On the hamiltonians for magneto-optical intensities

A multipolar semi-classical hamiltonian for magneto-optical intensities is derived by a canonical transformation taking Feynman's formulation of the conventional Pauli hamiltonian as the point of departure. Only interactions up to the order of electric quadrupole and magnetic dipole terms are retained. The resulting hamiltonians are divided into their respective time-independent, single photon and double photon parts, and the difference in the appearance of magnetic field dependent contributions in the perturbation terms is analysed. On the basis of this analysis it is argued that the magnetic field dependent term in the magnetic dipole transition moment operator may lead to a unique single photon process with an amplitude proportional to the static magnetic field. This process leads, amongst others, to transitions between totally symmetric atomic states, in contrast to the standard multipolar selection rules of ordinary spectroscopy.     

Spherical magnetic multipole moments system of currents

Concepts of spherical magnetic multipoles that represent distributions of electric currents over a spherical surface are introduced. Vector potentials of magnetic multipoles meet solenoidal- and harmonic-field conditions outside of the spherical surface and are continuous on it. Within the sphere, the vector potential of currents flowing outside of it is represented by the sum of vector potentials of basis magnetic multipoles with coefficients expressed by spherical multipole moments of system of currents. This expansion of the vector potential is in many respects analogous to the multipole expansion known from electrostatics. The first three terms of the expansion represent components of the well-known magnetic moment, the next five terms represent components of the magnetic quadrupole moment, etc. Possible applications of the magnetic spherical multipole technique are discussed. Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 66–72, October, 1999.     

Nuclear hyperfine interactions in non-linear semi-rigid molecules

From the expression for the hamiltonian in molecular coordinates we obtained previously, the computation of an effective hamiltonian for a nondegenerate electronic state is performed to second order in degenerate perturbation theory. We thus obtain explicitly all dominant parameters for the spin-vibration and spin-rotation interactions; in addition, the parameters associated with the interactions between the magnetic moment induced by the molecular motion and an external magnetic field are computed. The vibrational dependence of these parameters is studied and the hamiltonian is written in a form adapted to the computation of an effective hamiltonian for an arbitrary vibrational state.     

Quantum Phase for an Electric Multipole Moment in Noncommutative Quantum Mechanics

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive.     

Core/shell/shell spherical quantum dot with Kratzer confining potential: Impurity states and electrostatic multipoles

An exactly solvable problem of impurity states is considered in core/shell/shell spherical quantum dot. Kratzer molecular potential is taken for confinement potential. The analytical expressions are obtained for the energy spectrum and wave functions of the impurity electron. The dependencies of the total energy and the binding energy of the impurity on the parameters of the confining potential are investigated. The possibility of the impurity electron leakage is shown in the external environment, due to the specific form of the Kratzer potential. The character of the electrostatic field created by the impurity and the electron is observed on the basis of obtained results. The multipole corrections caused by the dipole and quadrupole moments of the electron are calculated. It is shown that the dipole moment is absent, and the problem reduces to the calculation of only z component for the average values of the diagonal elements of the quadrupole moment tensor. The dependencies of the average values of the quadrupole moment on the Kratzer potential parameters are studied.     

Deformation energies of rare-earth nuclei in generator coordinate method

The deformations of rare-earth nuclei for the mean field Nilsson hamiltonian with the local approximation of the two-body interaction are estimated. The collective hamiltonian is obtained within the generator coordinate method and the gaussian overlap approximation. The zero-point correction to the collective potential energy is included. The deformation energies of nuclei are up to 1 MeV larger than those for the mean field potential. The multipole moments are in usual agreement to the experimental data.     

Pure multipoles from strong permanent magnets: analytic and experimental results

We present the construction of arbitrary multipole field configurations from strong permanent magnets for trapping charged or neutral particles. A general analytic method for the design of three-dimensional magnetic multipoles is discussed for an idealized continuously varying magnetisation taking advantage of the superposition principle. Simple recipes for constructing magnetic dipole and quadrupole fields are given with two types of elements, axially and radially magnetised rings. Cylindrical magnet components not only give free access to the experimental region of interest, but also allow for some tunability to reduce undesirable higher multipole orders. Measurements confirm theoretical predictions achieving useful magnetic fields of 1 T and steep gradients of 3 T/cm with high purity over several ccm.     

