Effect of the diamagnetic interaction on the intensity of the radiation lines of an atom in a magnetic field

Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum | Δl| ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields.     

Radiative properties of diamagnetic levels in atoms: Dependence of transition probability on magnetic field strength

We study the effect of diamagnetic interaction on the probability of radiative transitions of an atom from states split by a field. We write the analytic expressions for the diamagnetic corrections to the matrix elements of transitions belonging to the Lyman and Balmer series and of transitions between arbitrary nondegenerate states in hydrogen. We also discuss the perturbation theory for transitions from degenerate diamagnetic states. The theory is based on expanding in powers of the field strength the eigenfunctions and eigenvalues of the matrix of diamagnetic interaction in the subspace of states with given principal and magnetic quantum numbers. The field changes the coefficients in both the superposition and the degenerate basis. To derive the analytic expressions for the higher-order matrix elements, we use the Sturm expansion of the reduced Coulomb Green’s function. We also elaborate on the features of the frequency dependence of the corrections to the radiative matrix elements, which correlate with the structure of the diamagnetic spectrum of excited levels. Finally, we establish that the magnetic field acts selectively on the diamagnetic components of emission lines: as the field strength increases, an increase in the intensity of certain lines is accompanied by a decrease in the intensity of the other lines. Zh. éksp. Teor. Fiz. 116, 1161–1183 (October 1999)     

Rotational Rydberg states of polar molecules: Hund’s classification and Zeeman effect

The rotational Rydberg states of polar molecules, which arise as a result of the interaction of a Rydberg electron with core rotations, are considered. A large number of angular momenta in the core-electron system lead to a considerably greater number of possible coupling schemes of these momenta compared to the number of schemes determined by the classical five Hund’s cases for lower excited electron states of molecules. As a result of such detailed Hund’s classification, more than 30 different coupling schemes (Hund’s subcases) are constructed for rotational Rydberg states of molecules. The conditions of their realization are indicated in terms of the relative quantities of intramolecular interactions, for which analytical estimates are presented. For a large number of subcases, analytical expressions for the molecular matrix elements are found. These expressions can be useful in classification of the experimental spectra of highly excited molecules. As an application, for each of the subcases considered, analytical expressions are given, which describe the linear Zeeman effect and the Paschen-Back effect.     

Faraday effect in alkali-metal vapors in a strong bichromatic field of laser light

Results of a numerical study of the Faraday effect arising upon propagation of the light beams with the frequencies ω _L1 (resonant to the nS _1/2-nP _{1/2, 3/2} transitions) and ω _L2 (resonant to the nP _{1/2, 3/2}-(n+2)S _1/2 transitions) through alkali-metal vapors are presented. Characteristics of the magneto-optical rotation spectra at each of the frequencies are strongly affected by the second intense radiation field resonant to the adjacent transition. When the atoms interact with two strong light waves, resonant to adjacent transitions, and with a magnetic field, the shape of the Faraday rotation spectra depends on the energy shifts of the atomic states that arise due to the dynamic Stark effect and the Zeeman effect (the Paschen-Back or an intermediate-type effect), as well as due to the difference of populations of these states caused by the interaction of the atoms with the fields. The results obtained show that in the frequency selection method, based on the resonance Faraday effect, the frequency of the generated narrow-band beam can be tuned by the intensity of the strong wave, resonant to the transition between the excited states.     

Die Abhängigkeit innerer und äußerer Wechselwirkungen des TlF-Moleküls von der Schwingung,Rotation und Isotopie

The hyperfinestructure, Stark effekt and Zeeman effect of the TlF molecule have been measured with a molecular beam resonance apparatus. The apparatus uses electric four poles as deflecting fields and a homogeneous electric field parallel to a super-imposed magnetic field in the transition region. Electric dipole transitions withΔm _J =±1,ΔJ=0 (J rotational quantum number) were measured in the following (v, J) states (v vibrational quantum number): (0,1), (1,1), (2,1) and (0,2) of the molecule²⁰⁵Tl¹⁹F and (0,1) of the molecule²⁰³Tl¹⁹F. For these five states the following interaction constants were determined: The magnetic (and the electric) dipolemoment of the molecule, the scalar and the tensor nuclear dipole-dipole interaction, the nuclear spin-rotational interactions, the anisotropy of the diamagnetic susceptibility ξ_⊥?ξ_∥, the anisotropy of the diamagnetic shielding of the external field by the electrons at the position of the nuclei σ_⊥?σ_∥. From these quantities it was possible to calculate the quadrupole-moment of the electronic charge distribution. Furthermore, the dependence of the ratio of the isotopic electric dipolemoments on vibrational state was measured. A new method for determining the nuclear magnetic moments is described. The method consists of a molecular beam resonance apparatus with combined magnetic and electric transition fields and was used to measure the magnetic moments of the nuclei²⁰⁵Tl and¹⁹F. — On page 293 will be found a table of results.     

SS433 and hydrogen spectrum beyond the Paschen-Back region

We examine the hydrogen spectrum in intense magnetic fields beyond the Paschen-Back region. Unlike in the Zeeman and Paschen-Back regions, the perturbations from the normal hydrogen spectrum increase as the magnetic fielddecreases!     

