Static Magnetic Dipole Research Articles

Correspondences and quantum description of Aharonov–Bohm and Aharonov–Casher effects

We establish systematic consolidation of the Aharonov-Bohm and Aharonov-Casher effects including their scalar counterparts. Their formal correspondences in acquiring topological phases are revealed on the basis of the gauge symmetry in non-simply connected spaces and the adiabatic condition for the state of magnetic dipoles. In addition, investigation of basic two-body interactions between an electric charge and a magnetic dipole clarifies their appropriate relative motions and discloses physical interrelations between the effects. Based on the two-body interaction, we also construct an exact microscopic description of the Aharonov-Bohm effect, where all the elements are treated on equal footing, i.e., magnetic dipoles are described quantum-mechanically and electromagnetic fields are quantized. This microscopic analysis not only confirms the conventional (semiclassical) results and the topological nature but also allows one to explore the fluctuation effects due to the precession of the magnetic dipoles with the adiabatic condition relaxed.

Neutral Fermion with a Magnetic Moment in External Electromagnetic Fields

The interaction between a massive neutral fermion with a static (spin) magnetic dipole moment μ and an external electromagnetic field is described by the Dirac–Pauli equation. Exact solutions of this equation are obtained along with the corresponding energy spectrum for an axially symmetric external magnetic field and for some centrally symmetric electric fields. It is shown that the spin–orbital interaction of a neutral fermion with a magnetic moment determines both the characteristic properties of the quantum states and the fermion energy spectrum. It is found that (1) the discrete energy spectrum of a neutral fermion depends on the projection of the fermion spin on a certain quantization axis, (2) the ground energy level of a fermion in these electric fields as well as the energy levels of all bound states with a fixed value of the quantum number characterizing the projection of the fermion spin in the electric field E = er is degenerate and the degeneration order is countably infinite, and (3) the energy spectra of neutral fermions and antifermions with spin magnetic moments are symmetric in centrally symmetric fields. Bound states of a neutral fermion with a magnetic moment in an external electric field do exist even if the Dirac–Pauli equation does not explicitly contain the term with the fermion mass. In addition, in centrally symmetric electric fields, there exist a countably infinite set of pairs of isolated charge-conjugate zero-energy solutions of the Dirac–Pauli equation.

Optical elements for slowly moving neutral atoms based on magnetic fields

Magnetostatic and quasi-magnetostatic devices can act as optical elements for the de Broglie waves of magnetic atoms, i.e. atoms with a net static magnetic dipole moment in the ground (or isomeric) state. Such magnetic atom optical elements complement, and are alternatives to, resonantly tuned laser atom optical elements which rely on dynamically generated electric dipole moments. The physical principles behind such magnetic devices are discussed briefly, as well as the potential problems of decoherence and its management. The way that these optical elements may be realized is also discussed, with special reference to mirrors and static and quasi-static gratings. Gratings are important to atom interferometry as they can act as beam-splitters.

Interacting boson approximation-2 analysis of the Pd and Ru chains. I. Mixed symmetry states ofFmax−1character in even palladium isotopes

An analysis of positive parity levels in the even palladium isotopes ${}^{100\ensuremath{-}116}$Pd has been carried out in the framework of the interacting boson approximation-2 model to identify states having large mixed-symmetry components. By means of numerical calculations, performed in the U(5) limit of the model, it has been possible to find simple relations obeyed by the eigenvalues of the generalized Majorana operator for the mixed-symmetry states having ${F=F}_{\mathrm{max}}\ensuremath{-}1.$ These results have been utilized as a starting point for our analysis. Experimental energies, static and transition electric quadrupole and magnetic dipole moments as well as mixing ratios and intensity ratios have been compared to the values calculated by using a realistic Hamiltonian. In the analysis only six out of the twelve model parameters have been varied as a function of the neutron number. A good overall agreement has been found. A detailed investigation of the level structure made it possible to identify whole groups of states of predominant mixed-symmetry character and to establish, in most cases, a close correspondence with states of the U(5) limit of the model.

Nontrivial aspects of the onset of nuclear collectivity: Static moments.

We consider several topics concerning static magnetic dipole and electric quadrupole moments ({mu} and {ital Q}) as signatures of the onset of nuclear collectivity. Having previously noted that in {sup 50}Cr there is an abrupt change of sign in {ital Q} of yrast states with {ital J}{sup {pi}}=10{sup +},12{sup +}, and 14{sup +} relative to lower {ital J} states, we discuss whether these states are oblate or prolate. We next show that configuration mixing leads to much larger changes in {ital Q} than in {mu}. We then look for other bands of interest in {sup 50}Cr. Finally we discuss the Jolos{endash}von Brentano relationship which relates {ital Q} of 2{sub 1}{sup +} states to {ital B}({ital E}2){close_quote}s for transitions from and to the 2{sub 1}{sup +} states. {copyright} {ital 1996 The American Physical Society.}

Full-symmetry and mixed-symmetry states in even ruthenium isotopes.

