sky map of the cluster polarization at z approximately 1 would allow us to better characterize the very large scale density fluctuations. While the horizon length is smaller in the past, two other competing effects significantly remove the contribution of the small scale fluctuations from the quadrupole polarization pattern at z approximately 1. For the standard LambdaCDM universe with vanishing tensor mode, the quadrupole moment of the temperature anisotropy at z = 0 is expected to have an approximately 32% contribution from fluctuations on scales below 6.3 h(-1) Gpc. This percentage would be reduced to approximately 2% level for the quadrupole moment of polarization pattern at z approximately 1. A cluster polarization would shed light on the potentially anomalous features of the largest scale fluctuations.     

Dirac Particle Polarization in Uniform Magnetic Field

For Dirac particles in a uniform magnetic field, the polarization operator projections onto three directions remain unchanged. If the orbital angular moment of particles is large with respect to 1, then the spin of moving particles retain the fixed orientation relative to the axes of the cylindrical coordinate system.     

Interrelationship between the polarization moments of different parity upon optical pumping of atoms under magnetic resonance conditions: III. Comparison of theory with experiment

The optical pumping of Cs atoms with light of the D ₁ line under magnetic resonance conditions is numerically calculated. This calculation is done to check the suggestion that an unexpectedly strong influence of the polarization of the pumping light on the resonance signals of transverse alignment, which we observed experimentally, is caused by the coupling between orientation and alignment by means of the magnetic field and/or the pumping light. This suggestion has been confirmed: upon circularly polarized pumping, the shape of the signal line of transverse alignment proved to be similar, as well as in the experiment, to the shape of the signal line of transverse orientation and was sharply different from the shape of the line of alignment observed upon linearly polarized pumping. For metastable 2³ S ₁ ⁴He atoms, in accordance with the experimental data, the calculated shape of the signal line of transverse alignment is found to be independent of the polarization of the pumping light. The calculations also confirm the possibility of a reverse effect: the influence of alignment on orientation, which manifests itself in the occurrence of orientation upon pumping with unpolarized light under magnetic resonance conditions. For Cs atoms exposed to a field of ～0.6 Oe, the largest contribution to this effect is yielded by the field coupling of orientation and alignment, whereas, for metastable 2³ S ₁ ⁴He atoms, the largest contribution is made by the light coupling of these polarization moments.     

Observation of the nuclear magnetic octupole moment of 133Cs

We describe our high-resolution measurements of the 133Cs 6p (2)P(3/2) state hyperfine structure. An optically narrowed diode laser excites perpendicularly a highly collimated atomic beam. The spectra are calibrated with a stable reference diode laser using a rf locking scheme allowing us to determine the splittings with an accuracy of < or =2 kHz, an order of magnitude better than previous results. The magnetic dipole a, electric quadrupole b, and magnetic octupole c hyperfine coupling constants are determined. The values we obtained are a=50.288 27(23) MHz, b=-0.4934(17) MHz, and c=0.56(7) kHz. This work represents the first observation of the magnetic octupole moment of the cesium nucleus. We carry out atomic-structure calculations and determine the nuclear electric quadrupole moment Q= -3.55(4) mb and nuclear magnetic octupole moment Omega=0.82(10) b x mu(N).     

Tensor polarization of 12C(2+), 24Mg(2+), and 28Si(2+) oriented nuclei

Measured and calculated angular dependences of components of the polarization tensor of a ¹²C nucleus in the 2⁺ state at 4.44 MeV formed in various reactions involving light particles, as well as ²⁴Mg(2⁺, 1.369 MeV) and ²⁸Si(2⁺, 1.78 MeV) nuclei formed in inelastic alpha-particle scattering, are presented. The experimental tensor polarization in question was reconstructed on the basis of the densitymatrix spin-tensors found previously for these nuclei. The parameters of the quadrupole and hexadecapole orientation of the nuclei under study were obtained. The experimental polarization features were compared with the results of calculations based on the coupled-channel method. Special features of the behavior of tensor polarizations in various reactions were discussed. The similarity of the experimental angular dependences of the components of tensor polarizations in inelastic deuteron and ³He scattering on ¹²C nuclei, as well as in inelastic alpha-particle scattering on ²⁴Mg and ²⁸Si nuclei, was demonstrated.     