Magnetic absorption of hexagonal crystals CdSe in strong and weak fields: Quasi-cubic approximation

The spectra of ultrathin free samples of hexagonal CdSe in a magnetic field up to 8 T are studied at 1.7 K. The fan-shaped diagram contains information on weak (the Zeeman effect and diamagnetic shift), as well as strong fields (transitions between Landau levels). As a result of the application of two theoretical models for combined interpretation of strong-and weak-field experimental data, two sets of (band and polaron) parameters are calculated for hexagonal CdSe in the quasi-cubic approximation. The values of the obtained polaron/band parameters are: the electron effective mass m _e =0.125/0.116m ₀, the Luttinger parameters γ₁=1.5/1.72, γ=0.29/0.37, κ=?0.63, and the effective electron g-factor g _e =0.7.     

g-Factors of group III impurities in germanium by Piezo-Zeeman spectroscopy

Experimental results are presented of the Zeeman spectrum of the stress components of the D and G lines of gallium impurity in germanium. The interpretation of the results based on symmetry unambiguously demonstrate that the g-factors of the ground state are essentially zero. From this and theoretical expressions for g-factors of Γ₈ states of T̄_d symmetry, experimental values have been determined for the g-factors of the excited states of the D and G transitions. These values compare well with those obtained by Zeeman observations on the unstressed material.     

Optical properties of semiconductor quantum dots in magnetic fields

Optical properties of semiconductor quantum dots in magnetic fields are reviewed. A theory is described based on a multi-band effective-mass approximation with a nonparabolic conduction electron dispersion, the direct Coulomb interaction, and the electron-hole exchange interaction taken into account. The transition from the quantum-confined Zeeman effect for a weak magnetic field to the quantum-confined Paschen-Back effect to a strong magnetic field is discussed in comparison with atomic spectra in magnetic fields. Experimental results of the optical properties of isolated CuCl, CdSSe, and Si quantum dots in magnetic fields are also discussed in conjunction with the theoretical results.     

On the Zeeman effect in electronic transitions of diatomic molecules

The Zeeman effect for diatomic molecules is calculated in a representation with Hund's case (a) wave functions as a basis set. The resulting expressions are simpler and easier to handle than those obtained from previous calculations on the basis of cace (b) wave functions. The calculations of intensities and polarization of Zeeman patterns is presented for transitions between doublet states with arbitrary spin-orbit (if Λ≠ 0) or spin-rotation (if Λ = 0) interaction, and for case (a)-case (a) transitions of any multiplicity. These calculations are in good agreement with observations.     

The assignment of molecular infrared spectra from a laser magnetic resonance spectrometer

Mathematical techniques are presented which have proved useful in assigning the laser magnetic resonance pure-rotation spectrum of HO₂, i.e., useful in assigning an absorption spectrum obtained when molecular energy levels are Zeeman shifted by an external magnetic field until transition frequencies coincide with a fixed-frequency radiation source. The techniques described should have general applicability to the laser magnetic resonance vibration-rotation spectrum of any molecule in an orbitally nondegenerate electronic state and a doublet electronic spin state ($\text{S =}\text{1}\text{2}$). Equations involving both Zeeman line positions and Zeeman line intensities are presented. These allow the assignment of M_J quantum numbers, the determination of the spin-rotation interaction constant γ and rotational quantum number N for both the upper and the lower state, and the determination of the zero-field transition frequency. The equations can be used without prior knowledge of the molecular structure or energy levels.     

Simple determination of electron densities in plasmas submitted to magnetic fields

A method is described to measure electron densities in plasmas with a sufficiently strong magnetic field superposed. The profiles of the spectral lines emitted by such a plasma are shaped by the Stark and Zeeman effect (Lorentz-triplet). Eliminating the central Zeeman component by a polarizer or observing in field direction, one gets a doublet, in which for a given spectral line and magnetic field strength the ratioI ₀/I _z of minimum to maximum intensities is only a function of the electron density. Measuring this ratio one finds the corresponding densities by means of calibration curves given below for the He I lineλ=5876 å. This calibration is independent of the spectral arrangement, when utilizing a polarizer for the spectral observation.     

Hyperfine anomaly arising from the nuclear spin-forbidden transition,and absolute sign determination of the zero-field splitting constant

It has been found in the triplet E.S.R. spectra of radical pairs in irradiated potassium deuterium fumarate that the hyperfine structure of the two transitions, M _s = 1?0 and M _s = 0?+1, are entirely different. This anomaly has been interpreted in terms of the forbidden transition arising from the mixing of the nuclear spin states by the anisotropic hyperfine interaction. The theory has been developed for multiplet electron spin systems and includes the nuclear Zeeman interaction which is often neglected. The theoretical predictions are in good agreement with the observed separations and intensities of the anomalous hyperfine lines. In addition, it has been found that since the forbidden lines of the electron spin multiplet system with S ≥ 1 appear strongly only in transitions which include some specific electronic spin states, the anomalous features of the spectra make it possible to determine the absolute sign of the zero-field or hyperfine splitting constant, if the sign for one of them is known. Using this principle, attempts have been made to determine the absolute sign of the zero-field splitting constant for a number of triplet E.S.R. spectra which exhibit a hyperfine anomaly arising from the proposed mechanism.     

