Gyromagnetic Factor Research Articles

Gyromagnetic Factors and Covalency in Iron-Series Complexes

The gyromagnetic factor appropriate to a transition-metal salt such as KNi${\mathrm{F}}_{3}$, is inspected in detail, with emphasis on extracting information concerning $3d$-electron covalent mixing from experiment. The necessary spin-orbit and Zeeman matrix elements are evaluated within the framework of Hund---Mulliken---Van Vleck molecular-orbital theory and, contrary to frequent usage, the orbital reduction effects appropriate to the two types of matrix elements are very different. [The two-center terms, originally considered by Stevens and Tinkham, are important to the matrix element (as they anticipated) but not to spin-orbit operator.] Taking $s$ and $\ensuremath{\sigma}$ bonding estimates from transferred hyperfine experiments, the observed $g$ shift for ${\mathrm{Ni}}^{2+}$ in KMg${\mathrm{F}}_{3}$ is used to deduce the $\ensuremath{\pi}$ bonding. The result is suprisingly large (${\ensuremath{\gamma}}_{\ensuremath{\pi}}=0.24$) and is extraordinarily sensitive to computational details. For example, a simple perturbation-theory treatment, linear in spin-orbit coupling, is inadequate. The result is very likely too high because of a suspected understimate in the $\ensuremath{\sigma}$ bonding. It and the parameters obtained from transferred hyperfine measurements appear to supply an adequate and internally consistent set for understanding the various experimental quantities affected by covalency. Some difficulty arises when one attempts to relate the results to recent $a$ priori estimates of covalency, and the implications of this for the model (underlying both the results and those estimates) are discussed.

A Network Model for Transmission Lines with Gyromagnetic Coupling

Reciprocal ensembles of coupled transmission lines have been studied for many years using matrix techniques. In this paper, the lossless multiconductor transmission line model is extended to permit a description of gyromagnetic coupling effects. The novel ingredient which allows such an extension is the incorporation of distributed gyrators into the elemental line-length prototype. These gyrators provide antireciprocal coupling between the ensemble conductors. The amount of coupling is expressed by a geometry-dependent factor which in effect measures a given structure relative to an ideal Faraday rotator in the same medium. The gyromagnetic coupling factor, in conjunction with the derived expressions for mode propagation factors and characteristic impedances, provides a means of interpolating between the known limits of no coupling and ideal Faraday rotation. General relations are derived for two-line systems and for symmetrical, quasi-TEM three-line systems.

Magnetic moments of some excited states of Sn and Pb isotopes

The gyromagnetic factor of the first 4 + state of the Pb isotopes and the first 5 − state of the Sn isotopes have been calculated in the quasi-particle model, using the wave functions of Arvieu et al. 1) and compared with experiment.

Gyromagnetic Factors and Spin—Orbit Coupling in Ligand Field Theory

It has been customary to compute the effect of spin—orbit coupling on the magnetic properties of transition metal ions in crystals with the expression taken over from atomic spectroscopy, although this expression is valid only in a spherically symmetric field. In the present work, we show how the use of a spin—orbit interaction Hamiltonian derived from the Bethe—Salpeter approximation to the relativistic Breit equation for a partly covalent complex leads to a dependence of the gyromagnetic factor on the spin—orbit coupling parameter of the ligand atoms. We develop an expression of g for a d8-ion in a cubic field and apply it to the case of KNiF3. The calculated g values agree very well with experimental results. Other differences between our expression and those found by other authors are discussed.

COLLECTIVE GYROMAGNETIC FACTOR OF THE NUCLEUS <sub>62</sub>Sm<sup>152</sup>

Following Belyaev's superconductor theory of nuclei, a calculational formula for the collective gyromagnetic factor of even-even nuclei is given on the basis of cranking model. Using Nilsson's model for deformed nuclei, the collective gyromagnetic factor of the nucleus 62Sm152 is computed. The agreement between the computed and the experimental value lends support to the superconductor theory of the nuclei.

Gyromagnetic factors of deformed odd-mass nuclei with 153 ≦ A ≦ 187

Recently available experimental data are combined to obtain accurate values of the reduced magnetic dipole transition probabilities between rotational states of deformed odd- mass nuclei. These results are interpreted on the basis of the rotational model to yield the gyromagnetic factors g R and g K . It appears that the values of g R vary rather smoothly with the atomic number and have a minimum at A ≈ 170, and that g R is smaller for odd neutron nuclei than for odd proton nuclei.

On the coupling of the elementary particles with the electromagnetic field

We are trying to build up a theory in which all the supplementary conditions are considered as constraint equations imposed on the wave function and implying that only 2s+1 (s=spin) of its components are really independent. In the already treated free field case, all the elementary particles obey the Klein-Gordon equation of motion. To introduce the electromagnetic field in a general way we consider a basic interaction involving the transformation matrix of the wave function. A process is described, by means of which a gauge invariant equation of motion can be constructed. The theory is renormalizable and describes particles having the normal gyromagnetic factor 2 for any spin value.