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.     

Nuclear moments. Concluding remarks

Studies of nuclear magnetic moments and nuclear weak interactions discussed in this Conference are reviewed. The importance of configuration mixing and meson exchange currents is examined, and it is emphasized that the second order configuration mixing (tensor correlation) is essential for the understanding of these phenomena. Recent results concerning nuclear quadrupole moments reported in this Conference are also discussed. Finally, the pairing effect in metal clusters is pointed out and the importance of measuring their spins and magnetic moments is mentioned.     

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.     

An ab initio analysis of electronic states associated with a silicon vacancy in cubic symmetry

The electronic orbitals localized in the vicinity of a vacancy in a silicon crystal are calculated by an ab initio method based on the density functional theory and analyzed in association with the elastic softening observed by the recent ultrasonic experiments, especially focused on an estimate of the electric quadrupole moments. The localized orbitals due to the existence of a vacancy show largely extended properties and the quadrupole moments calculated from the orbitals indicate the strong dependence on cell sizes up to 511 atoms in the basic cell. Asymptotic values of the quadrupole moments in the limit of large size are obtained by an extrapolating method. It is shown that the quadrupole moments are enhanced due to the extension of the orbitals and the ratio of the quadrupole moments of Γ₅ and Γ₃ symmetries agrees well with the value deduced from the experimental results.     

Optical rectification and frequency doubling in metal vapors

It is theoretically shown that, under conditions of two-photon absorption of radiation by metal vapors, the medium becomes considerably polarized and efficiently doubles the radiation frequency. Two physical mechanisms by which these effects can occur are detected. The first of them results from the ring frequency mixing, while the second one is caused by a polarization nonlinearity that is quadratic in the field amplitude and that is formed as a result of the electric quadrupole absorption due to the forbidden transition. The effects predicted can form the basis for new optical methods for measuring the electric quadrupole and magnetic dipole moments for forbidden atomic transitions.     

Precision measurements of nuclear quadrupole moments by muonic X-rays

The electric multipole hyperfine interaction in muonic atoms is discussed. In particular, the influence of the finite size of the nuclear electric multipole-charge distribution on the values of nuclear spectroscopic multipole moments that are extracted from muonic hyperfine measurements is considered. It is shown that nuclear electric quadrupole moments can be deduced from the observed hyperfine splittings of muonic M X-ray transitions with high precision and practically independently of the model nuclear quadrupole-charge density. Measurements of the ground-state electric quadrupole moments of 11 deformed nuclei in and near the rare-earth region are discussed.     

Precision measurement of 11Li moments: influence of halo neutrons on the 9Li core

The electric quadrupole moment and the magnetic moment of the 11Li halo nucleus have been measured with more than an order of magnitude higher precision than before, |Q| = 33.3(5) mb and mu = +3.6712(3)muN, revealing a 8.8(1.5)% increase of the quadrupole moment relative to that of 9Li. This result is compared to various models that aim at describing the halo properties. In the shell model an increased quadrupole moment points to a significant occupation of the 1d orbits, whereas in a simple halo picture this can be explained by relating the quadrupole moments of the proton distribution to the charge radii. Advanced models so far fail to reproduce simultaneously the trends observed in the radii and quadrupole moments of the lithium isotopes.     

Revision of spin echoes in pure nuclear quadrupole resonance

Goldman's spin-1/2 formalism has been used for describing the response of an I=3/2 spin system to a two-pulse sequence in a pure nuclear quadrupole resonance experiment. A detailed analysis of the polarization evolution and quadrupolar echo generation is carried out through the use of explicit expressions for secular homo- and heteronuclear dipolar interactions. In striking contrast with previous studies, it is predicted that Van Vleck's second moments governing a classical solid-echo or Hahn sequence differ from those obtained by equivalent means in magnetic resonance. In fact, it is shown that, although measured moments still complement each other, the combined use of standard sequences does not allow the separate determination of homo- and heteronuclear dipolar contributions to the linewidth, not even in an indirect manner. In this context, the importance and potential usefulness of a crossed coil probe are also briefly discussed.     

