Zeeman perpendicular

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

Besides a strongly coupled proton with a nearly isotropic hfc of Ah —20 MHz, two clearly separated nitrogen peaks between 15-26 MHz with unresolved quadrupole and nuclear Zeeman splittings have been observed along all three turning points of the g tensor (Fig. 39b). In the evaluation of the hf data collected in Table 12.1 it is assumed that the two metal-coordinated 14N exhibit roughly axial hfs tensors with the Ajj1 values oriented approximately perpendicular to each other. 

Fig. 3. Stark modulation spectrum of HDCO around 2850.62 cm", obtained with a Zeeman-tuned Xe laser line at 3.50 fim. The Stark field is perpendicular to the optical field and increases from the bottom towards the top of the figure resulting in an increasing splitting of the Stark levels therefore more and more components are separated. (From Uehara, K.T., Shimizu, T., Shimoda, K., ref. 85))...

The spin-dynamics method was applied to the intramolecular PRE in the case of aqueous and methyl protons in the Ni(II)(acac)2(H20)2 complex (acac = 2,4-pentanedione) (131,132). The two kinds of protons are characterized by a different angle between the principal axis of the static ZFS and the dipole-dipole axis. The ratio, p, of the proton relaxation rates in the axial (the DD principal axis coinciding with the ZFS principal axis) and the equatorial (the DD principal axis perpendicular to the ZFS principal axis) positions takes on the value of unity in the Zeeman limit and up to four in the ZFS limit. A similar spin-dynamics analysis of the NMRD data for a Mn(II) complex has also been reported (133). 

The influence of a magnetic field on gaseous atoms induces a splitting of each line into several polarised components. This phenomenon, which can be seen in the emission or absorption spectra of these atoms and is called the Zeeman effect, arises from perturbations in the energy states of electrons in the atom (Fig. 14.13). For example, the absorption wavelength of cadmium, situated at 228.8 nm, leads to three polarised absorption bands due to the Zeeman effect. One of these bands, the it component, retains the initial value of the wavelength whereas the other two, the a components, are symmetrically shifted by a few picometres relative to the 7r component in a 1-tesla field. The direction of polarisation of the 7r and a lines are perpendicular and the polarisation plane of the 7r component is parallel to the magnetic field (Fig. 14.14). 

The programming of the formulae needs a COMPLEX 16 arithmetic since the CF potential itself could be complex. Therefore, it is easy to implement the complex spherical transforms of the magnetic field, x and B, into the (complex) Zeeman matrix elements. With the magnetic field Eref aligned parallel to the principal rotational axis of an axial system, the Zeeman matrix stays real since then B](] = Bxef. Its counterpart for the perpendicular direction is also real, and this involves the following transforms x = - (l/V2)Bref and... 

Transitions between the two spin states (+1/2 and -1/2) can be induced by oscillating electromagnetic radiation (v in the microwave region) applied perpendicularly to 77. The energy-level splitting is referred to as the Zeeman effect, illustrated in Figure 16.1. Normally in the EPR measurements, v is maintained at a fixed value and 77 is permitted to vary until the resonance is matched. 

The fundamental principle governing the NMR technique centres on the induction of transitions between different nuclear Zeeman levels of a particular nucleus. To cause these transitions, a variable radiofrequency (RF), referred to as B, acts perpendicular to the applied magnetic field (B0), which is causing the nuclear alignments. When the frequency of the applied RF is identical to the precessional frequency (w0) of the nuclei being observed, a transition between nuclear spin states occurs. 

To maintain thermal stability, hence a condition EB/kBT= In (for) needs to be fulfilled. For z = 10 years storage, 109-10u Hz [28] and ignoring dispersions, i.e. assuming monodisperse particles, this becomes Es/kBT= 40-45. Reversal for isolated, well-decoupled grains to first order can be described by coherent rotation over EB. This simple model, as first discussed by Stoner and Wohlfarth in 1948 [29], considers only intrinsic anisotropy and external field (Zeeman) energy terms. For perpendicular geometry one obtains the following expression ... 

