Electric quadrupole interactions magnetic perturbation

Pure nuclear magnetic hyperfine interaction without electric quadrupole interaction is rarely encountered in chemical applications of the Mossbauer effect. Metallic iron is an exception. Quite frequently, a nuclear state is perturbed simultaneously by... 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

The low-temperature Mossbauer spectra of the spinel type oxides, NiCr204 [14,18] (Fig. 7.6b) and NiFe204 [3, 18], have been found to exhibit combined magnetic dipole and electric quadrupole interaction (Fig. 7.7). For the evaluation of these spectra, the authors have assumed a small quadrupolar perturbation and a large magnetic interaction, as depicted in Fig. 7.3 and represented by the Hamiltonian [3]... 

The interaction between the electrons and the nucleus causes a very small perturbation of the nuclear energy levels in comparison with the energy of the nuclear transition. Such interactions are called hyperfine interactions. The main hyperfine interactions are the following electric monopole, electric quadrupole, and magnetic dipole interactions between the nucleus and the electrons (shell electrons, ligands, etc.). Such interactions can be sensitively monitored by Mbssbauer spectroscopy. The measurement of hyperfine interactions is the key to the utilization of Mbssbauer spectroscopy in a wide range of applications. 

Often all three interactions, i.e. the electric monopole, magnetic dipole and electric quadrupole interactions, occur simultaneously. If the quadrupole interaction is small compared with the magnetic interaction (Eq j[i )> a correction to the interaction energy may be applied using first-order perturbation... 

If the electric field gradient tensor is axially symmetric and its principal axis makes an angle 6 with the magnetic axis, then a relatively simple solution exists providing that e qQ (iH in this case the quadrupole interaction can be treated as a first-order perturbation to the magnetic interaction. The eigenvalues are... 

Next, consider the energy levels of a spin-3/2 nucleus in a single crystal in the presence of an applied magnetic field and an electric field gradient so that the perturbation provided by the quadrupole interaction with the applied EFG is small a first order perturbation. We already considered this case in II.D.l. where we saw that the quadrupole interaction split the single line into three by shifting the 3/2<- l/2 and the -3/2 ->-1/2 lines in opposite directions. We state without... 

One of the two or both nuclei of a diatomic molecule may interact with rotation via their electric quadrupole moments, or their magnetic dipole moments may interact with the rotational magnetic field. The two nuclei may be coupled by the direct (tensorial) or indirect (electron-coupled scalar) magnetic dipole interaction which also influences rotation. Furthermore, in a state other than E the nuclei cause magnetic perturbations when their dipole moments interact with those of the unpaired - electron spins or with the orbital magnetic field. The energetic effects of these so-called hyperfine interactions can be quantified with the aid of interaction constants which in favorable cases can be determined from high-resolution spectra. 

Here eq denotes the largest component of the electric field gradient tensor and eQ the quadrupole moment. 0 is the angle between the field gradient and the magnetic field. A second-order perturbation treatment of the quadrupole interaction shows the central line to be shifted. 

It is this selective interaction which justifies the effort involved in constructing and transposing optimally adapted potentials in spherical, cylindrical, or rectangular coordinates. It is now permissible to limit the generally infinite secular determinant to a finite number of elements or to cut off the perturbation expansion after a finite number of terms. Each multipole considered increases the order of the respective secular determinant G(o), k) by four The multipole may be situated at particle 1 or 2 and may be electric or magnetic. Treating dipole interactions yields a secular determinant of order four, the inclusion of quadrupole interactions causes a secular determinant of order eight. 

The energy levels of the lanthanide ionic moment are perturbed somewhat by interaction with the magnetic dipole and electric quadrupole moments of its nucleus and to a lesser extent the nuclei of ligand ions. The magnetic hyperfine interaction has been described from the nuclear standpoint in section 1.2.1 where the hyperfine constant A was introduced in the hamiltonian 5(fhf = AI J of (18.8). In any subset of levels resulting from the CEF interaction (18.109) which are characterized by an effective spin S, the magnetic hyperfine interaction can be written in the form... 

In the last three sections we have considered the effect of a time-dependent external electric field r,t) and a magnetic induction B r,t) on the motion of an electron and denoted the corresponding potentials with 4> r,t) and A r,t). In the present section we want to collect all the terms and derive our final expression for the molecular electronic Hamiltonian. However, we will not restrict ourselves to the case of external fields because in the following chapters we want to study also interactions with other sources of electromagnetic fields such as magnetic dipole moments and electric quadrupole moments of the nuclei, the rotation of the molecule as well as interactions with field gradients. Therefore, we do not include the superscripts B and on the vector and scalar potential in this section. On the other hand, we will assume that the perturbations are time independent. The time-dependent case is considered in Section 3.9. 

It is expedient to employ the Rayleigh-Schrbdinger perturbation theory, or equivalent theoretical tools (e.g., equation-of-motion and propagator methods) to evaluate explicit expressions for the properties appearing in equations (4) and (5). In the presence of time-independent, spatially uniform external perturbations (e.g static homogeneous fields) or intramolecular perturbations (nuclear magnetic dipole or electric quadrupoles), described via first- and second-order interaction Hamiltonians and the expressions for the contributions to the energy up to fourth order can be written as... 

Hyperfine interactions, that is the interaction of a nuclear magnetic moment with extranuclear magnetic fields and the interaction of a nuclear quadrupole moment with electric field gradients from extranuclear charge distributions, are measured via time differential perturbed angular correlation (TDPAC) of y-rays emitted from radioisotopes. 

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