Recent developments and new trends in NMR on oriented nuclei

Recent developments in nuclear magnetic resonance on oriented nuclei (NMR-ON) are reviewed with the following main topics: (i) Measurement of magnetic moments. In this context the resonance shift of NMR-ON resonances with an external magnetic field is discussed critically. (ii) Resonance techniques for the measurement of electric quadrupole moments. It is shown that — with hcp-Co as host matrix — the techniques QI-NMR-ON (quadrupole-interaction-resolved NMR-ON) and MAPON (modulated adiabatic passage on oriented nuclei) have a tremendous potential for the measurement of quadrupole moments of radioactive nuclei. Data are presented for medium (Zr, Nb) and heavy elements (Ir, Pt, Au, Hg). With results on the 11/2^– isomers in Au it is shown that MAPON yields highly precise quadrupole moments of states with half-lives of the order of seconds, for which no other technique with comparable precision exists up to now. In the case of⁹⁰Nb it is demonstrated that MAPON allows also the measurement of very small quadrupole moments with high precision. (iii) Electric field gradients in cubic Fe, fcc-Co and Ni. MAPON experiments show a strong magnetic-field dependence of the effective quadrupole interaction; the implications are discussed. (iv)-decay-induced lattice site change identified by a double-resonance NMR-ON measurement. The resulting change of the hyperfme interaction has severe consequences for the interpretation of time-integral and even time-differential nuclear orientation measurements on nuclei far off stability. (v) Spin-lattice relaxation for nuclei on non-substitutional lattice sites. Recent experiments support the global character of the spin-lattice relaxation, in contrast to the local character of the static magnetic hyperfine interaction. (vi) Magnetic-field dependence of the spin-lattice relaxation. Recent experiments with hcp-Co as host lattice strongly support the so-called enhancement factor model and disfavour the one-, two- or three-magnon processes postulated in the literature.     

On the static quadrupole moments of the 21 states in Te and Te

The reorientation effect in Coulomb excitation was used to measure the static quadrupole moments of the first 2⁺ states in ¹²⁶Te and ¹²⁸Te. The particle-γ coincidence technique using a large NaI(Tl) crystal was employed to measure relative excitation probabilities at backward and forward projectile scattering angles. The Winther-de Boer multiple Coulomb excitation program was used to analyze the data. The influence of the deorientation effect was also determined. For positive interference via the second 2⁺ state the extracted quadrupole moments of the first 2⁺ states are; −0.20±0.09 b and -0.24±0.08 b for ¹²⁶Te and ¹²⁸Te respectively. The quadrupole moments of the first 2⁺ states of^{122,124,126,128,130}Te determined by different techniques are in excellent agreement with one another. The values are compared with recent theoretical calculations.     

Self-consistent calculation of the ground state properties of some rare-earth nuclei

Ground state intrinsic deformation properties of some rare earth nuclei are calculated within the Hartree-Fock approximation using a Skyrme effective interaction. After a careful optimization of basis parameters, calculations have been performed with a basis corresponding to 13 spherical oscillator shells. In order to obtain the multipole moments, good numerical convergence is necessary. Calculated quadrupole and hexadecapole moments are in agreement with available experimental data. Ground state binding energies are also well reproduced.     

The use of a non-spherical reference potential in statistical mechanical perturbation theory

A statistical mechanical perturbation theory for the pair correlation function and thermodynamic properties of molecular fluids is presented in which the reference potential function is non-spherical. With this choice the short-range molecular repulsive forces can be properly taken into consideration and attractive forces, such as those resulting from electric moments, treated as the perturbation. Calculations are presented for the first-order perturbation term to the Helmholtz free energy due to quadrupolar forces in models of liquid nitrogen and chlorine, and due to dipolar forces in liquid hydrogen chloride. For these calculations the rigid diatomic model and its modification appropriate to heteronuclear molecules were used for the reference potentials. It is found that the lowest-order perturbation terms here are proportional to the second power of the dipole or quadrupole moments, and not the fourth power as had been found previously using a spherical reference potential function. This second-order dependence on the electric moment is especially important in the case of mixtures, where it leads to an explanation for the occurrence of negative azeotropes in binary mixtures of species with quadrupole moments of opposite sign.     