Magnetic field effect on free and bound excitons in chalcopyrite CuInS<Subscript>2</Subscript>

The effect of a strong magnetic field (induction up to 10 T) on free and bound excitons in CuInS₂ single crystals is studied. A diamagnetic shift to higher energies is observed in the luminescence and reflectance spectra for free-exciton lines A_LPB ≈ 1.5348 eV, A_UPB ≈ 1.5361 eV, and BC ≈ 1.557 eV. The diamagnetic shifts of free-exciton lines A_LPB, A_UPB, and BC provide a basis for estimating the exciton reduced masses = 0.131m₀, = 0.13 4m₀, and μ_BC = 0.111m₀, respectively. Bound-exciton lines in luminescence spectra are split under the influence of the magnetic field. The magnitude of the Zeeman effect (g-factor of the magnetic splitting) is estimated. __________ Translated from Zhurnal Prikladnoi Spektroskopii Vol. 74, No. 3, pp. 373–377, May–June, 2007.     

Mössbauer absorption by soft ferromagnets in radio-frequency magnetic field

The simultaneous influence of periodical magnetic field reversals at the nucleus between the values ±h ₀ and of magnetostrictive vibrations on the shape of the Mössbauer absorption spectrum is analyzed. The effect of a constant external magnetic field is taken into account by assuming unequal durations of the states ?h ₀ and +h ₀. It is shown that such asymmetric reversals of the magnetic field lead to splitting of the absorption lines into Zeeman patterns corresponding to the time-averaged magnetic field h ₀ R, where R is the asymmetry parameter of the reversals. The calculations agree well with experiment.     

Near-field magneto-photoluminescence of quantum-dot-like composition fluctuations in GaAsN and InGaAsN alloys

Near-field magneto-photoluminescence scanning microscopy has been used to investigate the structural and optical properties of quantum-dot (QD)-like compositional fluctuations in GaAsN and InGaAsN alloys. Sharp spectral lines (halfwidth 0.5–2 meV) from these QDs are observed at T<70 K, and their Zeeman splitting and diamagnetic shifts are used to determine the size (r6–18 nm), density (100 μm⁻³), and nitrogen composition. Near-field scanning images reveal phase separation effects in the distribution of nitrogen, but little effect appears from the presence or absence of indium. Indium does have a strong effect on the exciton g-factor for observations in a magnetic field.     

Zeeman effect and magnetic anomalies in narrow-gap semiconductor quantum dots

We present a systematic theoretical study, based on the Kane–Weiler 8×8 k·p model, of the linear Zeeman splitting introduced by the interaction between the angular momentum and the magnetic field which can give a measure of the non-linear Zeeman effect associated with interband coupling and diamagnetic contributions. The conduction and valence bands g-factors are calculated for InSb spherical and semi-spherical quantum dots. The calculations of the g-factors showed an almost linear dependence, for the ground state, on the magnetic field. We have also found that the strong magnetic field dependence as well as the dependence on the dot size of the effective spin splitting can be unambiguously attributed to the strength of the inter-level mixing.     

Oscillations of echo amplitude in glasses in a magnetic field induced by nuclear dipole-dipole interaction

The influence of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the mutual position of nuclear spins at tunneling and the Zeeman energy E _H of their interaction with the external magnetic field lead to a nonmonotonic magnetic-field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E _d is much smaller than the Zeeman energy has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude).     

Selected States Magnetic Resonance Spectroscopy (SSMRS): Detection of Paramagnetic Element Dynamics

Abstract

Magnetic resonance (MR) response obtained in a strongly heterogeneous magnetic field with a linear gradient is analysed. It is shown that the employment of strong magnetic field gradients enables the MR spectroscopy to be accomplished in a system with selectively populated energy states (SSMRS). The method can be applied for measuring such physical quantities as the spin diffusion coefficient, D, spin-lattice, T_1m and spin-spin, T_2m, relaxation times and mobility, p_m, of paramagnetic elements in individual Zeeman energy states.

     

Third-order diamagnetic susceptibilities of hydrogenlike atoms

We develop a method for calculating diamagnetic susceptibilities based on higher-order perturbation theory for the wave function and energy of the excited states of the hydrogen atom with degeneracy of arbitrary multiplicity. We derive analytical expressions for third-order matrix elements in the spherical states |nlm〉 with fixed principal quantum number n and magnetic quantum number m. The formulas for the susceptibilities of doubly degenerate levels are represented in the form of radical-fractional relationships containing polynomials in the principal quantum number. We establish the existence of a monotonic interdependence between the absolute values of susceptibilities of the first three orders. We also present the results of numerical calculations for the states with n⩽6 and m⩽3 mixed by the field. Finally, for Rydberg states with large n and small m we detect the existence of a discontinuity in the interdependence of the susceptibilities at the boundary between the doublet and equidistant parts of the spectrum of diamagnetic sublevels with opposite parities. Zh. éksp. Teor. Fiz. 116, 838–857 (September 1999)