Gyromagnetic Factor Research Articles

On the electromagnetic interaction and the anomalous term in the Duffin-Kemmer-Petiau theory

The problem of vectorial mesons embedded in an electromagnetic field via Duffin-Kemmer-Petiau (DKP) formalism is reinvestigated. Considering the electromagnetic interaction as a minimal coupling, an incorrect value is identified for the gyromagnetic factor (g-factor). Furthermore, it is shown that it is cumbersome to find analytical solutions due to the presence of the so-called anomalous term for the spin-1 sector of the DKP theory. Suspecting that the anomalous term results from an incomplete version of the DKP equation to describe the electromagnetic interaction, we consider the addition of a non-minimal coupling. This leads to the correct g-factor and, as a consequence, the anomalous term becomes proportional to an external four current. As an application, the DKP equation with a static uniform magnetic field is considered, yielding the corresponding Landau levels.

Dirac equation and its contribution to atomic fine structure

This article aims to establish the comprehensiveness of the Dirac equation as an effective modification of quantum mechanics for the analysis of electrons and atomic fine structure. The Dirac equation is applied to investigate two scenarios involving electron interactions with different potentials. In the case where =0, the Dirac equation aligns naturally with electron theories and yields an electron gyromagnetic factor of g_s=2. With additional radiative corrections, it is possible to bring this value into closer proximity to experimental results. On the other hand, when considering spin-orbit coupling within a central field of V=(-e^2)r, the spin-orbit Hamiltonian derived from the Dirac equation is shown to match calculations based on Larmor and Thomas interactions. These cases collectively demonstrate the superior utility of Diracs theory when dealing with spin-1/2 particles like electrons, underscoring Diracs historical success in addressing the complexities of the time. His achievements in elucidating atomic fine structure and spin-orbit coupling hold pivotal significance for advancing technologies rooted in these theories. However, it is important to note that the Dirac equation primarily remains valid in weak external field situations, as observed in electron orbital motion, while challenges persist in unifying it with general relativity in stronger external field contexts.

Stringent test of QED with hydrogen-like tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 1015 V cm−1 for the innermost electrons1. Especially in few-electron, highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the past several decades2,3. Another approach is the measurement of gyromagnetic factors (g factors) in highly charged ions4–7. However, so far, either experimental accuracy or small field strength in low-Z ions5,6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118Sn49+. The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT)8 and injected into the ALPHATRAP Penning-trap setup9, in which the bound-electron g factor was measured with a precision of 0.5 parts per billion (ppb). For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about 0.012%, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests by means of the Lamb shift and, with anticipated advances in the g-factor theory, surpass them by more than an order of magnitude.

Anomaly in the electron orbital gyromagnetic factor: QED and radiative interactions

Using standard Quantum Electrodynamics (QED), we have calculated the anomaly in the electron orbital g-factor, which is in reasonable agreement with experimental data. For second-order corrections, the anomaly in the orbital g-factor is of the order α/3π, while for approximations to the same order, the well-known anomaly in the electron spin g-factor where α = 1/137 is the structure constant. Unlike the spin-g anomaly, the orbital-g anomaly is not intrinsic, but depends on the atomic state, and on Z, the atomic mass. Thus, the orbital anomaly is actually (α/3π)D, where D includes the effect of the magnetic field and/or the atomic properties. Hence, we have shown that radiative interactions, which are the sources of the spin-g anomaly, also produce an orbital anomaly. It is physically reasonable to expect that radiative interactions that modify many physical properties of electrons in electromagnetic fields will also modify the orbital magnetic moment of the electron.

Recycled and Nickel- or Cobalt-Doped Lead Materials from Lead Acid Battery: Voltammetric and Spectroscopic Studies.