Permanent and interaction-induced far-infrared spectra of CO in dense Ar: a molecular dynamics approach

Permanent and electric multipole induced contributions to the far-infrared absorption spectrum of CO in Ar for dense gas and liquid densities have been calculated by means of classical molecular dynamics simulations. The comparison of the simulated spectra with experiments let us to give an estimation of some multipole moments of CO: quadrupole, octupole and hexadecapole. Although the experimental profiles lack of a fine rotational structure, the results of the simulations and their comparison with previous theoretical works, indicate that at low temperatures, the consideration of a quantum time correlation function for the dipole moment is necessary to get a good agreement with experiments. Finally, it is shown that the permanent-induced and induced-induced cross terms in the absorption coefficient, that usually are difficult to calculate from a theoretical viewpoint, are not very relevant for this system.     

The fine structure splitting of the level of lithium in Rydberg states

The Hamiltonian of the four-body problem for a lithium atom is expanded in series. The level shift and level formula of a lithium atom in Rydberg states are achieved by means of the calculation of polarization of the atomic core (including the contribution of dipole, quadrupole and octupole components). We also consider the effect of relativity theory, the orbital angular momentum L and the spin angular momentum S coupling scheme (LS coupling) and high-order correction of the effective potential to the level shift. The fine structure splitting (N=5-12, L=4-9, J=L±1/2) and level intervals in Rydberg states have been calculated by the above-mentioned formula and compared with recent experimental data.     

Using ion imaging to analyze higher-order moments of the angular distributions of photofragments

We investigate the effect of the hexadecapole (K=4) polarization moment on the spatial distributions of angular momenta for atoms produced during the photodissociation of diatomic or triatomic molecules by polarized radiation. We derive general expressions for the angular distributions of the atomic density matrix for K = 2, 4 and expressions for the corresponding anisotropy parameters that contain all information on the photodissociation dynamics. We show that these anisotropy parameters can be experimentally determined by using ion imaging. We consider oxygen atoms in the ¹ D ₂ state aligned with respect to the orbital angular momentum as an example and provide ion images of the signals that correspond to the population of the atomic magnetic sublevels ¦m¦ = 0, 1, 2. We show the contributions from the second-and fourth-rank state multipoles to the angular distributions of the atomic density matrix to be comparable in magnitude and significantly different in form.     

Nondipole optical scattering from liquids and nanoparticles

Nondipolar contribution to optical scattering in liquids and nanoparticle suspensions has been discerned for the first time from the dominant electric dipole scattering by assigning the observed polarization and azimuthal angular distribution of scattered polarized light to pure magnetic dipole and/or electric quadrupole radiation and ruling out other (the impurity of laser polarization, multiple scattering, optical activity, and optical anisotropy) explanations. The observed scattering has potential use in the optical study of nanoparticles.     

Electric quadrupole and magnetic octupole moments of the light decuplet baryons within light cone QCD sum rules

The electric quadrupole and magnetic octupole moments of the light decuplet baryons are calculated in the framework of the light cone QCD sum rules. The obtained non-vanishing values for the electric quadrupole and magnetic octupole moments of these baryons show nonspherical charge distribution. The sign of electric quadrupole moment is positive for Ω⁻, Ξ^*−, Σ^*− and negative for Σ^*+, which correspond to the prolate and oblate charge distributions, respectively. A comparison of the obtained results with the predictions of non-covariant quark model which shows a good consistency between two approaches is also presented. Comparison of the obtained results on the multipole moments of the decuplet baryons containing strange quark with those of Δ baryons shows a large SU(3) flavor symmetry breaking.