Electric hyperfine structure

In the same way as a magnetic dipole acquires an orientational energy in a magnetic field, a non-spherically symmetric charge distribution will acquire such an energy in an electric field gradient (Fig.2.17). 

Atomic nuclei can be stretched like cigars (prolate shape) or compressed like discs (oblate shape). The deformation is described by the electric quadrupole moment Q (prolate Q 0 oblate Q 0). The principal interaction is, of course, the normal electrostatic (Coulomb) force on the charged nucleus (monopole interaction). The differential interaction, which depends 

In analogy with the magnetic dipole interaction constant a the electric quadrupole interaction constant b is a product of a nuclear quantity Q, the electric quadrupole moment, and an electronic quantity qj, which is proportional to the electric field gradient. Thus, with the b factor experimentally determined, information on the nucleus or the electronic shell can be obtained. The electric hyperfine structure is of the same order of magnitude as the magnetic one, but generally somewhat smaller. It exhibits itself as a deviation from the Lande interval rule. In Fig.2.18 two examples of the combined action of magnetic and electric hyperfine structure are shown. 

If the nucleus has no spin, i.e. 1 = 0, there is neither a magnetic nor an electric hyperfine structure. For 1=1/2 only a magnetic interaction is possible whereas the occurrence of electrical hyperfine structure requires I 1 

In analogy with the magnetic dipole interaction constant a the electric qua-drupole interaction constant 6 is a product of a nuclear quantity Q, the electric 

Orientation energy of an electric quadrupole in an electric field gradient 

If the nucleus has no spin, i.e. I — 0, there is neither a magnetic nor an electric hyperfine structure. For I — lj2 only a magnetic interaction is possible, whereas the occurrence of electrical hyperfine structure requhes I 1 and J 1. Hyperfine stmctiue and the determination of nuclear moments have been discussed in [2.47]. Extensive data on nuclear moments have been listed in [2.48, 2.49] hfe data for the extensively studied alkali atoms have been compiled in [2.50] and the theoretical aspects of atomic hyperfine interactions have been covered in [2.51-2.54]. 

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Atomic nuclei can be stretched like cigars (prolate shape) or compressed like discs (oblate shape). The deformation is described by the electric quadrii-pole moment Q (prolate Q > 0 oblate Q < 0). The principal interaction is, of course, the normal electrostatic (Coulomb) force on the charged nucleus monopole interaction). The differential interaction, which depends on the structure of the nucleus and on the valuation of the field across its finite extension, is of course very much smaller quadrupole interaction). It gives rise to an electric hyperfine structure. The energy contribution depends on the direction of the nuclear spin in relation to the electric field gradient. For the electric hyperfine interaction one obtains... 

Discuss electrical hyperfine structure. What is its origm What can be learned from it Under what circumstances (quantum numbers etc.) can it be observed ... 

The electric hyperfine structure of rotational levels is observed if at least one of the nuclei in the molecule has a spin quantum number / > 1, because the multipole expansion of the electrostatic interaction between the nuclei and electrons gives the quadrupole term as the next non-vanishing term after the monopole. This part can be written in the eoneept of spherical tensor operators [57Edm]... 

Quadrupole coupling constants for molecules are usually determined from the hyperfine structure of pure rotational spectra or from electric-beam and magnetic-beam resonance spectroscopies. Nuclear magnetic resonance, electron spin resonance and Mossbauer spectroscopies are also routes to the property. There is a large amount of experimental data for and halogen-substituted molecules. Less data is available for deuterium because the nuclear quadrupole is small. 

Fig. 3. (a) Partially resolved nuclear hyperfine structure in the p.SR spectrum for Mu in GaAs in an applied field of 0.3 T. The structure occurs in the line corresponding to 0 = 90° and Ms = —1/2. (b) Theoretical frequency spectrum obtained by exact diagonalization of the spin Hamiltonian using the nuclear hyperfine and electric quadrupole parameters in Table I for the nearest-neighbor Ga and As on the Mu symmetry axis. Both Ga isotopes, 69Ga and 71Ga, were taken into account. From Kiefl et al. (1987). 

The energies of the electric quadrupole (Wg) and magnetic dipole (W ) interactions, which determine the hyperfine structure, are calculated as follows [11,20] ... 

A Mi = 0, 1, A Ms = 0. Lines with A Mi = 0 are plane polarized with electric vector parallel to the direction of the applied magnetic field those with A Mi — 11 are plane polarized with components perpendicular to the field. See also Atomic Spectra and Hyperfine Structure. 

The hyperfine structure (splitting) of energy levels is mainly caused by electric and magnetic multipole interactions between the atomic nucleus and electronic shells. From the known data on hyperfine structure we can determine the electric and magnetic multipole momenta of the nuclei, their spins and other parameters. 

The operator of the hyperfine structure, caused by electric multipole radiation, may be presented in the form... 

In formulas (22.12) and (22.13) k acquires only even values for k = 2 we have the usual electric quadrupole interaction, whereas for k = 4 we have the electric hexadecapole interaction, already observed in [145]. The expressions for the matrix elements of the hyperfine structure operators considered above for the closed shells follow straightforwardly from the... 

Prior to about 1955 much of the nuclear information was obtained from application of atomic physics. The nuclear spin, nuclear magnetic and electric moments and changes in mean-squared charge radii are derived from measurement of the atomic hyperfine structure (hfs) and Isotope Shift (IS) and are obtained in a nuclear model independent way. With the development of the tunable dye laser and its use with the online isotope separator this field has been rejuvenated. The scheme of collinear laser/fast-beam spectroscopy [KAU76] promised to be useful for a wide variety of elements, thus UNISOR began in 1980 to develop this type of facility. The present paper describes some of the first results from the UNISOR laser facility. 

Abstract. CPT invariance is a fundamental property of quantum field theories in flat space-time. Principal consequences include the predictions that particles and their antiparticles have equal masses and lifetimes, and equal and opposite electric charges and magnetic moments. It also follows that the fine structure, hyperfine structure, and Lamb shifts of matter and antimatter bound systems should be identical. 

A further structure effect, the proton polarizability, is only estimated to be < 4 ppm [28], of the same order than the value above. The agreement between theory and experiment is therefore only valid on a level of 4 ppm. Thus, we can say that the uncertainty in the hyperfine structure reflects dominantly the electric and magnetic distribution of the proton, which is related to the origin of the proton anomalous moment, being a current topics of particle-nuclear physics. 

In the 2s1/2 - 2px/2 system there are transitions in the electric field between the s and p hyperfine structure sublevels with total angular momentum projections 1, 0... 

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