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.

scholarly journals Evolution of quasi-bound states in the circular n–p junction of bilayer graphene under magnetic field

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Haijiao Ji ◽  
Yueting Pan ◽  
Haiwen Liu
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Bound States ◽  
Local Density ◽  
Energy Levels ◽  
Bilayer Graphene ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Weak Magnetic Fields ◽  
The Magnetic Field

Abstract Electron in gapless bilayer graphene can form quasi-bound states when a circular symmetric potential is created in bilayer graphene. These quasi-bound states can be adjusted by tuning the radius and strength of the potential barrier. We investigate the evolution of quasi-bound states spectra in the circular n–p junction of bilayer graphene under the magnetic field numerically. The energy levels of opposite angular momentum split and the splitting increases with the magnetic field. Moreover, weak magnetic fields can slightly shift the energy levels of quasi-bound states. While strong magnetic fields induce additional resonances in the local density states, which originates from Landau levels. We demonstrate that these numerical results are consistent with the semiclassical analysis based on Wentzel–Kramers–Brillouin approximation. Our results can be verified experimentally via scanning tunneling microscopy measurements.

scholarly journals Equatorial Geodesics Around the Magnetars

2017 ◽  
Vol 45 ◽  
pp. 1760050
Author(s):  
Viviane A. P. Alfradique ◽  
Orlenys N. Troconis ◽  
Rodrigo P. Negreiros
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Neutron Stars ◽  
Complete Solution ◽  
Compact Object ◽  
Relativistic Effects ◽  
Schwarzschild Solution ◽  
Soft Gamma Repeaters ◽  
Definition Of ◽  
The Magnetic Field

Neutron stars manifest themselves as different classes of astrophysical sources that are associated to distinct phenomenology. Here we focus our attention on magnetars (or strongly magnetized neutron stars) that are associated to Soft Gamma Repeaters and Anomalous X-ray Pulsars. The magnetic field on surface of these objects, reaches values greater than [Formula: see text] G. Under intense magnetic fields, relativistic effects begin to be decisive for the definition of the structure and evolution of these objects. We are tempted to question ourselves to how strengths fields affect the structure of neutron star. In this work, our objective is study and compare two solutions of Einstein-Maxwell equations: the Bonnor solution, which is an analytical solution that describe the exterior spacetime for a massive compact object which has a magnetic field that is characterize as a dipole field and a complete solution that describe the interior and exterior spacetime for the same source found by numerical methods). For this, we describe the geodesic equations generated by such solutions. Our results show that the orbits generated by the Bonnor solution are the same as described by numerical solution. Also, show that the inclusion of magnetic fields with values up to [Formula: see text]G in the center of the star does not modify sharply the particle orbits described around this star, so the use of Schwarzschild solution for the description of these orbits is a reasonable approximation.

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

Relaxation Attenuation of Ultrasound by the Jahn-Teller Centers in ZnSe:Cr in High Magnetic Fields

2015 ◽  
Vol 233-234 ◽  
pp. 125-128 ◽  
Author(s):  
N.S. Averkiev ◽  
I.B. Bersuker ◽  
V.V. Gudkov ◽  
S. Zherlitsyn ◽  
S. Yasin ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Ultrasonic Attenuation ◽  
Energy Levels ◽  
Orbital Interaction ◽  
Spin Orbital ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
The Magnetic Field ◽  
Good Agreement

The magnetic field dependence of ultrasonic attenuation α (B) of slow shear waves in the ZnSe:Cr2+crystal at a number of fixed temperatures fromT=1.4 K to 20 K in magnetic fields of up toB=14 T were investigated. For magnetic fieldsBabove 5 T we found that the attenuation increases with B monotonically, and at a given temperature it is proportional to the magnitude of relaxation attenuation atB=0. We show that the magnetic field dependent attenuation is due to the change in populations of the lowest energy levels of the impurity centers CrZn4Se, produced by the Jahn-Teller effect and split by the spin-orbital interaction and the magnetic field. The calculations carried out without fitting parameters are in good agreement with the experimental data.

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.

scholarly journals Genetic algorithm coupled with Bézier curves applied to the magnetic field on a solenoid axis synthesis

2016 ◽  
Vol 65 (2) ◽  
pp. 361-370 ◽  
Author(s):  
Marcin Ziolkowski ◽  
Stanislaw Gratkowski
Keyword(s):  
Magnetic Field ◽  
Genetic Algorithm ◽  
Magnetic Fields ◽  
Uniform Magnetic Field ◽  
Optimal Shape ◽  
Point Of View ◽  
Theoretical Point ◽  
Bezier Curves ◽  
Bézier Curves ◽  
The Magnetic Field

Abstract Electromagnetic arrangements which create a magnetic field of required distribution and magnitude are widely used in electrical engineering. Development of new accurate designing methods is still a valid topic of technical investigations. From the theoretical point of view the problem belongs to magnetic fields synthesis theory. This paper discusses a problem of designing a shape of a solenoid which produces a uniform magnetic field on its axis. The method of finding an optimal shape is based on a genetic algorithm (GA) coupled with Bézier curves.

