Zeeman energy pattern

Fig. 5 Influence of the JT interaction (defined by the vibronic coupling parameter v) on the Zeeman energy pattern in a perpendicular magnetic field (//HC3)...

Note that if L = 0 in equation (67) then J = S and g = 2, the spin-only-value . The energy pattern of Figure 27 is linear in H there is no second-order Zeeman effect unless other states are considered. Application of equation (64) to this system is fairly straightforward since it yields... 

Fig. 5.2. Zeeman energy level pattern for the OD A2T,+, v = 0, IV = 1, J = 3/2 level as a function of magnetic field.

Fig. 3.39 5 = 1/2 ESR line pattern for an / = Vi nucleus with an anisotropic hyperfine coupling and a nuclear Zeeman term of comparable magnitude. The intensities 1 and Ip depend on the values of Va and vp and the nuclear Zeeman energy vn in frequency units according to Eqs. (3.38) and (3.39)...

The hyperfine pattern of a sample may differ at different microwave frequencies due to the difference in the nuclear Zeeman energy, with Bn 0. 5 mT at X-band, 1.8 mT at Q-band for the H- hfc in a free radical (g 2.00). An example is shown in Fig. 4.21(a) for the hydrazine cation radical discussed in Chapter 1. For the magnetic field oriented along the N—N (Y) bond the four hydrogen atoms are accidentally equivalent giving a normal quintet of lines at X-band. The hfc due to the two... 

Notice that in both case (d) and case (e) there is no molecular projection quantum number. An example of case (e) coupling, probably the first, has been observed [60] for vibration rotation levels of the HeKr+ ion which lie very close to the dissociation limit. The Kr+ atomic ion has L = 1 and S= 1/2, so that. Ja is 3/2 or 1 /2, and the spin orbit interaction is strong. When a very weak bond is formed with a He atom,. Ja remains a good quantum number, at least for the most weakly bound levels, but there are nevertheless series ofrotation levels, with rotational energy BR(R + 1). The details are described in chapter 10, where we show that case (e) coupling is identified, both by the observed pattern of the rotational levels, and by the measured Zeeman effects and effective g factors for individual rotational levels. 

The high-resolution spectroscopy of OH has been perhaps the most important test bed for the development of the theory of the molecular energy levels, both in zero field and in the presence of applied magnetic fields. In this section, we concentrate on the A-doubling and hyperfine structure, as probed by the molecular beam studies. In chapter 9 we discuss the complex theory of the Zeeman effect, and in chapter 10 deal with rotational transitions. Our discussion therefore follows a pattern similar to that adopted for the NO molecule. 

The physical origins of the effect can be illustrated from Figure 2, which shows the energy level scheme for an I = 1 nucleus, such as coupled to an S = 1/2 electron spin. In the case considered here (i.e., the electron-nuclear interaction, the nuclear Zeeman interaction, and the nuclear quadrupole interaction, all of the same order), microwaves can induce both allowed and semi-forbidden transitions between states in the Mj = 1/2 manifold (a) and the Ms = - 1/2 manifold (/ ). Simultaneous excitation of both kinds of transitions by the echo generating microwave pulses gives rise to interference effects, which manifest themselves as variations in the echo amplitude and thus cause the modulation of the echo envelope. Where a number of nuclei are coupled to the same electron spin, the level scheme becomes more complicated, but it is possible to factor out contributions due to coupling with each nucleus in the overall modulation pattern. If v(U l2>" n) is the modulation function due due to coupling with n nuclei, then... 

The QI can be treated as a first- and second-order perturbation of the fundamental Zeeman interaction that describes nuclear spin energy levels in a magnetic field. The QI leads to a significant increase in i powder pattern... 

In cases where molecular motion is restricted [wr is not 1) the situation is more complex. Such cases arise when the alkali metal is bound to the surface of a large molecule such as a protein or membrane surface and thereby has its motion restricted. The quadrupolar interaction with the nucleus shifts the energies of the Zeeman levels according to the square of the quantum number to a first approximation. Thus, the energy level splittings for a nucleus with 1 = (e.g. Li, Na, and Tlb) become as illustrated in Figure 1. With rapid isotropic motion, as described above, the multiple line pattern will... 

Similar to the situation in [Ru(bpy)3] (Sect. 3.3.1), 11), II), and III) represent zero-field spUt components, which result in their main contributions from the same orbital parentage or fi om one specific MLCT state. This is indicated (1) by the fact that the splitting pattern does not strongly depend on the matrix, though the absolute energies are shifted over a range of more than 250 cm, when the different matrices are compared (Table 8) (2) states 11) and II) exhibit a strong Zeeman interaction (Sect. 4.1.4 [92]) and (3) both states are -within Umits of experimental error of < 1 cm /kbar - equally shifted under... 

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