The experimental data on positive parity, low-lying levels of the even ruthenium isotopes {sup 98--114}Ru have been analyzed in the framework of the IBA-2 model, with the aim of identifying states having a large mixed-symmetry component. Energies, static and transition electric quadrupole and magnetic dipole moments as well as mixing and branching ratios of the relevant levels have been considered. It appears that the properties of all low-lying levels in these isotopes, for which the comparison between experiment and theory is possible, can be satisfactorily described by the standard IBA-2 model, provided proper account is taken of the presence at low energy of states having a mixed-symmetry character. It seems possible to identify, in each isotope, a few states having such a character, the lowest ones being the 2{sup +}{sub 3} and 3{sup +}{sub 1} levels. Some indications for the presence above the 3{sup +}{sub 1} level of a band of states having {ital J}{sup {pi}}=5{sup +}{sub 1},7{sup +}{sub 1},9{sup +}{sub 1} and a comparable degree of mixed symmetry are pointed out for the heavier nuclei of the chain.

Effects of collective rotation on the magnetic dipole states in deformed nuclei

Effects of collective rotation on the magnetic dipole states in deformed nuclei

Spin-flip magnetic dipole states in deformed nuclei

The spin-flip magnetic dipole states in deformed nuclei in the rare earth region are calculated within the quasi-particle random phase approximation. In all cases we obtain a concentration of spin-flip strength around 8 MeV, and in some of the nuclei a second bump appears about 2 MeV lower.

Low-collective scissors mode

Realistic microscopic RPA calculations for156Gd with a deformed Woods-Saxon mean field, quadrupole-quadrupole, spin-spin and symmetry-restoring residual interactions show that the purely collective scissors mode of the two-rotor model is fragmented over orbital isovector 1+ states, lying at 2–7 MeV. The strongest experimentally observed magnetic dipole state is interpreted as performing a low-collective scissors-type of geometrical motion. This conclusion evolves from the identification of the above state with the strongest RPA excitation, which reproduces well the experimental energy,B(M1) value and (e, e′) form factor, has the largest overlap with the scissors state and can be represented as a low-collective scissors type vibration.

Symmetry-restoring interactions for Kπ = 1 + isovector vibrations

The low-lying isovector 1 + states are studied by a symmetry-restoring RPA approach in some rare-earth nuclei. A new velocity-dependent residual interaction is proposed in order to restore the rotational invariance of the hamiltonian in the quasiparticle random-phase approximation with an axially-symmetric Woods-Saxon potential. A new quadrupole interaction is introduced with a self-consistently determined coupling strength. Calculations for six rare-earth nuclei ( 154Sm, 156,158Gd, 164Dy, 168Er, 174Yb) show a good agreement with the experimental energies and B(M1) values. The M1 transitions, corresponding to the experimental strong magnetic dipole states, have in all apart from one case a predominant orbital contribution. The largest orbital contribution (90%) is found in 154Sm. About half of the low-energy ( E < 5MeV, B(M1)↑>0.1 μ N 2) states in each nucleus have an orbital character with a (10–40)% spin admixture. The M1 strength is concentrated in the region 2–9 MeV with a maximum around 5 MeV and corresponds to ΔN osc = 0 transitions.

Proton particle-hole states in 208Pb

Differential cross sections for the 209Bi(d, 3He) 208Pb transitions to the proton particle-proton hole states in 208Pb were obtained with the 45 MeV analyzed deuteron beam from the JULIC cyclotron and the high resolution spectrograph BIG KARL. 72 states up to 6.6 MeV were studied with an overall resolution of 12 to 15keV. Spectroscopic factors were extracted relative to the simultaneously measured calibration reaction 208Pb(d, 3He) 207Tl. For 26 states new parity assignments were possible on the basis of the measured angular distributions. The deduced inclusion into one of the four multiplets put limits on the possible spins of the states in question. With the help of sum rule arguments the spins of 12 states were assigned. The comparison with shell model calculations give only rough agreement as they predict the energies of the respective states about 300 keV too high. The magnetic dipole state at 5.846 MeV was observed with a Spectroscopic factor C 2 S = 0.17. From this, together with the transition probability B(M1↑) = (1.6 ± 0.5) μ N 2 from a ( γ, γ′) experiment we derived size and relative sign of the dominant neutron and proton spin-flip amplitudes. The result gives clear evidence for the isoscalar character of this state in accordance wtih TDA and RPA predictions. The matrix elements of the two-body residual interaction were derived unambiguously for the h 9 2 ∗ s 1 2 and h 9 2 ∗ d 3 2 multiplets. For the h 9 2 ∗ h 11 2 and h 9 2 ∗ d 5 2 multiplets uncertainties are larger because of assumptions of some of the spins for the states of high excitation energy. The four monopole terms are found close to the average of −308 keV. They are dominated by the Coulomb contributions of ≈ − 216 keV. The deduced J-dependence of the matrix elements differs from those found in other systematic investigations indicating more complicated underlying nuclear forces must contribute.