基于环磁美特材料的无线传能系统

传统的四线圈磁共振耦合无线传能系统已在移动电子设备、电动汽车无线充电中得以应用,然而,其传能效率仍然因其磁场空间分布的发散性而难以提高.为了克服上述缺点,我们提出了一种基于环磁美特材料、磁场更为局域的高效无线传能系统.该系统将四线圈系统中的一对磁谐振耦合线圈替换为具有环磁谐振特性的四个非对称开口谐振环.该环磁模式具有高Q值、低金属损耗以及辐射抑制的特性.实验结果表明,相对于四线圈系统,该系统的磁场更为集中,能量传输效率更高.     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Numerical calculations of potential distribution in non-ideal quadrupole trap and simulations of anharmonic oscillations

A quadrupole ion trap consisting of electrode structures symmetric about z-axis is an important tool for conducting several precision experiments. In practice the field inside the trap does not remain purely quadrupolar, and can be calculated using numerical methods. We have used boundary element method to calculate the potential inside the truncated as well as symmetrically misaligned quadrupolar ion trap. The calculated potential values are fitted to multipole expansion and the weights of multipole moments have been evaluated by minimizing the least square deviation. The higher-order multipole contribution in the fabricated hyperbolic electrodes due to truncation and machining imperfections is discussed. Non-linear effects arising due to the superposition of octupole moment manifest as anharmonic oscillations of trapped ions in the non-ideal Paul trap. Theoretical simulations of non-linear effects have been carried out.      

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.     

Cranking Calculation in the sdg Interacting Boson Model

A self-consistent cranking calculation of the intrinsic states of the sdg interacting boson model is performed. The formulae of the moment of inertia are given in a general sdg IBM multipole Hamiltonian with one- and two-body terms. In the quadrupole interaction, the intrinsic states, the quadrupole and hexadecapole deformation and the moment of inertia are investigated in the large N limit. Using a simple Hamiltonian, the results of numerical calculations for ¹⁵²,¹⁵⁴Sm and ^154-160 Gd satisfactorily reproduce the experimental data.     

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.     

Novel isotope effects observed in polarization echo experiments in glasses

In recent years unexpected magnetic field effects have been observed in dielectric measurements on insulating glasses at very low temperatures. Polarization echo experiments have indicated that atomic tunneling systems are responsible for these effects and that the nuclear properties of the tunneling particles are of importance. Subsequently, it was suggested that the magnetic field effects are caused by tunneling systems carrying a nuclear quadrupole moment. Now we have studied the isotope effect in echo experiments on fully deuterated and ordinary glycerol clearly showing the crucial role of the nuclear quadrupole moments for the magnetic field effects. In addition, we have observed a new effect in the decay of spontaneous echoes in zero magnetic field for the deuterated samples which can be explained in terms of a quantum beating involving the quadrupole levels.     

Relativistic theory of the electric quadrupole moment of a hydrogen-like atom in the <Emphasis Type="Italic">s</Emphasis>1/2 and <Emphasis Type="Italic">p</Emphasis>1/2 states

Relativistic analytical expressions are derived for the electric quadrupole moment induced by the hyperfine interaction of the electron with the nucleus of a hydrogen-like atom in the ns_1/2 and np_1/2 states. The magnetic dipole and electric quadrupole hyperfine interactions are taken into account. The calculations are performed using the generalized virial relationships for the Dirac equation in a central field. The dependences of the electric quadrupole moment on the nuclear charge Z and the principal quantum number n are analyzed. The induced quadrupole moments are compared with the nuclear quadrupole moments.     

Goldanskii-Karyagin effect and external magnetic field method as tools to measure anisotropy of the recoilless fraction in amorphous materials

Diffraction of X-rays or neutrons can not be used to obtain details about the atomic vibrational anisotropy in the case of amorphous materials due to the lack of well-defined Bragg reflections. Mössbauer spectroscopy can yield some information in such cases, either via the Goldanskii-Karyagin effect or by applying a magnetic field, preferably along the beam axis. The latter method can be applied to the (preferably diamagnetic) samples exhibiting an electric quadrupole interaction (preferably non-axial) and the magnetic field should be chosen in such a way as to produce significant off-diagonal elements in the hyperfine hamiltonian. The external magnetic field method is capable of yielding much more information than the Goldanskii-Karyagin effect in most cases, provided sufficiently strong magnetic fields are available. Some examples of the¹²⁹I Mössbauer spectra have been calculated to show the usefulness and sensitivity of the external magnetic field method.     

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.     

Concept of multipole magnetic field rotation in ECRIS

The conventional type of magnetic well is formed by superposition of two types of magnetic field, axial bumpy field and radial multipole field. It is used to contain plasma that consists of neutrals, ions and electrons. These particles are in constant motion in the well and energetic electrons create plasma by violent collisions with neutrals and ions. The confined electrons are constantly heated by ECR technique in the presence of magnetic field. In this paper it has been shown theoretically that how the electron motion is influenced in terms of heating, containment and azimuthal uniformity of plasma, by the axial rotation of the multipole magnetic field [1,2]. Afterwards, the feasibility of achieving a rotating magnetic multipole field is discussed to some extent. And it is seen that it is not beyond the capability of the scientific community in the present scenario of the advanced technology. Presently, it can be achieved for lesser field and slightly larger size of the multipole electromagnet and can be used for improvement of the ECR ion source (ECRIS).