Emergence of Twisted Magnetic Flux Related Sigmoidal Brightening

2000 ◽  
Vol 179 ◽  
pp. 263-264
Author(s):  
K. Sundara Raman ◽  
K. B. Ramesh ◽  
R. Selvendran ◽  
P. S. M. Aleem ◽  
K. M. Hiremath
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Ultra Violet ◽  
Active Regions ◽  
Morphological Properties ◽  
Energy Storage And Conversion ◽  
The Sun ◽  
X Rays ◽  
The Magnetic Field

Extended AbstractWe have examined the morphological properties of a sigmoid associated with an SXR (soft X-ray) flare. The sigmoid is cospatial with the EUV (extreme ultra violet) images and in the optical part lies along an S-shaped Hαfilament. The photoheliogram shows flux emergence within an existingδtype sunspot which has caused the rotation of the umbrae giving rise to the sigmoidal brightening.It is now widely accepted that flares derive their energy from the magnetic fields of the active regions and coronal levels are considered to be the flare sites. But still a satisfactory understanding of the flare processes has not been achieved because of the difficulties encountered to predict and estimate the probability of flare eruptions. The convection flows and vortices below the photosphere transport and concentrate magnetic field, which subsequently appear as active regions in the photosphere (Rust & Kumar 1994 and the references therein). Successive emergence of magnetic flux, twist the field, creating flare productive magnetic shear and has been studied by many authors (Sundara Ramanet al.1998 and the references therein). Hence, it is considered that the flare is powered by the energy stored in the twisted magnetic flux tubes (Kurokawa 1996 and the references therein). Rust & Kumar (1996) named the S-shaped bright coronal loops that appear in soft X-rays as ‘Sigmoids’ and concluded that this S-shaped distortion is due to the twist developed in the magnetic field lines. These transient sigmoidal features tell a great deal about unstable coronal magnetic fields, as these regions are more likely to be eruptive (Canfieldet al.1999). As the magnetic fields of the active regions are deep rooted in the Sun, the twist developed in the subphotospheric flux tube penetrates the photosphere and extends in to the corona. Thus, it is essentially favourable for the subphotospheric twist to unwind the twist and transmit it through the photosphere to the corona. Therefore, it becomes essential to make complete observational descriptions of a flare from the magnetic field changes that are taking place in different atmospheric levels of the Sun, to pin down the energy storage and conversion process that trigger the flare phenomena.

scholarly journals An 84-μG Magnetic Field in a Galaxy at Z=0.692?

2008 ◽  
Vol 4 (S254) ◽  
pp. 95-96
Author(s):  
Arthur M. Wolfe ◽  
Regina A. Jorgenson ◽  
Timothy Robishaw ◽  
Carl Heiles ◽  
Jason X. Prochaska
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Faraday Rotation ◽  
Large Scale ◽  
Dynamo Model ◽  
Magnetic Field Generation ◽  
Interstellar Gas ◽  
Splitting Technique ◽  
Average Value ◽  
The Magnetic Field

AbstractThe magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars (Beck 2005). The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ≈ 3 μG (Han et al. 2006). The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars (Kronberg et al. 2008) suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain.Here we report a measurement of a magnetic field of B ≈ 84 μG in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 μG in the neutral interstellar gas of our Galaxy (Heiles et al. 2004). This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past, rather than stronger (Parker 1970).The full text of this paper was published in Nature (Wolfe et al. 2008).

Magnetic Field Spectroheliograms from the San Fernando Observatory

1971 ◽  
Vol 43 ◽  
pp. 329-339 ◽  
Author(s):  
Dale Vrabec
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Spiral Structure ◽  
Longitudinal Component ◽  
Solar Telescope ◽  
Solar Magnetic Fields ◽  
San Fernando ◽  
Field Lines ◽  
The Magnetic Field ◽  
Field Network

Zeeman spectroheliograms of photospheric magnetic fields (longitudinal component) in the CaI 6102.7 Å line are being obtained with the new 61-cm vacuum solar telescope and spectroheliograph, using the Leighton technique. The structure of the magnetic field network appears identical to the bright photospheric network visible in the cores of many Fraunhofer lines and in CN spectroheliograms, with the exception that polarities are distinguished. This supports the evolving concept that solar magnetic fields outside of sunspots exist in small concentrations of essentially vertically oriented field, roughly clumped to form a network imbedded in the otherwise field-free photosphere. A timelapse spectroheliogram movie sequence spanning 6 hr revealed changes in the magnetic fields, including a systematic outward streaming of small magnetic knots of both polarities within annular areas surrounding several sunspots. The photospheric magnetic fields and a series of filtergrams taken at various wavelengths in the Hα profile starting in the far wing are intercompared in an effort to demonstrate that the dark strands of arch filament systems (AFS) and fibrils map magnetic field lines in the chromosphere. An example of an active region in which the magnetic fields assume a distinct spiral structure is presented.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

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