The active mass of the plates of aspent car battery with higher wear after an efficient desulfatization can be used as sources of a new electrode. This paper proposes the recycling of spent electrodes from a lead acid battery and the incorporation of NiO or Co3O4 contents by the melt-quenching method in order to enrich the electrochemical properties. The analysis of X-ray diffractograms indicates the gradual decrease in the sulfated crystalline phases, respectively, 4PbO·PbSO4 and PbO·PbSO4 phases, until their disappearance for higher dopant concentrations. Infrared (IR) spectra show a decreasing trend in the intensity of the bands corresponding to the sulfate ions and a conversion of [PbO3] pyramidal units into [PbO4] tetrahedral units by doping with high dopant levels, yielding to the apparition of the PbO2 crystalline phase. The observed electron paramagnetic resonance (EPR) spectra confirm three signals located on the gyromagnetic factor, g~2, 2.2 and 8 assigned to the nickel ions in higher oxidation states as well as the metallic nickel nanoparticles. This compositional evolution can be explained by considering a process of the drastic reduction in nickel ions from the superior oxidation states to metallic nickel. The linewidth and the intensity of the resonance lines situated at about g~2, 2.17, 4.22 and 7.8 are attributed to the Co+2 ions from the EPR data. The best reversibility of the cyclic voltammograms was highlighted for the samples with x = 10 mol% of NiO and 15 mol% of Co3O4, which are recommended as suitable in applications as new electrodes for the lead acid battery.

Hadronic light-by-light scattering contribution to the muon g − 2 from lattice QCD: semi-analytical calculation of the QED kernel

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor g of the muon to deviate from the value of two predicted by Dirac’s theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon (g − 2). Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at https://github.com/RJHudspith/KQED.

Investigation of the high-spin yrast band structure of Pu236–246 isotopes

The available data on some actinide nuclei point to certain significant features of the rotational yrast band and other excited bands. The rotational properties of plutonium isotopes ($^{236--346}\mathrm{Pu}$) were studied via projected shell model (PSM). Calculations are based on the Hamiltonian of the PSM which includes the formed part of a single particle, the $Q\ensuremath{-}Q$ force, and the residual interaction of monopole and quadrupole pairings. The results of the calculated energy levels of the yrast band are then compared with available experimental data and a good agreement has been found. The crossing between two-quasiparticle (2qp) excited bands and the ground state band (g band) in the high-spin regions has been analyzed in terms of band diagrams. The upbendings observed in the kinematic moments of inertia (${j}^{(1)}$ MOI) curves for $^{236--346}\mathrm{Pu}$ isotopes are due to the effect of two aligning nucleons that occupy excited bands and the $\ensuremath{\nu}({j}_{15/2}$), $\ensuremath{\pi}({i}_{13/2}$) high-$j$ intruder orbits. The PSM successfully reproduces the observed upbending in ${j}^{(1)}$ as well as the upturning and downturning in ${j}^{(2)}$. For the $^{240}\mathrm{Pu}$ isotope, the PSM predicts a simultaneous alignment of neutrons ${\ensuremath{\nu}}^{2} [1/2,\ensuremath{-}7/2] {K}^{\ensuremath{\pi}}$ = ${4}^{+}$ and protons ${\ensuremath{\pi}}^{2} [\ensuremath{-}3/2,5/2] {K}^{\ensuremath{\pi}}$ = ${1}^{+}$ bands cross the g band at spin $I=22$. We expect it to be mainly responsible for the disagreement at $I=22$. Furthermore, electric quadrupole transition probabilities $B(E2)$ and the gyromagnetic factor ($g$ factor) for the yrast band energy levels are also studied.

Testing standard-model extensions with isotope shifts in few-electron ions

When collecting spectroscopic data on at least four isotopes, nonlinearities in the King plot are a possible sign of physics beyond the standard model. In this work, an improved approach to the search for hypothetical new interactions with isotope-shift spectroscopy of few-electron ions is presented. Careful account is taken of the small nuclear corrections to the energy levels and the gyromagnetic factors, which cause deviations from King linearity within the standard model and are hence a possible source of confusion. In this approach, the experimental King nonlinearity is not compared to the vanishing prediction of the standard model at the leading order, but to the calculated full standard model contribution to King nonlinearity. This makes searching for beyond-the-standard-model physics with King linearity analysis possible in a high-precision experimental regime, avoiding confusion. The bounds which can be set on beyond-the-standard-model parameters remain limited by the uncertainties on the small standard model nuclear corrections which cause King nonlinearity. Direct comparison between theory and experiment on a single pair of isotopes is advocated as a more suitable approach for few-electron ions.

