scholarly journals Sum rules for an atomic hyperfine structure in a magnetic field

2006 ◽  
Vol 84 (9) ◽  
pp. 801-811
Author(s):  
Savely G Karshenboim
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Hyperfine Structure ◽  
Uniform Magnetic Field ◽  
Sum Rules ◽  
Magnetic Moments ◽  
Energy Levels ◽  
Linear Combinations ◽  
Nuclear Magnetic Moments ◽  
The Magnetic Field

The sum rules for the energy levels of a hyperfine multiplet in a constant uniform magnetic field are presented. It is found that for any value of the electron angular moment and the nuclear spin there are certain linear combinations of energy levels that do not depend on the magnetic field and can be used to determine the unperturbed hyperfine-structure separation in the presence of a perturbing magnetic field. It is also demonstrated that there are other linear combinations that are linear with the external magnetic field and hence can be used to determine bound values of the electron and nuclear magnetic moments. The accuracy of the approximation within which the result is valid is also discussed.PACS Nos.: 32.10.Fn, 32.60.+i1

scholarly journals Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 467
Author(s):  
Fayçal Hammad ◽  
Alexandre Landry ◽  
Parvaneh Sadeghi
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Total Mass ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Schwarzschild Solution ◽  
Relativistic Regime ◽  
The Magnetic Field

The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the particles are derived as functions of the magnetic field, the radius of the massive sphere and the total mass of the latter. As no assumption is made on the relative strengths of the particles’ interaction with the gravitational and magnetic fields, the relevance of our results to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense, is discussed.

Infinite solitons in ferromagnetic materials with an internal magnetic field

2021 ◽  
pp. 2150413
Author(s):  
Hamdy I. Abdel-Gawad
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
External Field ◽  
Model Equation ◽  
Graphical Representation ◽  
Magnetic Moments ◽  
Soliton Solutions ◽  
Internal Magnetic Field ◽  
Multiple Soliton Solutions ◽  
The Magnetic Field

The ferromagnetism induced by an external magnetic field (EMF), in (3+1) dimensions, is governed by Kraenkel–Manna–Merle system (KMMS). A (1+1) dimension model equation was derived in the literature. The magnetic moments are parallel to the magnetic field in ferromagnetism as they are aligning in the same direction of the external field. Here, it is shown that the KMMS supports the presence of internal magnetic field. This may be argued to medium characteristics. The objective of this work is to mind multiple soliton solutions, which are obtained via the generalized together with extended unified methods. Graphical representation of the results are carried. They describe infinite soliton shapes, which arise from the multiple variation of the arbitrary functions in the solutions. It is, also, shown that internal magnetic field decays, asymptotically, to zero with time.

Characteristics of Ultrasound Propagation in a Magnetic Fluid Under Uniform Magnetic Field

2003 ◽  
Author(s):  
Masaaki Motozawa ◽  
Tatsuo Sawada
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fluid ◽  
Uniform Magnetic Field ◽  
Colloidal Particles ◽  
Magnetic Field Intensity ◽  
Magnetic Field Direction ◽  
Ultrasound Propagation ◽  
Ultrasonic Propagation ◽  
The Magnetic Field

When an external magnetic field is applied to a magnetic fluid, some of the colloidal particles coagulate and form chain-like clusters. Properties of ultrasonic propagation wave are changed by these chain-like clusters. We carried out measurement of the ultrasonic propagation velocity in a magnetic fluid. Measurement were made by changing the magnetic field intensity from 0 mT to 570 mT, and the angle between the magnetic field direction and direction of the ultrasound propagation from 0° to 180°. The ultrasound frequencies were 1 MHz, 2 MHz and 4 MHz. Some of experimental results for the characteristics of ultrasound propagation in a magnetic fluid under a uniform magnetic field were reported.

scholarly journals Magnetic Quantum Otto Engine for the Single-Particle Landau Problem

2017 ◽  
Author(s):  
Francisco J. Peña ◽  
Alejandro González ◽  
A.S. Nunez ◽  
Pedro Orellana ◽  
René G. Rojas ◽  
...  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Field Intensity ◽  
Compression Ratio ◽  
Single Particle ◽  
Magnetic Field Intensity ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Adiabatic Processes ◽  
The Magnetic Field

We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic quantum Otto engine. The scheme of the cycle is composed of two quantum adiabatic processes and two quantum isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.

scholarly journals A Rapid Magnetofluidic Micromixer Using Diluted Ferrofluid

2016 ◽  
Author(s):  
Majid Hejazian ◽  
Nam-Trung Nguyen
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
External Magnetic Field ◽  
Uniform Magnetic Field ◽  
Body Force ◽  
Low Cost ◽  
Magnetic Field Gradient ◽  
Mixing Efficiency ◽  
Biological Assays ◽  
The Magnetic Field

Effective and rapid mixing is essential for various chemical and biological assays. The present work reports a simple and low-cost micromixer based on magnetofluidic actuation. The device takes advantage of magnetoconvective secondary flow, a bulk flow induced by an external magnetic field, for mixing. A paramagnetic stream of diluted ferrofluid and a non-magnetic stream are introduced to a straight microchannel. A permanent magnet placed next to the microchannel induced a non-uniform magnetic field. The magnetic field gradient and the mismatch in magnetic susceptibility between the two streams create a body force, which leads to rapid and efficient mixing. The micromixer reported here could achieve a high throughput and a high mixing efficiency of 90 % in a relatively short microchannel.

scholarly journals Magnetic Engine for the Single-Particle Landau Problem

2017 ◽  
Author(s):  
Francisco J. Peña ◽  
Alejandro González ◽  
A.S. Nunez ◽  
Pedro A. Orellana ◽  
René G. Rojas ◽  
...  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Field Intensity ◽  
Compression Ratio ◽  
Single Particle ◽  
Magnetic Field Intensity ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Adiabatic Processes ◽  
The Magnetic Field