Temperature and field dependence of the order parameter in the antiferroquadrupolar phase of CeB6 from mu+ Knight shift measurements

The Fermi contact hyperfine contribution to the Knight shift of positive muons, implanted at the interstitial 3d sites in CeB6, is found to exhibit the same temperature dependence below T(Q) in phase II as the quadrupolar order parameter determined from resonant and nonresonant x-ray scattering. Furthermore, the contact coupling parameter is shown to be anisotropic and field dependent. These unanticipated features are interpreted to arise from the RKKY induced conduction electron spin polarization, which depends on the orientation and expectation value of the ordered 4f quadrupole moments.     

Magnetic multipole moments

Literature definitions of magnetic multipole moment operators are shown to be at variance, and new definitions are formulated which are consistent with a general multipole interaction hamiltonian and with the radiation field of a dynamic charge distribution. The applicability of traceless multipole moments is examined.

The multipole hamiltonian is used to derive expressions for some magnetic quadrupole distortion tensors. For those describing the quadrupole moment induced by a magnetic field and by a field gradient the number of independent components for various molecular symmetries is evaluated.     

Spectroscopic properties of fission isomers

Our present understanding of the spectroscopic properties of fission isomers is discussed. Recent progress has been achieved by applying newly developed and improved experimental techniques such as the charge plunger method and the recoil shadow technique to measure quadrupole moments, moments of inertia, and spins of fission isomeric states. The data establish the evidence for shape isomerism in the actinide region and a second minimum in the fission potential.     

Temperature and angular momentum dependence of the quadrupole deformation in sd-shell

Temperature and angular momentum dependence of the quadrupole deformation is studied in the middle of the sd-shell for ²⁸Si and ²⁷Si isotopes using the spherical shell model approach. The shell model calculations have been performed using the standard universal sd-shell (USD) interaction and the canonical partition function constructed from the calculated eigensolutions. It is shown that the extracted average quadrupole moments show a transitional behaviour as a function of temperature and the infered transitional temperature is shown to vary with angular momentum. The quadrupole deformation of the individual eigenstate is also analysed.     

Measurement of quadrupole moments of unstable nuclei during channeling and the possibility of revealing the effect of vector polarization of tensor-polarized beams of nuclei

General relations are deduced which describe the spin dynamics of beams of nuclei with the initial tensor and vector polarizations upon planar channeling in bent crystals. Our analysis demonstrates the possibility of revealing the effect of vector polarization, as predicted by Baryshevsky and Sokolsky, which occurs upon the planar channeling of a beam of nuclei with initial tensor polarization. The planar channeling of a beam of nuclei with the initial tensor and vector polarizations may be used to determine the quadrupole moments of unstable nuclei with a small lifetime of up to the order of 10^?7 s. The quadrupole moments of nuclei with a lifetime on the order of 10^?7 s cannot be measured by known techniques, including optical methods.     

Finite-field calculation of electric quadrupole moments of ~2P_(3/2),~2D_(3/2,5/2),and ~2F_(5/2,7/2) states for Yb~+ ion

Electric quadrupole moments of low-lying excited states of Yb~+ are calculated by relativistic coupled-cluster theory with perturbations from external fields.The field-dependent energy differentiation provides accurate values of the electric quadrupole moments o f~2P_(3/2),~2D_(3/2,5/2),and~2F_(5/2,7/2) states which agree well with experimental values.The important role of the electronic correlation to the electric quadrupole moments is investigated.Our calculations indicate the early dispute of the electric quadrupole moment of the Yb~+(~2F_(7/2))state for which the measured and theoretical values have a large discrepancy.These electric quadrupole moment values can help us to determine the electric quadrupole shifts in start-of-the-art experiments of the Yb~+ ion.     

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.     

Orbital dynamics of the 4f shell in DyB2C2

For the first time, fluctuations in the Dy quadrupole (orbital) moment have been observed in DyB(2)C(2) using inelastic neutron scattering. The observed quasielastic response is decomposed into two components, one reflecting transitions within the doublets (narrow) and the other transitions between the doublets (broad) of the effective Dy quartet ground state. The widths of the narrow and broad components are shown to arise from fluctuations in the magnetic dipole and the electric quadrupole moments, respectively.