Corrections to the gyromagnetic factor in very special relativity

We consider Very Special Relativity corrections to the energy spectrum of a $C-$invariant Dirac Fermion in a static and homogeneous magnetic field $\vec B$. First, in the case of $\vec B$ parallel to the spatial VSR preferred direction $\vec n$, finding that the expression for the energy spectrum stays the same, except for a correction to the mass arising from the VSR contribution. Then, we relax the parallelism condition, finding a new equation for the energy spectrum. We solve this equation perturbatively. With a Penning trap's experiment in mind, we derive the first order VSR corrections to the electron's $g-2$ factor. Finally, using the current errors on the electron's $g$-factor measurements in Penning trap's experiments, we obtain an upper bound to the VSR electron mass parameter, and therefore also to the VSR electronic neutrino mass, of $0.824 \, eV$. This result does not contradict the possibility for VSR to be the origin of neutrino masses.

Magnetic dipole moments as a strong signature for alpha -clustering in even-even self-conjugate nuclei

We investigate the magnetic dipole moments in even-even self-conjugate nuclei from ^{12}C to ^{48}Cr. For these nuclei, the measured gyromagnetic factors of excited states turn out to assume the same value of g approx + 0.5 within statistical errors. This peculiar feature can be interpreted on the basis of collective excitations of alpha -clusters. Analogously, the behaviour of the same observable is studied for all isotopes obtained by adding one or two neutrons to the considered self-conjugate nuclei. It is found that for the N = Z + 1 isotopes the alpha -cluster structure hardly contributes to the observed negative g- factor value, corroborating molecular alpha -cluster models. The addition of a further neutron, however, restores the original alpha -cluster g-factors, except for the semi-magic isotopes, in which the deviations from g approx + 0.5 can be associated with the relevant shell closures. Secondly, we analyze the same observable in the framework of a macroscopic alpha -cluster model on a finite lattice of side length L. We focus on the discretization effects induced in the magnetic dipole moments of the 2_1^+ and the 3_1^- states of ^{12}C at different values of the lattice spacing a.

Theoretical investigations on the defect structures and g factors for V4+ in 30PbO-5Bi2 O3 -(65-x)SiO2 glasses at different concentrations.

For 3d1 (V4+ ) impurity in 30PbO-5Bi2 O3 -(65-x)SiO2 glass systems with different concentrations x of V2O5, the defect structures and gyromagnetic factors are theoretically investigated by using the perturbation formulas of g factors for a tetragonally compressed octahedral 3d1 group. The concentration dependences of d-d transition band and g factors are suitably explained from the Fourier type concentration functions of the cubic crystal field parameter Dq, covalency factor N and relative tetragonal compression ratio ρ. The above concentration dependences of these quantities are suitably illustrated by the modifications of the local crystal field strength and electron cloud distribution with increasing x. The concentration variations of the electrical conductivity and dielectric relaxation are further analyzed from the stability of the systems in view of two competitive factors (increasing network polymerization and bulk stability at low concentrations and decreasing former SiO2 and stability at high concentrations).

Dynamic effect to gyromagnetic factors of the compressed tetragonal molybdenum (V) tetrahedral center in the light-irradiated lead molybdate crystal

The dynamic effect concerning small mixing of first-excited state to ground state due to the ligand vibration (which can bring about a twinkling tetrahedral change from compression to elongation) is introduced to calculate the gyromagnetic (g) factors of the second compressed tetragonal molybdenum (V) tetrahedral center in the light-irradiated lead molybdate crystal. The computed results agree well with the observed values, and the large deviation of the observed g // from ge (≈2.0023, the free electron g factor) is therefore interpreted. The outcomes (particularly, the percentage in time for the twinkling tetrahedral change from compression to elongation) are discussed.