We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic engine. The scheme of the cycle is composed of two adiabatic processes and two isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.

scholarly journals Acoustic Properties of Magnetic Fluids Based on Transformer Oil Under Magnetic Field

2013 ◽  
Vol 64 (6) ◽  
pp. 381-385 ◽  
Author(s):  
Jozef Kúdelčík ◽  
Peter Bury ◽  
Peter Kopčanský ◽  
Milan Timko ◽  
Vlasta Závišová
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Structural Changes ◽  
Magnetic Moments ◽  
Magnetic Fluids ◽  
Transformer Oil ◽  
Acoustic Properties ◽  
Acoustic Spectroscopy ◽  
Long Time ◽  
The Magnetic Field

Abstract The structural changes in magnetic fluids based on transformer oil TECHNOL and MOGUL upon the effect of an external magnetic field and temperature were studied by acoustic spectroscopy. When a magnetic field is increased, the interaction between the magnetic field and the magnetic moments of the nanoparticles leads to the aggregation of magnetic nanoparticles and following clusters formation. However, the temperature of magnetic fluids has also very important influence on the structural changes because of the mechanism of thermal motion that acts against the cluster creation. The live time of clusters have relative long time scale for the magnetic fluid based on TECHNOL, while for MOGUL is quite short.

A THEORETICAL INVESTIGATION OF THE NUCLEAR RESONANCE ABSORPTION SPECTRUM OF Al27 IN SPODUMENE

1953 ◽  
Vol 31 (6) ◽  
pp. 1010-1014 ◽  
Author(s):  
G. Lamarche ◽  
G. M. Volkoff
Keyword(s):  
Magnetic Field ◽  
Theoretical Investigation ◽  
Transition Matrix ◽  
Uniform Magnetic Field ◽  
Dimensionless Parameter ◽  
Energy Levels ◽  
Resonance Absorption ◽  
Matrix Elements ◽  
Transition Matrix Elements ◽  
The Magnetic Field

A theoretical investigation is presented of the energy levels of a nucleus of spin I = 5/2, a given magnetic moment μ, and electric quadruple moment eQ, placed in a uniform magnetic field H0, and a crystalline electrostatic potential [Formula: see text] without axial symmetry. The dependence of the energy levels, line frequencies, and transition matrix elements on the dimensionless parameter [Formula: see text] is calculated for Al27 for one orientation of a spodumene crystal in the magnetic field H0 over the interesting range of the parameter R linking up the pure quadrupole with the Zeeman spectrum. Other orientations of the crystal are discussed briefly.

SCATTERING OF RADIO WAVES BY AN IONIZED GAS IN THERMAL EQUILIBRIUM IN THE PRESENCE OF A UNIFORM MAGNETIC FIELD

1961 ◽  
Vol 39 (5) ◽  
pp. 716-740 ◽  
Author(s):  
J. A. Fejer
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Thermal Equilibrium ◽  
Uniform Magnetic Field ◽  
Debye Length ◽  
Density Fluctuations ◽  
Total Power ◽  
Radio Waves ◽  
Ionized Gas ◽  
The Magnetic Field

In an earlier paper (Fejer 1960) a theory was developed for the scattering of radio waves by the electron density fluctuations that exist in an ionized gas in thermal equilibrium. The theory treated only the extreme cases where the "characteristic scale" of the scattering irregularities is either very much larger or very much smaller than the Debye length. The presence of only one type of singly charged ion was considered and the ion and electron temperatures were assumed equal. The effects of an external magnetic field were not taken into account.These earlier limitations are removed in the present paper and the effects of an external magnetic field are taken into account.It is shown that the total power is independent of the magnetic field and an expression for the frequency spectrum of scattered power in the presence of a uniform magnetic field is obtained. Useful approximations to this expression are derived for various limiting cases of interest.It is concluded that the magnetic field need not be taken into account in the interpretation of past observations by Bowles (1958, 1959) and by Pineo, Kraft, and Briscoe (1960). In future experiments, however, particularly at great heights, the effect of the magnetic field could be considerable.

The Effect of Magnetic Field on the Hydration of Nanoscopic Hydrophobic N-Alkane Plates

2011 ◽  
Vol 228-229 ◽  
pp. 1007-1011
Author(s):  
Wei Wei Zhang ◽  
Long Qiu Li ◽  
Guang Yu Zhang ◽  
Hui Juan Dong
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dynamics Simulation ◽  
Free Energy Barrier ◽  
Confined Water ◽  
Magnetic Exposure ◽  
Hydrophobic Solutes ◽  
The Magnetic Field ◽  
Density Of Water ◽  
Induced Adsorption

The effect of an external magnetic field on the hydration behavior of nanoscopic n-octane plates has been extensively investigated using molecular dynamics simulation in an isothermal-isobaric ensemble. The solute plates with different intermolecular spacing have also been considered to examine the effect of the topology of hydrophobic plates on the adsorption behavior of confined water in the presence of an external magnetic field with an intensity ranging from 0.1T to 1 T. The results demonstrate that magnetic exposure decreases the density of water for the plates with intermolecular spacing of a0 = 4 and 5 Å. This suggests that the free energy barrier for evaporation can be lowered by the applied field, and the hydrophobic solutes consisting of condensed n-octane molecules are apt to aggregate in the aqueous solution. In contrast, the magnetic field improves the dissolution or wetting of solutes comprised of loosely packed n-octane plates of a0=7Å. A magnetic-field-induced adsorption-to-desorption translation, which is in agreement with the experimental results provided by Ozeki, has also been observed for the plates with intermolecular spacing of a0 = 6 Å.

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