We have calculated exactly the Zeeman effect for the levels IS, 3S and 3P. Indeed it is necessary to know the shift for all the hyperfine levels very well. These calculations are very classical and we just present the results in a Zeeman diagram (see Fig. 5). The most important part in the diagram is the crossing between the 38 2 (F=l, mp=-l) and 3P1/2(F=1, mj =0) levels, because the quadratic Stark effect is proportional to the square of the induced electric field and inversely proportional to the difference of energy between the two considered levels. Moreover the selection rules for the quadratic Stark effect in our case (E perpendicular to B) impose Am.F= l. So it is near this crossing that the motional Stark shift is large enough to be measured. In our calculations the Stark effect is introduced by the formalism of the density matrix [4] where the width of the levels are taken into account. The result of the calculation presented on... 

There are few published reports of experiments on the Zeeman effect in nitrogen quadrupole resonance. In her study of p-bromoaniline, Minematsu 41) showed that the Ox and Oy axes of the electric field gradient tensor lie in the molecule plane, with Oy being directed along the molecule axis of symmetry and Ox perpendicular to it. 

This would imply a very simple linear Zeeman effect but, as we show in chapter 8, additional terms describing the nuclear spin rotation interaction and the spin-spin interaction make the system much more interesting. The nuclear spin transitions are induced by an oscillating magnetic field applied perpendicular to the static magnetic field, the perturbation being represented, for example, by the term... 

Somewhat similar conclusions apply to the rotational magnetic moment g tensor for a diatomic molecule. The component of the moment of inertia tensor along the intemuclear axis is zero, and the two perpendicular components are, of course, equal. Consequently the rotational magnetic moment Zeeman interaction can be represented by the simple term... 

A simple extension of the Stark analysis given above enables one to derive an expression for the intensities of the electric dipole transitions. The oscillating microwave electric field is applied perpendicular to the static magnetic field, so that the Zeeman levels experience a time-dependent perturbation, represented by the operator... 

Figure 10.73. Observed Zeeman pattern and theoretical reconstruction for a J = 3/2 —> 3/2 transition in HeAr+, with a rest frequency of 35 092.7 MHz [211]. The magnetic field was 4.85 G, using the TE10 mode with parallel ion beam and microwave propagation, but perpendicular microwave electric field and static magnetic field (AM/ = 1).

In the microwave ion beam experiments described in this section, it is important to identify the microwave mode corresponding to the resonance line studied in a magnetic field. For a TM mode the microwave electric field along the central axis of the waveguide is parallel to the static magnetic field. We then put p = 0 in equation (10.161) so that the Zeeman components obey the selection rule AMj = 0. Alternatively in a TE mode the microwave electric field is perpendicular to the static magnetic field and the selection rule is A Mj = 1. This is the case for the Zeeman pattern shown in figure 10.73 each J = 3/2 level splits into four Mj components and the six allowed transitions should,... 

Figure 11.24. Experimental arrangement used by Ernst and Kindt [44] in their pump/probe microwave/optical double resonance study of a rotational transition (18.2 GHz) in the ground state of CaCl. The photomultiplier tubes which monitor fluorescence are situated on the axis perpendicular to both the laser beam and the molecular beam. The C region, where the molecular beam is exposed to microwave radiation, is magnetically shielded to minimise stray Zeeman effects. The microwave power was amplitude modulated at 160 Hz and the modulated fluorescence detected by photomultiplier B. 

Pieter Zeeman was the first to study the effect of an applied magnetic field on atomic emission spectra. Since a perpendicular applied field was subsequently typically used within Zeeman (excited state emission) spectroscopy the normal Zeeman effect is usually described in terms of parallel (II) and perpendicular (J.) plane polarized bands (Figure 1). It should be noted, however, that Zeeman also studied the parallel magnet alignment used within MCD spectroscopy. In Zeeman s words during his Nobel prize lecture in 1902 describing results obtained for emission from the 5d orbital of Cd to the 5p orbital,. But let us first consider the rays... 

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