Golden Quartic Polynomial and Moebius-Ball Electron

A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚ twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (ge = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.

Magnetic moment of the 11/2− isomeric state in Mo99 and neutron spin g factor quenching in A≈100 nuclei

The gyromagnetic factor of the low-lying ${E}_{x}=684.10(19)\phantom{\rule{4pt}{0ex}}\mathrm{keV}$ isomeric state of the nucleus $^{99}\mathrm{Mo}$ was measured using the time-dependent perturbed angular distribution technique. This level is assigned a spin and parity of ${J}^{\ensuremath{\pi}}=11/{2}^{\ensuremath{-}}$, with a half-life of ${T}_{1/2}=742(13)\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$. The state of interest was populated and spin-aligned via a single-neutron transfer on a highly enriched $^{98}\mathrm{Mo}$ target. A magnetic moment ${\ensuremath{\mu}}_{\mathrm{expt}.}=\ensuremath{-}0.627(20){\ensuremath{\mu}}_{\mathrm{N}}$ was obtained. This result is far from the Schmidt value expected for a pure single-particle $\ensuremath{\nu}{h}_{11/2}$ state. A comparison of experimental spectroscopic properties of this nucleus is made with results of multishell Interacting boson-fermion Model (IBFM-1) calculations. In this approach, the ${J}^{\ensuremath{\pi}}=11/{2}^{\ensuremath{-}}$ isomeric state in $^{99}\mathrm{Mo}$ has a pure $\ensuremath{\nu}{h}_{11/2}$ configuration. Its magnetic moment, as well as that of other two excited states could be reasonably well reproduced by reducing the free neutron spin $g$ factor with a quenching factor of 0.45. This low value is not appropriate only for this case, similar values for the quenching factor being also required in order to describe magnetic moments in other nuclei from the same mass region.

EPR Spectra of Sintered Cd1-xCrxTe Powdered Crystals with Various Cr Content.

In this paper, we show a simple method of producing ferromagnetic materials with a Curie temperature above room temperature. The electron paramagnetic resonance (EPR) spectra of Cd1−xCrxTe (0.002 < x < 0.08) were measured with a dependence on temperature (82 K < T < 381 K). Obtained EPR lines were fitted to a Lorentz-shaped curve. The temperature dependencies of the parameters of the EPR lines, such as the peak-to-peak linewidth (Hpp), the intensity (A), as well as the resonance field (Hr), were studied. Ferromagnetism was noticed in samples at high temperatures (near room temperature). For a sample with a nominal concentration of chrome of x = 0.05, a very strong intrinsic magnetic field is observed. The value of the effective gyromagnetic factor for this sample is ge = 30 at T = 240 K. An increase of chrome concentration above x = 0.05 reduces the ferromagnetic properties considerably. Analysis of the temperature dependencies of the integral intensity of EPR spectra was carried out using the Curie–Weiss law and the paramagnetic Curie temperature was obtained.

Studying the Magnetocaloric Effect in Nd0.55Sr0.45MnO3 Manganite by the Mean-field Model

In this paper, we exploited the mean field model to simulate the magnetocaloric effect (MCE) in Nd0.55Sr0.45MnO3 manganite which undergoes second-order ferromagnetic (FM)-paramagnetic (PM) phase transition. A scaling method, based on mean field theory, leads to a direct estimation of the exchange parameter (λ), the saturation magnetization (M0), the total angular momentum (J) and the gyromagnetic factor (g) of Nd0.55Sr0.45MnO3 sample. These parameters were used for simulating the magnetic isotherms, M (H, T), and the magnetic entropy change, −∆SM(T). The theoretical calculations are compared with the experimental behavior.

Relationship between the gyromagnetic anisotropy and tetragonal distortion for d 1 ions in octahedral clusters

The gyromagnetic (g) factors of vanadium (IV) (V4+) tetragonally-distorted octahedra in ‘bulk’ (where g-anisotropy Δg = g //−g ⊥>0) and surface (where Δg < 0) of metal oxides are studied from complete diagonalization method and perturbation theory method. The calculated g factors for small and large tetragonal distortions agree with the observed values of V4+ in ‘bulk’ and surface of metal oxides, respectively. So the sign of Δg for d 1 octahedra depend upon the magnitude of tetragonal distortion rather than the ground state as in the complementary d 9 octahedral clusters. Similar case can also be found for d 9 ions in tetragonally-distorted tetrahedral clusters.

