Zero-field components

An equivalent form is given by Englefield.11 It is possible to find quite a variety of phases for the transformation coefficients of Eq. (6.18).10-13 The phase depends on the phase conventions established for the spherical and parabolic states. The choice of phase in Eq. (6.18) is for spherical functions with an /, as opposed to (-r)e, dependence at the origin and the spherical harmonic functions of Bethe and Salpeter. A few examples of the spherical harmonics are given in Table 2.2. The parabolic functions are assumed to have an ( n) ml/2 behavior at the origin and an e m angular dependence. This convention means, for example, that for all Stark states with the quantum number m, the transformation coefficient (nni>i2m nmm) is positive. To the extent that the Stark effect is linear, i.e. to the extent that the wavefunctions are the zero field parabolic wavefunctions, the transformation of Eqs. (6.17) and (6.18) allows us to decompose a parabolic Stark state in a field into its zero field components, or vice versa. 

The most precise measurements of the fine-structure parameters D and E have in fact been carried out using zero-field resonance. Figure 7.6 shows the three zero-field transitions in the Ti state of naphthalene molecules in a biphenyl crystal at T = 83 K. In these experiments, the absorption of the microwaves was detected as a function of their frequency [5]. The lines are inhomogeneously broadened and nevertheless only about 1 MHz wide. Owing to the small hnewidth of the zero-field resonances, the fine-structure constants can be determined with a high precision. This small inhomogeneous broadening is due to the hyperfine interaction with the nuclear spins of the protons (see e.g. [M2] and [M5]). For triplet states in zero field, the hyperfine structure vanishes to first order in perturbation theory, since the expectation value of the electronic spins vanishes in all three zero-field components (cf Sect. 7.2). The hyperfine structure of the zero-field resonances is therefore a second-order effect [5]. 

A second direct optical-detection method for selective population and depopulation is microwave-induced delayed phosphorescence in zero field (Bq = 0) [25]. Figure 7.26 shows the phosphorescence intensity from quinoline in a durene (tet-ramethyl benzene) host crystal at T= 1.35 K as a function of the time after the end of the UV excitation. The phosphorescing zero-field component here is Tz). Its lifetime is considerably shorter than those of the other two zero-field components, from which furthermore no phosphorescence is emitted. If the zero-field transition... 

Ty -o- Tz is rapidly saturated by a short resonant microwave pulse (1000.5 MHz) after the end of the UV excitation, thus when the radiative component Tz) has already mostly decayed, then the radiative component Tz) will again be populated from the non-radiative component Ty), thus inducing renewed phosphorescence. With a still longer delay of the microwave pulse, the increase in the phosphorescence intensity is smaller. From this, the lifetime of Tf) can be derived. With this method, the decay constants of all three zero-field components can be determined. 

Table 7.4 Rate constants for the population and depopulation of the three zero-field components Th), (u =x,y,z) of the quinoxaline triplet states in a N-d quinoxaline crystal. Sq is the applied field at which the measurement was carried out. The rate constants in zero field can be uniquely computed from those measured in a magnetic field see Eq. (7.13).

Note that although an ion may speed up or slow down as it passes through intermediate lenses before it reaches the QMF, such lenses do not themselves influence the axial velocity within the QMF. In practice, fringing flelds always exist near the entrance and exit of the QMF. These give rise to non-zero field components in the z direction, and will therefore alter the axial velocity. The influence of these flelds extends into the mass Alter to a distance of about 3ro from the entrance and exit. For simplicity this influence is largely ignored in this treatment, which applies specifically to ion motion in a perfect quadrupole field (but see Section 2.1.1.9). 

The behavior of the field g caused by masses of the layer is shown in Fig. 1.14c. Thus, for negative values of z the field component g inside the layer is positive, since the masses in the upper part of the layer create a field along the z-axis, and this attraction prevails over the effect due to masses located below the observation point. At the middle of the layer, where z = 0, the field is equal to zero. Of course, every elementary mass of the layer generates a field at the plane z = 0, but due to symmetry the total field is equal to zero. For positive values of z the field has opposite direction, and its magnitude increases linearly with an increase of z. As follows from Equations (1.146-1.148) the field changes as a continuous function at the layer boundaries. 

The value is derived from a zero-field spectrum recorded at 150 K. A q could not be determined at 4.2 K because the compound is in the limit of slow paramagnetic relaxation and the strong unquenched orbital moment forces the internal field into the direction of an easy axis of magnetization. As a consequence, the quadrupole shift observed in the magnetically split spectra results only from the component of the EFG along the internal field and the orientation of the EFG is not readily known dbabh is a bulky N-coordinating amide... 

For the d, 32 system the effects of the zero field splitting on the susceptibility have been elucidated by Prins, Van Voorst, and Schinkel (92), and the expressions given by these authors are readily derived as outlined below. Thus, if the two components of the... 

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