On-line nuclear orientation

Low-temperature nuclear orientation has for many years been a productive technique for obtaining nuclear spectroscopic information from radioactive decays. Decay-scheme studies have revealed spin-parity assignments of ground and excited states, multipolarities of alpha, beta, and gamma transitions, and static magnetic dipole and electric quadrupole moments of ground states and isomers. A new development in this field has been the coupling of a dilution refrigerator to an isotope separator and in turn to a heavy-ion accelerator, thus permitting the production, implantation, and orientation of a variety of short-lived nuclei, especially those very far from stability. Technological details of such facilities are discussed and examples of recent results from three operating on-line facilities are given.

Collective magnetic dipole transitions: Dependence of the energies and rates on the nuclear effective interaction

The dependence on the properties of the effective interaction of the energies of and excitation strengths to magnetic dipole states in open shell nuclei is studied. In particular the single j-shell for 48Ti is used as an example. In this case there are two 1 + states with isospin T = 2 and one with isospin T = 3. The conditions for having a strong low-lying collective 1 + state are examined. Focus is also given on the excitation strength to the analog T = 3 state since this is of relevance also to β + Gamow-Teller reactions and to double beta decay. It is found that in the rotational limit there is no strength to the T = 3 state and there is an overly strong low-lying 1 + T = 2 state. This is almost also true for a quadrupole-quadrupole interaction. At the other extreme, as shown by Halse, with a pairing interaction all the strength goes to the T = 3 state. Other interactions considered are pairing plus quadrupole, spin-dependent delta and Kuo-Brown bare and renormalized, and matrix elements taken from the spectrum of 42Sc. It is found that the β + strength can be reduced either by making the two-body J = 2 T = 1 matrix element or J = 1 T = 0 matrix element more attractive, just as was shown by others in heavier nuclei. However such parameter changes have effects on other properties of the 1 + spectrum, which can serve as indicators as to whether or not these changes are justified.

Correction to "Fast Nonrecursive Method for Estimating Location and Dipole Moment Components of a Static Magnetic Dipole"

Correction to "Fast Nonrecursive Method for Estimating Location and Dipole Moment Components of a Static Magnetic Dipole"

Fast Nonrecursive Method for Estimating Location and Dipole Moment Components of a Static Magnetic Dipole

This paper presents a method of estimating the position and moment components of a static magnetic dipole based on measurements of the magnetic field component normal to an arbitrary plane in which measurements are obtained. The largest local maximum and smallest local minimum of the field component and the corresponding positions in the plane are all the data necessary to obtain the solution. The solution is accurate, nonrecursive, robust, fast enough to be carried out by a 16-bit microprocessor in a fraction of a second, and makes no assumptions about the orientation of the dipole. The method in most cases gives good results for total field data, too. Results of a computer simulation study, which was performed to evaluate the method using simulated but realistic data, are presented. It is found for both total and vector magnetic field data that accuracy of component estimates are nearly independent of magnetic sensitivity (for S/N ratios greater than 28 dB) and sensor positional errors in the plane of measurement (if less than 5 percent of the dipole depth). Percentage error in estimates of dipole position and moment components is approximately equal to the percentage error in sensor position orthogonal to the plane of measurement (if less than 5 percent of the depth).

Microscopic calculation of the restoring force for scissor isovector vibrations

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.

On the nature of low-lying collective 1 + states in the heavy deformed nuclei 154Sm, 156Gd and 164Dy and in the [formula omitted] shell nucleus 46Ti

High resolution inelastic proton scattering at 201 MeV on 154Sm, 156Gd and 164Dy is used to clarify the nature of low-lying magnetic dipole states previously observed in inelastic electron scattering. An upper limit on the spin contribution to these collective magnetic dipole excitations is presented. The roles of spin and convection currents are also studied by inelastic proton and electron scattering to the low-lying 1 + state at 4.319 MeV in the f 7 2 - shell nucleus 46Ti. A substantial orbital contribution is observed in all cases.

Non-proportional cross sections of 50Ti(p, p′) and 49Ti(d, p) reactions for magnetic dipole states of 50Ti

A shell-model calculation is carried out for the B(M1) values of magnetic dipole states in 50Ti and the spectroscopic strengths of a 49Ti(d, p) 50Ti reaction with an f 5 2 -neutron transfer leading to 1 + states of 50Ti. The calculation accounts qualitatively for the experimental data. The 1 + states at E x ≈ 10 MeV which are strongly excited by inelastic scattering are not necessarily populated by a 49Ti(d, p).

Variational approach to magnetic dipole core polarization: Applications to moments and transitions

A variational approach to magnetic dipole core polarization is discussed which goes beyond the usual perturbative treatment and takes the coupling between the collective magnetic dipole state and single particle states into account. Using various spin-dependent effective interactions simple expressions for corrections to the g-factors of the free nucleons are derived. The effect of the coupling of the collective M1 state in 48Ca, 90Zr and 208Pb to single particle M1 moments and transitions in the neighbouring A=48±1, 90±1 and 208±1 nuclei, respectively, is pointed out.

GR and gK factors in deformed nuclei

The static and dynamic magnetic dipole moments of odd-mass and even-mass nuclei with 150<A<190 have been compiled and analyzed in a systematic way, in order to extract the best set of collective rotational g-factors gR and intrinsic g-factors gK.