Insights into nature of a magnetization plateau of 3d-4f coordination polymer [Dy2Cu2]n from a spin-1/2 Ising-Heisenberg orthogonal-dimer chain

The ground state and magnetization process of an exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with two different gyromagnetic factors of the Ising and Heisenberg spins are investigated in detail. It is shown that the investigated quantum spin chain exhibits up to seven possible ground states depending on a mutual interplay of the magnetic field, intra- and inter-dimer coupling constants. More specifically, the frustrated and modulated quantum antiferromagnetic phases are responsible in zero-temperature magnetization curves for a zero magnetization plateau. The intermediate 1/11- and 5/11-plateaus emerge due to the frustrated and modulated quantum ferrimagnetic phases, while the intermediate 9/11- and 10/11-plateaus can be attributed to the quantum and classical ferrimagnetic phases. It is conjectured that the magnetization plateau experimentally observed in a high-field magnetization curve of 3d-4f heterobimetallic coordination polymer [{Dy(hfac)2(CH3OH)}2{Cu(dmg)(Hdmg)}2]n (H2dmg = dimethylglyoxime; Hhfac = 1,1,1,5,5,5-hexafluoropentane-2,4-dione) could be attributed to the classical and quantum ferrimagnetic phases.

Investigations on the g factors and local structure for the trigonal Ce3+ center in YAl3(BO3)4 crystal

Abstract The perturbation formulae of the EPR gyromagnetic factors g // and g ⊥ for the lowest Kramers doublet of a 4f1 ion in trigonal symmetry are established. By using the above perturbation formulae, the anisotropic g factors and the local structure for the trigonal Ce3+ center in YAl3(BO3)4 crystal are theoretically studied. From the studies, this center is attributed to the impurity Ce3+ occupying the trigonal prism Y3+ site in YAl3(BO3)4. The Ce3+–O2− bond is found to undergo an angular variation Δθ(≈ 1.72°) related to the C3 axis. The calculated g factors based on the above impurity angular distortion display consistence with the measured results. The anisotropic g factors and the trigonal distortion of the Ce3+ center are analyzed with respect to the host Y3+ site in YAl3(BO3)4.

In-beam γ -ray and electron spectroscopy of Md249,251

The odd-$Z$ $^{251}$Md nucleus was studied using combined $\gamma$-ray and conversion-electron in-beam spectroscopy. Besides the previously observed rotational band based on the $[521]1/2^-$ configuration, another rotational structure has been identified using $\gamma$-$\gamma$ coincidences. The use of electron spectroscopy allowed the rotational bands to be observed over a larger rotational frequency range. Using the transition intensities that depend on the gyromagnetic factor, a $[514]7/2^-$ single-particle configuration has been inferred for this band, i.e., the ground-state band. A physical background that dominates the electron spectrum with an intensity of $\simeq$ 60% was well reproduced by simulating a set of unresolved excited bands. Moreover, a detailed analysis of the intensity profile as a function of the angular momentum provided a method for deriving the orbital gyromagnetic factor, namely $g_K = 0.69^{+0.19}_{-0.16}$ for the ground-state band. The odd-$Z$ $^{249}$Md was studied using $\gamma$-ray in-beam spectroscopy. Evidence for octupole correlations resulting from the mixing of the $\Delta l = \Delta j = 3$ $[521]3/2^-$ and $[633]7/2^+$ Nilsson orbitals were found in both $^{249,251}$Md. A surprising similarity of the $^{251}$Md ground-state band transition energies with those of the excited band of $^{255}$Lr has been discussed in terms of identical bands. Skyrme-Hartree-Fock-Bogoliubov calculations were performed to investigate the origin of the similarities between these bands.